The theory of Homo comperiens, the firm’s market price, and the

The theory of Homo comperiens, the firm’s market price, and the
Doctoral Thesis No. 128 Joachim Landström The theory of Homo comperiens, the firm’s market price, and the implication for a firm’s profitability 2007
ISSN 1103-8454
Universitetstryckeriet, Uppsala 2007
Företagsekonomiska institutionen
Department of Business Studies
The theory of Homo
comperiens, the firm’s
market price, and the
implication for a firm’s
profitability
Joachim Landström
Doctoral
Thesis
No. 128
2007
Företagsekonomiska institutionen
Department of Business Studies
The theory of Homo
comperiens, the firm’s
market price, and the
implication for a firm’s
profitability
Joachim Landström
Dissertation presented at Uppsala University to be publicly examined in Hörsal 2, Ekonomikum,
Uppsala, Friday, October 26, 2007 at 13:15 for the degree of Doctor of Philosophy.
ABSTRACT
Landström, J., 2007, The theory of Homo Comperiens, the firm’s market price, and the implication
for a firm’s profitability, Doctoral thesis / Företagsekonomiska institutionen, Uppsala universitet 128, 259 pp.,
Uppsala.
This thesis proposes a theory of inefficient markets that uses limited rational choice as a central trait
and I call it the theory of Homo comperiens. The theory limits the alternatives and states that the
subjects are aware of and only allow them to have rational preference relations on the limited action
set and state set, i.e. limited rationality is introduced. With limited rational choice, I drive a wedge
between the market price and the intrinsic value and thus create an arbitrage market.
In the theory, the subjects are allowed to gain knowledge about something that they previously were unaware of. As the discovery proceeds, the arbitrage opportunities disappear, and the
market prices regress towards the intrinsic values.
The theory is applied to firms and market-pricing models for a Homo comperiens environment is a result. The application of the theory to firms also leads to testable propositions that I test
on a uniquely comprehensive Swedish accounting database that cover the years 1978—1994.
Hypotheses are tested which argues that risk-adjusted residual rates-of-returns exist. The null
hypotheses argue that risk-adjusted residual rates-of-returns do not exist (since they assume a noarbitrage market). The null hypotheses are rejected in favor of their alternatives at a 0.0 percent significance level. The tests use approximately 22,200 observations.
I also test hypotheses which argue that risk-adjusted residual rates-of-returns regress to zero
with time. The null hypotheses are randomly walking risk-adjusted residual rates-of-returns, which
are rejected in favor of the alternative hypotheses. The hypotheses are tested using panel regression
models and goodness-of-fit tests. I reject the null hypotheses of random walk at a 0.0 percent significance level.
Finally, the results are validated using out-of-sample predictions where my models compete
with random-walk predictions. It finds that the absolute prediction errors from my models are between 12 to 24 percent less than the errors from the random walk model. These results are significant at a 0.0 percent significance level.
Joachim Landström, Uppsala University, Department of Business Studies, Box 513, SE-751 20 Uppsala, Sweden.
ISSN 1103-8454
© Joachim Landström
Printed in Sweden 2007 by Universitetstryckeriet, Ekonomikum, Uppsala
To Maria for being at my side at all times.
TABLE OF CONTENTS
CHAPTER 1 —INTRODUCTION ...................................................................................................................... 17
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Background ........................................................................................................................................................................ 17
The efficient market hypothesis ...................................................................................................................................... 18
The standard state-space-and-partition model, ignorance, and equilibrium .............................................................. 19
Empirical research ............................................................................................................................................................. 21
The relation of the thesis to other research ................................................................................................................... 22
Expected contribution ...................................................................................................................................................... 23
Outline of thesis ................................................................................................................................................................ 24
CHAPTER 2 —THE THEORY OF HOMO COMPERIENS: LIMITED RATIONAL CHOICE ................. 25
2.1 Introduction ....................................................................................................................................................................... 25
2.2 The limited rational choice ............................................................................................................................................... 27
2.2.1
The perfectly rational choice, the starting point............................................................................................................... 28
2.2.2
Actions, ignorance of available actions, and limited rationality ....................................................................................... 28
2.2.3
Limited rationality versus bounded rationality............................................................................................................... 30
2.2.4
Consequences, ignorance, and the subjective action function in certainty ........................................................................... 31
2.2.5
Consequences, ignorance, and the subjective action function in uncertainty ....................................................................... 32
2.3 The limited rational choice’s utility representation ....................................................................................................... 36
2.4 Learning and the limited rational choice ........................................................................................................................ 40
2.4.1
Learning as a resolution of uncertainty ......................................................................................................................... 40
2.4.2
Learning as discovery ................................................................................................................................................... 42
2.4.3
Human action and Homo comperiens ........................................................................................................................... 44
2.5 Summary ............................................................................................................................................................................. 46
CHAPTER 3 —HOMO COMPERIENS AND PRICE THEORY ..................................................................... 49
3.1 Introduction ....................................................................................................................................................................... 49
3.2 A point of departure for the application of Homo comperiens to price theory ....................................................... 49
3.3 A micro analysis of limited rational choice .................................................................................................................... 53
3.3.1
Optimization of Homo comperiens’ subjective expected utility maximization problem ..................................................... 53
3.3.2
Interpretation of the optimization ................................................................................................................................. 54
3.4 A macroanalysis of limited rational choice..................................................................................................................... 55
3.4.1
The dynamics of learning .............................................................................................................................................. 55
3.4.2
The adaptation processes .............................................................................................................................................. 58
3.5 Homo comperiens and Walras’ tâtonnement process .................................................................................................. 60
3.6 Summary ............................................................................................................................................................................. 62
CHAPTER 4 —HOMO COMPERIENS AND THE FIRM ............................................................................... 65
4.1 Introduction ....................................................................................................................................................................... 65
4.2 The firm as a choice entity in the theory of Homo comperiens ................................................................................. 65
4.3 Certainty, subjective certainty, and uncertainty ............................................................................................................. 67
4.4 Homo comperiens and firm market-pricing models in subjective certainty ............................................................. 68
4.5 Homo comperiens and the firm’s risk and return ......................................................................................................... 70
4.5.1
Homo comperiens and the firm’s rate-of-return in the subjectively certain choice ............................................................... 70
4.5.2
The firm’s rate-of-return in the objective uncertain choice ................................................................................................ 73
4.5.3
Homo comperiens and the firm’s rate-of-return in the subjectively uncertain choice ........................................................... 75
4.6 Summary ............................................................................................................................................................................. 78
CHAPTER 5 —THE EMPIRICAL DATA AND THE FINANCIAL STATEMENTS .................................... 81
5.1 Introduction ....................................................................................................................................................................... 81
5.2 A description of the empirical data ................................................................................................................................. 82
5.3 Operationalization of the financial statements .............................................................................................................. 84
5.3.1
Operationalization of the clean surplus relationship, book value of equity, and paid net dividends ................................... 84
5.3.2
Operationalization of the balance sheet ......................................................................................................................... 86
5.3.3
Operationalization of the income statement ................................................................................................................... 90
5.4 Summary ............................................................................................................................................................................. 94
CHAPTER 6 —HYPOTHESES TESTS AND THE TEST VARIABLES ......................................................... 95
v
6.1 Introduction ....................................................................................................................................................................... 95
6.2 Operationalization of the risk-adjusted subjective expected residual accounting rates-of-returns ........................ 95
6.2.1
Ex ante and ex post rates-of-returns ............................................................................................................................ 96
6.2.2
The residual accounting rates-of-returns......................................................................................................................... 97
6.2.3
The risk-premiums and biased accounting ..................................................................................................................... 98
6.2.4
Descriptive statistics of risk-adjusted RROE and RRNOA from 1978 to 1994 .......................................................101
6.3 Do risk-adjusted residual accounting rates-of-returns exist? .....................................................................................103
6.3.1
The hypotheses to be tested .........................................................................................................................................103
6.3.2
Results from the robust double-sided t tests ..................................................................................................................104
6.4 Does the market learn through discovery? ..................................................................................................................108
6.4.1
The tested hypotheses..................................................................................................................................................109
6.4.2
Results of the tests of the hypotheses ............................................................................................................................109
6.5 Summary ...........................................................................................................................................................................115
CHAPTER 7 —ASSESSING HOMO COMPERIENS’ PREDICTIVE ACCURACY ...................................... 117
7.1 Introduction .....................................................................................................................................................................117
7.2 The method for assessing the theory’s external validity .............................................................................................118
7.2.1
The prediction models.................................................................................................................................................118
7.2.2
The out-of-sample predictive method ............................................................................................................................120
7.2.3
The pooling of forecast errors and the forecast error statistic ..........................................................................................124
7.3 Results from the predictions ..........................................................................................................................................126
7.3.1
Results from using the risk-adjusted RROE ..............................................................................................................128
7.3.2
Results from using the risk-adjusted RRNOA ...........................................................................................................130
7.3.3
Conclusions from the external validation .....................................................................................................................132
7.4 Summary ...........................................................................................................................................................................133
CHAPTER 8 —CONCLUDING DISCUSSION................................................................................................ 135
8.1 Introduction .....................................................................................................................................................................135
8.2 Research problems and the research design ................................................................................................................135
8.3 The theory of Homo comperiens..................................................................................................................................136
8.4 Summary of the hypotheses tests ..................................................................................................................................140
8.4.1
Does an arbitrage market exist? ................................................................................................................................140
8.4.2
Is discovery part of human action? ..............................................................................................................................141
8.5 The external validity of the theory of Homo comperiens..........................................................................................142
8.6 Directions for future research........................................................................................................................................143
8.7 The implications for the role of accounting in society ...............................................................................................144
APPENDIX A —PERFECT RATIONALITY AND THE INTRINSIC VALUE OF THE FIRM IN AN
OBJECTIVE CERTAIN CHOICE ..................................................................................................................... 147
A.1
A.2
A.3
A.4
A.5
A.6
A.7
A.8
A.9
Introduction .....................................................................................................................................................................147
A point of departure........................................................................................................................................................148
Choice of consumption over time in objective certainty ...........................................................................................148
His or her preference relation and the objective utility function in objective certainty ......................................... 150
His or her objective opportunity set in objective certainty ........................................................................................153
His or her optimization problems in objective certainty............................................................................................157
The competitive equilibrium ..........................................................................................................................................162
The intrinsic value rule for firms in objective certainty..............................................................................................166
Summary ...........................................................................................................................................................................176
APPENDIX B —HOMO COMPERIENS AND THE MARKET PRICE OF THE FIRM IN A
SUBJECTIVE CERTAIN CHOICE ................................................................................................................... 179
B.1
B.2
B.3
B.4
B.5
B.6
B.7
Introduction .....................................................................................................................................................................179
The subject’s opportunity set .........................................................................................................................................179
The subject’s optimization problems ............................................................................................................................181
The market price and the subjective dividends ...........................................................................................................184
The market price based on subjective residual income ..............................................................................................186
The market price based on accounting rates-of-returns.............................................................................................188
Summary ...........................................................................................................................................................................189
APPENDIX C —PROOF OF PROPOSITION 2-3 ............................................................................................ 191
C.1 Structuring the problem..................................................................................................................................................191
C.2 Derivation .........................................................................................................................................................................192
C.3 Discussion ........................................................................................................................................................................194
vi
APPENDIX D —OPERATIONALIZATION OF GROUP CONTRIBUTION AND OF UNTAXED
RESERVE............................................................................................................................................................. 195
APPENDIX E —TRACING FIRMS .................................................................................................................. 197
E.1 Introduction .....................................................................................................................................................................197
E.2 Tracing firms and identifying each firm’s opening balance sheet ............................................................................. 197
E.3 Finding usable firm-year observations ..........................................................................................................................201
APPENDIX F —OPERATIONALIZATION OF THE BALANCE SHEET ................................................. 205
APPENDIX G —OPERATIONALIZATION OF THE INCOME STATEMENT ........................................ 207
APPENDIX H —FIELDS IN THE DATABASE .............................................................................................. 209
APPENDIX I —THE INDUSTRY-SPECIFIC ACCOUNTING RATES-OF-RETURNS ............................. 211
I.1
I.2
I.3
Introduction .....................................................................................................................................................................211
Estimation of the industry year’s ex post accounting rates-of-returns ..................................................................... 211
Classifying the industry ...................................................................................................................................................214
APPENDIX J — HYPOTHESES TESTS USING ALTERNATIVE OPERATIONALIZATIONS OF
INCOME .............................................................................................................................................................. 215
J.1
J.2
J.3
Introduction .....................................................................................................................................................................215
The result from panel regression on alternative specification of CNI ..................................................................... 216
The results from panel regression on alternative specification of COI ...................................................................217
APPENDIX K —THE ROBUST T-TEST ASSESSING IF NON-ZERO RISK-ADJUSTED RESIDUAL
ACCOUNTING RATES-OF-RETURNS EXISTS ............................................................................................ 219
APPENDIX L —THE PANEL REGRESSION TEST METHOD .................................................................. 221
L.1
L.2
L.3
L.4
L.5
Introduction .....................................................................................................................................................................221
Three panel regression models ......................................................................................................................................221
Alternative covariance structures for the fixed effect method ..................................................................................222
Formation of panels, the identification, and the treatment of outliers in the fit periods ...................................... 229
Summary ...........................................................................................................................................................................232
APPENDIX M —PANEL REGRESSION SPECIFICATION TESTS ............................................................ 233
M.1
M.2
M.3
M.4
M.5
M.6
M.7
Introduction .....................................................................................................................................................................233
Specification test plan .....................................................................................................................................................233
The Breusch-Pagan LM test for presence of random effects....................................................................................233
The F-test for the presence of firm effects ..................................................................................................................235
The Hausman test for correlation between random firm effects and the regressors .............................................237
The likelihood test for the presence of panel heteroscedasticity in the fixed-effect model ..................................238
Conclusions from the specification tests ......................................................................................................................239
APPENDIX N —DOES RANDOM WALK IN THE RISK-ADJUSTED RESIDUAL ACCOUNTING
RATES-OF-RETURNS? ..................................................................................................................................... 241
N.1
N.2
N.3
N.4
N.5
N.6
The hypotheses to be tested...........................................................................................................................................241
The goodness-of-fit test..................................................................................................................................................242
A multi-period goodness-of-fit-test ..............................................................................................................................243
Test method .....................................................................................................................................................................244
Results from the multi-period goodness-of-fit tests ...................................................................................................245
Conclusions from the multi-period goodness-of-fit tests ..........................................................................................249
ACKNOWLEDGEMENTS ................................................................................................................................. 251
REFERENCES .................................................................................................................................................... 253
vii
LIST OF TABLES
Table 5-1: A specification of the balance sheet’s components. ................................................................................ 87
Table 5-2: Estimated yearly marginal tax in Sweden from 1977—1996. ................................................................ 89
Table 5-3: A specification of the type of components of the income statement ................................................... 91
Table 5-4: The one-year risk-free rate-of-return in Sweden (Source: SCB 1979—1984; Svenska Dagbladet,
1984—1996). ..................................................................................................................................................................... 92
Table 6-1: Descriptive statistics for risk-adjusted RROE per year, [EQ 6-8]....................................................... 101
Table 6-2: Descriptive statistics for risk-adjusted RRNOA per year, [EQ 6-9]. .................................................. 102
Table 6-3: Summary of the double-sided t test of H0: Risk-adjusted RROE=0 for all firms vs. H1A: Riskadjusted RROE0 for at least one firm. .................................................................................................................... 105
Table 6-4: Comparison of the robust confidence interval t-test and the best location estimate double-sided t
test of H0: Risk-adjusted RROE=0 for all firms vs. H1A: Risk-adjusted RROE0 for at least one firm. ....... 106
Table 6-5: Summary of the double-sided t test of H0: Risk-adjusted RRNOA=0 for all firms vs H1B: Riskadjusted RRNOA0 for at least one firm. ................................................................................................................. 107
Table 6-6: Comparison of the robust confidence interval t-test and the best location estimate double-sided t
test of H0: Risk-adjusted RRNOA=0 for all firms vs H1B: Risk-adjusted RRNOA0 for at least one firm. . 107
Table 6-7: Estimated serial correlation in the fixed-effects panel regressions and fit statistics for the fixedeffects panel regression using the risk-adjusted RROE with PCSE when assuming AR(1) errors. ................. 110
Table 6-8: Parameter estimates from the fixed-effects panel regression using the risk-adjusted RROE with
PCSE and AR(1) errors. ................................................................................................................................................ 111
Table 6-9: Estimated serial correlation in the fixed-effects panel regressions and fit statistics for the fixedeffects panel regression using the risk-adjusted RRNOA with PCSE and assuming AR(1) errors. ................. 112
Table 6-10: Parameter estimates from the fixed-effects panel regression using the risk-adjusted RRNOA with
PCSE and AR(1) errors. ................................................................................................................................................ 113
Table 7-1: A summary of the relationships between holdout sample length, forecast length, and the minimum
required predictions per firm at maximum forecast length. .................................................................................... 123
Table 7-2: The data matrix of forecast errors (e) with N predictions per firm having forecast horizon H with
M firms. ............................................................................................................................................................................ 124
Table 7-3: The parameter estimates from the pooled regression model for risk-adjusted residual rates-ofreturns. ............................................................................................................................................................................. 127
Table 7-4: The MdRAE-statistic for all holdout samples using the risk-adjusted RROE. ................................. 128
Table 7-5: The results from paired t tests used to discriminate between the transitory earnings model, the
semi-transitory earnings models, and McCrae & Nilsson’s (2001) model. ........................................................... 129
Table 7-6: The MdRAE statistic for all holdout samples using the risk-adjusted RRNOA. ............................. 130
Table 7-7: The results from paired t tests used to discriminate between the transitory earnings model, the
semi-transitory earnings model, and McCrae & Nilsson’s (2001) model. ............................................................. 131
Table E-1: The total number of limited companies (firms) in the empirical data. .............................................. 197
Table E-2: A summary of the number of structurally stable and structurally instable firms for the empirical
data.................................................................................................................................................................................... 201
Table E-3: The number of imputed firm in the data set using industry averages. .............................................. 202
Table E-4: The number of imputed firm in the data set using previous year’s financial data. .......................... 202
Table E-5: Summary of number of firm-year observations. ................................................................................... 203
viii
Table E-6: The time-series of structurally stable non-imputed firms. ................................................................... 203
Table I-7: Tail-weight indices for different distributions. ........................................................................................ 212
Table I-8: Robust estimates for the industry-year’s accounting rates-of-returns per industry size. .................. 213
Table J-9: Parameter estimates from the fixed-effects panel regression using the risk-adjusted RROE with
PCSE and AR(1) errors for alternative operationalizations of CNI. ..................................................................... 216
Table J-10: Parameter estimates from the fixed-effects panel regression using the risk-adjusted RRNOA with
PCSE and AR(1) errors for alternative operationalizations of COI. ..................................................................... 217
Table L-11: The dynamics of relative risk-adjusted RRNOA measured using number of observations and the
relative risk-adjusted RRNOA. .................................................................................................................................... 230
Table M-12: The outcome of the Breusch-Pagan LM tests for presence of random effects using the variables
risk-adjusted RROE and risk-adjusted RRNOA....................................................................................................... 234
Table M-13: The results of the F-tests for presence of firm effects measured using both risk-adjusted RROE
and risk-adjusted RRNOA. ........................................................................................................................................... 236
Table M-14: The results from the Hausman test for correlation between random firm effects and the
regressors when estimated using both the risk-adjusted RROE and the risk-adjusted RRNOA. .................... 238
Table M-15: Test for the presence of panel heteroscedasticity using both the risk-adjusted RROE and the
risk-adjusted RRNOA. .................................................................................................................................................. 239
Table N-16: The conditional probabilities ................................................................................................................. 245
Table N-17: Number of deleted complete firm times-series. ................................................................................. 245
Table N-18: Number of used complete firm time series that is available for the goodness-of-fit tests. These
time series are the time series available after the trimming explicated in Table N-17. ....................................... 246
Table N-19: Number of empirical observations (Obs) and the expected number of observations (Exp) per
bin for t=5. ...................................................................................................................................................................... 246
Table N-20: Number of empirical observations and the expected number of observations per bin for t=4. 247
Table N-21: Number of empirical observations and the expected number of observations per bin for t=3. 247
Table N-22: Summary statistics for the goodness-of-fit tests where t=5. ............................................................ 248
Table N-23: Summary statistics for the goodness-of-fit tests where t=4. ............................................................ 248
Table N-24: Summary statistics for the goodness-of-fit tests where t=3. ............................................................ 248
Table N-25: Summary statistics for the goodness-of-fit tests where t=2. ............................................................ 249
ix
SYMBOLS AND ABBREVIATIONS
Note that this is selection and not a comprehensive list of symbols and abbreviations.
\a,b^
a and b are the elements of a set.
‘
Logical not.
ab
a when b.
a ‰A
a is an element of set A.
aŠA
a is not an element of set A.

The empty set.
For all.
There exists.
’
Logical and.
‚
Intersection.
ƒ
Union.
a vb
a is not equal to b.
A
*a
i
i
A is the set of the union of all a:s.
S8
The objective (i.e., the universal) state set. Subscript 8 always denotes the universal set.
SK
The subjective state set. Subscript K is mnemonic for known. SK S8 4 I S
IS
The ignorance of states set. The states that the subject is unaware of.
A8
The objective actions set. I.e., the objective set of alternatives to choose from
AK
The subjective action set. A.k.a. the set of alternatives that is known. AK A8 4 I A
IA
The ignorance of actions set. The alternative that the subject is unaware of.
C8
The objective consequence set.
CK
The subjective consequence set
A‡B
A is a strict subset of B. I.e., At least one element of B is not part of A.
AˆB
A is a weak subset of B. I.e., All element of B may be part of A
AºB
A implies B but B does not necessarily imply A. A is a sufficient condition for B.
A”B
A is equivalent to B. I.e., A implies B and B implies A. A is a sufficient and necessary
condition for B.
A5B
Set theoretical minus. I.e., The part of set A that is not part of set B.
‰A
The complement set to set A.
a \b
A weak preference relation. I.e., a is either preferred to b or indifferent to b.
a ;b
A strict preference relation. I.e., a is preferred to b.
a b
Real value a is greater than the real value b.
a ‰ < 0,1>
0 ba b1
x
a ‰ 0,1>
0 a b1
a ‰ < 0,1
0 ba 1
a ‰ 0,1
0 a 1
f :AlB
The real function f maps domain A to its co-domain B.
f Du
The composition of real functions f and u.
f a The real value of the real function f at a.
\
The real line.
\
The positive real numbers.
\L
The real space having L dimensions.
t 1 ROEt
The firm’s return on equity for the period starting at the end of t 1 to the end of t .
I
t 1 ROEt
The industry’s return on equity for period t.
t 1 RROEt
Residual return on equity.
t 1 RNOAt
Return on net operating assets.
*
t 1 RROEt
The ex post risk-adjusted residual return on equity.
*
t 1 RRNOAt
The ex post risk-adjusted residual return on equity.
&0 <¸>
The objective expectation at present.
&K 0 <¸>
The subjective expectation at present.
&*K 0 <¸>
The risk-adjusted subjective expectation at present.
&0 < t 1rt >
The objective expected market rate-of-return, also denoted objective MROR.
t 1rt
Simplified notation for the objective market rate-of-return.
&K 0 < t 1rKt >
The subjective expected market rate-of-return, also denoted subjective MROR.
t 1rKt
Simplified notation for the subjective market rate-of-return.
t 1 pt
The objective price at time t-1 for delivery at time t. It is also denoted
p * when
t 1 pKt
optimization is considered.
The subjective price.
T
T

The product symbol. E.g., 0 pT 0 p1 ¸ 1 p2 ¸ ! ¸ T 1 pT V0
The intrinsic value of a firm at present.
P0
The market price of a firm at present.

t 1 pt
t 1
t1
xi
LIST OF CENTRAL DEFINITIONS
Definition 2-1: Definition of ignorance of actions: Let the subject be unaware of at least one action in the
objective action set, i.e. the subject’s ignorance set is nonempty, I A Š  , and a strict subset to the objective
action set, I A ‡ A8 . .......................................................................................................................................................... 29
Definition 2-2: Definition of limited knowledge of actions. A subject’s knowledge of alternative actions is
limited when the subject has a nonempty ignorance set according to Definition 2-1. ......................................... 29
Definition 2-3: Definition of the subjective action set. The subjective action is defined as AK A8 4 I A . ...... 29
Definition 2-4: Definition of limited rationality: A subject that has a rational preference relation, i.e. a
preference relation that is complete and transitive on the subjective action set (Definition 2-3) is a limited
rational subject. ................................................................................................................................................................. 30
Definition 2-5: Let the subject be unaware of at least one state in the objective state set, i.e., the subject’s
ignorance set is nonempty, I S Š  , and a strict subset to the objective action set, I S ‡ S8 . ............................. 33
Definition 2-6: Definition of limited knowledge of states. A subject’s knowledge of potential states is limited
when the subject has a nonempty ignorance set of states according to Definition 2-5........................................ 33
Definition 2-7: Definition of the subjective state set. Let the subjective state set be SK S8 4 I S . ................ 33
Definition 2-8: Definition of limited rationality in the uncertain choice. In addition to Definition 2-4, a
subject exhibits limited rationality when the subject has a rational preference relation on uncertain
consequences that are limited because of limited knowledge of states (Definition 2-6). ..................................... 35
Definition 2-9: Definition of learning as discovery. Discovery takes place when the subject that acts
according to Definition 2-4 and Definition 2-8 and that faces the next choice in a sequence of choices
expands his or her subjective state set and/or the subjective action set. Discovery takes place because of the
subject’s experience from previous choices: Formally, learning as discovery means that the previous
subjective state and/or action sets are strict subsets to the current subjective state set and/or action sets. With
symbols, learning as discovery is defined as SKt 1 ‡ SKt , AKt 1 ‡ AKt , or when both situations occur and this
is because discovery make certain that I At 1 ‡ I At and I St 1 ‡ I St . ........................................................................ 44
Definition 4-1: The firm’s action set is defined as the union of all subjects’, who participate in the firm’s
I
endeavor, action sets. That is, AFirm * A , where i ‰ I
i
is a subject. .................................................................. 66
i 1
xii
LIST OF PROPOSITIONS
Proposition 2-1: When knowledge limits the actions inferred as available by the subject, it can, but must not,
reduce the subject’s set on subjective consequences. That is, AK ‡ A8 º C K ˆ C 8 . ............................................ 32
Proposition 2-2: There exists at least one subjective state probability that differs from the objective state
probability when the subject faces a strict subset of states: That is, QKs v Q8s where QKs , Q8s ‰ 1K ‚ 18 ,
when SK ‡ S8 . .................................................................................................................................................................. 35
Proposition 2-3: When the subject has a preference relation on the subjective consequence sets, which are
complete, transitive, continuous, state uniform, independent, and that follow the Archimedean assumption, it
is possible to express the subject’s choice as if he or she makes his or her choice based on an action’s
QKs ¸ uK cs , where cs ‰ C Ks , and QKs ‰ 1K . 38
subjective expected utility: EK 0 ¢¡U K c1, !cS ; QK 1, ! QKS ¯±° œ
s ‰SK
Proposition 2-4: Homo comperiens is a subject who is limited rational (Definition 2-4, Definition 2-8), that
learns using Bayesian learning and through discovery (Definition 2-9). The subject has a complete, transitive,
insatiable, continuous weak preference relation, which under uncertainty also is independent, state-uniform
and that follows the Archimedean conjecture. ............................................................................................................ 45
Proposition 3-1: Learning through discovery (Definition 2-9) ascertains that lim AK x A8 and
lim SK x S8
t ld
t ld
since the ignorance sets decrease. This implies that the subjective price approaches the
objective price as t goes to infinity. That is lim t 1 pKt x t 1 pt .............................................................................. 57
t ld
Proposition 3-2: Suppose that the Pareto optimal equilibrium price is fixed, which is reasonable since the
objective action and state sets are assumed to be fixed and since inflation is not conjectured. Then, with
Proposition 3-1 in mind, I propose that price convergence can be described as follows: Let the subjective
price be a function of the objective price p
and a fraction of the previous period’s discrepancy between the
subjective price and the objective price. That is,
K
t 1 pt
pC¸
t 2 ptK1 p
Ft
where C ‰ < 0,1
and
where Ft is a white noise disturbance. ............................................................................................................................ 59
Proposition 4-1: Since the subjects in a firm face subjective action sets according to Definition 2-3, and since
the firm’s knowledge is the union of its entire subject’s knowledge (Definition 4-1), the firm faces a subjective
action set that is a weak subset of the objective action set, i.e. AKFirm ˆ A8Firm . ....................................................... 66
Proposition 4-2: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences and
a mild regulatory assumption (cf. Appendix B, p. 188 for details), the market price of a firm is:
d
P0 0 pKt ¸ &K 0 <dKt > . ............................................................................................................................................. 69
œ
t 1
Proposition 4-3: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences, the
clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 188 for details), the market
d
price of a firm is: P0 EQ0 0 pKt ¸ &K 0 <RI t > , where &K 0 <RI t > &K 0 <CNI t > &K 0 < t 1rt > ¸ EQt 1 . ............ 69
œ
t 1
Proposition 4-4: Conjecturing Assuming the theory of Homo comperiens (Proposition 2-4), homogenous
preferences, the clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 188 for
d
d
details), the market price of a firm is: P0 EQ0 0 pKt ¸ &K 0 <ROI t > 0 pKt ¸ &K 0 <RIEt > where
&K 0 <ROI t > &K 0 <OI t > &K 0 < t 1rt > ¸ NOAt 1 ,
œ
t 1
œ
t 1
and &K 0 <RIEt > &K 0 <IEt > &K 0 < t 1rt > ¸ NFLt 1 . ............................. 70
Proposition 4-5: In a subjectively certain market that meets the assumptions of Homo comperiens
(Proposition 2-4, Proposition 3-2), with unbiased accounting, the subjective expected RROE and RRNOA
regress until, in the limit, they are zero. That is, lim &K 0 < t 1RROEt >
0 , and lim &K 0 < t 1RRNOAt >
0 . .. 72
t ld
t ld
Proposition 4-6: In a market that meets the conjectures of the theory of Homo comperiens (Proposition 24), and with unbiased accounting, there exists non-zero risk-adjusted subjective expected RROE and
xiii
RRNOA because of arbitrage opportunities. That is, &*K 0 < t 1RROEt > &K 0 <net arbitrage rate of returnt > v 0 , and
&*K 0 < t 1RRNOAt > &K 0 <operating arbitrage rate of returnt > v 0 ................................................................................................ 77
Proposition 4-7: In a market that meets the conjectures of the theory of Homo comperiens (Proposition 2-4,
Proposition 3-2) and with unbiased accounting the limit values of risk-adjusted subjective expected RROE
and RRNOA are zero. That is: lim &*K 0 < t 1RROEt >
0 , and lim &*K 0 < t 1RRNOAt >
0 . .............................. 78
t ld
t ld
xiv
LIST OF COROLLARIES
Corollary 4-1: The firm, populated by subjects who act according to Definition 2-7, faces a subjective state
set that is a weak subset of the objective state set, i.e. SKFirm ˆ S8Firm . ..................................................................... 66
Corollary 4-2: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences, the
clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 190 for details), the market
d
price of a firm is: P0 EQ0 0 pKt ¸ &K 0 < t 1 RROEt > ¸ EQt 1 , where
œ
t 1
&K 0 < t 1RROEt > &K 0 < t 1ROEt > &K 0 < t 1r >t
. ............................................................................................................. 69
Corollary 4-3: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences, the
clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 191 for details), the market
d
d
price of a firm is: P0 EQ0 0 pKt ¸ &K 0 < t 1 RRNOAt > ¸ NOAt 1 0 pKt ¸ &K 0 < t 1RNBC t > ¸ NFLt 1 ,
œ
t 1
œ
t 1
where &K 0 < t 1RRNOAt > &K 0 < t 1RNOAt > &K 0 < t 1rt > and &K 0 < t 1RNBC t > &K 0 < t 1NBCt > &K 0 < t 1rt > . ..... 70
xv
“Ignorance is like subzero weather: by a significant expenditure its effects upon people can be kept within
tolerable or even comfortable bounds, but it would be wholly uneconomical entirely to eliminate all its effects. And, just as an analysis of man’s shelter and apparel would be somewhat incomplete if cold weather
is ignored, so also our understanding of economic life will be incomplete if we do not systematically take
account of the cold winds of ignorance.” (Stigler 1961, p. 224)
CHAPTER 1—INTRODUCTION
“Thought is only a flash in the middle of a long night, but the flash that
means everything” Poincaré (1854-1912)
1.1 Background
At least three areas within market-based accounting research use the efficient market hypothesis
(EMH) as a reference point. Accounting researchers who correlate contemporaneous accounting
information with contemporaneous stock prices (e.g., the earning response coefficient literature)
(e.g., Collins and Kothari, 1989; Easton and Zmijewski, 1989; Liu and Thomas, 2000) need a model
to identify normal earnings to be able to study how actual market prices move regarding unexpected
earnings. The earning response coefficient literature conjectures market efficiency to find normal
earnings.
Researchers that test market efficiency demand models for earnings prediction in order to be
able to form hedge portfolios on this type of information (e.g., Abarbanell and Bushee, 1998; Piotroski, 2000). This research also makes heavy use of the EMH.
Positive accounting theorists seek to explain accounting choice based on management’s opportunistic behavior (e.g., Watts and Zimmerman, 1986). In addition, these researchers need to establish a level of normal earnings, which leads them to assume market efficiency.
In fact, when reading the market-based accounting review articles by Lev and Ohlson (1982),
Bernard (1989), and Kothari (2001), it appears as if the bulk of market-based accounting research
conjectures the EMH.
Lee (2001, p. 237) argues that research that builds on the efficient market hypothesis “is akin
to believing that the ocean is flat, simply because we have observed the forces of gravity at work on
a glass of water. No one questions the effect of gravity, or the fact that water is always seeking its
own level. But it is a stretch to infer from this observation that oceans should look like millponds on
a still summer night. If oceans were flat, how do we explain predictable patterns, such as tides and
currents? How can we account for the existence of waves, and of surfers?”
Nowadays, there are even calls for a theory of inefficient markets. Kothari (2001, p. 191)
writes, “while much of the research concludes market inefficiency, further progress will be made if
researchers develop a theory that predicts a particular return behavior and based on that theory design tests that specify market inefficiency as the null hypothesis.” Lee (2001, p. 251) writes: “Rather
than conjecturing market efficiency, we should study how, when, and why price becomes efficient
(and why at other times it fails to do so).” Even an adamant proponent of EMH, such as Malkiel
17
(2003, p. 80), admits that the market has pricing irregularities, predictable patterns, and is not perfectly efficient.
The growing awareness of the problems with the EMH provides an opportunity to develop
new theories of inefficient markets. This thesis develops and tests such a theory of market inefficiency, which uses a limited rational choice as a point of departure. I call this theory 1 the theory of
Homo comperiens and it allows me — continuing with Lee’s metaphor — to account for the existence of waves. It further explains how these waves disappear in the world of markets.
The theory of Homo comperiens is general but thesis applies it to financial economics to
maintain a connection to EMH. By applying it to financial economics, I derive firm valuation model
assuming ignorance. Some propositions from the theory are also tested on Swedish accounting data
that places it in the market-based accounting field.
Before I present and discuss any details of the research presented in this thesis, it is necessary
to put the research into its proper context. Therefore, what follows is an initial discussion of EMH
and consequences of applying EMH onto market-based accounting research. This chapter closes by
fencing this research from other non-equilibrium theories and with the disposition of the thesis.
1.2 The efficient market hypothesis
Fama (1965a, p. 94) proposes the EMH and defines an efficient market as “…a market where prices
at every point in time represent best estimates of intrinsic values. This implies in turn that, when
intrinsic value changes, the actual price will adjust ‘instantaneously’…”
Fama’s initial definition of the efficient market is changed in Fama (1970, p. 383) to a market
“…in which prices always ‘fully reflect’ available information.”
The second definition presumes the first definition but opens for gradual dissemination of
information into the market. Fama (1970) also endows the definition with testable properties.
The first definition is an application of the rational expectations hypothesis onto the financial
market in that it refers to best estimates. The rational expectations hypothesis conjectures that the
subject makes unbiased forecasts (e.g., Huang & Litzenberger 1988, p. 179, 185). A rational expectation model is Pareto optimal if and only if the forecasts are unbiased (Huang & Litzenberger 1988,
p. 191-193). Indeed, the rational expectations hypothesis is flexible enough to ensure that a Pareto
optimal equilibrium exists even when information is asymmetrically distributed among the subjects
in a market (Grossman 1981). Therefore, it follows that EMH is valid if the hypothesis about rational expectations is valid since it yields a Pareto optimal equilibrium.
1
Indeed, I call it theory in a narrow sense since it purports to be “…a set of statements, organized in a characteristic
way, and designed to serve as partial premisses for explaining as well as
predicting an indeterminately large (and usually varied) class of economic phenomena (Nagel, 1963, p. 212).”
18
The unbiasedness comes from the fact that the subject continuously updates his or her expectations based on the realizations from a stochastic process (Grossman 1981, p. 543-544). The
updating of expectations follows a Bayesian learning procedure (e.g., Huang & Litzenberger 1988, p.
179-182, Congleton 2001, p. 392), which implies the use of a the standard state-space-and-partition
model 2. Even under information asymmetry, the asymmetry is limited to be on the events within the
standard state-space-and-partition model (e.g., Grossman 1981).
The standard state-space-and-partition model allows the subject to learn by introducing a
finer and finer partition of the state set until the limit scenario occurs where the partition only holds
a unique state. This means that the subject gradually resolves previous uncertainty and traverse from
knowing that the subject does not know (as Modica and Rustichini, 1999, p. 266 put it, the subject
faces a conscious uncertainty), to knowing that the subject knows (i.e., certainty).
To conclude, for EMH to be valid it follows that the rational expectations hypothesis must
be valid, the subjects’ forecasts must be unbiased for the rational expectations hypothesis to be valid,
and the subjects’ knowledge must be able to be captured using the standard state-space-and-partition
model for the forecasts to be unbiased. When this chain of conjectures holds, it implies that the
market is in a Pareto optimal equilibrium. A Pareto optimal equilibrium is a situation where there
does not exist arbitrage opportunities (e.g., Ohlson 1987, p. 17).
1.3 The standard state-space-and-partition model, ignorance, and equilibrium
The use of standard state-space-and-partition model permeates financial economics (e.g., Eichberger
& Harper 1997; Debreu 1959; Demski 1972; Dothan 1990; Duffie 1992; Fishburn 1979; Huang &
Litzenberger 1988; Ohlson 1987; Pliska 1997; Silberger & Suen 2000). Another way to express this is
that financial economics generalizes consumer theory with the use of state-contingent commodities
(Silberger & Suen 2000, p. 399).
A state is in this perspective “a description of the world, leaving no relevant aspect undefined” Savage ([1954] 1972, p. 9). The true state is the state that “does in fact obtain” Savage ([1954]
1972, p. 9). The standard state-space-and-partition model envisions the state space as exhaustive and
consisting of mutually exclusive states. Whichever state obtains is beyond the control of the subject.
The use of the standard state-space-and-partition model is necessary for a Pareto optimal
equilibrium solution in financial economics when uncertainty is present (e.g., Ohlson 1987, p. 8-25).
No arbitrage opportunities are necessary to derive at the Capital Asset Pricing Model
(CAPM) (e.g., Ohlson 1987, p. 71-94). Existence of no arbitrage opportunities is necessary to derive
the firm valuations models used in financial economics (e.g., Feltham & Ohlson 1999), and the standard state-space-and-partition model is an integral part to the no-arbitrage solution.
2 I borrow the use of the concept “standard state-space-and-partition model” from Dekel, Lipman & Rustichini (1998, p.
164) and Samuelson (2004, p. 399).
19
The standard state-space-and-partition model assumes that the subject can identify everything that the he or she does not know (Dekel, Lipman & Rustichini 1998, p. 164; Rubinstein 1998,
p. 47; Samuelson 2004, p. 372, 398). This is known as the axiom of awareness (Samuelson 2004, p.
372) or the axiom of wisdom (Samuelson 2004, p. 398), or that the subject “knows all tautologies”
(Dekel, Lipman & Rustichini 1998, p. 164).
The axiom of wisdom ascertains that the subject can never be surprised and that the arrival
of new information allows him or her to reduce his or her uncertainty about what is (Samuelson
2004, p. 398). That is, the subject was aware of this possibility before but with the arrival of new
information, the subject knows it with certainty. This means that the subject first knows that he or
she does not know but with the arrival of new information, the he or she learns such that he or she
knows that he or she knows.
The axiom of wisdom ascertains that the subject is not unaware of anything (Samuelson
2004, p. 399). In fact, the main result of Dekel, Lipman, and Rustichini (1998) is that the standard
state-space-and-partition model cannot cope with the subject’s ignorance of some state. That is, for
the subject to be ignorant of a state requires that the subject cannot identify the state, but the standard state-space-and-partition model conjectures that the subject can identify all states.
This may not be a problem when a unique subject’s choice is considered, but considering a
market means that the problem expands into a multi-subject setting with the implication that the
other subjects’ choices become part of the uncertainty of the focal subject’s choice-problem (Samuelson 2004, p. 388). This means that the standard state-space-and-partition model’s axiom of wisdom requires each subject to have a complete understanding of all other subjects’ plans for choices— i.e. perfect knowledge.
The discussion above shows that models in financial economics, such as the CAPM and
firm valuation model, require every subject in the market to have perfect knowledge about everyone
else’s supply and demand plans. Anything short of that implies ignorance of at least a state and the
existence of ignorance ascertains arbitrage opportunities, which mean that the market no longer
satisfies the requirement for a Pareto optimal equilibrium.
Some may argue that requiring all individuals to be rational with perfect knowledge is overly
restrictive. Two alternative explanations are that irrational subjects’ trades are random and cancel
each other, or even if they do not cancel each other, rational arbitrageurs in the market eliminate
their influence on prices (Shleifer 2000).
If irrational subjects’ trades are random and cancel each other, it follows that at least two individuals in the market are surprised with their consumption-investment plans. This means that at
least one individual continues to jostle to improve his or her well-being, with possible changes to the
price as a result, i.e. this is not a Pareto optimal equilibrium. The additional weakness with such a
20
hypothesis is that it lacks theoretical coherence: Why would irrational subjects trade random so that
they cancel each other? The existing no-arbitrage theory does not support such a proposition since it
imposes the axiom of wisdom.
The second argument surmises that rational arbitrageurs in the market eliminate irrational
subjects’ influence on prices. Again, such a proposition lacks credible formal theoretical foundation.
Such a proposition requires a choice theory where rational subjects are given certain traits and where
irrational subjects are given other traits, and where it leads to a Pareto optimal equilibrium. I still
have not seen a formal theory that solves this problem.
1.4 Empirical research
Much empirical research is devoted to investigate different operationalizations of EMH and it appears as if stock markets are efficient in the short run (Kothari 2001, p. 187-204).
Tests for stock market efficiency are mainly conducted on U.S. stock market data: for example, Beaver (1968), Landsman, and Maydew (2002). How smaller markets behave is less clear (e.g.,
Graflund (2001) showed market inefficiency for the Swedish stock market and Jacobsen and Voetmann (1999) found market inefficiency in the Danish stock market. The efficiency in the market for
ownership in non-public firms is even less understood, but there are reasons to expect them to be
not as efficient as organized stock markets because of less well-developed market microstructures
(e.g., liquidity and lack of transparency).
The efficiency tests of organized stock markets use, e.g., short-window event studies. Event
studies having short windows in which they study stock market reactions are studies that test if
short-run arbitrage opportunities exist in the stock market and, if present, how fast they disappear.
Short-run market efficiency tests cannot separate between the effect from an inefficient market and the effect from deviations from the no-arbitrage condition in the market. This is due to the
joint hypothesis of market efficiency tests: Any test of a market’s efficiency has to be jointly tested
with a no-arbitrage asset-pricing model (Fama 1970, 1991).
CAPM is applied as the no-arbitrage asset-pricing model when the market’s efficiency is
tested. If the market is in disequilibrium (e.g., because of less-than perfect knowledge) while CAPM
is applied, it means that a miss-specified asset-pricing model contaminates the market efficiency test.
This implies that such tests cannot distinguish between effects from a miss-specified asset-pricing
model and effects from market inefficiency.
Deficiencies in the tests of short-run market efficiency have led to long-horizon event studies
(e.g., DeBond and Thaler 1985; Abarbanell and Bushee 1997, 1998). Long-horizon tests of market
efficiency find conflicting results to those in the short-run tests, with the results indicating that the
stock market is unable to adjust for long-horizon arbitrage opportunities (Kothari 2001, p. 188-189).
21
Anecdotic evidence of long-horizon mispricing effects abound: e.g., the 17th century tulip
mania in Holland, the stock market crash in the 1930s, the October 1987 stock market crash, the
Japanese stock market price bubble from the 1980s, and the Internet stock price bubble from the
1990s.
Low-frequency events as those above create the long-horizon post-event anomalies and are
observable in other markets as well (e.g., the real-estate markets’ price bubbles in Sweden and the
UK in the 1980s).
For several reasons (e.g., the long-run indicators of market inefficiency) there is a longstanding and growing unease among empirical market-based accounting and finance researchers in
the EMH (e.g., Lev & Ohlson 1982; Bernard 1989; Daniel et al. 1998; Barberis et al. 1998; Hong &
Stein 1999). Moreover, it is this unease that led Kothari (2001) and Lee (2001) to start to ask for a
theory of inefficient markets.
1.5 The relation of the thesis to other research
This thesis is a response to Kothari (2001) and Lee (2001). It is an attempt to develop and empirically test a theory of inefficient markets using accounting data. I call the choice theory for Homo comperiens. It uses Dekel, Lipman, and Rustichini’s (1998) findings that the standard state-space-andpartition model cannot cope with the subject’s ignorance, and Modica and Rustichini’s (1999) result
that shows that a state-space-and-partition model allowing for ignorance is still partional.
It is well known that there exist innumerable ways to be in non-equilibrium, i.e. that potentially there exist innumerable theories of inefficient markets. Examples of inefficient market theories
are theories that posit that the subjects are not price takers (monopoly theory and oligopoly theory).
Then there is the tradition in behavioral economics that focuses on bounded rational choices in the
form of modeling the choice process in a non-perfect manner. Research that uses a bounded rational framework focus on, e.g., heuristics, framing or other types of market inefficiency (Kahneman
2003; Shefrin 2002; Shleifer 1999).
The theory of Homo comperiens presented in this thesis is part of behavioral economics research in the sense that it focuses on the subject’s bounded rationality. It separates itself from the
core of behavioral economics (e.g., Simon 1955; Kahneman & Tversky 1979; Tversky and Kahneman 1981) since it does not model the choice process. It positions itself deliberately close to the
core financial economics (e.g., Debreu 1959; Demski 1972; Dothan 1990) and empirical marketbased accounting research (e.g., Abarbanell & Bushee 1998; Collins & Kothari 1989; Liu & Thomas
1999a, b; Piotroski 2000) by conjecturing rational preference relations. It is also closely related to
parts of game theory research (e.g. Halpern 2001; Modica & Rustichini 1999) insofar that it allows
for ignorance. Modica and Rustichini (1999) defines ignorance as a situation where the subject only
22
is aware of a subset of the “grand” set of states. Moreover, these authors show that even such a
state-space model is partional.
The only central conjecture that is modified in Homo comperiens as compared with mainstream economics is the completeness axiom. By changing only one central conjecture in mainstream economics, a new world opens, which is a world in which disequilibrium becomes the rule
and not the exception. Nevertheless, it is at the same time a world that also exhibits equilibrating
forces. Alternatively, the theory predicts the existence of waves and how they disappear.
In this thesis I attempt to falsify the theory by empirically testing two testable hypotheses.
Since they are based on the firm valuation models conjecturing ignorance that stems from the theory
of Homo comperiens, they conjecture market inefficiency. Therefore, the empirical tests do not
focus on tests of stock market efficiency. However, again inspired by Kothari (2001, p. 191), in a test
of the theory’s validity, I let predictions of return behavior from a rational expectations model compete with predictions of return behavior from the theory of Homo comperiens.
Because the market is theorized as being inefficient, market prices are expected to be the
same as intrinsic values, implying that there is nothing to be gained from using market prices as part
of the empirical tests, as is the standard operating procedure in market-based accounting research.
1.6 Expected contribution
Both the economist and the accounting researcher should find an interest in this research since it
proposes a formal theory of limited rational choice that yields inefficient markets. The empirical
section of this thesis can also interest users, producers, auditors, and regulators of accounting.
Users of accounting are the existing and potential equity subjects in firms. They can use the
results of this research as they analyze the intrinsic value of Swedish manufacturing firms. They can
also apply the same basic models, but with different parameter estimates, to other industries and to
other countries.
Producers of accounting variables can use the models from several perspectives. As the
models reveal how the accounting rate-of-return is affected by discovery, this can provide ideas of
how to use a firm’s financial control mechanism. It could also be used as a strategic tool for guiding
the choice of top-management.
Regulators have use of the empirical accounting research in this thesis since it sheds light on
how acquired goodwill changes over time. Consequently, this research can affect the regulation of
goodwill.
The thesis also provides a tool for auditors when analyzing firms’ impairment test of goodwill in that it provides clues on how to evaluate a firm’s forecasted earnings capacity for the acquired
assets.
23
1.7 Outline of thesis
This thesis consists of eight chapters and appendices. The thesis can be read in many ways depending on interest. I propose three alternative reading strategies.
The first strategy is aimed at theoretically interested readers who wonder what the theory of
Homo comperiens is and how it relates to economic theory. Such a reader is primarily interested,
after having read Chapter 1, in reading Chapter 2—4 and Appendices A - C.
With such an interest, I would advise the reader to read Appendix A before reading Chapter
2. While reading Chapter 2, it is advisable to also read Appendix C.
Having read Appendix A, Chapter 2, and Appendix C, the reader should proceed to Chapter
3, Appendix B, and Chapter 4, in that order. While reading Appendix B, it is advisable to again skim
Appendix A because of their similarities.
Then, as closure, I would take a quick look at the empirical findings and conclusions of the
thesis by reading the summaries in Chapters 6 and 7 and the concluding discussion in Chapter 8.
The second strategy is designed for the non-theoretically interested accounting researcher,
the non-theoretically interested industrial economics researcher, and accounting practitioners, including users, producers, regulators, and auditors.
Such people should, after having read Chapter 1, read Chapter 5 and 6 and Appendix D—N.
Chapter 5 is read with frequent cross-referencing into Appendix D—H. Those appendices provide
the operationalizations of the variables to the database names and discuss how the database was set
up.
Chapter 6 makes final operationalizations of the testable propositions and reports the tests
and test results. While reading the chapter there are plentiful cross-references into Appendix I – N
that I urge the reader to follow. Those appendices provide further operationalizations (Appendix I),
technical discussion on test procedures (Appendix K, L, and M) and complementary tests in
Appendix J and N. I also urge such a reader to read the concluding discussion in Chapter 8.
The third strategy focuses on the reader who has an interest in the whole thesis. I would like
to advise such a reader to follow both reading strategies, perhaps after first having read Chapter 1
and the concluding discussion in Chapter 8.
Others, with only a cursory interest in thesis, can focus on the first and last chapters and possibly on each chapter’s summary
24
CHAPTER 2—THE THEORY OF HOMO COMPERIENS:
LIMITED RATIONAL CHOICE
“…there are known knowns; there are things we know we know. We also
know there are known unknowns; that is to say we know there are some
things we do not know. But there are also unknown unknowns -- the ones
we don’t know we don’t know.” (Rumsfeld 2002)
2.1 Introduction
This thesis aims to develop and test a theory of market inefficiency. At the heart of the debate regarding market efficiency and market inefficiency, lays the conjecture of the subject’s rationality.
Chapter 1 argues that the nucleus to a theory of market inefficiency should be based on a limited
rational choice and not on other limitations such as non-atomistic actors. The purpose of this chapter is to develop a theory of limited rational choice that can be applied to such areas as financial
economics and market-based accounting research.
Before I introduce the details, consider the following story 3. Before you leave home in the
morning, you consider whether to wear a raincoat or not. The choice depends on whether it rains or
not. You look at the window and if there are raindrops on the window, you take the raincoat because that signal implies that it is raining. If there are no raindrops on the window, you do not wear
the raincoat since it implies that it is not raining. When you look at the window, you see there are no
raindrops and consequently you do not wear the raincoat when you open the door.
This short story is a choice problem with a set of alternative actions that contains two elements \raincoat, ‘raincoat^ . The action set stands in relation to a set of consequences with elements
\wet, dry^ and this relation is intercepted by the following state set \rain drops, ‘ rain ‘drops^ .
The state set is presented in an event way such that the event with drops on the window allows you
to learn whether it is raining or not.
However, when you open the door and leave the house, after having received the signal no
drops, without wearing the raincoat, you find yourself walking in a rain shower. Walking wet in the
rain you realize that you were unaware of the fact that it could rain even when you receive the signal
no drops. Therefore, when you prepare to walk to your job the next morning, you consider the expanded state set \ rain drops, rain ‘drops, ‘ rain ‘drops^ when choosing what to wear. This time
you receive the signal drops and therefore conclude that it is raining and wear the raincoat. When
you leave the home, you realize that it does not rain because the drops on the window come from a
neighbor watering his lawn, which is a possibility that you somehow where unaware of. Again, you
learn from your experience so that the next day you consider an even more complete state
3
This story originally appeared in Rubinstein (1998, p. 41) but it is here modified to allow for ignorance.
25
set \ rain drops, rain ‘drops, ‘ rain ‘drops, ‘ rain drops^ when choosing whether to wear the raincoat.
Making these choices, you are unaware of the possibility that it might or might not rain regardless of the signal, and this leads you to incorrect inferences. However, you are not only unaware
of the possibility that the signal may not indicate that it rains, you are also unaware of the fact that
you are unaware of this. Consequently, you are completely amiss making your choice, i.e. there are
uncertainties that are not anticipated – unknown unknowns.
Through the learning effect, you are able to expand the consequence set such that the unknown unknowns become known unknowns, i.e. you know that you do not know whether it is raining after having received either the no drops or the drops signals and the uncertainties are therefore
anticipated.
Not only are there unknown unknowns in this simple problem depicting themselves as limited state sets, but the set of alternatives to choose from is also limited. The choice problem is
restricted to choose only whether to wear or not to wear a raincoat based on the drops on the window signal. When you learn that this is not an appropriate signal (i.e., unknown unknowns are now
known unknowns), you realize that by opening the front door you can judge whether it is raining or
not. The set of choice alternatives is therefore limited and by expanding the action set it becomes
possible to convert the known unknowns to known knowns, i.e. to remove the uncertainty altogether by redefining the choice problem to include more alternatives in the action set. The set of alternatives can of course be expanded to cover other options too such as bringing an umbrella in case it
begins to rain, etc.
Restricting rationality is not novel. Simon (1955, p. 101, 104; 1990, p. 7) notes that there are
basic physiological constraints to a subject’s choice making on both the subject’s computational ability and the subject’s memory that physically prohibits perfect rationality. Rubinstein (1998, p. 3)
notes that it is not until recently that bounded rationality has affected economics. However,
bounded rationality focuses on the elements of the process of choice and hence not specifically on
the type of limitations considered above (Rubinstein 1998, p. 1, 192-193; Simon 1993, p. 156). Lipman (1995, p. 43) notes that there are only a few papers that explore the implications of bounded
rationality, but that there are many modeling approaches, which may be due to lack of agreement as
to what bounded rationality is.
To the best of my knowledge, there are no formal bounded rationality models in economics
that have been applied to financial economics models. There is a vast literature in behavioral economics inspired by bounded rationality arguments (see, e.g., Shiller (2003) for a review of behavioral
finance and Conlisk (1996) for a review of bounded rationality research). However, as Kahneman
(2003) notes, behavioral economics typically addresses only a particular observed market anomaly at
26
a time, whereas this thesis aims to be more general in scope with its approach to model choice as
choosing from a set of alternatives.
It is possible to argue that theory already exists in Austrian economics since Kirzner (1973)
and Congleton (2001) restrict choice due to ignorance. Neither Kirzner nor Congleton treats the
ideas in a manner such that it can be transformed into a theory of market inefficiency that is precise
enough to allow it to be formally tested. The theory of Homo comperiens builds particularly on
Kirzner’s ideas but takes the analysis further in such a direction that it becomes a testable theory of
human action.
In developing the theory I sought vital inspiration from the work of Hayek (1936, 1945),
Kirzner (1973), and Simon (1955, 1956). Since the model is mathematically grounded leading to the
subjective utility maximizing behavior (which is only similar to a [objective] utility maximizing behavior that appears in a general equilibrium), it is also inspired by the general equilibrium researchers
Debreu (1959) and Demski (1972). Rubinstein (1998) and Samuelson (2004) provide inspiration for
the chapter’s discourse.
Chapter 2 is organized as follows: After the introduction, a subsection follows in which rational choice and limited rational choices are discussed. This subsection focuses on developing the
main body of the theory. The ensuing subsection converts the limited rational choice into a utilitybased limited rational choice. Learning is introduced before the closure of the chapter, which is a
central trait to Homo comperiens. It leads to the sought-for equilibrating forces in a sequence of
choices that can best be described as being in a state of disequilibrium.
2.2 The limited rational choice
This section proposes a model of human choice-making that allows for ignorance on both the action and the state set. It does so using an axiomatic approach, which is suggested by Lipman (1995,
p. 64) to be an especially promising route in the bounded rationality research.
Lipman (1995, p. 64) points out that it is important to try to apply these models to empirical
data, but that there has been very limited attempts in that direction. The goal with this section, and
the rest of the chapter, is to be specific enough such that it is possible to use the results to build
tractable firm valuation models in uncertainty conjecturing ignorance that can be empirically tested.
The section retains all the traits of a perfectly rational subject but forces those choices to be
made on a limited set of alternatives and by considering a limited state set. Thus, the chapter discusses human action that is rational but where any choice is made on a strict subset of the objective
set of available alternatives and on a strict subset of the objective set of available consequences.
An intriguing result with this section is that human action, as described by Homo comperiens, can be thought of as if it follows a principle of maximizing the subjective expected utility. This
27
is similar yet it differs from human action according to the perfectly rational choice. A perfectly rational choice can be described as if it follows a utility maximization principle, which I here call the
objective expected utility. First follows the perfectly rational choice that acts as a frame of reference
and then follows the limited rational choice model.
2.2.1 The perfectly rational choice, the starting point
First, as in economics, I conjecture a complete preference relation, which is similar to e.g., Kreps
(1988), Mas-Colell et al. (1995, p. 6). That is, the subject knows 4 of all the alternatives that the subject can choose among, and the subject can choose between them. Formally, that means a \ b ,
or b \ a , or both a, b ‰ A .
Second, I conjecture again, as in economics (e.g., Kreps 1988; Mas-Colell et al. 1995, p. 6),
that the subject’s preference relation is transitive. That is a \ b , b \ c º a \ c a, b, c ‰ A .
A preference relation that is complete and transitive is, according to Mas-Colell et al. (1995,
p. 6), a rational preference relation.
The set of alternatives above is generic and hence more structure is needed. Therefore, let
A8 be the subject’s nonempty objective 5,6 action set, i.e. the set of all available alternatives for a sub-
ject. Since there are no a priori limitations to the objective action set, it can be infinite.
A subject who holds a rational preference relation on the objective action set is a perfectly rational subject.
A perfectly rational subject can make any necessary transformations so that the subject can
rank all the alternatives. Since the objective action set is potentially infinite, there can be neither
bounds to the subject’s physiological storage capacity of information nor any limitations to the subject’s computational abilities necessary to achieve transitivity.
2.2.2 Actions, ignorance of available actions, and limited rationality
Suppose that the subject is unaware of at least one action in the objective action set. To be more
precise I define this ignorance below.
4
By knowing I mean that when the subject knows, e.g., that it is raining, it means that it is true that it is raining. Knowing is therefore not the same as believing, which may or may not turn out to be true. Knowing is to be aware of, or to
perceive. Similarly, not knowing is equivalent to be unaware of, equivalent to be ignorant of, and equivalent to not perceive.
5 The words objective and subjective sets are used in this thesis. Modica and Rustichini (1999) use them with the same
meaning, i.e. when they differentiate between the universal set and a subset of it.
6 Objective is also used by Hayek (1936, p. 39) in the meaning of objective data, where objective data is exogenous data
common to all subjects in the market. This should be understood as if there is an objective reality with “real” alternatives
and “real” consequences. That is, a world that is not socially constructed. This departs from sociological research that
frequently sees the world as being a social construct.
28
Definition 2-1: Definition of ignorance of actions: Let the subject be unaware of at least one action in the
objective action set, i.e. the subject’s ignorance set is nonempty, I A Š  , and a strict subset to the objective action set, I A ‡ A8 .
With the introduction of the ignorance of actions set, it is also possible to define a subject’s
limited knowledge of action, as done below.
Definition 2-2: Definition of limited knowledge of actions. A subject’s knowledge of alternative actions
is limited when the subject has a nonempty ignorance set according to Definition 2-1.
Using Definition 2-1 together with the objective action set, it is also possible to define the
subject’s subjective action set.
Definition 2-3: Definition of the subjective action set. The subjective action is defined as AK A8 4 I A .
Definition 2-1 to Definition 2-3 can be verbally explained as follows. When a subject has limited knowledge of actions, the subject does not know of all the alternative actions that exist. All the
actions that are available are found in the objective action set. Those actions that exist but that the
subject does not know of constitute the ignorance of action set. The actions that the subject knows
of make up the subjective action set, which is defined as the difference between the objective action
set and the ignorance of actions set.
Note that A8, I A Š  ’ I A ‡ A8 º AK Š  . The fact that the subjective action set and the
ignorance of action set are non-empty implies that AK ‡ A8 , and so it follows that any choice that
the subject makes is based on an incomplete description of the available alternatives. Since AK is
nonempty, it means the model conjectures that the subject always knows of at least one alternative
to choose from.
Conjecture that the subject holds a rational preference relation on AK . Note that that if
AK A8 is possible, it implies that the subject makes a perfectly rational choice. The strict subset
conjecture therefore ascertains that there is a difference between the two choice models.
Simon (1955, p. 101, 104; 1990, p. 7) notes that there are basic physiological constraints to a
subject’s potential choice making capacity because of the subject’s computational ability and because
of the subject’s limited short-term memory. If Simon is correct, it is reasonable to conjecture that a
subject can be ignorant of some of the elements of the objective action set. A subject’s ignorance of
alternative actions is also something that both Hayek (1936, 1945) and Kirzner (1973) use.
It is possible to conceive that other factors than the subject’s physiological constraints can
restrict a subject’s subjective action set such that it becomes a strict subset of the objective action
set. In particular, legislative restrictions may prohibit some goods and services from being traded
(e.g., nuclear weapons). These legislative restrictions create incomplete markets, which is a phenomenon already appreciated in economics (e.g., Pliska 1997, p. 58). The subjective action set dis29
cussed above is not of this kind, however: It is a subset that only exists because of limited knowledge. Had the subject had perfect knowledge, the subject would have had the possibility to evaluate
all the possible actions rationally. This is guaranteed by the completeness axiom. From this it also
follows that incomplete markets may appear due to limited knowledge and does not only depend on
legislative measures.
The definition of ignorance of actions in connection with the definition of the objective and
the subjective action set leads to limited knowledge of the available alternatives. Limited knowledge
of the available alternatives is used to define limited rationality.
Definition 2-4: Definition of limited rationality: A subject that has a rational preference relation, i.e. a
preference relation that is complete and transitive on the subjective action set (Definition 2-3) is a limited
rational subject.
2.2.3 Limited rationality versus bounded rationality
The concept of limited rationality can itself be loosely seen as a strict subset to bounded rationality.
Consider the definition of bounded rationality by Simon (1993, p. 156):
“Human beings (and other creatures) do not behave optimally for their fitness, because they are wholly incapable of acquiring the knowledge and making the calculations that would support optimization. They do
not know all of the alternatives that are available for action; they have only incomplete and uncertain
knowledge about the environmental variables, present and future, that will determine the consequences of
their choices; and they would be unable to make the computations required for optimal choice even if they
had perfect knowledge.”
That is, when Simon (1955) introduces bounded rationality as a critique to perfect rationality,
it is clear that the subject not only limits his or her action set but the he or she also limits the process
of making a choice. The subject does so by introducing, e.g., a satisfying behavior. In research, the
concept of bounded rationality has become a waste basket into which almost any sort of non-perfect
rationality is deposited (see, e.g., Conlisk (1996) for a review of the diverse field of bounded rationality research). Rubinstein (1998, p. 1) notes that bounded rationality sometimes is even used to depict
situations having incomplete or bad models. Rubinstein challenges Kreps to come up with a definition of bounded knowledge, but Kreps acknowledges his inability to provide a precise definition
(Kreps 1990, p. 150-156).
Even though Simon (1955, 1993) includes choices based on limited actions as part of
bounded rationality, it is clear from Simon (1955, 1956, 1986, 1993) and from Simon’s correspondence with Rubinstein (1998, p. 192-193) that bounded rationality primarily focuses on the process
of making a choice and the physiological as well as the psychological limitations that guide the process. In fact Simon (1986) even calls this procedural rationality.
Limited rationality does not consider procedural rationality but retains the economics view
that the model (hopefully) describes the subject’s choice as if it is limited rational, i.e. as will become
30
clear as the analysis proceeds, limited rationality focuses on the optimization of given means to given
ends, to use Kirzner’s (1973) word, but here the means and ends are subsets to the objective sets.
With this definition of limited rationality, it clearly demarcates itself from both perfect rationality and bounded rationality. Perfect rationality never implies limited rationality. Bounded rationality may imply limited rationality. Limited rationality implies bounded rationality. But limited
rationality and bounded rationality are not equivalent models of a choice problem.
2.2.4 Consequences, ignorance, and the subjective action function in certainty
So far, nothing has been said about how the subject forms his or her preference relation. It is as-
sumed, as in economics (e.g., Rubinstein 1998, p. 9) that a subject forms his or her preference relation based on the consequences of the choice alternatives. An action can only lead to one possible
consequence when certainty is present. This subsection maintains the certainty conjecture. A subsequent subsection (2.2.5) introduces the uncertain choice.
Let C 8 be the nonempty objective consequence set, which is the set whose elements are the
outcomes from choosing among the objective action set. Let the objective action function be
f8 : A8 l C 8 , which attaches a consequence to each action. The unique element in the consequence
set is also written as f8 a to indicate that it is the real value of the function f8 at a .
A (mathematical) function is a special type of correspondence between two sets of which one
set is the domain and the other set is the co-domain. It is a correspondence defined once for each
element in the domain. To each element in the domain exactly one element is attached in the codomain. Every element in the domain must be accounted for only once, but to each element in the
co-domain there can be attached more than one element from the domain. It is possible that not all
the elements in the co-domain are associated with elements in the domain. The essential feature is
that each element in the domain must be used once, and once only, to form an association with a
unique element in the co-domain. The association is the function’s arguments (see, e.g., Sydsaeter et
al. (1999) for such a discussion).
Since f8 : A8 l C 8 is a function, it follows that it is a one-to-one relation, which implies that
the subject is a priori certain about the outcome of a particular choice. Hence, it is a certain choice.
Since it is a one-to-one relation, it follows that it is a surjective function, i.e. every element of the codomain is used at least once.
Conjecture that the subject does not know of at least one consequence in the objective consequence set. Let the subject have a subjective consequence set, which is defined as the difference
between the objective consequence set and the set of consequences that the subject is unaware of.
That is, C K
C 8 4 IC
, where IC ‡ A8 and IC Š  . This is analogous to Definition 2-1 to Definition
31
2-3, but since this subsection is an expansion of the more general choice structure in the previous
subsection, no formal definitions are introduced.
Since the subject then has a subjective consequence set, the subject has a subjective action
function fK : AK l C K .
With these definitions, it is possible to state the following proposition.
Proposition 2-1: When knowledge limits the actions inferred as available by the subject, it can, but must
not, reduce the subject’s set on subjective consequences. That is, AK ‡ A8 º C K ˆ C 8 .
The intuition underlying this proposition can be seen from this simple example: Conjecture
that A8 \a, b ^ and that f8 a f8 b . Furthermore, conjecture that AK \a ^ and I A \b ^ .
From this it follows that AK ‡ A8 , which implies that C K ‡ C 8 , but since f8 a f8 b , it also follows that C K C 8 , and so we have C K ˆ C 8 .
This means that even when the choice is limited because of ignorance of available actions, it
must not lead to a subjective consequence set that is a strict subset to the objective consequence set.
It also means that even when the number of alternatives to choose from increases, the subject may
nevertheless feel no significant difference in the choice situations since the subjective consequences
can remain unchanged.
Assume the following situation: A8 \a, b, c, d, e ^ but the subject’s subjective action set is
only AK \a, b, c ^ . The corresponding consequences are C 8 \f a , f b , f c , f d , f e ^ and
C K \f a , f b , f c ^ . Note that f8 ¸
fK ¸
f ¸
, i.e. the outcomes are objectively verifiable
such as, e.g., eating a meal. Furthermore, assume that f a f d and f b f c . If the subject
can make choices based on the objective action set, he or she would hold the following preferences f e ; f a f d ; f b f c . Such preference relations imply that e ; a d ; c b .
Since the subject’s knowledge of the available alternatives is restricted to AK , it implies that the
preference relations on the consequences are f a ; f b f c . This means that when knowledge
of the available alternatives and their consequences is limited, it follows that the choice can result in
a different choice. This, however, is not always true. Consider if C K \f a , f b , f c , f e ^ ; it
means that the choice in A8 is identical to that in AK Furthermore, since f a f d , the additional consequence that is attainable by expanding the subjective action set to the objective actions is
already attainable in the subjective actions set.
2.2.5 Consequences, ignorance, and the subjective action function in uncertainty
The previous subsection analyzes the certain choice. The subject knows at the point of choice what
the consequence is for each subjective action. This subsection focuses on the situation where the
32
subject, at the point of choice, infers that each subjective action can only lead to one consequence,
but where the consequence is uncertain. Uncertainty implies that the subject can specify each of the
inferred potential consequences for an action, but the subject cannot control which of the consequences that eventually unfolds 7.
The inference from an action to its consequence is, with the introduction of uncertainty, intercepted by exogenous factors. In the economics, the uncontrollable determinants of an action’s
consequence are captured by the concept of states (e.g., Debreu 1959; Demski 1972; Fishburn 1979;
Kreps 1988). Savage ([1954] 1972, p. 9) calls the state a “description of the world, leaving no relevant aspect undefined.”
A state is a complete description of the factors about which the subject is uncertain and
which are relevant to the consequences that are associated with the choice of an action. Let S 8 be
the subject’s nonempty objective set of states where s ‰ S 8 is a unique state. The set of states are
mutually exclusive and the objective set of states is S 8 *i si which is assumed closed and
bounded.
Since an action can lead to only one consequence but where the consequence a priori is
known to be unknown because the subject cannot know for sure the state that does in fact obtain, it
follows that the objective action function is state-dependent. That is, f8,s : A8 l C 8,s where f8,s denotes the state-dependent objective action function that attaches a unique state-dependent consequence to each action and where C 8,s is the objective consequence set for a specific state.
Conjecture that the subject is ignorant of at least one state in the objective state set and use
this to define the limited knowledge of states as below.
Definition 2-5: Let the subject be unaware of at least one state in the objective state set, i.e., the subject’s
ignorance set is nonempty, I S Š  , and a strict subset to the objective action set, I S ‡ S8 .
Definition 2-6: Definition of limited knowledge of states. A subject’s knowledge of potential states is
limited when the subject has a nonempty ignorance set of states according to Definition 2-5.
As with Definition 2-3 on page 29 it is possible to use the ignorance of states to define the
subject’s subjective state set as below.
Definition 2-7: Definition of the subjective state set. Let the subjective state set be SK S8 4 I S .
Again note that S 8, I S Š  ’ I S ‡ S 8 º S K Š  . Since the subjective state set is nonempty, it is a subset to the objective state set, and the fact that the ignorance of states set is also nonempty assures that the subjective state set always is a strict subset to the objective state set. This
7
This is, as in the case of certainty, completely in line with the use of uncertainty in microeconomics.
33
means that the subject always makes choices that are to some extent based on erroneous expectations.
When the subject faces the subjective rather than the objective state set, the action function
no longer is the objective state-dependent action function. Instead, it means that the subject faces
the subjective state-dependent action function, which is: fKs : AK l C K ,s . Note that fKs v f8s for
two reasons. First, the subject’s ignorance of actions leads to this difference. Second, the subject’s
ignorance of states also contributes to this difference.
The separation of the subjective state set from the objective state set resembles the work of
Modica and Rustichini (1999) who use a set-theoretical approach to model ignorance. Modica and
Rustichini (1999) see ignorance as non-full awareness and awareness is, according to the authors, the
union of certainty and conscious uncertainty. That is, awareness implies that either you know for
certain what is (e.g., it is for sure raining) or that you know that you do not know (e.g., that it is raining or not). Ignorance implies that the occurrence of rain, or of its opposite, is a surprise to the subject. In other words, it is an unknown unknown.
The definition of states and the state sets implies that each action has one consequence per
state. By gathering the consequences across states per action, all possible consequences for an action
are given.
Since the objective set of states is exhaustive and because the states are mutually exclusive, it
follows that it is possible to assign probabilities to each of the states. That is, it is possible to depict a
human choice under uncertainty as if the subject holds probability beliefs over the states. The objective state probability for a state is denoted Q8s ‰ 18 , and 18 is the objective state-probability set
(see, e.g., Sydsaeter et al. 1999 for the axioms of probability).
The subjective set of states consists of a subset of the objective state set. This means that the
subjective state set also consists of mutually exclusive states. Furthermore, since I S Š  , the subjective set of states differs from the objective state set, i.e. it cannot be exhaustive in the objective
sense. From the subject’s perspective, the subjective state set is exhaustive since the subject believes
that this is the objective state set, i.e. the subject believes that the subjective state set is exhaustive.
This implies that it is possible to assign state probabilities to the subjective states. For convenience, I
call these state probabilities subjective state probabilities.
When the subjective set of states is a strict subset of the objective set of states, it follows that
at least one element from the objective set of states is missing in the subjective set of states. Or, to
put it differently, S K ƒ I S S 8 . s ‰ S K ‚ S 8 are all the states that are common to both choice
situations. Since the subject can be thought to hold probability beliefs on the states, it follows that at
34
least one state of the states in S K ‚ S 8 must have a different subjective state probability belief,
QKs ‰ 1K than the objective state probability. The symbol 1K is the subjective state probability set.
Proposition 2-2: There exists at least one subjective state probability that differs from the objective state
probability when the subject faces a strict subset of states: That is, QKs v Q8s where
QKs , Q8s ‰ 1K ‚ 18 , when SK ‡ S8 .
Despite that there is a difference in the probability beliefs when a choice is made on the subjective or on the objective set of states, it follows from the previous definition of states and the set
of states that summing all of the subjective state probabilities yields exactly unity, as required by the
axioms of probability. The only problem is that at least one of these state probabilities is incorrect
and thus the subject makes an erroneous choice if his or her choice is described as if the subject
makes use of probability calculus.
With the definitions and the proposition above, it is possible to enlarge the definition of limited rationality as put forward in Definition 2-4. It is expanded here to encompass also ignorance
of states.
Definition 2-8: Definition of limited rationality in the uncertain choice. In addition to Definition 2-4, a
subject exhibits limited rationality when the subject has a rational preference relation on uncertain consequences that are limited because of limited knowledge of states (Definition 2-6).
With Definition 2-1 to Definition 2-8 , Proposition 2-1, and Proposition 2-2, I have set up
the nucleus to a choice theory that resembles the perfect rational choice but with significant differences. In my model, the subject makes a rational choice on a strict subset of the objective set of
alternatives while only considering a strict subset of the objective set of states. This subject has limited knowledge of the alternatives he or she can choose from and limited knowledge of the states
that does obtain, all of which leads to limited rational choices.
To the best of my knowledge, limited rational choice in the way I use it in this thesis is novel.
There exists game theoretical research that models unawareness, or the lack thereof (e.g., Dekel,
Lipman & Rustichini 1998; Halpern 2001; Modica & Rustichini 1994; Modica & Rustichini 1999),
but it is limited to the unawareness of states and not of the available actions. Furthermore, to the
best of my knowledge, none of the unawareness research has yet found its way into applied economics in terms of financial economics, and hence not into valuation models in uncertainty, which is
what I use here. My proposed theory of limited rational choice allows for unawareness of states and
of actions and it is precise enough to allow the posing of testable propositions in the area of financial economics and market-based accounting research. Moreover, my proposed theory allows for
learning as becoming aware (more precisely this implies that the ignorance set is reduced) in addition
to typical Bayesian learning, but that is the topic of section 2.4. The next section avoids the dynam-
35
ics that come from learning and focus on the static choice. It introduces utility to the limited rational
choice model.
2.3 The limited rational choice’s utility representation
Having established the core to my theory of limited rational choice in section 2.2, this section takes
the analysis forward to the point where it is possible to speak of a limited rational choice as if the
subject chooses an action based on a subjective expected utility maximization behavior. This should
not be confused with what is often subjective as an expected utility 8 maximizing behavior because
what is then thought of is what I call the expected utility maximizing behavior facing the objective
action and state sets. I call such a behavior for objective expected utility maximizing. To emphasize,
objective is in this research used to emphasize the special case where human action is based on perfect knowledge and hence where the subjective expectation of a subject is identical to the objective
facts of the choice problem.
Human action that can be explained using objective expected utility is contrived by theory of
choice that makes use of A8,C 8, S 8, 18 . This can be contrasted with human action that can be explained using subjective expected utility since such human action is contrived by the theory of Homo comperiens that makes use of AK ,C K , S K , 1K .
In deriving the subjective expected utility maximization behavior of Homo comperiens the
conjectures of continuous, insatiable preferences are imposed. The preferences are also supposed to
be state uniform, independent, and that abide to the Archimedean assumption. These conjectures
are usually invoked on the perfectly rational choice (e.g., Kreps 1988), but are equally applicable to
the situation at hand. With these additional conjectures, it is possible to apply the theory of Homo
comperiens to firm valuation.
To be able to connect the theory of Homo comperiens to firm valuation requires that it can
be described using real-valued (real) functions. This makes it necessary to be able to describe choice
as if it is based on a real number, which in economics is called utility. Utility is a numerical representation of the consequences, where it can be thought of as an index used to rank the consequences of
each action (Mas-Colell et al. 1995).
The reader should think when reading this section on how the choice problem is designed.
The subject faces a choice among alternative actions. The subject has to choose an action, and does
so, according to the previous section as well as the traditional theory of choice, based on the outcomes of the actions. The subject makes the choice by ranking the outcomes and this is done by the
subject no matter how diverse these outcomes may be. In this research the utility is merely an index
that conserves the ranking of outcomes performed by the subject. Accordingly, utility is merely an
8
Or, more specifically, von Neumann-Morgenstern’s expected utility.
36
analytical device derived from the ranking of the outcomes and thus has no value or importance in
itself. The index is given cardinal properties to ensure compatibility with real mathematics.
To be able to claim that a subject acts as if he or she chooses based on an action’s utility, i.e.
a ; c ” u a u c , a functional relation must exist between the action set and the consequence
set, as well as between the consequence set and the utility set. The previous section described the
choice as if the subject chooses an action based on consequences using such a functional relation
between the action set and the consequence set. This section focuses on the functional relation between the consequence set and the utility set.
A unique numerical representation is attached to each consequence, whether it is from C 8 ,
C K , C 8s , or C Ks . This representation is the subject’s utility for a particular consequence. Recall
from subsection 2.2.1 that the preference relation is conjectured weak and therefore there is the possibility that a subject is indifferent among alternative consequences. This implies that those consequences must have identical utilities; the utility otherwise fails to be a measure of how well off the
subject is 9. Based on this reasoning, it follows that each consequence must have only one corresponding element in the utility set, but that each element in the utility set may have more than one
consequence attached to it. This is equivalent to the discussion on the action function.
The preferences must be continuous to guarantee the existence of a functional relation between the consequence set and the utility set (Mas-Colell et al. 1995).
For simplicity, let the utility set span the complete real line, here denoted \ . Note that this is
unproblematic in that a functional relation does not require that all elements of the co-domain have
a corresponding element in the domain (Sydsaeter et al. 1999).
Conjecture that the consequence set is the subjective consequence set. The correspondence
between the subjective consequence set and the utility set satisfies all the necessary properties of a
functional relation: All the elements in the domain exists only once and to each element of the domain is attached a unique element in the co-domain. This means that the correspondence between
the subjective consequence set and the utility set is a functional relation. It further means that it is
possible to express this function as uK : C K l \ for a certain choice. When the choice is uncertain,
if follows that there exists a subjective state-dependent utility function that is uKs : C Ks l \ .
The utility function would be u8 : C 8 l had the certain choice not been limited since the
choice is based on the objective consequence set. Function u8 is the utility function normally used
in economics and it may be expressed as an objective state-dependent utility function also, which is
9
Utility is broad enough in this research to encompass both the subjective and the objective utility. The well-off-ness
should be interpreted relatively: Is the subject better or worse off by choosing an action before another?
37
u8s : C 8s l \ . Derivations of a traditional utility function can be found in many textbooks on mi-
croeconomics but also in more formal treatment in (e.g., Fishburn 1979).
The general theory of rational choice describes the subjects as if they rank their actions based
on their consequences. The action function makes it possible to describe choice as the choice of an
action based on the action’s consequence. Since the utility function is a real-valued function from
the consequence set to the utility set, it opens the possibility to view the choice of action as the
composition of the action and the utility function. That is, in certainty, the subjective action function
fK : AK l C K , maps an action into a unique subjective consequence. The utility function
uK : C K l , maps the subjective consequence into a unique real number. Thus, we have their
composition fK D uK : AK l , which maps an action into a unique real number.
This means that when the subject has limited knowledge, he or she exhibits a ; b if and only
if the he or she also exhibits fK D uK a fK D uK b , which occurs if and only if uK a uK b ,
where a,b ‰ AK . Consequently, uK a uK b is a necessary and sufficient condition for a ; c .
Limited rational choice is then possible to be described as if a subject’s choice is based on the action’s subjective utilities.
In uncertainty, there is no clear solution to the choice problem. For instance, it is possible to
sum the state-dependent utilities for each action and then compare these sums to each other since
the system is of an ordinal scale. A cardinal utility is needed to be able to sum the utilities, and according to Kreps (1988), it is necessary to conjecture that the subject’s preference of a consequence
is uniform across states to introduce cardinal utility. For example, winning a million is equivalent to
a subject whether it is won in a boom or in a recession.
In financial economics von Neumann-Morgenstern’s expected utility is used to derive the
value of the firm. This utility is called the objective expected utility in this research and is denoted
E ¢ U8 c1, !cS ; Q81, ! Q8S ¯± œ
s ‰S8
Q8s ¸ u8 cs . The objective expected utility is a cardinal utility
that is achieved by focusing on a setting meeting the criteria of the perfectly rational choice. The
focus on Homo comperiens in this chapter makes it necessary to derive a cardinal utility for a limited rational choice. According to the present thesis, the cardinal utility in uncertainty for Homo
comperiens is as follows:
Proposition 2-3: When the subject has a preference relation on the subjective consequence sets, which
are complete, transitive, continuous, state uniform, independent, and that follow the Archimedean assumption, it is possible to express the subject’s choice as if he or she makes his or her choice based on an
action’s subjective expected utility: EK 0 ¢¡U K c1, !cS ; QK 1, ! QKS ¯±° œ
s ‰SK
QKs ¸ uK cs , where cs ‰ C Ks ,
and QKs ‰ 1K .
See Appendix C (p. 191) for proof of Proposition 2-3.
38
Savage ([1954] 1972) proposes a subjective expected utility. This utility should not be confused with the subjective expected utility I propose since my subjective expected utility is a direct
effect of the subject’s limited knowledge, which means that even in certainty there is a difference in
utility functions. Savage focuses on the existence of the subject’s subjective probabilities in an uncertain choice and does not limit the action set as I do. Nor does Savage restrict the state set as I do.
Indeed, I suppose that Savage’s axioms can be applied to my setting transforming the Savage subjective expected utility function into a subjective subjective expected utility function. Such a development is outside the scope of this thesis and is therefore deferred into the future.
The subjective expected utility in Proposition 2-3 differs from the objective expected utility
in that at least one of the subjective state probabilities, QKs , differs from the objective state probability, and that the subjective Bernoulli utilities, uK cs , differ from the objective Bernoulli utilities.
The difference in the Bernoulli utilities is due to the subject’s failure to specify correctly the supremum and/or the infimum consequences. That is, the subjective supremum and infimum consequences are not the same as the objective supremum and infimum consequences. The failure of having incorrect subjective state probabilities, having an incorrect supremum consequence, and having
an incorrect infimum consequence are due to the subject’s limited knowledge of actions and states
(Definition 2-2 and Definition 2-6). These failures imply that the subject’s choice is erroneous when
compared with a choice made on perfect knowledge.
Proposition 2-3 should be interpreted as follows. A subject who faces a choice forms an understanding of the available actions that he or she may take. The subject also forms an understanding on what the ensuing consequences are and acts as if he or she assigns probabilities to the states
that he or she infers. The subject then acts as if he or she measures the subjective expected utility for
each action. With the construction of the action function, the subjective utility function, and the
composition thereof, it also follows that the subject acts as if he or she chooses the action that delivers the subjective expected utility that he or she prefers most,
i.e., a ; b ” fK D U K a fK D U K b ” U K a U K b .
This proposition rests on the conjecture that the subject has preferences that are complete
(on the subjective action sets and their associated states), transitive, state-uniform, continuous, independent, and that follow the Archimedean assumption. The only difference between this limited
rational choice and a perfectly rational choice is that in the limited rational choice the choice is restricted to a strict subset of the objective action set and to a strict subset of the objective state set.
Since this thesis is particularly concerned with firm valuation, it makes sense to think of the
consequence set as if it consists of monetary consequences. This is identical to the choice set in financial economics. Financial economics posits that the perfectly rational subject is never satiated. By
39
imposing the insatiability conjecture on the limited rational choice, I have a subject that appears to
maximize his or her subjective expected utility.
Financial economics rests on the subject that acts as if he or she maximizes his or her objective expected utility. This chapter alters this by introducing limited knowledge: A subject who acts
according to Proposition 2-3, is insatiable, has the ability to learn, and is a limited rational subject.
2.4 Learning and the limited rational choice
The previous sections focused on a single choice and not on a sequence of choices. This section
introduces sequential choices allowing for learning. Learning is considered here a two-fold process
in which the subject learns by Bayesian learning that allows him or her to resolve uncertainty and by
discovery. That is, the subject learns such that the unknown unknowns become known unknowns
and perhaps even known knowns.
2.4.1 Learning as a resolution of uncertainty
The standard state-space partition model allows the subject to learn by introducing a gradually re-
fined partition of the state set until the limit scenario occurs where the partition only holds a unique
state. This means that the subject gradually resolves previous uncertainty and traverse from knowing
that he or she does not know (facing a conscious uncertainty as Modica and Rustichini (1999, p.
266) put it) to the limit knowing that the subject knows (i.e., certainty).
Traversing from uncertainty to certainty uses Bayesian learning. In Bayesian learning, the
subject holds a prior probability on the states based on the available information. A search for more
information (or the gradual dissemination of more information as time passes) allows the subject to
update the probabilities based on the new information, which, in turn, allows the individual to update his or her prior probability to a posterior probability. Another way to explain this is that the
information partition above is gradually refined, i.e. it holds fewer groups of states. This process
repeats itself and if this search for new information is considered costless, it continues until all information is uncovered. When all information is uncovered, the information partition holds only
one state and thus all uncertainty has been resolved using Bayesian learning.
The rational expectations model (which EMH relies on) uses Bayesian learning since it presumes that the subject has perfect knowledge of the standard state-space partition model (Huang &
Litzenberger 1988, p. 179-182; Congleton 2001, p. 392). Rational expectations further assume that
the subject makes unbiased forecasts (Huang & Litzenberger 1988, p. 179, 185). A rational expectation model is Pareto optimal if and only if the forecasts are unbiased (Huang & Litzenberger 1988,
p. 191-193). Thus, it follows that EMH is valid if and only if the hypothesis about rational expectations is valid. The unbiasedness comes from the fact that the subject continuously updates his or her
expectations based on the realizations from a stochastic process (Grossman 1981, p. 543-544),
which means that Bayesian learning is present using the standard state-space model.
40
Dekel, Lipman and Rustichini’s (1998) central contribution is that they show that the standard state-space partition model cannot accommodate ignorance. The standard state-space partition
model requires that the axiom of wisdom is in place (Samuelson 2004, p. 399), which means that the
subject must know of every state in the objective state set. That is, the subject’s state set state must
be a complete description of the world, without leaving any important aspect overlooked.
Another way to put this is that ignorance of a state implies a zero prior probability for the
state on which the subject is unaware. A zero prior of a state implies that the posterior probability
also is zero for the state, implying that Bayesian learning does not reduce the ignorance of states.
In a multi-subject setting, this has even stronger implications. Since the subject can describe
the his or her uncertainty in the form of states and that he or she knows of each and every state that
is relevant for his or her choice, the subject must also know of each and every other action and state
that he or she makes. With such a perspective, the axiom of wisdom is very strong indeed.
With this perspective, it follows that the economic system is without external shocks since a
shock is something that was not anticipated and the standard state-space model, by definition, anticipates everything. Recall Savage’s ([1954] 1972, p. 9) words: The state is a “description of the world,
leaving no relevant aspect undefined.” Congleton (2001, p. 9) expresses this as “what is learned is
general, rather than anything truly unanticipated or new.”
The important contribution by Modica and Rustichini (1999) is that they show that the standard state-space partition model can be mended such that when the subject no longer is aware of the
objective state set, but is aware of a subset of the objective set, this subset is still partitional.
Modica and Rustichini (1999) therefore allow for a relaxation of the axiom of wisdom while
still allowing for learning in the Bayesian sense, where more information gives a finer partition of the
subjective state set, which allows the subject to update his or her priors and perhaps come to another choice. Note that the process is now restricted to take place on the subjective state set and not on
the objective state set. Traversing from the subjective to the objective state set cannot be accommodated through Bayesian learning.
This implies that the subject can engage in an information search, which, if the information
search is costless, can continue until everything within the confines of the subjective state set is identified. Indeed, it becomes possible to conceive of a limited rational expectations model in which the
subject makes unbiased forecasts about the future. However, since the existing knowledge is confined to be within the subjective state set, it means that it may not be, and probably is not, unbiased
in an objective sense. So, considering a rational expectations framework, even if we conjecture homogenous preferences such that all subjects in the market have access to the identical subjective
state set, it is not possible to conjecture unbiased forecasts. Thus, conjecturing Homo comperiens
41
implies conjecturing a limited rational expectations model that provides biased forecasts of the future.
Learning as a resolution of uncertainty therefore logically implies that nothing novel is ever
discovered since it is restricted to learn more about what is already known.
2.4.2 Learning as discovery
Suppose that the subject faces a sequence of choices, and at present he or she faces a choice wheth-
er or not to invest in a firm. The subject proceeds to investigate the firm and given all his or her
current and previous knowledge he or she finds that the firm’s current market price is below/above
its intrinsic value, so the subject invests in the firm. In this setting, the subject has three alternative
strategies to choose from: (1) investing in the firm, which implies buying the stock, (2) not buying
the stock, and (3) short selling the stock.
With all of the subject’s previous and current knowledge, he or she infers only two choices,
namely buying and refraining from buying the stock. This means that the subject’s subjective action
set is a strict subset of the objective action set. The subject is not aware of the possibility of borrowing the stock from someone else (and promising to return it after some time) and selling it in the
stock market. This is short selling and makes it possible for him to make a profit on a firm whose
market price is above its intrinsic value.
The firm that the subject considers to invest in is in the business of long-term storage of nuclear waste. Its main storage facility is going to be deep in the Swedish mountains in an area with solid rock, and in it, the firm plans to store highly radioactive waste from nuclear power plants. While
waiting for the facilities to be constructed it has a short-term storage facility somewhere in the middle of Sweden.
The company’s management has recently reviewed its insurance policy and has decided to
change the conditions of the insurance for the firm in order that it is not insured against acts of terrorism. The choice to scrap the insurance against acts of terrorism is not publicly disclosed since
management does not consider this important.
The subject has, given all of his or her previous and current knowledge, an understanding of
the likely states that can occur. The subject can infer various states that incorporate different levels
of recessions, boom periods, earthquakes, and so on. But the subject is not aware that there is an
immediate risk of a terrorist attack on the firm’s facilities and that such an attack can destroy the
storage facility in such a fashion that radioactive dust is sent up into the air where it pollutes the
whole Stockholm region to such a degree that it must be evacuated for hundreds of years. Nor is the
subject aware that in such an event the firm goes bankrupt. This means that the subject has a limited
comprehension of all the available states. Consequently, the subject makes his or her choice based
on a subjective state set, which is a strict subset of the objective state space. To be able to span the
42
objective state set the subject would have to know if there were any terrorist considering committing
an act of terror against this facility, that such an act could destroy the building, and that the destruction would pollute the whole Stockholm region. The subject would also have to know that management had ruled out this possibility and discarded the terrorist insurance.
With the entire subject’s knowledge, he or she finds that the company is priced below its intrinsic value and thus purchases the stock. The next week a terrorist blows up the facility such that it
sends a radioactive dust cloud into the air, which drifts into the Stockholm region where it rains
down and pollutes the whole area. Since the firm is missing an insurance that covers such an act of
terrorism, it means that the firm is sued for the damages that resulted, and the firm goes bankrupt.
Thus, the subject loses his or her entire investment.
Had the subject been aware of the fact that a terrorist was planning an attack on the facility,
or aware of the fact that a terrorist could be planning such an attack on the facility, that such an attack would blow up the building, and that the company was uninsured against such an accident, the
subject would probably have reached another choice and thus refrained from investing in the firm.
However, even refraining from investing is an action that is not optimal since the subject was not
aware of the third possibility of going short. Had the subject instead been aware of the objective
state and action space, the subject could have short-sold the stock and made a profit on the event of
an act of terrorism.
After having made this disastrous investment, the subject has discovered the possibility of
having terrorists attacking such facilities, with severe and lethal consequences. This knowledge becomes a part of the subjective state set as the subject makes his or her next choice.
The aim with this story is to exemplify how this thesis views learning as discovery. When a
choice is made, the result of this choice is communicated to everyone (they discover) that is affected
by the choice. Some people make a good choice, implying that the consequence is matched with its
anticipation. Others may find consequences that are even better than expected, while some people
become disappointed because they have made an erroneous choice.
The knowledge of the effects of the choice above allows people to alter their expectations
over and above the effect from Bayesian learning and maybe their behavior as the next round of
choices commence. That means that when a subject makes his or her next choice, he or she has a
better appreciation of the subjective state and action sets, i.e. the subjective action and state sets are
expanded and approaches the objective sets. In my view, discovery concerns the expansion of the
subjective sets towards the objective sets.
Conjecture that the objective action and state sets are fixed. A sequence of choices lead to
that the subjective sets in the limit approach the objective sets, but since they are defined as strict
subsets, it also follows that despite the fact that the subject discovers more states, there is always
43
more to become aware of. That is, lim AK x A8 and lim SK x S8 . Learning as discovery is
t ld
t ld
therefore defined as follows:
Definition 2-9: Definition of learning as discovery. Discovery takes place when the subject that acts according to Definition 2-4 and Definition 2-8 and that faces the next choice in a sequence of choices expands his or her subjective state set and/or the subjective action set. Discovery takes place because of the
subject’s experience from previous choices: Formally, learning as discovery means that the previous subjective state and/or action sets are strict subsets to the current subjective state set and/or action sets.
With symbols, learning as discovery is defined as SKt 1 ‡ SKt , AKt 1 ‡ AKt AKt 1 ‡ AKt , or when both
situations occur and this is because discovery make certain that I At 1 ‡ I At and I St 1 ‡ I St .
A subtlety with Definition 2-9 is that it implies that the subject, by design, always learns from
a sequential choice and that he or she never forgets. Never forgetting is known as perfect recall in
game theory (Rubinstein 1998, p. 68-69). Had the definition been such that the previous subjective
state and/or action sets are allowed to be just subsets to the current subjective state set and/or action sets, i.e. SKt 1 ˆ SKt , AKt 1 ˆ AKt , learning would also encompass non-learning, i.e.
S Kt 1 S Kt , and/or AKt 1 AKt . However, even such a weaker definition of learning excludes de-
learning (forgetting) since that, in the strict sense, requires that SKt 1 „ SKt and/or AKt 1 „ AKt .
Central conjectures in the analysis above are that both A8 and S 8 are fixed. Another route
to follow can perhaps be to allow the objective sets to be strict subsets of some universal objective
sets, e.g., A8t ‡ A8 and S 8t ‡ S 8 . This implies that when the subject makes a choice he or she
faces objective action and state sets that are strict subsets to some universal action and state sets, and
the subjective sets are strict subsets to the objective sets that exist at the point of choice. Allowing
the objective set to be non-fixed as suggested here can again open the possibility of external shocks
since the change S8t 1 ‡ S8t , and A8t 1 ˆ A8t can be allowed to be the defining trait of external
shocks.
Conjecturing the objective sets constant allows for treating the optimal solution as a fixed
point, and tractable solutions to learning as discovery can be devised. This makes the external shock
endogenous to the model in the form of the discovery. I am at this point not certain that tractable
solutions can be modeled when the objective sets are allowed to be non-fixed. It can provide an
interesting future development for the theory of Homo comperiens.
2.4.3 Human action and Homo comperiens
The ignorance 10 that exhibits itself as a subjective state and action sets diminish from a choice to
another because of discovery. That is not to say that all ignorance disappears at once. The speed in
10
Ignorance is borrowed from Austrian Economics. Ignorance is central for Kirzner (1973). The subject uses it, e.g., to
discuss disequilibrium (1973, p. 69): “Market participants are unaware of the real opportunities for beneficial exchange
44
learning may be different among different subjects and the decrease of ignorance is thus unique for
each subject. While the subject makes more choices and experiences the consequences, he or she
discovers more about the objective action and state sets. The subjective action and state sets are in
the limit (when discovery has run its course to the end) nearly identical to the objective sets. In other
words, the subject still makes limited rational choices but with only a small amount of ignorance
when the discovery process has run its course.
Suppose that the market consists of many subjects. A subject’s choice of action then depends
on his or her anticipation on how the other subjects plan to act. Since choice is in this thesis assumed to be compatible with Homo comperiens, it follows that any subject has an incomplete understanding of the others’ plans. In addition, since the market consists of many subjects, it follows
that ignorance permeates the market. Even when some ignorance is discovered and dealt with, there
is always more ignorance in the market to be discovered and dealt with. In my view, it is unreasonable to expect that a subject will ever be able to infer the objective action and state sets since it implies that all subjects must do so, and to do so at the same time. Any choice is and will always be
limited rational.
As the subject goes through life making choices, he or she gathers knowledge that is specific
to the choices that he or she has made. This means that a subject follows his or her own unique
choice path. Then, it also follows that any subject must be endowed with his or her own unique set
of knowledge. It implies that every subject that faces an identical choice makes that choice based on
inferences from his or her own unique subjective action and state sets. The difference can sometimes be minimal, but at other times, it is immense and induces vastly different choices.
Since subjects are likely to interpret a situation in their own unique way, this implies that as a
subject scrutinizes another subject’s choice, he or she may feel that the choice appears illogical. Nevertheless, it must be remembered that it is only illogical in the eyes of the beholder. Given that the
subject’s actions can be described as following the theory of Homo comperiens, he or she made a
limited rational choice according to his or her own unique knowledge.
The discussion hitherto has added increasing structure to the proposed theory of limited rational choice. Given the definition of learning as discovery and learning as resolution of uncertainty,
all the pieces of the theory of Homo comperiens are in place. I therefore propose the theory of
Homo comperiens:
Proposition 2-4: Homo comperiens is a subject who is limited rational (Definition 2-4, Definition 2-8),
that learns using Bayesian learning and through discovery (Definition 2-9). The subject has a complete,
transitive, insatiable, continuous weak preference relation, which under uncertainty also is independent,
state-uniform and that follows the Archimedean conjecture.
which are available to them in the market. The result of this state of ignorance is that countless opportunities are passed
up.”
45
2.5 Summary
This chapter develops a theory of choice that I call Homo comperiens. The theory is suppose to,
using Nagel’s (1963, p. 212) words, “…serve as partial premises for explaining as well as predicting
an indeterminately large (and usually varied) class of economic phenomena.” Further, structure is
needed to make it applicable to financial economics and market-based accounting research. Such a
structure is provided in the next chapter.
The theory of Homo comperiens stems from this proposition:
Proposition 2-4: Homo comperiens is a subject who is limited rational (Definition 2-4, Definition 2-8),
that learns using Bayesian learning and through discovery (Definition 2-9). The subject has a complete,
transitive, insatiable, continuous weak preference relation, which under uncertainty also is independent,
state-uniform and that follows the Archimedean conjecture.
The theory of Homo comperiens uses the following core definitions:
Definition 2-4: Definition of limited rationality: A subject that has a rational preference relation, i.e. a
preference relation that is complete and transitive on the subjective action set (Definition 2-3) is a limited
rational subject.
Definition 2-8: Definition of limited rationality in the uncertain choice. In addition to Definition 2-4, a
subject exhibits limited rationality when the subject has a rational preference relation on uncertain consequences that are limited because of limited knowledge of states (Definition 2-6).
Definition 2-9: Definition of learning as discovery. Discovery takes place when the subject that acts according to Definition 2-4 and Definition 2-8 and that faces the next choice in a sequence of choices expands his or her subjective state set and/or the subjective action set. Discovery takes place because of the
subject’s experience from previous choices: Formally, learning as discovery means that the previous subjective state and/or action sets are strict subsets to the current subjective state set and/or action sets.
With symbols, learning as discovery is defined as SKt 1 ‡ SKt , AKt 1 ‡ AKt AKt 1 ‡ AKt , or when both
situations occur and this is because discovery make certain that I At 1 ‡ I At and I St 1 ‡ I St .
Definition 2-4 and Definition 2-8 rests on separate definitions of the subjective action and
state set that are:
Definition 2-3: Definition of the subjective action set. The subjective action is defined as AK A8 4 I A .
Definition 2-7: Definition of the subjective state set. Let the subjective state set be SK S8 4 I S .
And the subjective action and state sets depend on the definitions of the ignorance sets.
Definition 2-1: Definition of ignorance of actions: Let the subject be unaware of at least one action in the
objective action set, i.e. the subject’s ignorance set is nonempty, I A Š  , and a strict subset to the objective action set, I A ‡ A8 .
Definition 2-5: Let the subject be unaware of at least one state in the objective state set, i.e., the subject’s
ignorance set is nonempty, I S Š  , and a strict subset to the objective action set, I S ‡ S8 .
46
The ignorance sets are also used to define limited knowledge: The limited knowledge definitions are:
Definition 2-2: Definition of limited knowledge of actions. A subject’s knowledge of alternative actions
is limited when the subject has a nonempty ignorance set according to Definition 2-1.
Definition 2-6: Definition of limited knowledge of states. A subject’s knowledge of potential states is
limited when the subject has a nonempty ignorance set of states according to Definition 2-5.
A static limited rational choice is achieved by forcing the subject to make his or her choices
based on limited knowledge that lead to a choice based on a limited action set and, where uncertainty is present, also on a limited state set. These limited sets are strict subsets to their universal counterparts. The limited sets are referred to as subjective sets where the universal sets are the objective
sets. The axioms of rational choice are imposed on the subjective sets.
This means that choice, as pictured in my theory of Homo comperiens, meets the comparability, transitivity, insatiability, and continuous preference relation conjectures. In the uncertain
choice, the conjectures of independent, state-uniform preferences, and the Archimedean conjecture
is also added to the conjectures on the preference relation.
With this structure on choice, it is possible to explain human action as if the subject maximizes his or her subjective expected utility. That is,
Proposition 2-3: When the subject has a preference relation on the subjective consequence sets, which
are complete, transitive, continuous, state uniform, independent, and that follow the Archimedean assumption, it is possible to express the subject’s choice as if he or she makes his or her choice based on an
action’s subjective expected utility: EK 0 ¢¡U K c1, !cS ; QK 1, ! QKS ¯±° œ
s ‰SK
QKs ¸ uK cs , where cs ‰ C Ks ,
and QKs ‰ 1K .
The difference between subjective expected utility and von Neumann and Morgenstern’s
expected utility resides in different probabilities and different Bernoulli utilities. In the theory of
Homo comperiens they are referred to as subjective probabilities and subjective Bernoulli utilities.
The subjective probability differs from the objective probability because of the limited state
set and the subjective Bernoulli utilities differ from the objective Bernoulli utilities because of erroneous specification of the supremum and the infimum consequences. These errors are due to the
limited action set, which is a direct effect of limited knowledge. All the erroneous choices can therefore be traced back to my introduction of limited knowledge as the ignorance of actions and states,
which can be thought of as an unawareness conjecture. For proof of Proposition 2-3 see Appendix
C (p. 191).
The dynamics in the theory of Homo comperiens comes as a convergence of market prices
to the intrinsic values. This is achieved through the introduction of learning using both Bayesian
learning and discovery. Discovery is the aftermath of choice: Having made a choice, the effect of it
47
is experienced and when it yields an unanticipated consequence, it is incorporated into the choice set
of the next choice. Alternatively, more formally the subjective action and state sets for the previous
choice are strict subsets to the current choice.
This means that the subject initially is unaware that he or she is unaware. As the subjects
learn through discovery, they learn that they do not know for sure what the consequences are because of the exogenous factors, which means that the subjects face an uncertain choice. By engaging
in an information search, the subjects use Bayesian learning to the point where they know that they
know and so face a certain choice.
48
CHAPTER 3—HOMO COMPERIENS AND PRICE THEORY
“Only two things are infinite, the universe and human stupidity, and I’m not
sure about the former.” Einstein (1879-1955)
3.1 Introduction
This thesis aims to develop a theory of inefficient markets applicable to financial economics and
market-based accounting research. Chapter 2 served to develop the proposed theory of limited rational choice while the present chapter applies it to price theory. This is necessary since it creates a
structure precise enough that it allows market-pricing models of firms to be derived. Such models
are necessary for traversing from economics into market-based accounting. The results of this chapter are applied to firm valuation in the next chapter with associated appendices.
When a market consists of subjects who act according to the proposed the theory of Homo
comperiens, it follows that the necessary conditions for a general equilibrium is not met and thus the
market is in disequilibrium: Disequilibrium becomes the rule and equilibrium the exception.
The main interest in this chapter is the market price. What is it and does it differ from the
market price in the perfectly rational theory?
This chapter’s applied limited rational choice model is first specified, followed by a microanalysis and finally a macroanalysis that allows for discovery and price adaptation.
3.2 A point of departure for the application of Homo comperiens to price theory
The micro analysis restricts itself to a one-period choice with only exchange to avoid too much unnecessary detail. Thus, the analysis focuses on consumer theory. The reader may think of this chapter as an application of the theory to financial markets. Its application follows the standard application of microeconomics on financial markets (Huang & Litzenberger 1988, Silberger & Suen 2000),
with one important exception: This thesis posits that human action meets the conjectures stated in
Chapter 2, i.e. choice is limited rational and not perfectly rational. A similar analysis assuming a perfectly rational choice is for reference included in Appendix A (p. 147). Note that Chapter 2 argues
that the rational expectations hypothesis yields biased expectations in a Homo comperiens’ setting.
It therefore follows that such an analysis is not implemented in this chapter. This chapter’s analysis
mode makes instead use of state-contingent consumption following, e.g., Huang & Litzenberger
(1988) and Silberger & Suen (2000).
More than one period is used in the macroanalysis so that it can incorporate the learning
conjectures in Chapter 2. The one-period context should be interpreted as if the subjects make their
choice today about their consumption plans for today and tomorrow.
49
The analysis follows standard economics procedures and it assumes that the subject can
choose among several subjective consumption bundles (actions) that all delivers consequences,
which are measured in a numerarie good. The first good is defined as the numerarie; the price for
the numerarie is 1, which, in practical terms, can be thought of as money.
The subject has preferences on the consumption bundles according to the definition of Homo comperiens (Proposition 2-4, p. 45). The choice is bounded from above and below since the
Homo comperiens assumes that the subject makes choices that are restricted to span the subjective
action and state sets that are themselves by design bounded. The choice variable follows the symbols
used in Appendix A. Note that all the sets are the objective sets in Appendix A, but this chapter
conjectures Homo comperiens and hence are all the states part of the subjective state set.
This chapter’s subject chooses among different portfolios of current consumption and portfolios of future consumption (the subject’s subjective action set). The goods are denoted l ‰ LK
where the superscript is mnemonic for known. The subjective set of goods is a strict subset of the
objective set of goods, LK ‡ L8 having L goods for consumption because of Definition 2-3 (p. 29).
Chapter 2 also conjectures that the subject’s subjective state set is a strict subset to the objective
state set (Definition 2-7, p. 33). The subjective state set has S states and a state is designated by
s ‰ SK .
The portfolio of current consumption is symbolized by cK 0 cK 01, !, cK 0L 11 and a portfolio of future consumption is represented by cK0 . The focus of the analysis is on the subjective consumption bundle, designated CK cK 0 , cK 1 . The subjective consumption bundle differs from the
objective consumption bundle in that the subject has limited knowledge of the available consumption alternatives. That is, the subject knows only of LK and not of L8 .
The cost of current consumption of a good is cK 0l 0 pK 0l ¸ q 0l and the cost of the current
consumption portfolio is cK 0 QF0 ¸ 0 PK 0 , where QF0 <q 01, !, q 0L > is the transpose of the column
matrix with the quantities of current consumption goods held by the subject. This is a new meaning
of the symbols compared with Appendix A, where c0 represents the portfolio of quantities of goods
for current consumption. The shift in meaning is due to this thesis’ focus on the cost of consumption and not on quantities per se. Another difference pertains to the fact that Appendix A uses all
goods and services in L8 as available consumption alternatives, i.e. knowledge of available alternatives are not restricted.
11 The reader is reminded that bold upper case letters are the general representation of a matrix. The exception is the
column matrix that uses lower bold case letters as symbols. To reduce space requirement in the text this thesis writes
column matrixes as vectors. The inner product of two vectors, S ¸ c , can also be written in matrix notation, SF ¸ c ,
where SF denotes the transpose of column matrix S .
50
The subject can hold negative, nil, or positive quantities of goods for current consumption.
When the subject holds negative quantities, the subject holds a debt that must be cleared some day.
Nil indicates that the subject does not hold this particular good for current consumption, whereas a
positive sign on the quantity variable indicates that the subject holds this good for current consumption.
The current unit price for each good is summarized into the column matrix whose transpose
is symbolized by 0 PKF0 < 0 pK 01, !, 0 pK 0L > . Note that it retains the superscript K to signify that it
really is subjective current unit prices. The current price for a good, 0 pK 0l , is the good’s spot price,
which can be interpreted as the price paid today for the delivery of a good today, measured in terms
of the numerarie.
Today’s consumption is certain but tomorrow’s consumption is uncertain. The uncertainty is
subjective and not objective. Using the state-space-model, makes it possible to describe the uncertain subjective future consumption portfolio as a column matrix of subjective state-dependent future
consumption. The transpose of the uncertain subjective future consumption portfolio column matrix can be described as cKF 1 cK 11, !, cK 1S , where cK 1s designates the subjective cost of a future
consumption portfolio for a state. The subjective cost of the future consumption portfolio for each
subjective state is a column matrix and consists of its own bundle of state-contingent consumption,
cK 1s cK 1s , !, cKls .
Since the model is a one-period model, the subjective cost of the state-contingent consumption of a specific good is equal to the subjective payoff of a unit of this good times the quantity of
claims to future consumption of this good, i.e., cKls ql ¸ rKls , where Q1 <q1, ", qL > is all the current holdings of claims to the future consumption of goods. Note that Q1 is state-independent: It is
a legal claim that the holder has today to the consumption of goods in the future. What can vary
with the state is the subjective payoff of the claim. The payoff, rKls , is the subjective payoff (in consumption measured in the numerarie) for a unit of a particular good in a particular state. The total
subjective payoff for a particular state is then RKs rK 1s , ", rKLs The subjective payoff matrix above is for the future consumption in a state and since the
subject knows of S states, if follows that the subjective payoff matrix needs to be enlarged to cover
all known states. That is,
rK 11 " rKL1 ¯
¡
°
RKF <R K 1, !, RKS > ¡ #
%
# °
¡rK 1S " rKLS °
¢¡
±°
The subjective payoff shown above should be interpreted as all potential payoffs that the
subject can perceive in the future given his or her restrictions through the subjective set of states
51
and the subjective action set. It is therefore designated RK in this research, which is the subject’s
subjective payoff set. Note that the subjective payoff set is a strict subset to the objective payoff set.
It is restricted both in the number of columns (goods and services known to be available in the future) and in the number of rows (states that the subject believes that the market can enter into as the
future unfolds) since both the action set and the state set are the subjective and not the objective
sets.
With the definitions above, it is possible to reconsider the subjective cost of a bundle of
claims for consumption of goods delivered tomorrow. It can now be written as:
cK 1 ¯ rK 11 " rKL1 ¯ q1 ¯
¡
° ¡
° ¡ °
cK 1 ¡ # ° ¡ #
%
# ° ¸ ¡ # ° RKF ¸ Q1 ” cKF 1 Q1F ¸ RK
¡cKS ° ¡rK 1S " rKLS ° ¡qL °
¡¢
°± ¡¢
°± ¡¢ °±
I initially propose that the subject chooses among different strategies that deliver different
subjective consumption bundles, where the bundle is depicted cK 0 , cK 1 . With the setting above, it
can instead be described as QF0 ¸ 0 PK 0 , Q1F ¸ RK .
Chapter 1 makes a critical assumption that thesis rests on. It assumes that the actors in the
market are price takers. This implies that the research sets the current price matrix to be exogenously
determined. The subjective payoff matrix is also exogenous since production is not considered here.
Hence, the subject’s choice of strategies only affects the quantity of current consumption and the
quantity of claims held on future consumption goods.
The subject can only acquire the claims to future consumption at a subjective price which is
to the best of his or her knowledge beyond his or her control (again part of fundamental premises of
the thesis). The price today for one claim on a good to be delivered tomorrow is 0 pK 1l (futures
price) and the total futures price that the subject has to pay to get his or her bundle of claims for
future consumption is
œ
LK
q
l 1 l
¸ 0 pK 1l . The column matrix 0 PK 1 < 0 pK 11, ", 0 pK 1L > represents all
unit futures prices.
The subject has at the outset the choice a limited endowment of goods and of claims to future goods that are exogenous and cannot be affected by any choice. Together with the spot and
futures prices they make up in this research exogenous subjective wealth:
F
c QF0 ¸ 0 PK 0 Q1 ¸ 0 PK 1 . Any choice must be equal to the subject’s subjective wealth. The budget
F
restriction for Homo comperiens is therefore: QF0 ¸ 0 PK 0 Q1F ¸ 0 PK 1 QF0 ¸ 0 PK 0 Q1 ¸ 0 PK 1 . This
system allows the subject to hold negative quantities of claims to future goods as well as positive
quantities of claims to future goods.
52
3.3 A micro analysis of limited rational choice
Faced with having to choose among different consumption bundles, the subject chooses in a manner that may be described as if he or she chooses the consumption bundle that maximizes his or her
subjective expected utility (cf., Proposition 2-3, p. 38 and the insatiability discussion). This can be
expressed as a mathematical constrained optimization problem.
3.3.1 Optimization of Homo comperiens’ subjective expected utility maximization problem
Using Lagrange’s technique allows the problem to be posed as:
max
cK 0 ,cK 0 ,M
L c0 , c1 max E K0 ¡U K QF0 ¸ 0 P0K , Q1F ¸ R K ¯° M ¸ QF0 ¸ 0 PK 0 Q1F ¸ 0 PK 1 c 0
¢
±
Q0 ,Q1 ,M
[EQ 3-1]
The symbol M is Lagrange’s multiplier. Differentiating L with respects to the quantities of
current consumption goods and setting the derivative to zero give:
sL
0
sq 0l VK cK 0 , cK 1 M ¸ 0 pK 0l 0 , l ‰ LK
[EQ 3-2]
Differentiating L with respects to the claims to future consumption goods and setting the derivative to zero give:
sL
sq1l œ
s ‰SK
VK1 cK 0 , cK 1s ¸ rKls M ¸ 0 pK 1l 0 , l ‰ LK
[EQ 3-3]
Differentiating L with respects to Lagrange’s multiplier and setting the derivative to zero
give:
sL
F
F
sM Q0 ¸ 0 PK 0 Q1 ¸ 0 PK 1 c 0
[EQ 3-4]
Dividing [EQ 3-3] with [EQ 3-2] and solving for the ratio between the subjective futures
price and the current price show:
0 pK 1l
0 pK 0l
œ
s ‰SK
VK1 cK 0 , cK 1s ¸ rKls
, l ‰ LK
VK0 cK 0 , cK 1 [EQ 3-5]
Specifically, by focusing the analysis of [EQ 3-5] on the numerarie (money), it is clear that the
subject’s subjective future’s price for the numerarie is the marginal rate of substitution between consumption and saving 12. In symbols it is:
0 pK 11
1¸
œ
s ‰SK
VK1 cK 0 , cK 1s ¸ 1
VK0 cK 0 , cK 1 [EQ 3-6]
The subjective marginal utilities, VK0 c0K , c1Kl and VK1 c0K , c1Ks have more meaning because of
Proposition 2-4:
VK0 cK 0 , cK 1 12
sE K0 ¢U K cK 0 , cK 1 ¯±
QKs ¸ uKs cK 0 , cK 1 , l ‰ LK
scK 0l
s ‰SK
œ
[EQ 3-7]
Saving is the equivalent to postponed consumption.
53
VK1 cK 0 , cK 1s sE K0 ¢U K cK 0 , cK 1 ¯±
QKs ¸ uK cK 0 , cK 1 , s ‰ SK
sc1Ks
[EQ 3-8]
3.3.2 Interpretation of the optimization
When the subjective price is exogenous to the model, it follows that the subject can only adjust his
or her consumption quantities that he or she demands and supplies according to the prevalent subjective price. The particular quantities of consumption that the subject chooses is the quantities that
satisfy [EQ 3-4] and [EQ 3-5]. This means that the quantities are chosen so that the subject’s subjective marginal rates of substitution equal the subjective prices and that the subject does not waste
goods and services.
The subjective marginal rates of substitution are themselves functions, where the arguments
are based on the subject’s inference on the subjective state probabilities as well as on the subject’s
assignment of subjective Bernoulli utilities to consumption. This is expressed by [EQ 3-7] and
[EQ 3-8]. From this, it follows that as soon as the subjective action set is limited, the subjective state
set is limited, or when both occur, the subject chooses to trade erroneous amounts of current and
future goods: The subject makes an erroneous choice when compared with the situation where the
subject has access to the objective action and state sets. Had the subject made his or her choice
based on the objective sets, the choice would be identical to a choice using a von NeumannMorgenstern utility function as in financial economics.
The erroneous choice has profound implications on the macroanalysis as seen in the next
section. But first follows some important reflections on what effects the above analysis has for financial economics and the parts of market-based accounting research that needs valuation models
and a capital asset pricing model.
First, assume that the preferences are homogenous in the population and hence that it is
possible to analyze the situation using the representative individual conjecture, which is used in financial economics when e.g., deriving the CAPM (e.g., Huang & Litzenberger 1988, or Ohlson
1987, for a discussion of the conjectures underlying CAPM).
Even when there is no exogenous change as time passes, the representative subject’s utility
function changes since the representative subject learns through discovery (Definition 2-9, p. 44), i.e.
since the subjective action and state sets change. When the subjective sets change, it implies that the
representative subject’s subjective state-probabilities change and that the subjective Bernoulli utilities
change as well. The subjective Bernoulli utilities change since the representative subject becomes
better at specifying the supremum and infimum consequences.
This means that [EQ 3-7] and [EQ 3-8] change as time passes, even when there is no exogenous change and when a representative subject is assumed. Since they change, it also means that
the relative prices change, i.e. [EQ 3-5] and [EQ 3-6].
54
So, even when conjecturing a representative subject, it is without merit to push the analysis
into a subjective CAPM model since it is unique for each time and therefore cannot be given empirical content.
Furthermore, since each subject has his or her own unique understanding of which actions
are available and the states that can occur, it is fallacious to assume that all subjects in the market can
be assigned identical utility functions so that every subject has the same marginal utilities, which is
what is assumed by the representative subject conjecture.
So when the world consists of subjects who are limited rational it follows that, e.g., the conjectures for CAPM are violated and models that posit it, such as tests of EMH, invariably fail to
provide valid and reliable results.
3.4 A macroanalysis of limited rational choice
A downside with the microanalysis is that it posits that the subjective price is exogenous. To include
the formation of a subjective price into the model it is necessary to stop seeing the subject as a Robinson Crusoe (although with the possibility of trading): When the subject trades, he or she trades
with other subjects, and these subjects make up his or her environment in which he or she interacts.
The macroanalysis conjectures that the world is populated by more than one subject, that
they trade between each other, and that from the outset there exist an exogenous price, but as trading is allowed between the subjects, it becomes endogenously determined. The exogenous initial
subjective price can also be thought of as a subjective price that prevails in an already existing market as a subject enters. All the subjects in the analysis behave according to Homo comperiens
(Proposition 2-4, p. 45).
The microanalysis shows that when a subject acts as Homo comperiens he or she, given the
opportunity, decides on a subjective price that deviates from the price he or she would have decided
on had he or she had access to the objective action and state sets. In Chapter 1 where learning is
discussed, it is argued that each subject, which learns by making choices and experiencing their consequences, accumulates a unique composition of knowledge that dictates how he or she perceives
the world and its accompanying choices.
3.4.1 The dynamics of learning
The subject’s unique composition of knowledge implies that each subject assigns a unique subjective
price to a good, regardless if it is consumed today or tomorrow. This is because it is a function of
the subject’s utility function, which is a function of the subjective state probabilities and the subjective Bernoulli utilities, which are themselves functions of the subject’s limited knowledge.
If the subjective price, on the other hand, is exogenous and there are several subjects who
make up the market, they can adjust their quantities so that each of them supply and demand goods
55
that make their subjective marginal rate of substitution equal to the quoted subjective prices. The
subjective marginal rate of substitution is a function of the subjective state probabilities and the subjective Bernoulli utilities, which also means that each subject’s supplied and offered quantities are
not the same as if they had had access to the objective action and state sets. When all subjects’ demand and supply plans are aggregated, the planned supply of goods does not match the demanded
quantities of goods since the subjects fail to consider the peers’ demand and supply plans: The demand and supply plans fail to dovetail (except by chance) and the failure causes erroneous choices
that are manifested as excess supply and excess demand of goods and services. Only when all subjects make their choices on the objective action and state sets and when all subjects know each other’s choice rules, can we expect to see perfectly dovetailing supply and demand plans.
Since the subjects all have their own unique inference of what the available actions are and
what states that can occur, it follows that it is incomprehensible that all subjects, at the same time
and by chance, happen to infer the objective action and state sets. However, since Homo comperiens learns from past mistakes, it also follows that there is a sequence of choices of demand and
supply plans for the subjects from which the subjects learn.
Consider the following two examples: Each round of demand and offer plans are followed
by transactions based on these plans and hence are any failure and success with the plans transmitted among the subjects through the transactions. Some subjects succeed in carrying out their plans
while others fail to do so. The order in which the subjects’ demand and offer plans are cleared in any
given round of transactions is then important for the subjects. For instance, imagine that there is an
excess demand of a particular good. This implies that the last subject(s) cannot carry out his or her
(their) demand plan(s) as imagined, and end(s) up being dissatisfied. Conversely, in the case of
excess supply there is at the end some subject(s) who end(s) up not being able to sell all the goods
that he or she (they) planned and he or she (they) will also be dissatisfied. The dissatisfaction among
subjects induces them to make revised plans for the next round of transactions. The sequence of
choices of demand and supply plans is therefore where the subject gradually learns about other subjects’ demand and offer plans, as well as about what actions are available.
Taken together, the dynamics lead to a better and better match among the subjects’ aggregated demand and supply plans. When enough transactions have taken place, learning has reduced
excess demand and supply to almost nil, and the market approaches perfectly dovetailing demand
and offer plans since lim AK x A8 and lim SK x S8 . When this has happened, the market nears
t ld
t ld
a general equilibrium in which each subject can carry out his or her demand and supply plans almost
exactly according to his or her intentions. Thus, I propose the following:
56
Proposition 3-1: Learning through discovery (Definition 2-9) ascertains that lim AK x A8 and
t ld
lim SK x S8 since the ignorance sets decrease. This implies that the subjective price approaches the
t ld
objective price as t goes to infinity. That is lim t 1 pKt x t 1 pt .
t ld
Note that even though we fix the objective action and state sets, which implies a fixed price
situation, it is not correct to think of the objective price as a fixed and certain price. All I say is that
in the limit the subject knows of (almost) all states and of (almost) all actions that are part of the
choice. I do not say that the subject knows exactly which state will come true because that requires
me to conjecture that the objective state set is a singleton, and I have not imposed such a conjecture
here. Therefore, in the limit it is more correct to think of the objective price as a variable that is approximately randomly walking.
Proposition 3-1 also implies that I do not conjecture hog-tail like situations where the subjective price gradually gravitates away from the objective price in the theory of Homo comperiens. Instead, the subjective price gradually regresses to the objective price.
This can be expressed more precisely as below:
Definition 2-1, Definition 2-5, and Definition 2-9 º lim I A x  , and lim I S x 
t ld
t ld
lim I A x  º lim AK x A8
[EQ 3.9]
lim I S x  º lim S K x S 8
[EQ 3.10]
[EQ 3.9] º lim uK cK 0 , cK 1 x u c0 , c1 [EQ 3.11]
[EQ 3.9] º lim uK cK 0 , cK 1s x u c0 , c1s [EQ 3.12]
[EQ 3.10] º lim 1K x 18
[EQ 3.13]
[EQ 3.13] º lim QKs x Qs
[EQ 3.14]
t ld
t ld
t ld
t ld
t ld
t ld
t ld
t ld

ž sE K0
t ld ž
žŸ
U K cK 0 , cK 1 ¯ ¬­ sE U c0 , c1 ¯
¢
± ­­ x
¢
±
­
scK 0l
sc0l
®­
[EQ 3.15]
[EQ 3.12], and [EQ 3.14] º lim žž
 sE U c , c ¯ ¬­ sE U c , c ¯
0 1 ±
ž K0 ¢ K K 0 K 1 ± ­
¢
­­­ x
t ld ž
žŸ
sc1Ks
s
c
1l
®
[EQ 3.16]
[EQ 3.15] ” lim VK0 cK 0 , cK 1 x V 0 c0 , c1 [EQ 3.17]
[EQ 3.16] ” lim VK1 cK 0 , cK 1s x V1 c0 , c1 [EQ 3.18]
[EQ 3.12], and [EQ 3.14] º lim žž
t ld
t ld
 p
¬
[EQ 3.17], and [EQ 3.18] º lim žž 0 K 1l ­­­ x 0 1l
t ld ž
Ÿ 0 pK 0l ­®
0 p0l
[EQ 3.18], 0 pK 01, 0 p01 1 º lim t 1 pKt x
t ld
p
t 1 pt
l 1 Q.E.D.
57
That is, in the long run the subjective price converges towards the objective price since the
subjective state-dependent probabilities and the subjective Bernoulli utilities approach their objective
counterparts, all of which because the subject’s ignorance decreases because of discovery, i.e. limited knowledge becomes perfect knowledge.
3.4.2 The adaptation processes
It is conceivable to think of the subjective price as the information carrying device that brings supply
and demand plans to dovetail. This is because it is the subjective price that decides how much a subject is prepared to demand and how much the subject is prepared to offer (cf. section 3.3). So, as
subjects craft and attempt to execute erroneous demand and offer plans, excess demand and supply
situations occur. The hitherto erroneous plans are taken into account as the next set of demand and
offer plans are crafted. The resulting change reduces the excess supply and demand in the market,
with the market price changing accordingly. As the sequence of choices continues, the subjective
price changes to accommodate the decreasing excess demand and excess supply plans.
When there is an excess demand, subjects are prepared to buy more of the good than what
the current supply plans allow. Since subjects are insatiable, it follows that in the next round the
suppliers increase the subjective price to counter the excess demand. It is also conceivable that the
offered quantity is increased at the given subjective price, which also delivers a decrease in the excess
demand. Any combination thereof can also be concocted.
The increase in offered quantities is an effect of discovery: Because the supplier has learned
more about conceivable actions and states, the supplier makes the new choice (of increased/decreased offered quantities) based on a new utility function (it is defined on a new and
greater action/consequence set that maps into a greater utility set). The ability to overlook larger
action and consequence sets changes the subject’s perception (i.e. the marginal utilities and hence
the subjective marginal rate of substitution changes) and he or she is willing to supply larger quantities at a given subjective price.
If there is an excess supply, is follows from the non-satiation conjecture that the subjective
prices must drop so that the demand increases (and the supply decreases) to a level where the excess
supply disappears. It is also conceivable that there is an adjustment of the supply plans so that it, at a
given price, better corresponds to the demanded quantities, or there can be a combination of the
two alternatives. The quantity adjustment is motivated analogous to the preceding quantity adjustment analysis that can take place when there is excess demand.
From above, it should be clear that the subjective price is not an equilibrium price since subjects are limited rational and the subjective price changes in response to new choices that are made
based on more knowledge, i.e. the subjective action set and the subjective state set approach the
objective sets.
58
Proposition 3-1 suggests that lim t 1 pKt x
t ld
t 1 pt
. This proposition thus suggests an adap-
tive expectations model of the price. There are many such suggestions in economics starting with
Fisher (1930) through, e.g., Nerlove (1958; 1972), but it can also be found in market-based accounting research (Ohlson 1995). These adaptive expectations models are, to use Grossman’s (1981, p.
543) words, ad hoc models. That is, the models lack theoretical support since they do not derive
from the basic theory of choice. The theory of Homo comperiens, however, suggests such a behavior based on the subjects’ choices since it proposes that lim t 1 pKt x
t ld
t 1 pt
.
Economics have instead followed another direction with the introduction of rational expectations (Muth 1960), which implies that the price process follows a stochastic structure such that
pt & pt p1, p2 , !
(Grossman 1981, p. 543). The rational expectations imply that prices follow
random walk, but at present not even Malkiel (2003, p. 80) believes that prices do so to such an extent that markets are perfectly efficient.
Grossman (1981, p. 543-544) shows that a rational expectations equilibrium can be obtained
even when subjects face asymmetric information. This finding critically uses the unbiasedness conjecture by conjecturing that the expected price equals the price that comes true. Grossman calls this
perfect foresight (Grossman 1981, p. 543). However, [EQ 3-5] show that prices depend on the subjective sets, i.e. as the subject discovers new actions and/or new states, prices change non-randomly.
Chapter 2 argues that it is conceivable to talk about a limited rational expectation model since
the theory of Homo comperiens is general enough to allow for Bayesian learning. This means that it
is general enough to allow for random release of new information about the subjective state set,
which implies that in the event of no discovery we have a situation where the price follows random
walk, but in the event of discovery (of new actions and/or states) prices no longer follow random
walk. Perhaps it is conceivable to think of the price movements as following a random walk with
drift, where the drift follows in the direction of discovery.
I therefore suggest a non-random adaptation of the subjective price such that it regresses to
the equilibrium price, i.e. towards the objective price.
Proposition 3-2: Suppose that the Pareto optimal equilibrium price is fixed, which is reasonable since the
objective action and state sets are assumed to be fixed and since inflation is not conjectured. Then, with
Proposition 3-1 in mind, I propose that price convergence can be described as follows: Let the subjective
price be a function of the objective price p and a fraction of the previous period’s discrepancy between
the subjective price and the objective price. That is,
K
t 1 pt
pC¸
t 2 ptK1 p
Ft
where C ‰ < 0,1
and where Ft is a white noise disturbance.
The adaptation process proposed above suggests that if there initially is a price discrepancy,
i.e.
ptK1
p v 0 , there will be an adjustment process since C ‰ 0,1
. If C 1 , the process is a ran59
dom walk that suggests there is no learning by discovery. If C 0 , it implies that the learning
process is very fast and complete after one period. Having C ‰ 1, 0
implies an oscillating process
with overreactions but where the subjective price nevertheless regresses to the equilibrium price.
Having C 1 implies a never-ending oscillating process with constant over- and under-reactions,
which, consequently, do not allow the subjective price to regress towards the equilibrium price.
Since the theory of Homo comperiens suggests that lim t 1 pKt x
t ld
t 1 pt
it is reasonable to expect to
have C ‰ <0,1
, i.e. the market gradually discovers such that the subjective price regresses towards
the equilibrium price without an oscillating behavior. The pace of learning is kept unspecified from
being very quick C 0 to being very slow C x 1 .
The suggested adaptive model resembles Nerlove’s (1958, p. 231) model as well as Ohlson’s
(1995, p. 667-668) model with some exceptions. Nerlove’s model does not focus on an adaptive
process that leads to an equilibrium price but it is instead a gradual adjustment of the expected normal price based on the difference between the actual price and what was previously expected to be
normal. The model proposed above sets the expectation for t 1 to be the equilibrium price plus a
fraction of a difference between the actual price and the equilibrium price.
Ohlson’s (1995) model is similar to that which is proposed above with an important exception. Ohlson’s (equation 2A, p. 668) model focuses on Vt only and it assumes that the autoregressive process is intercepted by other non-random value-relevant effects that have an autoregressive
pattern. Furthermore, Ohlson presumes that the range of the two autoregressive parameters is nonnegative and less than one.
My proposed model is more tractable insofar that any other information is assumed random
and enters through the white noise residuals. I think that it is a reasonable assumption since two
types of learning is assumed to be present. First, there is Bayesian learning and the release of such
information (i.e. information about something that the subject knows that he or she does no know
about) is assumed to be random. If that conjecture is correct, it follows that such learning feeds into
the model’s white noise residuals. The second type of learning is learning through discovery, which
is what ascertains that lim AK x A8 and that lim S K x S8 , and thus lim t 1 pKt x
t ld
t ld
t ld
t 1 pt
. Ac-
cordingly, it cannot be a white noise process. Learning through discovery is therefore captured in
the model by having C ‰ <0,1
.
3.5 Homo comperiens and Walras’ tâtonnement process
Assuming perfect rationality suggests that there is neither excess demand nor any excess supply, but
with the introduction of limited rational choice, there exists excess demand and supply in the mar-
60
ket. Excess demand or supply is a sufficient and necessary condition for an arbitrage opportunity to
exist in the market.
This means that the existence of arbitrage opportunities is a defining characteristic of a market when limited rational choice is conjectured. The general equilibrium theory was developed by
Walras ([1874] 1954) in which the author argues that the equilibrium price is a price that equates the
demanded and the offered quantities of goods (Walras [1874] 1954).
Since a general equilibrium requires no-arbitrage, it follows that existence of arbitrage opportunities invalidates equilibrium analysis, and since general equilibrium analysis lies at the heart of
traditional economics, any arbitrage opportunity is assumed nonexistent (e.g., Debreu 1959). Walras
([1874]1954, p. 166-172), e.g., discusses what happens if there is an arbitrage opportunity.
According to Walras, it is possible to describe the market in terms of its subjects, their initial
endowments, their utility functions, and the market prices. If there is disequilibrium, the market adjusts itself by increasing the price of the goods that are in excess demand, and by decreasing the
goods that are in excess supply until the demand and supply are in balance for all goods. This takes
place in what Walras calls a tâtonnement process, and is in the subject’s book conceived to occur
without any outside interference. Walras, however, does not explain how it can happen.
Walras’ tâtonnement process has come to be described as if there is a Walrasian auctioneer
responsible for balancing the demand and supply of goods (e.g., Gravelle & Reese 1998). The balancing process is assumed to follow a pattern such as the following: The Walrasian auctioneer calls
out to all subjects in the market the price for each current and future good. Every subject takes these
prices as given and submits to the auctioneer his or her demand and supply plans for each good. All
plans for all subjects in the society are summarized so that the auctioneer can determine for each
good if there is excess demand, excess supply or if the demand and supply is in balance. If there is
imbalance, the auctioneer calls out a new set of prices and the subjects again submit their supply and
demand plans at the given price. If there still is an imbalance in the system, the auctioneer commences another round. This continues until there is a price that equates the demand with the supply
for all goods in the market. Once the set of equilibrium prices has been found, all plans are executed
and trading takes place.
An interesting feature of this Walrasian auctioneer and the tâtonnement process is that it presumes that there is a subject (or perhaps a machine?) that is smarter than all other subjects and who
can act as the auctioneer. 13 Since the subjects in the market fail to make choices that are perfectly
dovetailing, there is a need for someone else to step in and correct the erroneous demand and
13
More carefully put, it is argued that the Walrasian auctioneer is an aberration in the general equilibrium analysis. It is
inserted ad-hoc to guarantee a solution to the general equilibrium’s system of simultaneous linear equations.
61
supply plans. How is this possible when the general equilibrium theory assumes that the world is
populated by subjects who are omniscient (e.g. Mas-Colell et al. 1995, p. 547-548)?
These are in fact mutually contradictory conjectures: In perfect rationality subjects already
know everything there is to know about the alternatives and their consequences that they face, although they may not know it for sure since there is uncertainty. This means that subjects cannot
make an erroneous choice while disequilibrium is due to such erroneous choices! This fact has indeed been appreciated long before today; e.g., Kirzner (1973, 1992) discussed this and came to the
conclusion that a market is in disequilibrium precisely because subjects fail to make demand and
supply plans that dovetail. A drawback with Kirzner’s analysis is that he does not formally a structure the analysis such that he can explain the existence of ignorance and hence why markets are in
disequilibrium. This means that the practical use of the subject’s thoughts remains elusive. The
theory of Homo comperiens explains why markets are in disequilibrium and what the process is that
guides the market process (Chapter 2).
By allowing limited rational choice as defined by Homo comperiens, there is a structure that,
by design, creates a market that from the outset is in disequilibrium and where the market process is
a gradual adjustment to a general equilibrium while it retains the familiar traits of von Neumann Morgenstern’s utility function. A market that is constituted by subjects who act according to Homo
comperiens does also, as seen in section 3.3, neatly fit Walras’ tâtonnement process without having
to make a cumbersome, contradictory, ad-hoc conjecture about a Walrasian (near omnipresent) auctioneer, which has become a standard operating procedure in the application of general equilibrium
analysis.
3.6 Summary
This chapter applies the theory of Homo comperiens to a pure exchange market. It shows that the
subjective marginal rate of substitution between current and future consumption is:
0 pK 1l
0 pK 0l
œ
s ‰SK
VK1 cK 0 , cK 1s ¸ rKls
VK0 cK 0 , cK 1 The subjective marginal rate of substitution between current and future consumption is different to the objective marginal rate of substitution between current and future consumption, which
is (e.g. Ohlson 1987, p. 23):
0 p1l
0 p0l
œ
s‰
V1 c0 , c1s ¸ rls
V 0 c0 , c1l The difference resides in the difference between the marginal utilities for current and future
consumption. The subjective marginal utilities for current and future consumption are:
62
VK0 cK 0 , cK 1 sE K0 ¢U K cK 0 , cK 1 ¯±
QKs ¸ uKs cK 0 , cK 1 scK 0l
s ‰SK
VK1 cK 0 , cK 1s œ
sE K0 ¢ U K cK 0 , cK 1 ±¯
QKs ¸ uK cK 0 , cK 1 sc1Ks
The reason that subjective marginal utilities for current and future consumption differ from
the objective marginal utilities for current and future consumption is because of two reasons. First,
there is a difference between the subjective state-dependent probabilities and the objective statedependent probabilities. Second, the subjective Bernoulli utilities are different. That is,
QK ,s v Q8,s , u c0K , c1K v u c0 , c1 , and u c0K , c1,Ks v u c0 , c1s See section 2.3 (p.36) and Appendix C (p. 191) for a further discussion on this topic.
Chapter 2 shows that the subjective state probabilities and the subjective Bernoulli utilities differ
from the objective state probabilities and the Bernoulli utilities. From this, it follows that as soon as
the subjective action set is limited, the subjective state set is limited, or when both occur, the subject
chooses to trade erroneous amounts of current and future goods.
Since the subjective marginal rate of substitution between current and future consumption
differs from the objective marginal rate of substitution between current and future consumption, it
follows that the subjective prices (i.e. market prices) differ from the objective prices (i.e. intrinsic
values).
The chapter also demonstrates that the quantities demanded and quantities supplied of goods
and services are chosen so that the subjective marginal rates of substitutions of the goods and services equal the subjective prices. This is a deviation from microeconomic theory that rests on perfect
rationality, where the quantities chosen depend on equality between the objective marginal rates of
substitutions and the objective prices.
The chapter then focuses on the endogenous determination of the subjective price and concludes that it is not set independently of historical subjective prices (i.e. subjective prices are not
expected to follow a random walk process) but instead proposes:
Proposition 3-1: Learning through discovery (Definition 2-9) ascertains that lim AK x A8 and
t ld
lim SK x S8 since the ignorance sets decrease. This implies that the subjective price approaches the
t ld
objective price as t goes to infinity. That is lim t 1 pKt x t 1 pt .
t ld
Or, to put it another differently: The market prices approach the intrinsic values since the
subjects learn through discovery from sequential choices when there is no exogenous change that
interferes. This also leads to this chapter’s next proposition.
63
Proposition 3-2: Suppose that the Pareto optimal equilibrium price is fixed, which is reasonable since the
objective action and state sets are assumed to be fixed and since inflation is not conjectured. Then, with
Proposition 3-1 in mind, I propose that price convergence can be described as follows: Let the subjective
price be a function of the objective price p and a fraction of the previous period’s discrepancy between
the subjective price and the objective price. That is,
K
t 1 pt
pC¸
t 2 ptK1 p
Ft
where C ‰ < 0,1
and where Ft is a white noise disturbance.
The discovery variable
C
is assumed to be less than one but greater than or equal to zero,
which provides for a gradual adaptation process that does not overreact. If the adaptation variable
were less than zero, it indicates overreactions; had it been minus one, it implies random walk as it
does when it is one.
Another subtle but yet important element of this chapter is that it shows that the market
price for money is:
0 pK 11
1¸
œ
s ‰S K
VK1 cK 0 , cK 1s ¸ 1
VK0 cK 0 , cK 1 This differs from the intrinsic value of money (cf. A.6.1, p. 158, for the intrinsic value of
money in certainty). And, as A.8.2 (p. 169) shows, the market rate-of-return (MROR) in equilibrium
is a function of the intrinsic value. It follows that MROR is a function of the market price. This has
important implications for valuation theory since MROR is at the core of it, as Appendix A shows.
Chapter 3 argues that a market that assumes Homo comperiens is a market with arbitrage
opportunities, which is in opposition to a general equilibrium market that, by design, excludes arbitrage. This has an important bearing on the existence of a firm and its profits and also precludes
economic analysis based on general equilibrium conditions.
64
CHAPTER 4—HOMO COMPERIENS AND THE FIRM
Homo comperiens’ effect on the firm’s market price and accounting
variables
4.1 Introduction
Chapter 2 and Chapter 3 focus on the subjects and on how they create the market. Less is said about
the firm, which is the focus of the present chapter. This chapter presents limited rational market
pricing models for firms by conjecturing Homo comperiens. It also discusses the effect that the
theory of Homo comperiens has on the firm’s income and on its accounting rate of return (ARR).
The previous chapters present a theory of limited rational choice that is tested using accounting data in latter chapters. Thus, there is a need to connect theory to accounting data. This chapter
provides the formal link and poses operationalizable propositions.
Appendix B provides details to this chapter’s market pricing model propositions and corollaries.
4.2 The firm as a choice entity in the theory of Homo comperiens
In the theory of Homo comperiens the micro unit is the subject and not the firm. The firm is only
an analytical device that assembles the supply activities in the market.
The implication is that each subject can also be a firm, and when this occurs, the firm meets
the assumptions underlying the theory of Homo comperiens. Therefore, when the market consists
of one subject, it follows that the firm in the market, i.e. the market’s supply activities, also has limited knowledge.
However, firms are in practice more often seen as separate units operating in a market. When
this occurs, that unit is created, populated, and enacted by subjects.
Assume that the market has many subjects and all meet assumptions of the theory of Homo
comperiens. Assembling all their supply activities into a single firm is the analytical equivalent to a
planned market. Will such a firm also have limited knowledge and thus be limited rational?
It is possible that the subjects’ knowledge in the union of the market is the equivalent to perfect knowledge. The question can then be formulated as follows: Is it possible to bring together the
knowledge of all subjects into a single choice body such that it has perfect knowledge?
If it is possible to assemble the market’s subjects’ knowledge into a single firm such that it
becomes endowed with perfect knowledge, that firm becomes omniscient and can decide the supply
of goods and services such that a Pareto optimal equilibrium is obtainable. However, it is enough
65
that the firm fails to gather some of the complementary knowledge for the firm to have limited
knowledge.
This view on the subject and the firm’s knowledge leads to a proposition on the firm’s action
set and a corollary on the firm’s state set, but first comes a definition of the firm’s action set.
Definition 4-1: The firm’s action set is defined as the union of all subjects’, who participate in the firm’s
I
endeavor, action sets. That is, AFirm * A , where i ‰ I
i
is a subject.
i 1
Definition 4-1, which should be seen as a general definition, does not define whether the action set is the subjective or the objective action set.
Every subject in the firm faces, according to Definition 2-3 (p. 29), a subjective action set
that is a strict subset of the objective action set. Since the firm’s action set is the union of its subject’s action set, it follows that:
Proposition 4-1: Since the subjects in a firm face subjective action sets according to Definition 2-3, and
since the firm’s knowledge is the union of its entire subject’s knowledge (Definition 4-1), the firm faces a
subjective action set that is a weak subset of the objective action set, i.e. AKFirm ˆ A8Firm .
Proposition 4-1 implies that the firm knows of a weak subset of the objective action set, i.e. it
can be possible to endow it with perfect knowledge of available actions. In practice, it is not likely
that the union of all subjects’ knowledge becomes perfect knowledge. Even in the event that such a
conjecture is incorrect, it is not likely that all such knowledge can be collected without any friction
losses.
This means that the weak subset in Proposition 4-1 can be treated is if it is a strict subset. It
also means that not even in the boundary case, when all subjects in the population are part of a gigantic firm, the firm is able to make perfectly rational choices. Hence, a firm must make its choices
based on limited knowledge of the available actions, i.e.
Firm
AK
ˆ A8Firm .
Chapter 2 discusses the uncertain choice using the states-and-partition-model. It finds that
the subject’s subjective state set is a strict subset of the objective state set because of limited knowledge. This also leads to the following corollary.
Corollary 4-1: The firm, populated by subjects who act according to Definition 2-7, faces a subjective
state set that is a weak subset of the objective state set, i.e. SKFirm ˆ S8Firm .
Corollary 4-1 in practice is also likely to be even stricter and is it probable that a firm’s subjective state set is a strict subset to the objective state set,
Firm
SK
ˆ S8Firm
(cf. above).
The latter part of Chapter 3 finds that a market populated by subjects whose action meets
the conjectures of Homo comperiens is an arbitrage market. Proposition 4-1 and Corollary 4-1 ascertain that a firm’s choice follows the analysis set forth in Chapter 2 and Chapter 3.
66
The firm is therefore an actor in the market that faces limited knowledge when considering
both the action and the state sets. Thus, it is not possible to insert the firm into the market and expect that it can act as an omniscient equilibrating mastermind: the firms and the subjects all face and
act on arbitrage opportunities. This has important implications on the risk and returns of firms,
which is what is treated in the rest of the chapter.
4.3 Certainty, subjective certainty, and uncertainty
The conjecture of perfect rationality ascertains that the firm makes choices based on the objective
action and state sets. Since the firm can take into consideration all possible states that can occur, it
follows that the choice is a certain choice when the state set only contains one element. Using standard vocabulary, it is a certain choice.
Another version of a certain choice occurs - assuming a state-independent utility function when the firm foresees more than one element in the state set, but where the state-dependent consequences are constant.
Homo comperiens conjectures limited knowledge, which means that the firm faces subjective action and state sets. The choice is then seemingly a certain choice when the firm’s subjective
state set contains one element. However, since some elements are ignored because of the firm’s limited knowledge, it follows that the choice no longer meets the criteria for a certain choice and the
choice is only anticipated to be certain. Hence, as the consequences unfold, there is room for unanticipated consequences for the firm because of failure to account for all conceivable states. I call
such a scenario for a subjectively certain choice.
A subjectively certain choice also occurs when the firm correctly accounts for all states that
can occur but fails to realize that the state-dependent consequences are not constant (again conjecturing a state-independent utility function).
Facing an uncertain choice, the difference between the perfect rational choice and the limited
rational choice is less clear, but it is useful to distinguish between uncertainty in the objective sense
and uncertainty in the subjective sense.
Objective uncertainty is present in a choice when the firm faces the objective state set and
when the set contains more than one element. It occurs when the conjectures of perfect rationality
are applied. If Homo comperiens is assumed, subjective uncertainty is the choice when the firm faces the subjective state set and when it contains more than one element.
Section 4.4 focuses on presenting the disequilibrium market-pricing models that the present
thesis uses. The details of their derivations are found in Appendix B.
67
4.4 Homo comperiens and firm market-pricing models in subjective certainty
Equation [EQ A-52] shows that the intrinsic value (i.e. the objective price) of a firm equals the
product of the numerarie’s objective futures price and the objective expected future dividends,
V10 0 p11
¸ d11 , where 0 p11
is the numerarie’s objective futures price. Conjecturing Homo compe-
riens, the market price of the firm is in analogy (cf. Appendix B, p. 179 for details):
P10 0 pK 11 ¸ &K 0 <dK 11 >
[EQ B-23]
That is, the market price of a firm equals the product of the numerarie’s subjective futures
price and the objective expected future dividends.
The subjective futures price differs from the objective futures price since the subject exhibits
a subjective and not an objective utility function (cf. Proposition 2-3, p. 38).
Appendix A shows that the objective futures price of a unit of the numerarie is in equilibrium equal to the objective marginal rate of substitution between the numerarie tomorrow and the
numerarie at present, [EQ A-19]. Assuming Homo comperiens, the subjective futures price of the
numerarie equals the subjective marginal rate of substitution between the numerarie tomorrow and
the numerarie at present (cf. Appendix B, p. 179 for details):
0 pK 1
0 pK 0
‹U K cK 1 ‹U K cK 0 [EQ 4-1]
The subjective marginal rate of substitution is a function of the marginal rates of substitutions, which are functions of the subjective consequence set, U K : C K l \ . The subjective consequence set is itself a function of the subjective action set, fK : AK l C K .
The objective action set equals the consumption set X \ L0 q \ L1 after further restrictions
(the objective budget hyperplane and transformation frontier) are added. The subjective action set
equals the subjective consumption set X K , which is a strict subset to the objective consumption set
X K ‡ X 8 after further restrictions (the subjective budget hyperplane and transformation frontier)
are added.
For more detailed information, turn to sections 2.3 and 3.3 for an analysis of the utility function, its relationship to the action set and consequence set and section, and for optimization. See
Appendix A for an analysis that assumes perfect rationality and Appendix B for an analysis that assumes limited rationality.
The subjective expected dividends in [EQ 4-1] differ from objective expected dividends because of the subject’s subjective action set, i.e. the subject may have false anticipations. This means
that the subjective expected dividends need not be the dividends that come true even though the
subject perceives the choice as certain. Again, this shows how the rational expectations hypothesis
assumption of unbiased forecasts is not possible to apply in the limited rational choice.
68
Appendix A argues that the firm’s intrinsic value in a certain choice is equal to the present
value of the firm’s expected dividends. It also reasons that it is equal to the firm’s current book value
of equity and its present value of expected future residual income. Finally, the appendix states that
the firm’s intrinsic value is equal to the firm’s present book value of equity and its present value of
expected future residual operating income after it is adjusted for its present value of expected future
residual interest expense (cf. [EQ A-58], [EQ A-65], and [EQ A-68]). This is knowledge already
known (see Feltham & Ohlson, 1999, for a rather technical yet interesting set of derivations under
stochastic interest rates).
When subjects meet the conjectures in the theory of Homo comperiens, there exist equivalent market-pricing models. Assuming homogenous preferences means that the market price of a
firm is as follows.
Proposition 4-2: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences
and a mild regulatory assumption (cf. Appendix B, p. 186 for details), the market price of a firm is:
P0 œ
d
t 1
0 pKt
¸ &K 0 <dKt > .
As in Appendix A, the subscript identifying the numerarie good is excluded from the subscript in Proposition 4-2 to reduce cluttering. The only difference with a market price according to
above and the intrinsic value according to [EQ A-58] is that the subjective futures prices, 0 pKt , are
different from the objective futures prices (hence, we have biased rational expectations) and that the
subjective expected future dividend is different from the objective expected future dividend.
Another way to express the market price of a firm is as a function of the subjective expected
residual net income.
Proposition 4-3: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences,
the clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 186 for details), the
market price of a firm is: P0 EQ0 œ
d
t 1
0 pKt
¸ &K 0 <RI t > , where
&K 0 <RI t > &K 0 <CNI t > &K 0 < t 1rt > ¸ EQt 1 .
It is also possible to express Proposition 4-3 using accounting return on equity.
Corollary 4-2: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences,
the clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 188 for details), the
market price of a firm is: P0 EQ0 œ
d
t 1
0 pKt
¸ &K 0 < t 1RROEt > ¸ EQt 1 , where
&K 0 < t 1RROEt > &K 0 < t 1ROEt > &K 0 < t 1r >t .
Using the value additivity principle of Modigliani and Miller (1958) allows the market price of
equity to be described as a function of residual operating income as shown below.
69
Proposition 4-4: Conjecturing Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences, the clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 186
for details), the market price of a firm is: P0 EQ0 œ
d
t 1
0 pKt
¸ &K 0 <ROI t > œ
d
t 1
0 pKt
¸ &K 0 <RIEt >
where &K 0 <ROI t > &K 0 <OI t > &K 0 < t 1rt > ¸ NOAt 1 , and &K 0 <RIEt > &K 0 <IEt > &K 0 < t 1rt > ¸ NFLt 1 .
It is also possible to express Proposition 4-4 using accounting return on net operating assets.
Corollary 4-3: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences,
the clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 189 for details), the
market price of a firm is:
P0 EQ0 œ
d
t 1
0 pKt
¸ &K 0 < t 1RRNOAt > ¸ NOAt 1 œ
d
t 1
0 pKt
¸ &K 0 < t 1RNBC t > ¸ NFLt 1 , where
&K 0 < t 1RRNOAt > &K 0 < t 1RNOAt > &K 0 < t 1rt > and &K 0 < t 1RNBC t > &K 0 < t 1NBCt > &K 0 < t 1rt > .
Proposition 4-3 differs from [EQ A-65] and Proposition 4-4 differs from [EQ A-68] in that
the expected residual income, &K 0 <RI t > , the expected residual operating income, &K 0 <ROI t > , and
the expected residual net interest expense, &K 0 <RIEt > , are the subjective and not objective.
Since this is a subjectively certain choice, it follows that the firm, as in subsection A.8.3’s certain choice, uses an identical subjective market rate-of-return
t 1 rKt
for Proposition 4-2 to
Proposition 4-4 and that it is equal to the risk-free market rate-of-return.
With Proposition 4-3, Proposition 4-4, Corollary 4-2, and Corollary 4-3, it is possible to discuss what bearing they have on a firm’s income, accounting rate-of-return, and risk. This is considered in section 4.5.
4.5 Homo comperiens and the firm’s risk and return
This section analyzes what is expected from a firm’s accounting rates-of-returns and risk when
Homo comperiens is assumed. The section is divided into two subsections where subsection 4.5.1
focuses on a subjectively certain choice and subsection 4.5.2 deals with the subjectively uncertain
choice.
Appendix A discusses the intrinsic values, income, and accounting rates-of-returns assuming
unbiased accounting. This section and Appendix B retain the conjecture assumption of unbiased
accounting.
4.5.1 Homo comperiens and the firm’s rate-of-return in the subjectively certain choice
Appendix A argues that no residual income is a defining trait of no-arbitrage. Invoking the theory of
Homo comperiens implies that there are innumerable arbitrage opportunities ascertaining the existence of residual income. This means that in such a market there exists subjective expected residual
income, residual operating income, and residual interest expense.
70
In equilibrium the comprehensive net income is equal to the product of the objective market
rate-of-return and the beginning-of-period equity. The comprehensive operating income is equal to
the product of the objective market rate-of-return and the beginning-of-period net operating assets.
Moreover, the comprehensive net interest expense is equal to the product of the objective market
rate-of-return and the beginning-of-period net financial liabilities.
In a Homo comperiens setting, they are functions of the subjective market rate-of-return and
of arbitrage income. Since whole market is in disequilibrium, arbitrage income can be earned within
any part of the firm. Therefore:
&K 0 <CNI t > &K 0 < t 1rt > ¸ EQt 1 &K 0 <net arbitrage incomet >
[EQ 4-2]
&K 0 <OI t > &K 0 < t 1rt > ¸ NOAt 1 &K 0 <operating arbitrage incomet >
[EQ 4-3]
&K 0 <IEt > &K 0 < t 1rt > ¸ NFLt 1 &K 0 < financial arbitrage incomet >
[EQ 4-4]
The expected net arbitrage income &K ,0 <net arbitrage incomet > in [EQ 4-2] is the sum of the arbitrage income expected in [EQ 4-3] to [EQ 4-4].
These equations can be measured using accounting rates-of-returns according to the equations below. The analysis focuses on the return on equity and the return on net operating assets
since they provide the accounting explanation of the capital growth of the firm when it is either financially leveraged or financially unleveraged (cf. subsection A.8.4.2, p. 174). To focus the analysis
the financial accounting rate-of-return is ignored.
From [EQ 4-2] and [EQ 4-3], it is clear that the subjective expected return on equity and the
subjective expected return on net operating assets is, given the definitions in Appendix B, functions
of the subjective expected market rate-of-return and of the subjective expected arbitrage rate-ofreturn:
&K 0 < t 1 ROEt > &K 0 < t 1rt > &K 0 <net arbitrage rate of returnt >
[EQ 4-5]
&K 0 < t 1 RNOAt > &K 0 < t 1rt > &K 0 <operating arbitrage rate of returnt >
[EQ 4-6]
Appendix B also uses the residual accounting rates-of-returns. The residual accounting ratesof-returns are in the subjectively certain choice:
&K 0 < t 1 RROEt > &K 0 < t 1 ROEt > &K 0 < t 1rt > &K 0 <net arbitrage rate of returnt >
[EQ 4-7]
&K 0 < t 1 RRNOAt > &K 0 < t 1 RNOAt > &K 0 < t 1rt > &K 0 <operating arbitrage rate of returnt >
[EQ 4-8]
Model [EQ 4-2] to [EQ 4-8] holds in expectations since the subjectively certain choice is a
chimera because of limited knowledge. As the future unfolds, there can be a difference between the
expectation and the outcome because the subject’s expectation is based on the subjective state set
and not on the objective state set, or because the subjective state-dependent consequence was not
71
constant. The ex post variation of [EQ 4-2] to [EQ 4-8] is therefore affected by events that the firm
is ignorant of and we thus have accounting affected by unexpected income:
CNI Kt t 1 rt
¸ EQt 1 net arbitrage incomet unexpected incomet
[EQ 4-9]
OI t t 1 rt
¸ NOAt 1 operating arbitrage incomet unexpected incomet
[EQ 4-10]
IEt t 1 rt
¸ NFLt 1 financial arbitrage incomet unexpected incomet
[EQ 4-11]
t 1 ROEt
t 1 RNOAt
t 1 RROEt
t 1 RRNOAt
t 1 rt
t 1 rt
[EQ 4-12]
operating arbitrage rate of returnt unexpected rate of returnt
t 1 ROEt
t 1 RNOAt
net arbitrage rate of returnt unexpected rate of returnt
[EQ 4-13]
t 1rt net arbitrage rate of returnt unexpected rate of returnt
[EQ 4-14]
t 1rt operating arbitrage rate of returnt unexpected rate of returnt
[EQ 4-15]
The residual return on equity and the residual return on net operating assets are in expectations equal to the arbitrage rates-of-returns obtained by the firm. When they are measured ex post,
there is noise affecting them since there are occurrences that the firm is unaware of when making its
choice.
Homo comperiens is endowed with the capacity to discover (cf. Definition 2-9 and its corresponding section), and it is argued in Chapter 2 that the subject, and hence the firm, through discovery makes choices on subjective action and state sets that are increasingly more similar to their
objective counter parts. Given enough transactions, the subjective and the objective sets become
almost identical. This implies that the limited rational choice in limit becomes almost as a perfect
rational choice, with the market close to equilibrium.
This means that the market prices trend towards the Pareto optimal prices (cf. Proposition 32, p. 59), which implies that the subjective expected RROE [EQ 4-7] approaches zero when the
numbers of transaction increase since the subjective expected ROE approaches the objective expected ROE. The same applies to the subjective expected RRNOA [EQ 4-8] and since the subjective expected RNOA approach the objective expected RNOA.
Proposition 4-5: In a subjectively certain market that meets the assumptions of Homo comperiens
(Proposition 2-4, Proposition 3-2), with unbiased accounting, the subjective expected RROE and
RRNOA regress until, in the limit, they are zero. That is, lim &K 0 < t 1RROEt >
0 , and
t ld
lim &K 0 < t 1RRNOAt >
0 .
t ld
The ex-post RROE and RRNOA are thus only affected by the unexpected rate-of-return. If
the subjective state sets meet their objective counterpart, it implies that the unexpected rates-ofreturns also diminish as the number of transactions increases. It is consequently also likely that the
limit values of ex post RROE and RRNOA approach zero assuming subjective certainty.
This subsection takes as a point of departure the case where the subject and the firm perceive
a certain future. That is, when they believe that they know for sure what the future payoffs are going
72
to be. There is a difference between ex ante and ex post even in this scenario because of limited
knowledge. The following section analyses a more complete scenario in which subjectively uncertainty affects the formation of expectations.
4.5.2 The firm’s rate-of-return in the objective uncertain choice
This subsection expands the problem from analyzing market pricing of firms in subjective certainty
to analyzing market pricing of firms in subjective uncertainty. The analysis takes as its point of departure perfect rationality, as in the previous subsection.
Typical estimation of a firm’s intrinsic value in an uncertain choice assumes constant market
rate-of-return (MROR) and that it can be estimated using CAPM (e.g., Penman 2004). CAPM is a
general equilibrium model using constant MROR (Ohlson 1987). Section 4.4 allows for nonconstant MROR, which is similar yet different to Feltham and Ohlson (1999). Feltham and Ohlson
(1999) provide intrinsic valuation models for objective uncertainty with stochastic MROR. According to these authors, it is possible to find the firm’s intrinsic value using (p. 171 [DVR-f*], 172 [AVRf*], 176-178):
V0 œ
d
t 1
0 pt
¸ &*0 <dt > ” EQ0 œ
d
t 1
0 pt
¸ &*0 <RI t > ” EQ0 œ
d
t 1
0 pt
¸ &*0 < ROI t > œ
d
t 1
0 pt
¸ &*0 <RIEt >
The expectations operator &*0 <¸> is different from &0 <¸> since it is a risk-adjusted expectations
operator. For example, the expected dividend is the sum of the products of the state-dividend and
the objective state probability. Risk-adjusted expected dividend is the sum of the products of the
state-dividend and the risk-adjusted objective state probability.
A subject’s risk-adjusted objective state probability for a good in a given period is equal to
the product of the subject’s state price for this good and period and the risk-free return for the period. The state price of the numerarie equals the marginal rate of substitution between a claim to the
numerarie tomorrow and a claim to the numerarie today. The marginal rate of substitution stems
from the subject’s objective probability belief for the state to come true and on the claim’s objective
Bernoulli utility (see, e.g., Pliska (1997, p. 33-36) for more on the risk-adjusted probability function).
By using the risk-adjusted objective probabilities, it is possible to express the risk-adjusted
expected dividend according to (cf. e.g. Feltham & Ohlson 1999, p. 169, 171):
&*0 <dt > œd
st
¸ Qst* s‰
where
œd
st
¸ 0 pst ¸ 0 RtF
[EQ 4-16]
s‰
Qst* 0 pst ¸ 0 RtF
F
0 Rt

žžž
žŸ s ‰
œ
¬­1
­
®­
0 pst ­
73
In the equation above Qst* is the risk-adjusted state probability, 0 pst is the state price that reflects the subject’s risk aversion and beliefs, and 0 RtF is the risk-free return on a numerarie invested
at present until t.
All subjects have the same marginal rates of substitutions between saving and consumption
in general equilibrium and it is therefore no loss in generality to assume homogenous preferences,
i.e. the conjecture of the “representative subject”.
Assuming homogenous preferences means that the risk-adjusted expected dividend can be
expressed as a function of the expected dividend and a covariance term between the expected dividend and a risk adjustment index (Ohlson 1987, p. 85). The covariance term is negative for a riskaverse subject. That is,
&*0 <dt > &0 <dt > cov &0 <dt >,Q [EQ 4-17]
Adjusting for risk in valuation using a negative covariance between the payoff and a risk adjustment index is an accepted part of financial theory and can be found in, e.g., Rubinstein (1976).
Feltham & Ohlson (1999, p. 173) use this model for both the dividend valuation model and the residual income valuation model.
Adding additional structure to the subject’s utility function can lead to a setting in which the
familiar CAPM is found. The reader is referred to Ohlson (1987) for a comprehensive treatment of
the theory of security valuation in a no-arbitrage setting.
By using [EQ 4-17] it is possible to express the objective risk-adjusted expected residual income, residual operating income, and residual net interest-bearing expense as follows (cf. Feltham &
Ohlson (1999, p. 173) who apply [EQ 4-17] to the residual income valuation model).:
&*0 <RI t > &0 <RI t > cov &0 <RI t >,Qt [EQ 4-18]
&*0 <ROI t > &0 <ROI t > cov &0 <ROI t >,Qt [EQ 4-19]
&*0 <RIEt > &0 <RIEt > cov &0 <RIEt >,Qt [EQ 4-20]
A Pareto optimal equilibrium implies that there is no arbitrage opportunity, which means that
there are no strictly positive NPV investments. Unbiased accounting and zero NPV therefore imply
that the LHS in [EQ 4-18] to [EQ 4-20] are zero (e.g., Ohlson (2003) for a discussion of residual
income and NPV).
Given the previous definitions of the different alternative residual incomes models, this
enables the following relations:
&0 <CNI t > &0 < t 1rt > ¸ EQt 1 cov &0 <RI t >,Qt &0 < t 1rt > ¸ EQt 1 total risk premiumt
[EQ 4-21]
&0 <COI t > &0 < t 1rt > ¸ NOAt 1 cov &0 <ROI t >,Qt &0 < t 1rt > ¸ NOAt 1 operating risk premiumt
[EQ 4-22]
74
&0 <CIEt > &0 < t 1rt > ¸ NIBLt 1 cov &0 <RIEt >,Qt &0 < t 1rt > ¸ NIBLt 1 financial risk premiumt [EQ 4-23]
This means that the subject expects a firm to pay off at par with a risk-free investment for
any period, as well as an additional premium to cover for the objective uncertainty. It is possible to
rephrase this using objective expected ROE and objective expected RNOA.
&0 < t 1 ROEt > &0 < t 1rt > total risk premiumt
[EQ 4-24]
&0 < t 1 RNOAt > &0 < t 1rt > operating risk premiumt
[EQ 4-25]
The risk premium for [EQ 4-24] is cov &0 <RI t >,Qt ¸ EQt11
and it is different compared with
the risk premium in [EQ 4-25], which is cov &0 <ROI t >,Qt ¸ EQt11 since the covariances do not use
the same residual income variables.
The risk premium in [EQ 4-24] is the compensation that the subject requires because of the
objective operating uncertainty, i.e. the objective uncertainty that the firm faces if it is without financial leverage. The risk premium in [EQ 4-24] is a combination of the objective operating risk and the
objective financial risk. It thus follows that the objective expected ROE and RNOA differ in a financially leveraged firm. Another subtlety in the risk premiums is that they are non-constant: the risk
premiums must be constant if CAPM is applied since it is a one-period equilibrium model.
It is useful to note that in a perfect rational choice, [EQ 4-24] and [EQ 4-25] imply, given the
definitions of the objective expected RROE and RRNOA, that they are functions of the objective
risk premiums:
&0 < t 1 RROEt > &0 < t 1 ROEt > &0 < t 1rt > total risk premiumt
[EQ 4-26]
&0 < t 1 RRNOAt > &0 < t 1 RNOAt > &0 < t 1rt > operating risk premiumt
[EQ 4-27]
Appendix A finds that the objective expected RROE and RRNOA must be zero when objective certainty is present, i.e. conjecturing perfect rationality and certainty. This section finds that,
in the presence of objective uncertainty, the objective expected RROE and RRNOA are no longer
expected to be zero. Rather, they are equal to the corresponding non-constant objective risk premiums.
4.5.3 Homo comperiens and the firm’s rate-of-return in the subjectively uncertain choice
A similar analysis to that in 4.5.2 can be performed on choice that meets the assumptions of Homo
comperiens. This subsection assumes homogenous preferences, an assumption that enables a discussion of a market price rather than of a unique price of the firm for each subject. However, since
the subjects’ only have access to their limited action and state set, the market price is a disequilibrium price. Therefore, there is a difference between the market price and the intrinsic value.
75
The subject, acting according to the conjectures of Homo comperiens, therefore finds the
firm’s market price with the use of the risk-free market rate-of-return and with the use of riskadjusted subjective expected payoffs:
P0 œ
d
t 1
0 pKt
*
¸ &K
0 <dt > ” EQ0 œ
d
t 1
0 pKt
¸ &*K 0 <RI t > ” EQ0 œ
d
t 1
0 pKt
¸ &*K 0 <ROI t > œ
d
t 1
0 pKt
¸ &*K 0 <RIEt >
The key difference between section 4.4 and the perfect rational choice in uncertainty (subsection 4.5.2) centers on the risk-adjusted expectations operator and the subjective price.
The objective risk-adjusted expectations operator &*0 <¸> i.e., assuming perfect rationality, is
based on the objective state prices for the numerarie and on the objective risk-free return. The objective state prices equal the objective marginal rate of substitution between a claim to the numerarie
for that period and a claim to the numerarie today. Moreover, equilibrium forces all subjects to have
the same objective marginal rate of substitution between savings and consumption.
The risk-adjusted expectations operator &*K 0 <¸> is based, instead, on the subjective state prices for the numerarie and on the subjective risk-free return. The subjective state prices equal the subjective marginal rate of substitution between a claim to the numerarie for that period and a claim to
the numerarie today (cf. A.6.1 on page 157).
This means that the difference between &*0 <¸> and &*K 0 <¸> rests on the difference between the
objective and the subjective marginal rate of substitution between savings and consumption. The
objective marginal rate of substitution is the same across the population but the subjective marginal
rate of substitution is unique for each subject. It depends on the subject’s unique perception of the
available actions and on the subject’s subjective state set. These, in turn, depend on the subject’s
limited knowledge, which also depends on the subject’s unique transaction pattern.
Further, recall from [EQ 4-16] that the objective risk-free return for a period is a function of
the sum of the objective state prices for the numerarie in that period (Feltham & Ohlson 1999, p.
168-169). A corollary in the subjective uncertain choice is that the subjective risk-free return for a
period is a function of the subjective state prices for the numerarie in that period. In addition, this
implies that the subjective risk-free return is affected by the subjective marginal rate of substitution
between savings and consumption, which depends on limited knowledge of actions and states.
It is therefore possible to run a similar analysis to [EQ 4-17]—[EQ 4-25], assuming that the
effect of arbitrage opportunities enters in the same way as in subsection 4.5.1. Such an analysis gives
that the subjective expected ROE and RNOA are functions of the subjective risk-free rate-of-return,
a risk premium, and arbitrage rate-of-return. That is,
&K 0 < t 1 ROEt > &K 0 < t 1rt > &K 0 <net arbitrage rate of returnt > &K 0 <total risk premiumt >
[EQ 4-28]
76
&K 0 < t 1 RNOAt > &K 0 < t 1rt > &K 0 <operating arbitrage rate of returnt > &K 0 <operating risk premiumt >
[EQ 4-29]
The subjective expected RROE and RRNOA is a function of the respective arbitrage ratesof-returns and subjective risk premiums. That is, I define subjective expected RROE and RRNOA
as:
&K 0 < t 1 RROEt > &K 0 < t 1 ROEt > &K 0 < t 1rt >
[EQ 4.30]
&K 0 < t 1RRNOAt > &K 0 < t 1RNOAt > &K 0 < t 1rt >
[EQ 4.31]
Using [EQ 4.30] in [EQ 4-28] and using [EQ 4.31] in [EQ 4-29] gives the subjective expected RROE and RRNOA to be functions of the risk premiums and arbitrage profits.
&K 0 < t 1 RROEt > &K 0 <net arbitrage rate of returnt > &K 0 <total risk premiumt >
[EQ 4-32]
&K 0 < t 1RRNOAt > &K 0 <operating arbitrage rate of returnt > &K 0 <operating risk premiumt >
[EQ 4-33]
Subsection 4.3 finds that in subjective certainty the subjective expected RROE and RRNOA
trend towards zero as the number of transactions mounts. The argument is as follows: The subject
learns through discovery, which increases the subjective action and state sets until it in the limit almost reaches the objective action and state sets.
Define the risk-adjusted subjective expected RROE and RRNOA as:
&*K 0 < t 1 RROEt > &K 0 < t 1 RROEt > &K 0 <total risk premiumt >
[EQ 4.34]
&*K 0 < t 1 RRNOAt > &K 0 < t 1 RRNOAt > &K 0 <operating risk premiumt >
[EQ 4.35]
Substituting [EQ 4.34] into [EQ 4-32] and substituting [EQ 4.35] into [EQ 4-33], and rearranging show that [EQ 4.34] and [EQ 4.35] are non-zero because of the arbitrage rate-of-return. A
key difference between perfect rationality and limited rationality is therefore that the latter produces
non-zero arbitrage rates-of-returns that manifest themselves as non-zero risk-adjusted subjective
expected RROE and RRNOA.
Allowing the subjects to learn through discovery means that the risk-adjusted subjective expected RROE and RRNOA trend towards zero. They trend toward zero since the limited action and
state sets trend towards the objective sets that imply that the market trends towards a Pareto optimal
equilibrium. That is,
lim &K 0 < t 1 RROEt >
&K 0 <total risk premiumt >
[EQ 4-36]
lim &K 0 < t 1 RRNOAt >
&K 0 <operating risk premiumt >
[EQ 4-37]
t ld
t ld
Due to the analysis above, I pose these two propositions.
Proposition 4-6: In a market that meets the conjectures of the theory of Homo comperiens (Proposition
2-4), and with unbiased accounting, there exists non-zero risk-adjusted subjective expected RROE and
RRNOA because of arbitrage opportunities. That is, &*K 0 < t 1RROEt > &K 0 <net arbitrage rate of returnt > v 0 ,
and &*K 0 < t 1RRNOAt > &K 0 <operating arbitrage rate of returnt > v 0 .
77
Proposition 4-7: In a market that meets the conjectures of the theory of Homo comperiens (Proposition
2-4, Proposition 3-2) and with unbiased accounting the limit values of risk-adjusted subjective expected
RROE and RRNOA are zero. That is: lim &*K 0 < t 1RROEt > 0 , and lim &*K 0 < t 1RRNOAt > 0 .
t ld
t ld
With the propositions above, I have traversed from proposing a theory of choice in the
second chapter all the way into market-based accounting in a way that enables me to test the theory
of Homo comperiens. However, such tests need operationalization of the risk-adjusted subjective
expected residual accounting rates-of-returns. This is the topic of the next two chapters. They make
necessary operationalizations and pose testable hypotheses.
Proposition 4-6 and Proposition 4-7 imply there exists expected arbitrage residual income
and that such residual income decreases. A pertinent question is then how my market-pricing models with discovery that use residual income differ from the models proposed by Ohlson (1995) and
Feltham and Ohlson (1995).
It should be noted that I argue in A.8.4.3 (p. 174) that Ohlson’s model and Ohlson and Feltham’s model disallow the existence of expected residual income when the accounting bias is removed, i.e. they measure expected no-arbitrage residual income. This means that empirical investigations that use Ohlson’s and Feltham and Ohlson’s models critically assume no-arbitrage and zero
expected residual income of the sort that I model in here. Indeed, Feltham and Ohlson appreciate
this fact since they write (196, p. 209-210) “The resulting book value and accounting earning numbers are such that, for all periods, the book rate of return equals the cost of capital; that is, the firm
reports normal profits for all periods,” in a situation where we have unbiased accounting.
Since Ohlson’s and Feltham and Ohlson’s models assume no-arbitrage residual income, the
implication is that empirical assessments based on their models can only purport to explain residual
income because of accounting earnings only (i.e. when NPV is zero for all firms) and cannot purport
to explain residual income based on economic earnings (i.e. when NPV is non-zero for at least one
firm). This is something also noted by Lo and Lys (1999, p. 348), Lundholm (1995, p. 761), and
Beaver (2002, p. 458).
4.6 Summary
Chapter 4 discusses a firm’s market price in a market, assuming Homo comperiens. The firm’s market price is then different from the firm’s intrinsic value because the market is in disequilibrium. The
chapter poses the following propositions and corollaries.
Proposition 4-2: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences
and a mild regulatory assumption (cf. Appendix B, p. 186 for details), the market price of a firm is:
P0 œ
d
t 1
0 pKt
¸ &K 0 <dKt > .
78
Proposition 4-3: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences,
the clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 186 for details), the
market price of a firm is: P0 EQ0 œ
d
t 1
0 pKt
¸ &K 0 <RI t > , where
&K 0 <RI t > &K 0 <CNI t > &K 0 < t 1rt > ¸ EQt 1 .
Proposition 4-4: Conjecturing Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences, the clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 186
for details), the market price of a firm is: P0 EQ0 œ
d
t 1
0 pKt
¸ &K 0 <ROI t > œ
d
t 1
0 pKt
¸ &K 0 <RIEt >
where &K 0 <ROI t > &K 0 <OI t > &K 0 < t 1rt > ¸ NOAt 1 , and &K 0 <RIEt > &K 0 <IEt > &K 0 < t 1rt > ¸ NFLt 1 .
Corollary 4-2: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences,
the clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 188 for details), the
market price of a firm is: P0 EQ0 œ
d
t 1
0 pKt
¸ &K 0 < t 1RROEt > ¸ EQt 1 , where
&K 0 < t 1RROEt > &K 0 < t 1ROEt > &K 0 < t 1r >t .
Corollary 4-3: Assuming the theory of Homo comperiens (Proposition 2-4), homogenous preferences,
the clean surplus relationship, and a mild regulatory assumption (cf. Appendix B, p. 189 for details), the
market price of a firm is:
P0 EQ0 œ
d
t 1
0 pKt
¸ &K 0 < t 1RRNOAt > ¸ NOAt 1 œ
d
t 1
0 pKt
¸ &K 0 < t 1RNBC t > ¸ NFLt 1 , where
&K 0 < t 1RRNOAt > &K 0 < t 1RNOAt > &K 0 < t 1rt > and &K 0 < t 1RNBC t > &K 0 < t 1NBCt > &K 0 < t 1rt > .
The corollaries above make it possible to form propositions that, when operationalized, are
testable.
In a subjectively certain choice the firm has an opportunity to earn a subjective expected residual rate-of-return on equity (RROE) and a residual rate-of-return on net operating assets
(RRNOA). These opportunities exist because the market is an arbitrage market. However, the chapter also proposes that the opportunities dissolve because of the subjects’ propensity to discover.
Proposition 4-5: In a subjectively certain market that meets the assumptions of Homo comperiens
(Proposition 2-4, Proposition 3-2), with unbiased accounting, the subjective expected RROE and
RRNOA regress until, in the limit, they are zero. That is, lim &K 0 < t 1RROEt >
0 , and
t ld
lim &K 0 < t 1RRNOAt >
0 .
t ld
The proposition above is not testable since it takes place in subjective certainty and hence its
alternative formed in a subjectively uncertain choice. The propositions in subjective uncertainty are:
Proposition 4-6: In a market that meets the conjectures of the theory of Homo comperiens (Proposition
2-4), and with unbiased accounting, there exists non-zero risk-adjusted subjective expected RROE and
RRNOA because of arbitrage opportunities. That is, &*K 0 < t 1RROEt > &K 0 <net arbitrage rate of returnt > v 0 ,
and &*K 0 < t 1RRNOAt > &K 0 <operating arbitrage rate of returnt > v 0 .
79
Proposition 4-7: In a market that meets the conjectures of the theory of Homo comperiens (Proposition
2-4, Proposition 3-2) and with unbiased accounting the limit values of risk-adjusted subjective expected
RROE and RRNOA are zero. That is: lim &*K 0 < t 1RROEt > 0 , and lim &*K 0 < t 1RRNOAt > 0 .
t ld
t ld
80
CHAPTER 5—THE EMPIRICAL DATA AND THE FINANCIAL
STATEMENTS
An operationalization of the balance sheet, the income statement, and of
the clean surplus relation
5.1 Introduction
The previous chapter poses propositions based on Homo comperiens that uses accounting measures. This chapter operationalizes the empirical financial statements such that they can be used to
measure the components to ROE and RNOA, which are needed for hypothesis testing of the previous chapter’s propositions.
ROE is defined in [EQ A-71] (cf. also [EQ B-39]) and RNOA is defined in [EQ A-76] (cf.
also [EQ B-42]). Subsection A.8.3.2 on page 172 provides a further disaggegation and classification
of the components to ROE and RNOA. This chapter provides empirical content to these definitions and classifications.
The definitions of the accounting rates-of-returns are directly connected to theory. This
chapter’s operationalizations, together with Appendix D—Appendix H, attempt to determine if this
connection continues to exist. Having operationalized accounting rates-of-returns that maintain their
theoretical connections is not part of the mainstream in empirical market-based accounting research.
Empirical market-based accounting research using accounting rate-of-return often does not pay
close attention to the definitions and to the operationalization of the variables used. The research
often misses at least some of the dirty-surplus problem, the effects of extraordinary items, and the
effects that are due to discontinued operations. Other problems that often exist are measurement
inconsistencies (inconsistent definition of numerators and denominators in the accounting rates-ofreturns), and timing inconsistency (uses end-of-period balance sheet values).
The problems seem to very frequent in market-based accounting research (Albrecht et al.
1977; Ball & Watts 1972; Beaver 1970; Brooks & Buckmaster 1976; Fama & French 2000; Lookabill
1976; Ou & Penman 1989a,b; Penman 1991; Watt & Leftwich 1977). Notable exceptions are Penman & Zhang (2000) and Nissim & Penman (2001) who pay close attention to the definitions and
the operationalization of the variables.
Empirical industrial economics research also uses accounting rates-of-returns (Baginski et al.
1999; Brown & Ball 1967; Buzzell & Gale 1987; Brozen 1970; Cubbin & Geroski 1987; Jacobsen
1988; Jacobson & Aaker 1985; Geroski & Jacquemin 1988; Lev 1983; Lev & Sougiannis 1996; Mueller 1977; Mueller 1990; Waring 1996). This research has the same problems as the market-based
81
accounting research although the problems are even worse in empirical industrial economics research.
The chapter first presents the empirical data, followed by the operationalization of the clean
surplus relationship, the balance sheet, and finally, the operationalization of the income statement.
5.2 A description of the empirical data
The total sample of the present thesis covers 33,251 firm-year observations of which 25,245 are usable 14. The empirical data are acquired from Statistics Sweden (SCB). It covers the period 1977—
1996 but data only up to 1994 are used in this research. The data consist of active limited companies
in Sweden’s manufacturing industry. 15, 16
The study uses Swedish accounting data rather than, e.g., US data for two reasons. Focusing
on Swedish accounting data suggests that I will have a better understanding of the accounting principles and standards that allows me to operationalize the variables in a more valid manner. The
second reason is that there exist no such study of this scope on Swedish data but there exist quantitative accounting studies on a similar scope using, e.g., US accounting data.
The data cover a historical period. Using more up to date data would compromise the comparability since there was a major change in the collection and classification of the accounting data at
the end of the studied period. The fact that the accounting data are old does not materially affect
this research since I study a general phenomenon and thus it is not influenced by the choice of time.
To each firm-year observation is attached a balance sheet and an income statement, as well as
additional information (e.g., a standard industry classification code specified to the 4th digit). Each
firm-year observation has between 80—96 specified line items. See Appendix G for a full specification of the variables in the empirical data.
The data do not cover the consolidated financial statements but focus on the financial statements from the subject legal entities. A focus on legal entities rather than groups opens for the pos-
14 A usable firm-year observation is an observation that is structurally stable and that is not imputed. See Appendix C for
a description of the process of finding usable firm data from the total sample.
15 The focus on the Swedish manufacturing industry serves several purposes. First, it takes heed to Bernard’s (1989) call
for intra-industry research in accounting, and second, it takes into consideration McDonald and Morris’ (1985) caution
against inter-industry financial ratio analysis. In addition, because of a lack of comparable accounting standards, an international comparison is avoided.
16 Data from 1977—1978 use the whole population of limited Swedish manufacturing firms (LIMFs) having more than
50 employees and a sample from those LIMFs having less than 50 employees. The sampling method was designed by
SCB to keep the same firms in the sample over the years (Företagen 1978, p. 16-17). Between 1979 and 1994, the whole
population of LIMFs having more than 20 employees is used (Företagen 1994, p. 6). During the same period, a sample
of LIMFs having less than 20 employees is also used. In the period from 1995 to 1996, all LIMFs having more than 10
employees are in the sample, but LIMFs having less than 10 employees are still sampled (Erikson 2003, p. 2).
In this research the manufacturing industry is defined according to the standard industry classification from 1969
(SNI69) as SNI-code 38. From 1992, the new standard for industry classification, SNI92, is used. The old SNI-code 38
corresponds to the new SNI-codes 28—35. The re-definition of the manufacturing industry was developed in dialogue
with Statistics Sweden (SCB), which provided the raw data.
82
sibility of errors because of consolidation issues 17. However, these problems are small in comparison
with the benefit of having access to such a large database. I conjecture that, e.g., transfer pricing
errors even out as the empirical analysis focuses on several firms. Group contributions are operationalized as part of dividends and hence so do not affect the analysis.
SCB’s database is designed to meet the need of the national accounts in Sweden. Because of
its importance for economic statistics in Sweden, the quality of the information in the database is
high. I tested the data supplied by SCB for consistency at the point of delivery and it revealed hardly
any errors; errors that were found were not of a material size.
Erikson (2003) describes how SCB screen data collected from 1995. SCB first makes a consistency check that requires that the income statement and the balance sheet must sum up. If the
firm does not fulfill the consistency check, the income statement and the balance sheet are either
adjusted or considered as a non-response and have their data imputed. All large firms are manually
adjusted. Smaller firms are automatically corrected or left as non-response and imputed. The second
screening is designed to find extreme values and to validate single indicators. All firms that pass the
first step and that have at least one potential error according to the second screening are manually
checked. Finally, a model for changes in equity (EQ) is applied, and when its result is not good
enough to estimate the changes in EQ, a manual check is introduced.
Firms that SCB classifies as non-response after the first screening procedure are imputed. 18
SCB’s imputation either uses the firm’s last year data or uses the average values for the relevant SNIcode and size class. Data from the most detailed level of SNI-code are used in the imputation
process. I eliminate imputed firms using a method described in Appendix C, which reports the method applied for tracing firms and classifying them as usable.
To enable tracking of firms across years SCB has provided me with an extract from its database that also includes the firms’ names, organization numbers, and local unit information. This
enables me to detect, e.g., mergers, acquisitions, and divestments of whole or parts of firms, as well
as name changes and changes of organization numbers.
17 These issues can emanate from, e.g., transfer pricing, different measurement techniques in different legal entities for
assets and liabilities, accounting for foreign subsidiaries, etc.
18 For 1996 and SNI 10 to 37 and for all types of legal entity (from which the supplied raw data are a strict subset) imputation was carried out on 13.2 percent of all the firms. That accounted for 1.7 percent of the total sales for this group or
2.3 percent of the total employees. (Nv 11 SM9801:5)
In 1994, 16.7 percent of all the firms were imputed, accounting for 1.7 percent of sales and 2.8 percent of the employees. (Företagen, 1994:86)
In 1978 (SNI-code 3), 15 percent of the firms were imputed. Those firms represented 2.6 percent of total sales and
3.6 percent of total number of employees. (Företagen, 1978:19)
The vast majority of the imputations over the years 1977 to 1994 make use of the last year’s accounting data of the
firm instead of the industry average. E.g., only 1 percent of the imputed 16 percent in 1978 was based on industry averages. For 1996, representing the new method introduced from 1995 the relation was higher (6.3%/13.2%).
83
In section 5.3 the information from SCB’s is operationalized to meet the classifications in
subsection A.8.3.2 on page 172. Since the supplied income statements and balance sheets do not
meet the clean surplus relationship, the analysis from the previous chapter is also operationalized.
This determines that the firms in the database report comprehensive net income (CNI).
5.3 Operationalization of the financial statements
Transcending from theory to practice implies several interpretive problems that go beyond the problems with having dirty-surplus conservative accounting. Since the data span almost 20 years, they are
also exposed to introductions, changes, and scraping of GAAP. This is not unique for this thesis
since any study that faces time-series of accounting data is inevitably exposed to the problem. Associated to introduction and changes of accounting standards is also the problem of inconsistent implementation of the accounting standards across firms.
The problem with introductions, changes, and scraping of GAAP can be divided into two
parts. There is at first the problem of changing recognition and measurement rules. To solve this
problem requires individual adjustments of the financial reports for all firm-years, which is clearly
unfeasible. This problem is therefore acknowledged but it does not induce action. However, when
changing recognition and measurement rules creates dirty-surplus accounting, it is captured by
[EQ 5-10].
The second problem focuses on changes in the classification of assets and liabilities in the financial reports and the corresponding revenues and expenses. Those who use, e.g., Compustat database or Datastream do not face this problem since the database designers have already addressed it.
This thesis uses information from SCB and designs its own database. The implementations issues
are discussed in this section and accompanying appendices. Whenever possible a focus on substance
rather than form guides the operationalization.
The operationalization of the financial statements is discussed below in three subsections.
First, follows the operationalization of the clean surplus relationship, then the operationalization of
the balance sheet, and finally, the operationalization of the income statement. The operationalization
of the income statement is to some extent driven by the operationalization of the balance sheet.
5.3.1 Operationalization of the clean surplus relationship, book value of equity, and paid net
dividends
The clean surplus relationship is the relationship between the change in the balance sheet and the
income statement. Its importance means that it needs to be operationalized with care. This section
reports on the operationalization.
Appendix A uses unbiased accounting (i.e. an accounting system that is defined such that the
book value of assets and liabilities yields accounting rates-of-returns equal to the internal rates-ofreturns) that assumes that the clean surplus relation holds.
84
When theory meets practice, I therefore expose the models to accounting rules that do not
meet the conditions in Appendix A. Comprehensive income thus equals that period’s change in the
book value of EQ and any net dividend paid by the firm to the owner. This means that an operationalization of the clean surplus relationship implies operationalizations of CNI (CNI) and of net dividends.
Swedish firms do not report CNI so it must be inferred from the clean surplus relationship.
By defining, operationalizing, and measuring the net dividends paid to the owner and the change in
the book value of EQ, the firm’s CNI can be inferred. Using the definition of the clean surplus relationship in [EQ A-59] on page 172, the CNI for a period is defined as a function of the change in
EQ and the net dividends (d) that was paid to the owners during that period:
CNI t <EQt EQt1>dt
[EQ 5-1]
When the CNI is compared with the adjusted reported net income (NI) dirty-surplus accounting can be identified as the discrepancy between the two income measures 19 (see also
[EQ 5-10]).
It is necessary to operationalize the book value of EQ and the paid net dividends to have the
complete operationalized clean surplus relationship (this is done below).
The book value of EQ is usually defined unambiguously since it is part of the firm’s balance
sheet. However, in Sweden a firm can reduce its taxes by making appropriations (APR) that reduce
the taxable income, where the cumulative appropriations are reported in the balance sheet as an untaxed reserve.
The use of appropriations to manipulate taxable income implies that the untaxed reserve
consists of deferred tax and an EQ proportion of the untaxed reserve (EQUTR). The EQUTR is
classified here as part of the firm’s EQ. This means that the book value of EQ is in this thesis:
EQt eqt EQUTRt
[EQ 5-2]
where eq is the reported book value of EQ and EQUTR is the EQ proportion of the untaxed reserve. The database operationalization of the reported book value of EQ is found in
Appendix F (p. 205).
The EQ proportion of the untaxed reserve is identified using the full tax method, which is
used by, e.g., Runsten (1998). That is,
EQUTRt <1 tax ratet >¸UTRt
[EQ 5-3]
19
Adjusted reported NI is equal to reported NI adjusted for the equity proportion of the current period‘s appropriations. The adjustment follows the full tax method, which is an accepted principle in Sweden. It has been used by, e.g.,
Runsten (1998).
85
UTR is the untaxed reserve and the tax rate is marginal tax. For further specification of, e.g.,
the marginal tax rate, see subsection 5.3.2. Appendix D (p. 195) provides the database operationalizations of the untaxed reserve.
The net dividends paid summarize the transactions between the owners and the firm during
the year. This means that it includes dividends paid (PDIV), share issues (ISSUE) during the year.
Since the database uses legal entities, it is also affected by group contributions (GCs). GCs are also
classified as part of the paid net dividends. That is,
dt PDIVt GC t ISSUEt
[EQ 5-4]
Dividends paid are operationalized as variable UTD1 in the database. Operationalization of
the group contribution is given in Appendix D. The share issue is operationalized as variable UTD3
in the database. Appendix H (p. 209) provides a specification of all variables in the database.
With these operationalizations in place, it is possible to measure ROE but it is also necessary
to be able to measure RNOA, which requires an operationalization of net operating assets (NOA)
and of comprehensive operating income (OI). These operationalizations amount to operationalizations of the firm’s balance sheet and income statement, which is done next.
5.3.2 Operationalization of the balance sheet
According to [EQ A-67] in subsection A.8.3.2, the firm’s balance sheet equation uses EQ, NOA,
and net financial liabilities (NFL) as below:
EQt NOAt NFLt
[EQ A-67]
In this subsection NOA is first disaggregated another step so that it is the sum of operating
assets (OA) and of operating liabilities (OL):
NOAt OAt OLt
[EQ 5-5]
An OA is an asset that does not generate explicit or implicit interest income and OL are liabilities that do not carry explicitly or implicitly any interest expenses.
NFL are disaggregated into financial liabilities (FL) and financial assets (FA):
NFLt FLt FAt
[EQ 5-6]
As a corollary to the definitions of OA and OL are the financial assets. These are assets that
generate explicit or implicit financial revenue and financial liabilities are those liabilities that carry
explicit or implicit interest expenses.
This subsection provides empirical content to the four components of NOA and NFL.
The NOA consist only of the assets that are financed by the investors. The investors contribute with EQ and with NFL. With the classifications above, it is possible to view a firm’s net operating asset as financed from two investment sources (the debt market and the EQ market). Conse-
86
quently, this follows the tradition of Modigliani and Miller (1958) and allows for the application of
the value additivity principle.
The empirical balance sheets are converted to fit the classifications above since the existing
financial reporting follows the above classification. The operationalization is carried out for each
segment of the period between 1977 and 1996 in which the financial reports classification system is
fixed. In addition, the operationalization is carried out such that it facilitates longitudinal comparisons.
The conversion of the empirical balance sheets to the classification according to [EQ 5-5]
and [EQ 5-6] is made in two steps. This subsection discusses the first step and focuses on identifying stable assets and stable liability classes in the empirical balance sheets, as well as the assignment
of those to the classification scheme. The second step concerns the assignment of specific line items
in the database to this sections’ classification scheme. This step is reported in Appendix E (p. 197).
Below follows a table with a summary of the identification of the stable assets and liability
classes in the empirical balance sheets, as well as their assignment to the classification scheme.
THE BALANCE SHEET
EQUITY (EQ)
Operating assets (OA)
Share capital
Inventories and advance payments
Restricted reserves
Prepaid expenses and accrued income
Retained earnings
Intangible assets
Reported net income
Land and buildings
Equity proportion of the untaxed reserve
Plant and equipments
NET FINANCIAL LIABILITIES (NFL)
Construction in process and advance payments for
Financial liabilities (FL)
tangible assets
Accounts payable
Shares and participations in group companies
Advance payments from customers
Operating liabilities (OL)
Deferred tax proportion of the untaxed reserve
Other current liabilites
Pension liabilities
Provision for taxes
Other long term liabilities
NET OPERATING ASSETS (NOA)
Financial assets (FA)
Accounts receivables
Cash and bank balances
Other current receivables
Other long-term receivables
Bonds and other securities
Shares and participations in other firms
Table 5-1: A specification of the balance sheet’s components.
Liabilities are broadly divided into financial liabilities and OL. A financial liability is a liability
to which is attached a legal obligation to pay interest to the lender, whereas operating liability is a
liability that is not interest-bearing.
The financial liability can also be a liability to a lender who does not charge an explicit interest rate. This is the case with, e.g., accounts payable, where the supplier lends money to the customer and usually does not charge interest. Such a loan has an opportunity cost whom the lender pre-
87
sumably adds to the price of the goods. This suggests that the firm pays interest to its supplier.
However, it is not accounted for as an interest expense but as part of the cost of goods sold.
To have unbiased rates-of-returns measures require the classification of the accounts
payables as financial liabilities and that its implicit interest rate is identified and classified as an interest expense. This is done in subsection 5.3.3 where the income statement is operationalized.
Advance payments from customers are also considered as an implicit loan and thus treated in
a similar manner. For further information, see subsection 5.3.3.
The pension liability is also classified as a financial liability despite the fact that SCB assigns
the liability’s interest expense to operating cost. The reclassification follows the same method as for
accounts payable. For further information, see subsection 5.3.3.
This means that among the liabilities only deferred taxes and provision for taxes are classified
as non-interest-bearing liabilities for reasons discussed below.
In Sweden, firms are allowed to reduce its taxable income in order to reduce income taxes
paid. This is done using appropriations. The firms debit the untaxed reserve account, which is an
interest-free liability. Had the appropriation not existed, the firm would have to pay tax equal to the
marginal tax on the appropriation. The untaxed reserve is normally dissolved through the income
statement. Thus, the firm must pay tax on the reduction of the untaxed reserve. Operationalizations
of the appropriations and the untaxed reserve are found in Appendix F.
Using the full-tax method, the untaxed reserve is divided into a deferred tax proportion and
an EQ proportion. E.g., Runsten (1998) uses this method, where the deferred tax is estimated as the
product of the marginal tax rate and the untaxed reserve. The EQ proportion is what remains of the
untaxed reserve after the deferred tax has been removed.
In some research (e.g., Hamberg 2000) it is suggested that the untaxed reserve should be
classified as EQ. By using arguments such as in an inflationary market, the untaxed reserve will grow
in size. What is typical for an untaxed reserve is, however, that it can only be withheld from taxation
for a limited time. That means that income tax is eventually paid on the untaxed reserve, except in
those situations where the firm makes a loss, which it cancels against the untaxed reserve. The fulltax method is therefore applied in this research.
To apply the full-tax method it is necessary to estimate the marginal income tax. This research uses Runsten’s (1998, p. 117) estimation of the marginal income tax for the period 1977—
1993. From 1994— 1996 28 percent is used as a marginal income tax. During 1984 to 1990, there
was a profit sharing tax, but this is accounted for as an appropriation and thus is not included in the
measurement of the marginal tax. The marginal tax used in this research is found in Table 5-2.
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Year
1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
Tax rate 56% 57% 57% 57% 58% 58% 58% 53% 52% 52%
Year
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
Tax rate 52% 52% 40% 40% 30% 30% 30% 28% 28% 28%
Table 5-2: Estimated yearly marginal tax in Sweden from 1977—1996.
Deferred tax in Sweden refers to the sum of government-supported postponed income tax.
Since the government allows the firms to defer tax payments, it becomes a lender to the firm. However, the government does not require any interest payments from the firm because of the deferred
tax, and consequently, deferred tax in this research is treated as a non interest-bearing liability. The
treatment of deferred tax is consistent with, e.g., Penman (2004), Levin (1998), and Finansanalytikernas rekommendationer (1994).
Provision for taxes does not normally carry interest. It becomes interest bearing only when
its due date has expired. In the present research to pay taxes too late is considered unusual and the
provision for taxes is therefore classified as a non interest-bearing liability.
Additional to the treatment of accounts payable, deferred tax, and provision for taxes, there
are reasons to discuss the treatment of the shares and participations and the accounts receivable.
These are discussed individually below.
Accounts payable and the accounts receivables are often classified as OA and liabilities in financial analysis (cf., Levin 1998). In this research they are treated as part of the NFL. Accounts payable has already been discussed, but discussing accounts receivables remains. It is treated as analogous to the accounts payable, which means that the accounts receivables are seen here as created by
the firm when it decides not to require a cash payment from the customer at the point of sale. When
this occurs, the selling firm becomes a lender and incurs an opportunity cost on the loan. However,
only rarely will the selling firm charge an explicit interest on the loan; instead, part of the total invoiced amount will be an implicit interest on the loan. With a substance-over-form perspective, it
follows that the accounts receivables should be accounted for as interest-generating assets, and consequently, the implicit interest should be deducted from the sales and added to the firm’s interest
revenue. Penman (2004) also discusses this topic and proposes this method for adjusting the accounting.
As with the implicit interest expense on the accounts payable, the implicit interest revenue on
the accounts receivables is discussed in subsection 5.3.3, which focuses on income classification.
Other current receivables include other loans and claims that the firm has on its group (when
it is part of a corporate group). Loans typically carry interest, the claims on the group can be exchanged for cash, and so has an opportunity cost. It may also be the case that the group controls the
liquidity in the firm using these claims. Analogous to the accounts receivables, the other current
receivables are therefore classified as interest-generating assets.
89
Shares and participations are divided into two parts based on whether they are deemed an
integral part of the firm’s operations or not. Shares and participations in subsidiaries are seen as an
integral part of the firm’s operations. As a result, those assets are classified as non interest-generating
assets.
Shares and participations in other firms are not considered an integral part of the firm’s operations. Had the shares and participations been an integral part of the owning firm’s operations, it is
likely that the owning firm would acquire the other firm, or at least invest in it to the point where it
gains a controlling interest. When the firm gains the controlling interest in the other firm, its ownership is reclassified to shares and participations in subsidiaries. Since the owning firm has no controlling interest in the other firm, the shares and participations are classified as interest-generating assets.
Other long-term receivables, bonds and other securities, cash and bank balances are all classified as interest-generating assets, which should not be controversial. Next, follows that section on
the operationalization of the income statement.
5.3.3 Operationalization of the income statement
According to [EQ A-66] in subsection A.8.3.2, the firm’s CNI consists of the comprehensive
OI and the comprehensive net interest expense:
CNI t COI t CNIEt
Applying the clean surplus relationship to the firm’s operating activity implies that:
%NOA COI t FCFt ”
[EQ 5-7]
COI t %NOA FCFt
[EQ 5-8]
Defining the free cash flow, FCF, as did done below, allows COI to be measured according
to [EQ 5-8].
FCFt dt CNIEt %NFLt
[EQ 5-9]
The system above is using the same structure as used by Feltham and Ohlson (1995), Feltham and Ohlson (1999), Lundholm and O’Keefe (2001), and Penman (2004).
Net dividend paid is symbolized by dt . The net dividend is defined in subsection 5.3.1 as the
net of gross dividends, group contributions, and any new common stock issue. Gross dividends are
operationalized as the proposed dividend reported in the previous year according to Appendix G.
Group contributions are operationalized according to Appendix F. The new common stock issue is
defined in subsection 5.3.1, where it includes both the stocks’ face value and any agio. NFL are operationalized according to 5.3.3 and Appendix E. What remains is the operationalization of CNIEt .
This implies an operationalization of the income statement, which is the topic for the rest of this
subsection.
90
A guiding principle in the operationalization of the income statement is to have a consistent
treatment of assets, liabilities, revenues, and expenses. That is, the assets that are classified as financial assets must have their revenues classified as interest revenues. As an analogy, it follows that liabilities that are classified as financial liabilities must have their expenses classified as interest expenses. The revenues and expenses that are not identified as interest revenue or as interest expense
are classified as operating revenue or as operating expenses.
The transformation of the empirical income statement to an income statement comparable
to [EQ A-66] is made in two steps. This subsection discusses the first step and focuses on identifying stable revenue classes and stable expense classes in the empirical income statements, as well as
the assignment of those to a theoretical classification scheme. The second step is concerned with the
assignment of specific line items in the database to this subsections’ operationalized classification
scheme. This can be found in Appendix D.
Table 5-3 presents a summary of the identification of the stable revenue and expense classes
in the empirical income statements and their assignment to a theoretical classification scheme: after
the table follows a discussion on the previously signaled issues.
THE INCOME STATEMENT
COMPREHENSIVE OPERATING INCOME (COI) COMPREHENSIVE NET INTEREST EXPENSE (CNIE)
Adjusted sales
Adjusted interest revenue (IR)
Sales
Interest revenue
-Implicit interest revenue on AR
+Implicit interest expense on APL
Adjusted cost of material
- Cost of material
+Implicit interest expense on AP
+Implicit interest expense on PL
- Labor cost
- Depreciation
Dividends from the group
Government subsidies (GS)
Items affecting comparability (IAC)
Dirty-surplus accounting
Summation errors in OI (ERROI)
- Tax on COI
+Implicit interest revenue on AR
Adjusted interest expense (IE)
Interest expense
-Implicit interest expense on AP
-Implicit interest expense on APL
-Implicit interest expense on PL
Other dividends (ODIV)
Exchange rate difference (FXRD)
Summation errors in income (ERRFI)
- Tax on CNIE
Table 5-3: A specification of the type of components of the income statement
Credit sales inflate the firm’s reported operating revenue with the implicit interest revenue. A
credit purchase implies that the reported costs of goods sold are over estimated with the estimated
implicit interest expense. These issues were discussed in subsection 5.3.2 in conjunction with the
discussion of how to classify accounts receivables and accounts payable. The existence of implicit
interest is also acknowledged in national GAAP and in international GAAP (e.g., RR 3 and IAS 18).
This thesis deflates the overestimated operating revenue by decreasing it with the implicit interest revenue. The implicit revenue is thus reclassified as interest revenue. It also deflates the overestimated cost of material with the implicit interest expense, reclassifying it as interest expense.
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Following GAAP, the implicit interest rate charged to the accounts receivable would be equal
to the firm’s short-term lending rate, which equals a risk-free interest rate and a risk premium. However, since the accounts receivable typically have short duration and since conservatism requires that
uncertain claims to be immediately expensed, it is assumed that the disclosed value of accounts receivable is risk-free. This means that the correct opportunity cost for such a loan is the risk-free interest rate.
Estimating the implicit interest expense that is an effect of the accounts payable is only
slightly different. The implicit interest rate charged to the accounts payable should, in analogy to the
above, be equal to the firm’s short-term borrowing rate, which would equal the risk-free interest rate
and a risk premium. In view of the fact that the accounts payable typically has a short duration and
because it is not likely that a firm in deep financial trouble would be allowed to use credit purchases,
it is assumed that the risk-free rate-of-return can also be used as a proxy.
Advances from customers are also a loan that neither is interest free. It is assumed that customers do not finance a company’s activities free, and so demand a reduced price in compensation
for having to pay in advance. This reduced price is estimated similarly to the implicit interest expense above considering that these are rather short-term liabilities. The reduction is reversed and is
instead classified as an interest expense.
The cost for pension liabilities is usually according to Swedish GAAP classified as an interest
expense but SCB reclassifies the expense as an operating expense. I classify the pension liability as a
financial liability and consequently classify the expense as an interest expense. However, I lack detailed information of the size of the expenses and therefore need to assume it. I do this similarly by
using the one-year risk-free rate-of-return. This is probably a little bit too low considering that
pension liabilities are long-term but reclassifying it in this manner is better than no reclassification at
all. Additionally, the induced error is of a minor scale and I estimate that it will not have a significant
affect on the results.
Below follows the one-year risk-free interest rate that is used.
Year
Risk-free
Risk-free
Year
Risk-free
rate of return Year rate of return
rate of return
1978
8.00% 1985
11.80% 1992
12.55%
1979
6.50% 1986
12.50% 1993
9.49%
1980
9.00% 1987
9.55% 1994
6.41%
1981
10.00% 1988
9.73% 1995
9.35%
1982
11.00% 1989
10.87% 1996
8.20%
1983
10.00% 1990
13.02%
1984
11.80% 1991
13.85%
Table 5-4: The one-year risk-free rate-of-return in Sweden (Source: SCB 1979—1984;
Svenska Dagbladet, 1984—1996).
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In Table 5-4, the Swedish government’s “diskonto”, as of 1st of January, is applied a risk-free
rate-of-return for the period of 1978 —1983. Later periods use the yield-to-maturity on a one-year
T-bill as of 1 January.
When there are summation errors in the dataset supplied by SCB, these are part of OI. This
ensures that the clean surplus relationship is maintained after the dirty surplus adjustments are operationalized. Summation errors in the income statement occur in the raw data but are not frequent,
nor are they of material size.
Items affecting comparability include extra ordinary income, and for the period of 1994 to
1996, it incorporates capital gains from sales of fixed assets and write-downs of those assets. The
aggregation of capital gains from sales of fixed assets and write-downs of fixed assets with extra ordinary income into items affecting comparability reflects an effort of keeping a comparable accounting interpretation despite changing GAAP (cf. FAR No. 13 and its successor RR 4 in, e.g., FARs
Samlingsvolym 1994). Before 1994, capital gains from sales of fixed assets and write-downs of fixed
assets were usually included in extra ordinary income but they are not included in extra ordinary
income after 1994.
Items affecting comparability are treated as an OI even though it can contain revenues and
expenses that should be classified as financial income. When a firm makes a capital gain on the sale
of long-term financial assets, it is reported as extra ordinary income before 1994 and as OI after
1994. Since the data do not specify the components of extra ordinary income, or of capital gains
from sales of fixed assets, or of write-downs of fixed assets, they must be uniformly classified. Because the firms are manufacturing firms, it is assumed here that the bulk of items affecting comparability can be traced to operating activities and thus are concurrently classified as part of OI.
The effects of dirty surplus accounting are effects that occur when the accounting is not prepared on a clean surplus basis. In view of [EQ 5-8] with definition [EQ 5-9] and its operationalization and with the operationalized balance sheet it is possible to use [EQ 5-8] to measure comprehensive operation income directly.
Defining OI (i.e. as consisting of all line items in COI according to Table 5-3 except the dirty
surplus accounting), it is possible to measure the aggregate effect of dirty surplus accounting as:
DTSACTG COI OI
[EQ 5-10]
The firm’s adjusted total tax is allocated to the OI and the financial income. It follows standard procedures applied in, e.g., Copeland, Koller and Murrin (2000) and Penman (2004), which are
amended for effects of dirty surplus accounting. Tax on comprehensive net interest expense is estimated as the product of the marginal income tax rate and the pre-tax comprehensive net interest
expense.
The operationalization of income taxes is found in Appendix D.
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As discussed in the previous section, Swedish GAAP allows firms to reduce the income taxes
paid by making appropriations before the income tax is measured. The appropriation is undone in
the present research with the use of the full tax method. That means that the deferred tax is added
to the reported tax. The deferred tax is estimated as the product of the marginal income tax rate (see
Table 5-2) and the period’s appropriation. To get the adjusted total reported income tax the deferred
tax component is added to the reported tax.
The dividend from the group is exempted from tax and hence it is excluded from the tax
shield calculation.
5.4 Summary
This chapter bridges some of the gap between Appendix B and the empirical data. Bridging the gap
entails reclassification of assets into non interest-generating assets (also known as OA) and interestgenerating assets. It also entails reclassifying the liabilities into interest-bearing liabilities and non
interest-bearing liabilities.
The reclassification of the balance sheet follows standard procedures in financial analysis,
with the exception of the treatment of accounts receivables, accounts payable, and advance payments from customers. These are classified as financial assets and financial liabilities. This reclassification also carries over into the income statement that reclassifies some of the firm’s operating revenues to interest revenue because of the implicit interest revenue from accounts receivables. It reclassifies some of the firm’s cost of goods sold as interest expense because of the implicit interest expense from accounts payable. Further, it reverses the discount in sales from getting advance payments from customers and reclassifies it as an interest expense.
The reclassification of the income statement also entails changes that ascertain that the accounting follows the clean surplus principle. It also identifies summary errors in the raw data and
treats it as part of the income.
Since the data are based on legal entities rather than consolidated accounting, a firm reports
appropriations and untaxed reserves. These effects are also undone using the full-tax method.
Because of the operationalizations in this chapter and in Appendix D—Appendix G, all of
the components to ROE and RNOA are in place such that the ratios are measured on a clean surplus basis and the separation components to ROE and RNOA are done in the spirit of Modigliani &
Miller (1958).
94
CHAPTER 6—HYPOTHESES TESTS AND THE TEST
VARIABLES
“…it must be possible for an empirical scientific system to be refuted by
experience” (Popper 1959, p. 41)
6.1 Introduction
I evaluate the proposed theory of Homo comperiens in two ways. I test Proposition 4-6 and
Proposition 4-7 using hypotheses tests and I assess (to avoid committing a Type I error such that I
reject the null hypotheses when they are true) the theory’s predictive ability in out-of-sample tests.
This chapter is devoted to discuss the hypothesis tests and their results. Before I present the
testable hypotheses and results from the hypothesis tests, I first discuss the operationalization of the
risk-adjusted expected residual rates-of-returns. In Chapter 7, I discuss the predictive tests and their
results.
Because of their apparent similarities, in subsection 6.4.2.3 I relate my results with those
from empirical research based on Ohlson’s (1995) model. However, it should be noted that Ohlson’s model only purports to measure accounting residual income since it assumes zero arbitrage
residual income. If the markets are inefficient, it implies that empirical assessments based on Ohlson’s model, unintentionally, come to measure the combined effect of both arbitrage and accounting
residual income.
6.2 Operationalization of the risk-adjusted subjective expected residual
accounting rates-of-returns
Chapter 4 finds that if a market meets the assumptions of Homo comperiens, the market exhibits
arbitrage profits. The existence of arbitrage opportunities implies the existence of risk-adjusted residual accounting rates-of-returns. The existence of risk-adjusted residual accounting rates-of-returns
implies the existence of arbitrage opportunities. That is, they are equivalent expressions.
Two risk-adjusted subjective expected residual accounting rates-of-returns are defined in
Chapter 4. These include the risk-adjusted subjective expected residual return on equity,
&*K 0 < t 1ROEt >
(RRNOA),
and the risk-adjusted subjective expected residual return on net operating assets
&*K 0 < t 1RRNOAt > :
&*K 0 < t 1 RROEt > &K 0 < t 1 RROEt > &K 0 <total risk premiumt >
[EQ 4.34]
&*K 0 < t 1 RRNOAt > &K 0 < t 1 RRNOAt > &K 0 <operating risk premiumt >
[EQ 4.35]
95
The risk-adjusted subjective expected residual accounting rates-of-returns, as shown above,
are strictly theoretical and need to be attributed testable properties. This process is reported in section 6.2, with the assistance of the operationalization in Chapter 5 and relevant appendices.
Subsection 6.2.1 considers the expectations parameter, subsection 6.2.2 addresses the riskadjusted residual accounting rate-of-return, and subsection 6.2.3 considers both the risk premiums
and biased accounting. Section 6.2 concludes with descriptive statistics for the proxies to [EQ 4.34]
and [EQ 4.35].
Appendix I (p. 211) is related to section 6.2 in the sense that it operationalizes the industryspecific accounting rates-of-returns, which are necessary components to the testable proxies for the
risk-adjusted subjective expected residual accounting rates-of-returns.
6.2.1 Ex ante and ex post rates-of-returns
Chapter 4 finds that in subjective certainty ex ante and ex post rates-of-returns differ because the
subject makes choices on the subjective state set. The state that eventually emerges when the future
unfolds may not have been part of the subject’s subjective state set.
The distinction between ex ante and ex post rates-of-returns because of the subjective state
set’s interaction with the unfolding future is not only present in a subjective certain choice but it is
also present in a subjective uncertain choice. The effect from when an unnoticed (not part of the
subjective state set) state suddenly comes true is in the subjective uncertain choice subsumed by the
fact that only one of all states considered in the subjective state set can occur. Hence, there is by
design a difference between ex ante and ex post rates-of-returns in the subjective uncertainty. That
is, the uncertainty creates a difference between ex ante and ex post rates-of-returns even when the
true state is within the subjective state set.
Although ex ante and ex post rates-of-returns most likely differ between firms, it is difficult
to use ex post rates-of-returns to draw conclusions on ex ante rates-of-returns. However, the state
that comes true is, using the state-and-partition-model, uncontrollable by the subjects, which implies
that the state that comes true sometimes is better than expected and sometimes it is worse than expected. Because of uncertainty, ex ante and ex post rates-of-returns are different for individual firms
at individual times, but I suggest that the positive and negative effects cancel out as the number of
observations increase. That is, I assume that the ex post accounting rates-of-returns are, on average,
equal to the ex ante expected accounting rates-of-returns since the unfolding of the states is a random process.
Given that ex post and ex ante rates-of-returns are presumed to be comparable, ex post riskadjusted residual accounting rates-of-returns are used as proxies for [EQ 4.34] and [EQ 4.35] in the
empirical assessment of the theory. The ex post risk-adjusted residual accounting rates-of-returns
are:
96
*
t 1 RROEt
*
t 1 RRNOAt
t 1RROE t
t 1 RRNOAt
total risk premiumt
[EQ 6-1]
operating risk premiumt
[EQ 6-2]
The use of ex post rates-of-returns to make inferences of ex ante rates-of-returns follows a
long tradition in both economics and accounting and is therefore not controversial.
6.2.2 The residual accounting rates-of-returns
Appendix B defines the subjective residual accounting rates-of-returns in [EQ B-40] and in
[EQ B-43] as the difference between the subjective accounting rate-of-return and the subjective
market rate-of-return:
t 1 RROE Kt
t 1 ROE Kt
t 1rKt
t 1 RRNOAKt
t 1 RNOAKt
[EQ B-40]
t 1rKt
[EQ B-43]
The subjective ROE and the subjective RNOA are defined in Appendix B as:
t 1 ROE Kt
CNI Kt ¸ EQt11
[EQ B-39]
1
t 1 RNOAKt COI Kt ¸ NOAt 1
[EQ B-42]
Standard empirical ex post financial analysis (e.g., Penman 2004, Stickney & Brown 1999) use
average book values rather than beginning book values when accounting rates-of-returns are operationalized. The present research maintains theoretical connection by keeping theoretical definitions
of ROE and RNOA when operationalizing them.
Since the profit that a firm reports is compounded over the year, there may be large differences between these two capital definitions. Capital defined on beginning values implies that the risk
of having denominators close to zero increases and hence it is likely that the number of observations
having extreme ROE and RNOA increases. It is also likely that asset build-up is going to exacerbate
the volatility in the rate-of-return patterns since the small denominator effect quickly disappears.
However, the asset build-up problem is very small in this thesis because the empirical assessment is
done on a very large number of observations. The extreme effects from the capital definition are
subsumed by the effect from more normal behaviors.
The capital definition exacerbates the need to devise statistical measures that are insensitive
and to non-normal tails and efficient when the tails are non-normal since the extreme values that the
capital definitions likely generate create non-normal tails. Tolerance to non-normal tails is known as
robustness of validity, and high efficiency when non-normal tails are present is known as robustness
of efficiency (Mosteller & Tukey 1977). Robustness issues are considered in subsection I.2 and in
Appendix K.
Chapter 4 argues that a period’s subjective market rate-of-return is equal to the subjective
risk-free rate-of-return for that period, irrespective if the market rate-of-return is coming from the
definition of subjective RROE, [EQ 4.30], or coming from the definition of subjective RRNOA,
97
[EQ 4.31]. It is therefore possible to rewrite the risk-adjusted residual accounting rates-of-returns in
[EQ 6-1] and [EQ 6-2] to:
*
t 1 RROEt
*
t 1 RRNOAt
t 1ROE t
t 1RNOAt
t 1rtrisk free total risk premiumt
[EQ 6-3]
t 1 rtrisk free operating risk premiumt
[EQ 6-4]
The operationalization of the components to subjective ROE and RNOA is given in Chapter
5 and associated appendices.
6.2.3 The risk-premiums and biased accounting
The risk-adjusted subjective expected residual accounting rates-of-returns contain risk premiums
and assume unbiased accounting. This subsection addresses the issue of how the risk premiums and
the unbiased accounting can be operationalized such that [EQ 6-3] and [EQ 6-4] measure what they
should measure.
Subsection 6.2.3 first addresses the issue of proxies for risk premiums and then follows a discussion on proxies for unbiased accounting.
6.2.3.1
Proxies for the risk premiums
If the market had been in a Pareto optimal equilibrium, it would have been possible to measure the
risk-adjusted market rate-of-return by using CAPM and from CAPM it would have been possible to
find a firm’s total risk premium. Specifying the market so that CAPM can be applied also requires
that the market rate-of-return is constant, which implies a constant total risk premium.
When the subject makes limited rational choices according to the assumptions of Homo
comperiens, the total risk premium cannot be specified using an asset valuation model such as
CAPM, which is based on general-equilibrium. Thus, CAPM is not applicable to this research.
In view of the fact that, in this research, CAPM is not available in this respect, two strategies
remain. The first strategy implies the development of an asset-pricing model in a Homo comperiens
setting that provides the possibility to price subjective uncertainty. It is likely that such a model
needs to define operational proxies for the difference between subjective uncertainty and objective
uncertainty. This is clearly outside the scope of this thesis and hence is not considered any further.
Where the first strategy is deductive and uses theory to discern the risk premiums, the second
strategy uses empirical proxies for the risk premiums. This thesis uses empirical proxies for assessing
the risk premiums.
I assume that firms within the same industry sell similar products and have a similar production function. This assumption is similar to that of, e.g., Lev and Sunder (1979). The fluctuations in
the demand of the goods then affect the firms within the industry in a similar fashion because they
sell similar products. Having similar production functions means that the fluctuations in the factor
markets affect the firms within the same industry similarly. Together, these assumptions imply that
98
the fluctuations affect the firms’ profits similarly and hence also their accounting rates-of returns.
Gupta & Huefner (1972) find that cross-sectional variation of financial ratios is primarily related to
industry characteristics (see also Fieldsend, Longford & McLeay 1987, Lee 1985, McDonald &
Morris 1984, and McLeay & Fieldsend 1987 for similar results).
Suppose that it is possible to divide a firm’s operating risk premium into two components,
where the first component is the risk premium required by the investor for investing in a particular
industry and the second component is the firm-specific risk premium. This means:
operating risk premiumt firm - specific operating risk premiumt industry - specific operating risk premiumt
[EQ 6-5]
Assume that the firm-specific risk premium consists of two components. The firm-specific
risk premium’s first component is because the firm’s sensitivity to the market fluctuations is different from the industry’s sensitivity. The second component of the firm-specific risk premium is because the firm’s production function is not identical to the industry’s production function. Assume
that the firm-specific differences from the industry are small. This implies that the firm-specific risk
premium is approximately zero. The firm’s operating risk premium is then approximately equal to
the industry-specific risk premium.
There are studies showing that there is a relationship between a firm’s risk and its accounting
rates-of-returns (Beaver, Kettler & Scholes 1970; Beaver & Manegold 1975; Gonedes 1975; Lev
1974). I thus assume that an empirical proxy for industry-specific risk, assuming unbiased accounting and using an accounting-based risk perspective as a point of departure, is:
industry - specific operating risk premiumt where
I
t 1 RNOAt
I
t 1 RNOAt
t 1rtrisk free
[EQ 6-6]
is the industry’s return on net operating assets.
A similar argument can be used on total risk. Here it is assumed that the firm-specific total
risk is negligible and the firm’s total risk premium can therefore be measured using the industryspecific total risk premium. The assumption is that the industry-specific total risk premium can be
measured with the spread between the relevant accounting rate-of-returns and the risk-free rate-ofreturn:
industry - specific total risk premiumt where
I
t 1 ROEt
I
t 1 ROEt
t 1rtrisk free
[EQ 6-7]
is the industry’s return on equity (it is operationalized in Appendix I).
The risk-adjusted residual accounting rates-of-returns in [EQ 6-3] and in [EQ 6-4] can be
restated as functions of firm profitability and industry profitability since the firm-specific risk is negligible and because spread between the industry accounting rate-of-return and the risk-free rate-ofreturn is conjectured to be a proxy for industry-specific risk. The ex post risk-adjusted residual accounting rates-of-returns are then:
*
t 1 RROEt
t 1 ROEt
t 1 ROEtI
[EQ 6-8]
99
*
t 1 RRNOAt
t 1 RNOAt
t 1 RNOAtI
[EQ 6-9]
The present study uses industry accounting rates-of-returns as proxies for risk. This treatment presupposes that the accounting is unbiased. Unbiased accounting is unlikely and the subsection 6.2.3.2 addresses the issue of how biased accounting is treated in this study.
6.2.3.2
Biased accounting and ex post risk-adjusted residual accounting rates-of-returns
The accounting bias exists because the firm’s financial accounting is supposed to provide conservative estimations of the firm’s earnings and financial position. The accounting can be biased in many
ways. For instance, it is possible that there are opening (direct expensing of research outlays) and
closing (historical cost) valuation errors that affect the balance sheet. There can also be other types
of related bias such as late recognition of revenue (not at the point of contract but at the point of
delivery) or early recognition of costs (at the point of decision and not at the cash outlay). For a
discussion of how conservative accounting enter formal accounting models, see Feltham & Ohlson
(1996), Penman & Zhang (2002), and Cheng (2005).
The effects of conservatism are well known yet hard to empirically measure. Nonetheless,
there exist attempts exist to model and empirically estimate the bias. Runsten (1998), e.g., develops
an empirical permanent measurement bias (PMB) variable that is alleged to measure the accounting
bias. Runsten’s PMB model assumes no-arbitrage, which means that the model is not useful for my
purpose.
Subsection 6.2.3.1 reasons that firms within the same industry have similar products and similar production functions. If that is a valid assumption, it is reasonable to assume that firms within
the same industry are exposed to similar accounting rules and use similar accounting procedures
(e.g., approximately the same planned depreciation rate for fixed assets and similar operationalization of the revenue recognition principle). McDonald & Morris (1984) show that within-industry,
comparisons of accounting ratios are possible, but not intra-industry comparisons. Such a comparison would not be possible with a heterogeneous application of the accounting rules within an industry. Lee (1985) also reports significant industry effects. McLeay & Fieldsend (1987) and Fieldsend,
Longford & McLeay (1987) both report a significant industry effect in accounting ratios. On balance, this indicates that firms in an industry produce similar products, have similar production functions and apply the accounting rules in a similar manner. Thus, that kind of comparison of accounting data is valid within an industry.
With the accounting data within the industry being comparable, it should be possible to
sweep away the accounting bias from a firm’s accounting ratios by reducing them with the industry
ratio. This means that the adjustment in the ex post risk-adjusted residual accounting rates-ofreturns using [EQ 6-8] and [EQ 6-9] remove not only the risk premiums but also the biased accounting. Therefore, [EQ 6-8] and [EQ 6-9] are used as proxies for the risk-adjusted subjective ex-
100
pected residual accounting rates-of-returns [EQ 4.34] and [EQ 4.35]. The hypotheses tests are therefore performed using operationalizations [EQ 6-8] and [EQ 6-9].
The last component needed in the operationalization of the ex post risk-adjusted residual accounting rates-of-returns are the industry ex post accounting rate-of-returns, which are operationalized in Appendix I (p. 211).
6.2.4 Descriptive statistics of risk-adjusted RROE and RRNOA from 1978 to 1994
The components to risk-adjusted RROE, [EQ 6-8], and to risk-adjusted RRNOA, [EQ 6-9], are
ratios and this implies that as the denominator approaches zero for a component, the residual accounting rate-of-return values goes moves towards infinity. The denominators in the ratios are balance sheet data that can be erroneous and therefore outliers affect the data.
Table 6-1 and Table 6-2 present descriptive statistics for risk-adjusted RROE and for riskadjusted RRNOA for the whole set of firms in the data set.
Year
n
Max
Mean
Median
Locationbw
Min
StdDev
StdDevbw
QRange
Year
n
Max
Mean
Median
Locationbw
Min
StdDev
StdDevbw
QRange
Descriptive statistics for risk-adjusted RROE
1978
1979
1980
1981
1982
1983
1984
1985
1986
611
727
1356
1337
1342
1385
1436
1401
1444
6,560% 5,600% 4,340% 2,279% 36,683% 1,998%
3,804%
4,474% 9,924%
41%
10%
10%
-52%
54%
8%
26%
19%
27%
5.0%
9.4% 13.9%
12.5%
11.4%
13.0%
19.2%
13.2% 11.5%
5.4%
8.4% 15.8%
14.8%
12.7%
15.9%
21.2%
14.4% 11.7%
-2,562% -2,620% -3,357% -71,700% -3,268% -3,273% -5,066% -12,996% -3,624%
390%
295%
251% 1,992% 1,095%
216%
269%
378%
362%
34%
44%
33%
36%
36%
38%
40%
25%
25%
38%
41%
37%
39%
37%
39%
47%
30%
28%
1987
1988
1989
1990
1991
1992
1993
1994
1471
1453
1498
1412
1429
1351
1269
1278
6,314% 22,664% 1,969% 11,038% 72,357% 83,545% 105,119% 54,232%
20%
46%
26%
16%
47%
45%
126%
6%
9.5%
9.8% 21.8%
6.6%
13.6%
2.1%
11.0%
27.3%
11.3%
11.0% 23.3%
6.6%
13.5%
1.7%
12.6%
32.6%
-7,473% -1,249% -6,042% -8,045% -23,502% -13,564% -18,875% -108,200%
309%
634%
235%
392% 2,062% 2,379%
3,105%
3,419%
25%
25%
34%
28%
50%
46%
50%
54%
27%
27%
38%
29%
56%
51%
52%
68%
Table 6-1: Descriptive statistics for risk-adjusted RROE per year, [EQ 6-8].
Table 6-1 shows some descriptive statistics for the whole set of the available set of riskadjusted RROE on a per-year basis. In the table n is the symbol for the number of observations
available. Locationbw is the biweight location estimate. The mean is the arithmetic mean and so it is
the location estimate for a Gaussian-shaped distribution. StdDev is the standard deviation, i.e. the
scale measure for Gaussian shaped distributions, while the StdDevbw is the biweight estimation of
the scale. QRange is the interquartile range for the empirical distributions and thus describes the
spread between the 75th and 25th percentile observation.
101
From a visual inspection of the data, it is apparent that the yearly empirical distributions of
RROE have non-normal and fat tails because the interquartile range is small as compared with the
standard deviation and to the spread between the Max and Min observations. The effects of the
outliers are also seen in the mean estimates of the distributions that often are very far from the median observation. This means that outliers affect the yearly distributions, which prohibits the use of
Mean and StdDev for statistical tests.
Year
n
Max
Mean
Median
Locationbw
Min
StdDev
StdDevbw
QRange
Year
n
Max
Mean
Median
Locationbw
Min
StdDev
StdDevbw
QRange
Descriptive statistics for risk-adjusted RRNOA
1978
1979
1980
1981
1982
1983
1984
611
727
1356
1337
1341
1385
1436
4,030%
399%
792%
409% 1,423% 12,090% 3,790%
26%
8%
11%
10%
-17%
23%
21%
4.2%
5.7%
7.3%
7.5%
7.3%
7.7%
9.7%
4.5%
7.0%
8.3%
8.2%
7.9%
8.8%
12.1%
-600%
-279% -868%
-467% -35,714%
-772% -1,083%
193%
35%
43%
33%
981%
341%
149%
13%
15%
12%
13%
14%
15%
18%
16%
16%
14%
15%
15%
17%
21%
1987
1988
1989
1990
1991
1992
1993
1471
1453
1498
1411
1428
1351
1266
45,212% 7,892% 5,141% 27,220% 2,301% 396,709%
504%
-64%
9%
16%
-12%
12%
302%
12%
6.7%
6.6% 12.5%
5.9%
9.8%
5.9%
9.6%
7.5%
7.0% 13.4%
5.9%
10.6%
5.8%
11.3%
-155,870% -10,516% -2,525% -45,693% -2,697%
-345% -1,948%
4,246%
350%
175% 1,444%
123% 10,793%
83%
12%
12%
15%
13%
23%
21%
23%
14%
13%
18%
14%
25%
22%
25%
1985
1986
1401
1444
2,049% 3,667%
15%
2%
8.1%
7.0%
8.7%
7.6%
-734% -12,524%
81%
372%
11%
12%
13%
13%
1994
1277
1,161%
29%
17.6%
19.4%
-938%
78%
25%
30%
Table 6-2: Descriptive statistics for risk-adjusted RRNOA per year, [EQ 6-9].
Table 6-2 shows some descriptive statistics for risk-adjusted RRNOA. The table shows similar results as the table with descriptive statistics for risk-adjusted RROE. Thus, the yearly distributions of risk-adjusted RRNOA exhibit non-normal tails and thus the Mean and StdDev cannot be
used for statistical tests on the variable.
The arithmetic mean can possibly be replaced by the median but Mosteller & Tukey (1977)
show that the median’s efficiency in large samples is rather poor in comparison with the biweight
estimate, which has over 90 percent efficiency. An estimate having efficiency over 90 percent is very
difficult to distinguish from an estimate having 100 percent efficiency (Mosteller & Tukey 1977). A
100 percent efficiency is, e.g., the arithmetic mean in a Gaussian distribution (Mosteller & Tukey
1977).
The biweight estimate of location and scale uses c=9, which is equivalent to approximately 6
standard deviations, or 99.99 percent (Mosteller & Tukey 1977). This means that the biweight scale
and location estimate use all observations up to six standard deviations in its iterative procedure and
assigns a zero weight to the observations beyond the cut-off points. Therefore, by only excluding
102
the most extreme of the extreme values, the location estimate and the scale estimate change dramatically.
6.3 Do risk-adjusted residual accounting rates-of-returns exist?
Chapter 2 develops the theory of Homo comperiens. The theory of Homo comperiens proposes
that the subject is limited rational because he or she possesses limited knowledge of the available
action and state sets.
Even when assuming homogenous preferences, the theory of Homo comperiens implies that
the subjective expected utility function (Proposition 2-3) is different to the objective utility function.
This implies that the subjective marginal rate of substitution between savings and consumption differs from the objective marginal rate of substitution and we thus face an arbitrage market.
Chapter 4 finds that firms in the arbitrage market exhibit risk-adjusted subjective expected
RROE and risk-adjusted subjective expected RRNOA that are non-zero (Proposition 4-6). The empirically testable proxy for the risk-adjusted subjective expected RROE is [EQ 6-8] and it is [EQ 6-9]
for the risk-adjusted subjective expected RRNOA.
Following this analysis, it is possible to test Proposition 4-6 by analyzing [EQ 6-8] and
[EQ 6-9]. If some firms report these proxies as statistically non-zero, Proposition 4-6 is not falsified.
Subsection 6.3.1 operationalizes these alternative hypotheses and subsection 6.3.2 presents
the results. Appendix K (p. 219) presents the robust t-test that I use.
6.3.1 The hypotheses to be tested
An alternative hypothesis and its null hypothesis are stated per variable.
H1A. A market that meets the conjectures of Homo comperiens is an arbitrage market. In the
arbitrage market at least one firm earns arbitrage profits such that the risk-adjusted RROE is nonzero. This is a testable hypothesis based on Proposition 4-6 (p. 77), which focuses on the overall
residual earnings ability.
*
t 1 RROE it
v 0 Ft
i ‰ I ‰ M
where i is the firm, I is the industry, M is the market, t is the year, and t is a white noise residual.
H0A. The market is a no-arbitrage market and all firms thus report zero risk-adjusted RROE.
*
t 1 RROE it
0 Ft
i ‰ I ‰ M
where i is the firm, I is the industry, M is the market, t is the year, and t is a white noise residual.
H1B. A market that meets the assumptions of Homo comperiens is an arbitrage market. In
the arbitrage market at least one firm earns arbitrage profits such that the risk-adjusted RRNOA is
103
non-zero. This is a testable hypothesis based on Proposition 4-6 (p. 77), which focuses on the operating residual earnings ability.
*
t 1 RRNOAit
v 0 Ft
i ‰ I ‰ M
where i is the firm, I is the industry, M is the market, t is the year, and t is a white noise residual.
H0A. The market is a no-arbitrage market and all firms thus report zero risk-adjusted
RRNOA.
*
t 1 RRNOAit
0 Ft
i ‰ I ‰ M
where i is the firm, I is the industry, M is the market, t is the year, and t is a white noise residual.
6.3.2 Results from the robust double-sided t tests
Appendix K discusses the robust double-sided t test that is applied when assessing the hypotheses in
subsection 6.3.1. The hypotheses are tested using t tests on [EQ 6-8] and [EQ 6-9].
There is a risk that the operationalization of the financial statements in Chapter 5 can drive
the results and the hypotheses tests are thus performed under alternative specifications. The alternative tests are reported in Appendix J (p. 215).
There is a further risk that the results are affected by the measurement of the industry profitability confidence interval and therefore two alternative confidence interval methods are tested.
These are (1) the ‘best’ location estimate using the biweight scale estimate and (2) the biweight location using the biweight scale estimate. See Appendix I (p. 211) for details.
The tests of the hypotheses are with the alternative industry profitability operationalizations:
(i) H0: Risk-adjusted RROE is zero for all firms against the alternative hypothesis that risk-adjusted
RROE is non-zero for at least one firm. The industry ROE is estimated using subsection I.2: That
is, the ‘best’ location estimate and the biweight scale estimate are used to form the robust confidence intervals (RCI).
(ii) H0: Risk-adjusted RROE is zero for all firms against the alternative hypothesis that risk-adjusted
RROE is non-zero for at least one firm. The industry ROE is estimated with RCI using the biweight location and scale estimates. See Appendix K for details.
(iii) H0: Risk-adjusted RRNOA does not exist for any firm against the alternative hypothesis that riskadjusted RRNOA exists for at least one firm. The industry RNOA is estimated using subsection I.2:
That is, the ‘best’ location estimate and the biweight scale estimate are applied to form the RCI.
(iv) H0: Risk-adjusted RRNOA does not exist for any firm against the alternative hypothesis that riskadjusted RRNOA exists for at least one firm. The industry RNOA is estimated with RCI using the
biweight location and the biweight scale estimates. See Appendix K for details.
6.3.2.1
The data set for the tests of Proposition 4-6
According to Appendix C, the database has 33,251 firm-year observations when the full period from
1977 to 1996 is considered; of those, only 25,245 observations are structurally stable enough to test.
The tests of the hypotheses are further restricted to cover years up to and including 1994.
This is because of comparability problems of the data from 1995 forward with the previous periods.
104
All firms belonging to industry-years where there are fewer than five firms per year are excluded in order to provide a minimum acceptable level of firms in an industry-year.
The first year, 1977, is excluded from the test since the accounting rates-of-returns require
beginning of period capital and no such data are available for 1977.
An accounting rate-of-return is deleted if the data are missing or if the capital measure is zero
or negative. Traceable imputations are also deleted from the data set.
With these auxiliary restrictions, there are 22,200 observations available for testing the hypothesis whether
*
t 1 RROEit
is non-zero for at least one firm. There are 22,193 observations available
for testing the hypothesis whether
6.3.2.2
*
t 1 RRNOAit
is non-zero for at least one firm.
The results for the double-sided t test on risk-adjusted RROE
The t-statistic is measured for each observation according to [EQ K-2] and it is evaluated against a
robust threshold value according to the choice rule in Appendix K (p. 219). If the absolute value of
the t-statistic is greater than the threshold value, the null hypothesis is rejected in favor of the alternative hypothesis.
The test is evaluated at both the five and the one percent significance level in Table 6-3.
Supplementary results are also reported from tests at the significance level of two and ten percent.
The RCI method uses the biweight location and scale estimate with c 9 . RCI is used for
the tests of hypotheses that have significance levels set at five, two and, one percent.
The best location estimate (BLE) method is also used in the tests of the hypotheses that have
significance levels at five percent. Since the BLE uses the biweight scale estimate with c 9 and a
location estimate that is not a biweight estimate, the reliability of the test is not known in advance
and thus it might be like comparing apples and oranges. This problem is mended with Table 6-4
where the fit between the BLE and the RCI methods is listed.
The results from the hypotheses tests are presented in Table 6-3.
Risk-adjusted RROE=0 for all firms vs. H1A: Risk-adjusted RROE0 for at least one firm
RCI
RCI
BLE
RCI
RCI
=10%
=5%
=5%
=2%
=1%
Observations % Observations % Observations % Observations % Observations %
17,486 79%
16,710 75%
15,645 70%
15,786 71%
15,171 68%
Rejected H0
Not rejected
4,714 21%
5,490 25%
6,555 30%
6,414 29%
7,029 32%
22,200
22,200
22,200
22,200
22,200
Estimators
Significance
Table 6-3: Summary of the double-sided t test of H0: Risk-adjusted RROE=0 for all firms
vs. H1A: Risk-adjusted RROE0 for at least one firm.
The results from the tests reject the null hypothesis of risk-adjusted RRNOA=0 in favor of
the alternative hypothesis at a significance level of one percent for the great majority of observations. Approximately 68 percent of all the risk-adjusted RROE are non-zero at the one percent significance level, suggesting that the hypothesis test fails to reject Proposition 4-6 when both the
105
firm’s operating and financial activities are allowed to impinge on the results. Failure to reject
Proposition 4-6 means that it is not possible to exclude the possibility that there exists arbitrage opportunities in the market. These arbitrage opportunities may exist at the operative level, at the financial level, or at both the operative and financial levels of the firm. The additional hypothesis test uses
the risk-adjusted RRNOA and tests Proposition 4-6 when only operating activities are allowed to
affect the results.
RROE=0 vs RROE0
=5%
BLE
RCI
Observations
5,245
1,310
Reject H0
245
Reject H0
15,400
Reject H0 Reject H0
22,200
%
23.6%
5.9%
1.1%
69.4%
Table 6-4: Comparison of the robust confidence interval t-test and the best location estimate double-sided t test of H0: Risk-adjusted RROE=0 for all firms vs. H1A: Risk-adjusted
RROE0 for at least one firm.
The method of best robust location uses the best possible robust estimate of location while it
retains the biweight scale estimate. This could decrease its reliability, but as Table 6-4 shows, the fit
between the two alternative methods of estimating industry ROE is not seriously affecting the outcome of the tests.
The two methods of estimating the RCIs agree on the significantly non-zero risk-adjusted
RROE. Both methods find that in 15,400 of 22,200 the observation of risk-adjusted RROE is significantly non-zero. In only about seven percent is there dissimilarity between the methods.
Since both measurement methods arrive at the same conclusion for the vast majority of observations, the results are not materially affected by miss-specification of the RCI estimation method.
6.3.2.3
The results for the double-sided t test of risk-adjusted RRNOA
Risk-adjusted RROE is affected by the firms’ financial activities, which can drive the results in subsection 6.3.2.2. This section studies the results for the double-sided t test where the alternative hypothesis argues that risk-adjusted RRNOA is non-zero for at least one firm. This means that the firm’s
residual rates-of-returns are applied in the tests while excluding the effect of the firm’s financial activities.
Since risk-adjusted RRNOA requires NOA rather than EQ, more firms are likely to have zero or negative capital, which implies that they cannot be used in the analysis. This shows up in the
analysis as six fewer observations when risk-adjusted RRNOA is investigated than if risk-adjusted
RROE is investigated. Table 6-5 and Table 6-6 show the outcomes of these tests.
106
Risk-adjusted RRNOA=0 for all firms vs. H1B: Risk-adjusted RRNOA0 for at least one firm
RCI
RCI
BLE
RCI
RCI
Estimators
=10%
=5%
=5%
=2%
=1%
Significance
Observations % Observations % Observations % Observations % Observations %
17,676 80%
16,856 76%
15,725 71%
15,783 71%
15,179 68%
Rejected H0
Not rejected
4,517 20%
5,337 24%
6,468 29%
6,410 29%
7,014 32%
22,193
22,193
22,193
22,193
22,193
Table 6-5: Summary of the double-sided t test of H0: Risk-adjusted RRNOA=0 for all
firms vs H1B: Risk-adjusted RRNOA0 for at least one firm.
Table 6-5 corroborates the findings from Table 6-3 in that the vast majority of observations
(68 percent) reject the null hypothesis in favor of its alternative at the one percent significance level.
This suggests that the results reported in Table 6-3 do not depend on whether the residual accounting rate-of-returns includes or excludes the effect of the firms’ financial activities.
From Table 6-3 and Table 6-5, it appears to be rather normal for firms to report riskadjusted residual accounting rates-of-returns, an observation consistent with Proposition 4-6.
RRNOA=0 vs RRNOA0
=5%
BLE
RCI
Observations
5,066
1,402
Reject H0
271
Reject H0
15,454
Reject H0 Reject H0
22,193
%
22.8%
6.3%
1.2%
69.6%
Table 6-6: Comparison of the robust confidence interval t-test and the best location estimate double-sided t test of H0: Risk-adjusted RRNOA=0 for all firms vs H1B: Riskadjusted RRNOA0 for at least one firm.
The alternative hypothesis of having non-zero risk-adjusted RRNOA for at least one firm is
tested using (i) the biweight estimator for location and scale with c 9 and (ii) the BLE with the
biweight scale estimator. The difference between the two methods, which is small, is reported in
Table 6-6. Alternative (i) rejects about five percent more observations than what alternative (ii) does,
which is similar to the difference in methods using the risk-adjusted RROE.
6.3.2.4
Do risk-adjusted residual accounting rates-of-returns exist?
The tests whose results are presented on Table 6-3 to Table 6-6 fail to reject Proposition 4-6 and
thus they show that risk-adjusted residual accounting rates-of-returns permeate the firms’ financial
reporting. They also show that it appears to be the rule rather than the exception for firms to report
risk-adjusted residual accounting rates-of-returns. Thus, arbitrage opportunities are abundant and
that firms find and use those opportunities to earn arbitrage profits.
It also appears as if the majority of the arbitrage opportunities are found already at the firms’
operating level. No study has been carried out on the possibility to earn risk-adjusted residual accounting rates-of-returns from the firms’ financial activities and so it cannot be excluded that there
are possibilities for firms to earn arbitrage profits in their financial activities as well. Indeed, the re-
107
sults show that the market is in disequilibrium and thus it must be the case that financial activities
can also earn arbitrage profits.
Of 22,200 statistical tests based on the risk-adjusted RROE, 15,171 observations report a
risk-adjusted RROE significant non-zero at a significance level of 1 percent. 22,193 statistical tests
that use risk-adjusted RRNOA are available for tests of hypotheses. These tests reveal that 15,179
observations are significant non-zero at a one percent significance level, indicating that 68 percent of
all observations fail to falsify Proposition 4-6.
Dechow et al. (1999), Meyers (1999), McCrae & Nilsson (2001), Callen & Morel (2001), Gregory, Saleh, & Tucker (2005), and Giner & Iñiguez (2006) all report that residual income exists since
they find that residual income regresses. However, these studies operationalized the residual income
differently than the way I do in that they fail to distinguish between residual income that is due to
the accounting system and residual income that is due to arbitrage opportunities. Indeed, they even
assume no residual income because of arbitrage opportunities.
Instead, I remove the residual income pertaining to the accounting generated residual income
and focus on residual income whose source is arbitrage opportunities. From section 6.3.2, it is clear
that risk-adjusted residual rates-of-returns exist even after the bias from the accounting system is
removed and thus arbitrage-based residual income exists. Thus, I fail to reject Proposition 4-6.
6.4 Does the market learn through discovery?
Chapter 2 posits that individuals who are limited rational because of limited knowledge have the
capacity to learn from past mistakes in the form of discovery (Definition 2-9, p. 44). With discovery
as a learning process, Chapter 3 asserts that prices cannot be randomly walking; rather, they are partly a function of the price history that trends towards no-arbitrage prices (Proposition 3-1, p. 57;
Proposition 3-2, p. 59).
Chapter 4 takes the analysis further by proposing that limits values for risk-adjusted subjective expected residual accounting rates-of-returns are zero (Proposition 4-5 (p. 72) states it in a subjective certain choice and Proposition 4-7 (p. 78) states it in a subjective uncertain choice). The empirically testable proxy for the risk-adjusted subjective expected RROE is [EQ 6-8] and [EQ 6-9] for
risk-adjusted subjective expected RRNOA.
Proposition 4-7 implies that [EQ 6-8] and [EQ 6-9] should (i) approach zero as time passes
and (ii) not be randomly walking variables. Alternative (i) is equivalent to proposing that the firm’s
profitability approaches the industry profitability as time passes. This is what is tested in this chapter.
A goodness-of-fit test assesses alternative (ii) and is reported in Appendix N (p. 241).
Subsection 6.4.1 operationalizes the hypotheses and subsection 6.4.2 presents the results
from the tests.
108
6.4.1 The tested hypotheses
As in section 6.3, one alternative hypothesis is posed per variable.
H1A: Proposition 4-7 argues that the risk-adjusted subjective expected residual returns on equity (RROE) regress towards zero with time. Using the operationalized risk-adjusted RROE,
[EQ 6-8], it can be expressed as:
*
t RROEit 1
where
B C ¸ t 1 RROEit* Ft 1
i ‰ I ‰ M
[EQ 6-10]
C 1
and where B 0 , i is the firm, I is the industry, M is the market, t is the year, and t is a white
noise disturbance.
H0A: The risk-adjusted RROE do not diminish as time passes. That is, using [EQ 6-10] this
can be expressed as:
C .1
i ‰ I ‰ M
and where B 0 , i is the firm, I is the industry, M is the market, t is the year, and t is a white
noise disturbance.
H1B: Proposition 4-7 argues that the risk-adjusted subjective expected RRNOA regress towards zero with time. Using the operationalized risk-adjusted RRNOA, [EQ 6-9], it can be expressed as:
*
t RRNOAit 1
where
B C ¸ t 1 RRNOAit* Ft 1
i ‰ I ‰ M
[EQ 6-11]
C 1
and where B 0 , i is the firm, I is the industry, M is the market, t is the year, and t is a white
noise disturbance.
H0B: The risk-adjusted RRNOA do not diminish as time passes. Using [EQ 6-11] this can be
expressed as:
C .1
i ‰ I ‰ M
and where B 0 , i is the firm, I is the industry, M is the market, t is the year, and t is a white
noise disturbance.
Having B v 0 can imply many things. For example, it might imply that firms can earn sustainable risk-adjusted RROE and sustainable risk-adjusted RRNOA. However, it is equally plausible
that the test models are incorrectly specified and that there is an omitted variable problem.
6.4.2 Results of the tests of the hypotheses
The hypotheses in subsection 6.4.1 are tested using panel regressions. Many different panel regres-
sion models may be applicable. Dielman (1989), e.g., describes seven panel regression models from
the pooled regression model to models with time-varying and cross-sectional varying regression pa-
109
rameters. The choice of a panel regression model depends on the panel’s statistical properties or on
assumptions about those properties.
Dechow, Hutton & Sloan (1999), Gregory, Saleh, & Tucker (2005), McCrae & Nilsson
(2001) all use the pooled regression model. There is no information in their research about specification tests that assess the feasibility of such an assumption. Nor is there any explicit discussion on the
choice of panel regression model.
Empirical industrial economics research that applies panel regressions on accounting data
(e.g., Jacobsen 1988; Jacobson & Aaker 1985; Mueller 1977; Mueller 1990; Waring 1996) also applies
the pooled regression model without presenting support for it in the form of specification tests.
The panel regression model that I use is a fixed-effect panel regression model with panel corrected standard errors (PCSE) having AR(1) errors and not a pooled regression model. The choice
of a panel regression model is based on four specification tests whose results are reported in
Appendix M (p. 233). The panel regression models considered and the evaluation criteria are discussed in Appendix L (p. 221).
6.4.2.1
Results from panel regressions using risk-adjusted RROE
The results from the panel regressions are organized such that the fit statistics are first presented
followed by the results of the parameter estimates.
Table 6-7 reports the fit statistics for the panel regressions on the risk-adjusted RROE. See
[EQ L-18] for its definitions. RHOHAT is the estimated first-order serial correlation. DFE is the
degrees of freedom, SST is the total sum of squares, SSR is the regression sum of squares, and SSE
is the error sum of squares. MSE is the mean squared error, RMSE is the root mean squared error,
and RSQ is the coefficient of determination, which shows how large the proportion of the data set’s
variability can be explained by the econometric model. See subsection L.3.4 for definitions of the fit
statistics.
Field
RHOHAT
DFE
SST
SSR
SSE
MSE
RMSE
RSQ
1978
-0.141
899
117.0
56.6
60.4
0.068
0.262
48.4%
1979
-0.034
1,064
126.1
52.9
73.2
0.069
0.262
41.9%
1980
-0.068
1,907
243.0
97.9
145.2
0.076
0.276
40.3%
1981
-0.057
1,928
210.0
82.5
127.5
0.066
0.258
39.3%
1982
-0.059
1,970
191.3
67.3
124.0
0.063
0.251
35.2%
Fit origin
1983 1984 1985
-0.105 -0.009 -0.065
2,009 1,925 1,988
159.8 110.6 136.9
52.6 38.0 47.1
107.2 72.6 89.8
0.054 0.038 0.045
0.232 0.194 0.213
32.9% 34.4% 34.4%
1986
-0.065
1,850
130.5
48.8
81.7
0.044
0.211
37.4%
1987
-0.070
1,826
210.0
72.4
137.6
0.076
0.275
34.5%
1988
-0.037
1,748
241.7
86.0
155.7
0.089
0.299
35.6%
1989
-0.133
1,724
302.4
139.2
163.3
0.096
0.310
46.0%
1990
-0.114
1,856
408.1
192.6
215.5
0.118
0.343
47.2%
Table 6-7: Estimated serial correlation in the fixed-effects panel regressions and fit statistics for the fixed-effects panel regression using the risk-adjusted RROE with PCSE when
assuming AR(1) errors.
The most notable result in Table 6-7 is that the model appears to be able to explain rather
much of the variability in the data. The coefficients of determination range from 32.9 percent to
48.4 percent (average is 39 percent).
110
Dechow et al. (1999, p. 17) report a coefficient of determination of 34 percent, Gregory et al.
(2005, p. 509) 48 percent, and McCrae & Nilsson (2001, p. 328) 29 percent.
Meyers (1999) initiates another type of evaluation of the Ohlson (1995) and Feltham & Ohlson (1995) models that uses individual time-series regressions for each firm. Some of those articles
present coefficient of determination (Meyers and Callen & Morel do not). Gregory et al. (2005, p.
509) report an average coefficient of determination of 49 percent. Giner & Iñiguez (2006, p. 179)
report an average coefficient of determination of 51 percent.
It appears that the coefficients of determination that I report is approximately are comparable with previous research.
However, applying a pooled regression model with spherical disturbances to my data using
the risk-adjusted RROE only yields coefficients of determination ranging from 0.8 to 7.4 percent.
The random effect model on the same variable yields coefficients of determination from 0.3 to 5.3
percent.
Both of the alternative regression models deliver coefficients of determination that are much
lower than what the fixed effects model produces. As seen from the results of the specification tests
in Appendix M, the pooled regression model is not an applicable panel regression estimation model
for the data.
Table 6-8 shows the results from the panel regressions using the risk-adjusted RROE. In the
table, ESTIMATES are the estimated regression parameters. STDE is the regression’s standard error
and TVALUE_1 is the t-statistics according to definition [EQ L-1], i.e. the t-statistics for assessing
whether the estimated regression parameters are significantly less than one. PVALUE is the corresponding p-value. TVALUE_0 is the t-statistics for testing if the estimated regression parameter is
significantly different from zero and PVALUE_0 is the corresponding p-value assuming the twosided test.
Field
ESTIMATES
STDE
TVALUE_1
PVALUE_1
TVALUE_0
PVALUE_0
1978
-0.095
0.243
-4.50
0.00%
-0.39
69.5%
1979
-0.126
0.181
-6.21
0.00%
-0.69
48.8%
1980
-0.108
0.238
-4.66
0.00%
-0.45
65.0%
1981
-0.159
0.221
-5.24
0.00%
-0.72
47.1%
1982
-0.111
0.238
-4.67
0.00%
-0.47
64.1%
Fit origin
1983 1984
-0.065 -0.142
0.221 0.159
-4.82 -7.20
0.00% 0.00%
-0.29 -0.89
76.9% 37.1%
1985
-0.198
0.231
-5.19
0.00%
-0.86
39.1%
1986
-0.181
0.239
-4.94
0.00%
-0.76
44.9%
1987
-0.196
0.241
-4.96
0.00%
-0.81
41.5%
1988
-0.091
0.304
-3.59
0.02%
-0.30
76.6%
1989
-0.051
0.244
-4.31
0.00%
-0.21
83.4%
1990
-0.102
0.250
-4.41
0.00%
-0.41
68.4%
Table 6-8: Parameter estimates from the fixed-effects panel regression using the riskadjusted RROE with PCSE and AR(1) errors.
The estimated regression parameters are presented in Table 6-8. If the alternative hypotheses
are correct, they should be less than one and PVALUE_1 should be at least less than five percent.
The table reports that the estimated regression parameters are significantly less than one and not
111
significantly different from zero. Indeed the p-values indicate that the results are significant even at a
threshold level less than one percent and are consequently strong results.
Proposition 4-7 cannot be falsified based on the results reported in Table 6-8 since the null
hypothesis is rejected. This means that the test cannot falsify the notion that the market learns according to Proposition 3-2.
Proposition 3-2 (p. 59) is silent on how fast the actors in the market learn. All that it proposes is that they learn through discovery, i.e. that C ‰ <0,1
. If the process of learning is slow, C is
close to 1. If C is close to zero, it means that the firms learn fast.
If we have no-arbitrage, there are random walks in the rates-of-returns (e.g., Fama 1965a;
Fama 1965b), which implies that C 1 . Since the test finds that C 0 , it rejects randomly walking
risk-adjusted RROE.
6.4.2.2
Results from panel regressions using risk-adjusted RRNOA
This subsection focuses on the results from the panel regression using the risk-adjusted RRNOA.
Table 6-9 reports the results for the panel regressions using the risk-adjusted RRNOA. The coefficients of determination range from 34.1 to 54.1 percent (average is 42.5 percent)
The coefficients of determination are slightly higher for risk-adjusted RRNOA as compared
with their counterparts in subsection 6.4.2.1. A good explanation for this difference is probably that
the risk-adjusted RROE allows for financial leverage, which brings up a firm’s volatility in ROE as
compared with the volatility in RNOA. The high volatility in the underlying ratios therefore cascades
into greater problems for the regressions to minimize the squared errors. This is possible to see by
studying the SST, the SSR, and the sum of squared errors (SSE). SST and SSE are about 5 times
greater for risk-adjusted RROE than they are for risk-adjusted RRNOA, suggesting that the variability is much greater for risk-adjusted RROE than for risk-adjusted RRNOA, which makes it more
difficult to fit a straight-line through the cluster of observations while yielding low SSE.
Field
RHOHAT
DFE
SST
SSR
SSE
MSE
RMSE
RSQ
1978
-0.129
869
16.9
7.9
9.0
0.011
0.103
46.6%
1979
-0.084
1,061
21.5
9.6
12.0
0.011
0.106
44.5%
1980
-0.087
1,976
47.0
20.1
26.9
0.014
0.117
42.7%
1981
-0.035
1,919
41.9
17.1
24.8
0.013
0.114
40.9%
1982
0.005
1,931
39.9
14.0
26.0
0.013
0.116
35.0%
Fit origin
1983 1984 1985
-0.088 -0.067 -0.138
1,904 1,844 1,829
36.1 27.4 31.8
13.3 11.2 14.5
22.7 16.3 17.2
0.012 0.009 0.010
0.110 0.094 0.098
37.0% 40.7% 45.7%
1986
-0.126
1,664
28.4
12.7
15.7
0.010
0.098
44.8%
1987
-0.024
1,736
47.6
16.2
31.4
0.018
0.134
34.1%
1988
-0.027
1,679
57.9
21.3
36.6
0.022
0.148
36.8%
1989
-0.160
1,721
76.6
38.4
38.2
0.023
0.151
50.1%
1990
-0.187
1,880
107.3
58.0
49.3
0.027
0.165
54.1%
Table 6-9: Estimated serial correlation in the fixed-effects panel regressions and fit statistics for the fixed-effects panel regression using the risk-adjusted RRNOA with PCSE and
assuming AR(1) errors.
In Table 6-10 the parameter estimates and standard errors are presented for risk-adjusted
RRNOA. The t-values and p-values that the tests of the hypotheses use also appear in Table 6-10
112
The table shows that the null hypotheses C p 1 are rejected for all panels in favor of the alternative hypotheses C 1 . This means that also when risk-adjusted RRNOA is used to test empirically Proposition 4-7 the tests fail to falsify it. Thus, I cannot reject the possibility that firms learn
through discovery.
Field
ESTIMATES
STDE
TVALUE_1
PVALUE_1
TVALUE_0
PVALUE_0
1978
-0.072
0.251
-4.27
0.00%
-0.29
77.5%
1979
-0.127
0.222
-5.08
0.00%
-0.57
56.8%
1980
-0.122
0.258
-4.34
0.00%
-0.47
63.8%
1981
-0.215
0.245
-4.96
0.00%
-0.88
38.0%
1982
-0.145
0.252
-4.55
0.00%
-0.58
56.5%
Fit origin
1983 1984 1985
-0.057 -0.086 -0.157
0.248 0.160 0.239
-4.26 -6.78 -4.85
0.00% 0.00% 0.00%
-0.23 -0.54 -0.66
82.0% 59.1% 51.1%
1986
-0.183
0.230
-5.15
0.00%
-0.80
42.6%
1987
-0.161
0.246
-4.73
0.00%
-0.65
51.3%
1988
-0.039
0.309
-3.36
0.04%
-0.13
89.8%
1989
0.005
0.252
-3.95
0.00%
0.02
98.3%
1990
-0.054
0.254
-4.15
0.00%
-0.211
83.3%
Table 6-10: Parameter estimates from the fixed-effects panel regression using the riskadjusted RRNOA with PCSE and AR(1) errors.
As with the risk-adjusted RROE, the tests reveal that the parameter estimates are not significantly different from zero. This means that the actors learn fast, and within a year of public disclosure of the discovery of an arbitrage opportunity, the risk-adjusted RROE disappears.
To conclude, the null hypothesis of random walk is again rejected in favor of learning
through discovery that leads towards equilibrium. The variable PVALUE_1 shows that the tests are
all significant at a significance level less than one percent.
6.4.2.3
Does the market discover? — A discussion
All panel regressions using the risk-adjusted RROE and the risk-adjusted RNOA fail to reject
Proposition 4-7. Since the tests fails to reject Proposition 4-7 then Proposition 3-2 cannot be rejected. Because Proposition 3-2 cannot be rejected Proposition 3-1 could not be rejected. They
therefore fail to falsify that the market learns through discovery (Definition 2-9).
Another effect of the panel regressions is that they show that the variables do not behave as
if they are randomly walking, which is an EMH assumption.
The learning-through-discovery effect is so strong that it is complete within a year after discovery. This is completely at odds with random walk, and has important suggestions for forecasting
too: Since C is zero, or very close to zero, the best forecast of next year’s risk-adjusted residual accounting rate-of-return is zero.
This means that it is not correct to assume that a firm can make sustainable arbitrage profits.
Arbitrage profits are temporary by nature since the actors in the market discover and use the arbitrage opportunities. It implies that there are innumerable arbitrage profit opportunities in the market
but that those are fleeting, vanishing swiftly after they have been discovered and acted on.
Although it is difficult to compare research that uses similar yet different models, operationalizations, and estimation techniques, I nevertheless compare my results with those from Dechow,
Hutton, & Sloan (1999), Meyers (1999), McCrae & Nilsson (2001), Callen & Morel (2001), Gregory,
113
Saleh, & Tucker (2005), and Giner & Iñiguez (2006), all of whom perform tests using Ohlson’s
(1995) linear information dynamics model.
Dechow et al. estimate the parameter X in Ohlson’s model: RI t 1 XRI t Vt F1t 1
while assuming Vt 0 . Dechow et al. (1999, p. 16-17) appear to be using the pooled regression
model in the estimation and find that X 0.62 . I estimate my C 0 (which at face value is similar
to X ).
I believe there are at least four reasons for this difference between my results and those reported by Dechow et al. These differences are as follows: (i) I remove both risk and accounting bias
in my operationalization of the variables, whereas Dechow et al. only remove risk. (ii) They remove
risk naïvely since they assume that the cost of equity is 12 percent for all firms at all times (p. 14),
whereas I remove risk at different levels for different industries, even allowing it to be a time variable. (iii) They measure residual income from earnings before extraordinary items, whereas I maintain
the clean-surplus relation; (iv) I use a fixed effect regression model, whereas Dechow et al. use the
pooled regression model.
Indeed, I believe that the fourth reason is an important reason for the differences in results
since Table 7-3 in section 7.3 (p. 127) shows my parameter estimates using the pooled regression
model. These parameter estimates indicate that the median C is strictly positive. Indeed, Myers
(1999) corrects some of the above-mentioned problems and finds significant different results than
what Dechow et al. report.
Meyers (1999, p. 12) notes that the parameters “…must be a function of the firm’s economic
pressures, production technology, and accounting policies”. Meyers solves this problem by performing firm-by-firm time-series regressions. The author (1999, p. 15) also maintains that the naïve risk
adjustment is too simple and thus replaces it using an industry cost of equity estimation. Meyers’
method is not much unlike my own method since I adjust for these errors by sweeping away differences in economic pressures, production functions, accounting rules, and risks by using industry
rates-of-returns defined at the three-digit industry classification level. I addition, I use a more sophisticated panel regression model than both what Dechow et al. and Meyers use since I allow for fixed
effects in the panel regressions. I thus also allow for heterogeneity across the firms. Meyers (1999, p.
17) solves this problem by performing individual firm regressions and taking the median X that he
finds to be 0.23, which is much closer to my parameter estimates.
Differences still exist between Meyers’ and my results and I believe that part of this difference is possible to trace to Meyers’ firm-by-firm regressions, which only have 15—22 observations.
It is a problem for regressions to have so few observations and this is something that Meyers notes
(p. 26). This may bias Meyers’ results even though his median is based on 2,601 regressions. The
114
bias from such a procedure does not asymptotically regress to zero with an increased number of
individual regressions, but regresses to zero with an increased number of observations per firm.
The fixed-effect method that I use is not fault free since bias in dynamic fixed-effect models
do not asymptotically regress to zero with increasing number of firms. Its bias also regresses to zero
with an increase in the number of years in the panel (cf. the Nickell bias in dynamic fixed-effect regression models).
Thus, I conclude that Meyers’ method is a significant improvement to the method employed
by Dechow et al. Moreover, we can see that it changes the results from Dechow et al. levels towards
my levels. The remaining difference can be attributed to the fact that both Meyers and I have room
for technical improvements in our estimation methods.
Research that builds on Dechow et al. and Meyers includes the work of McCrae & Nilsson
(2001), Callen & Morel (2001), Gregory, Saleh, &Tucker (2005), and Giner & Iñiguez (2006).
McCrae & Nilsson report X 0.523 , Callen & Morel X 0.469 , Gregory et al. X 0.62 , and
Giner & Iñiguez X 0.55 .
These articles either use pooled regression models, which I find are not valid for my data and
that probably are not valid for any panel regression models using accounting data because of the
problems that I discuss in Appendix M, or they use cross-sectional regression, which still exposes
them to Meyers criticism of, e.g., differences that are due to differ accounting rules.
The cross sectional samples that Giner & Iñiguez use are small (ranges between 89 and 573
observations), which may make their results spurious. Callen & Morel use firm-by-firm regressions
but do not have more than 27 years of observations, which is very little for regression estimation.
Small samples (by cross section or by years) can be a factor that affects the results.
There may be additional factors that affect the difference between the cited research and my
findings, which is due to how I operationalize the risk-adjusted residual rates-of-returns. I remove,
e.g., accounting bias and risk by using the industry accounting rates-of-returns. It may be that industries also earn risk-adjusted residual rates of returns. If that is the case, I also remove those, whereas
Dechow et al., Meyers, McCrae & Nilsson, Callen & Morel, Gregory et al., and Giner & Iñiguez all
study the effect of jointly regressing both accounting and arbitrage residual incomes if one assumes
that the market is inefficient. This can be another explanation to account for the differences between studies.
6.5 Summary
Chapter 2 and Chapter 3 (with Appendix A—Appendix C) provide the core to the theory of Homo
comperiens. is the theory is applied to firms in Chapter 4, and it proposes market-pricing models for
firms. These models are not testable, but as the analysis in Chapter 4 shows it is possible to deduce
115
Proposition 4-6 and Proposition 4-7 from the market-pricing models. Proposition 4-6 and
Proposition 4-7 are testable. Chapter 6 presents the test method and the results of the tests.
Proposition 4-6 argues that the theory of Homo comperiens’ arbitrage market exhibits a certain trait, i.e. that firms (at least one) report risk-adjusted subjective expected residual accounting
rates-of-returns. This proposition is tested using robust double-sided t tests, the results of which are
presented in this chapter.
The proposition is evaluated using 22,200 (ex post) risk-adjusted return on equity observations and 15,171 of the observations reject the null hypothesis of significant zero risk-adjusted return on equity at the one percent significance level in favor of the alternative hypothesis of having
significant non-zero risk-adjusted return on equity.
The proposition is also evaluated using 22,193 risk-adjusted returns on net operating assets
observations and 15,179 of those observations reject the null hypothesis of significant zero riskadjusted return on net operating assets at the one percent significance level in favor of the alternative hypothesis of having significant non-zero risk-adjusted return on net operating assets.
The robust double-sided t tests therefore fail to falsify Proposition 4-6.
Proposition 4-6 assumes that the market has arbitrage opportunities and this allows for the
introduction of Proposition 4-7. Proposition 4-7 posits that the market’s actors learn from past mistakes through discovery and that this shows itself as diminishing risk-adjusted subjective expected
residual accounting rates-of-returns. This chapter applies a panel regression model to assess the
proposition.
Proposition 4-7 is evaluated on 13 panels of risk-adjusted residual return on equity and 13
panels having risk-adjusted RRNOA. This means there are 26 tests of the hypotheses tests that assess Proposition 4-7. In all these tests the null hypothesis of random walking risk-adjusted residual
accounting rates-of-returns is rejected in favor of its alternative hypotheses of diminishing riskadjusted residual accounting rates-of-returns.
The panel regression tests also find that the discovery is so strong that it appears as if firm’s
risk-adjusted residual rates-of-returns diminish within one year after discovery, which implies that
arbitrage opportunities are temporary (however, the results also show that they are abundant).
It is possible to reject the hypotheses without them being false (Type I error). To determine
that the results are not false it must be possible to create reproducible effects on other sets of empirical observations before a valid rejection of a theory can take place. That is, it is necessary to assess
theory’s external validity. Chapter 7 assesses the external validity of the theory of Homo comperiens
by testing its predictive accuracy using a fixed-size rolling-window out-of-sample forecasting method.
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CHAPTER 7—ASSESSING HOMO COMPERIENS’ PREDICTIVE
ACCURACY
“…a few basic statements contradicting a theory will hardly induce us to
reject it as false.” Popper (1959, p. 86)
7.1 Introduction
The theory of Homo comperiens is a theory that attempts to describe how choice is done and how
it affects the market. It is not a theory that seeks to make normative statements of how choice
should be made. This means that it is a positive theory that makes an endeavor to provide a system
of generalizations that can be used to make predictions about phenomena.
Some theorists propose that the appropriateness of a positive theory should be judged on its
internal validity (e.g., Mises 1949, p. 858). That is, the appropriateness of a theory is based on
whether it is consistent and exhaustive. Nevertheless, since positive theory tries to explain what will
happen as well as the consequences of actions, the meaningfulness of the theory must be primarily
based on its predictive ability even though the internal validity is of interest.
Popper (1959) argues that only theory that cannot be falsified using empirical observations
can endure. It is not enough to use tests of hypotheses, whose results are presented in Chapter 6
because such tests may lead to the rejection of the hypotheses when they are true. This is equivalent
to the Type I error in statistics or as Popper (1959, p. 86) says, “…a few basic statements contradicting a theory will hardly induce us to reject it as false.”
Popper (1959, p. 86) submits that a theory is rejected only when a reproducible effect that
rebuts theory is revealed. This means that tests that just establish the goodness-of-fit of empirical
observations to hypotheses are not enough to discard a theory. According to Popper, the results
must be reproducible on other sets of empirical observations before a valid rejection of a theory
takes place. Friedman’s (1953) view on positive theory resembles Poppers idea in that Friedman calls
for predictive tests.
An example of research that commit a Type I error is Ou & Penman (1989a) who reject the
null hypothesis of random walk in favor of non-random walk, and where a subsequent attempt by
Holthausen & Larcker (1992) to replicate the results on another data set fails.
This chapter presents a method for assessing the predictive accuracy and the results thereof
of the theory of Homo comperiens. The validation method is designed such that it assesses whether
it is possible to make forecasts on out-of-sample data based on the parameterization reported in
Chapter 6 that yield greater predictive ability than the random-walk model’s predictive ability.
117
Proposition 4-6 and Proposition 4-7 withstand the hypotheses tests in Chapter 6 and
Appendix N. If the propositions also withstand predictive tests, this provides considerable support
for the theory of Homo comperiens.
The chapter is organized such that the method for testing predictive accuracy is presented
first, followed by the section containing the results from the tests of predictive accuracy.
7.2 The method for assessing the theory’s external validity
Friedman (1953, p. 7) writes: “The ultimate goal of a positive science is the development of a
‘theory’ or, ‘hypothesis’ that yields valid and meaningful (i.e. not truistic) predictions about phenomena not yet observed.” Friedman appears to be inspired by Popper (1959). Further, it is apparent
that Friedman thinks that the development of a theory needs empirical corroboration and that such
external validation should be based on predictions.
Despite the need for validation, much research in both economics and market-based accounting often fails to validate their propositions and findings using predictive accuracy. Examples
from economics that do not validate the results include Brown & Ball (1967), Brozen (1970), Cubbin & Geroski (1987) Mueller (1977, 1990). Beaver (1970), and Fama & French (2000) are examples
from market-based accounting research that do not validate their results.
In the situation when it is used for external validation, the prediction is often done on the data set on which that models parameters where originally estimated on. This is referred to as insample validation. Research using this approach includes studies by Dechow et al. (1999), Freeman
et al. (1982), Giner & Iñiguez (2006), Gregory, et al. (2005), McCrae & Nilsson (2001), and Watts &
Leftwich (1977).
There is presently a consensus among forecasters that predictive models should be assessed
on out-of sample tests (Tashman 2000, p. 438). Out-of sample tests of predictive accuracy can, e.g.,
make predictions on a phenomenon, and then wait to see how the future unfolds. This is neither a
convenient nor a time efficient method. Holdout samples are presently a common way in which outof-sample tests are carried out (Tashman 2000, p. 438). A holdout sample is part of the data set that
was not used to estimate the model.
This thesis tests the predictive accuracy of the theory of Homo comperiens by making predictions on holdout samples that are compared with other predictions based on perfect rationality.
Next follows the tested models, which is followed by a description of the prediction method and the
evaluation criteria.
7.2.1 The prediction models
Proposition 4-7 (p. 78) reasons that the risk-adjusted residual return on equity (risk-adjusted RROE)
and the risk-adjusted residual return on net operating assets (risk-adjusted RRNOA) regress towards
118
zero. This is contrary to general equilibrium theory, which proposes randomly walking rates-ofreturns.
Proposition 4-7 does not predict how fast the learning process is and two alternatives for the
limited rational choice are offered based on Proposition 3-2 (p. 59). The first alternative suggests
that learning is immediate, i.e. within one period (here it is a year after discovery) and the second
alternative proposes that learning is a gradual process in which the risk-adjusted residual accounting
rates-of-returns regress over more than one period until they are zero.
This implies that I test three predictive models. The results reported in Chapter 6 differ from
those reported by Dechow, et al. (1999), McCrae & Nilsson (2001), Callen &Morel (2001), Gregory,
et al. (2005), and Giner & Iñiguez (2006).
Thus, I also compare the three predictive models with a fourth model that is based on the results reported by McCrae & Nilsson (2001). I compare my predictive models with McCrae & Nilsson rather than with Dechow et al. because the former authors use Swedish data.
The basic prediction model is:
x iT n BT x iT ¸ CT
[EQ 7.1]
Then we have the four prediction models based on [EQ 7.1]:
BT 0 , CT 1
i ‰ M
[EQ 7-2]
BT ‰ d, d
, CT ‰ 0,1
i ‰ M
[EQ 7-3]
BT 0 , CT 0
i ‰ M
[EQ 7-4]
BT 0.012 , CT 0.523
i ‰ M
[EQ 7.5]
where x iT is the last observed (in year T) risk-adjusted residual accounting rate-of-return for
firm i in the set of firms M. x iT n is the n-year predicted risk-adjusted residual accounting rate-ofreturn.
Note that when BT v 0 , the prediction model becomes more complex than a BT 0 prediction model as we forecast further into the future. This is because a three-year forecast is
xT 3 BT ¸ 1 CT CT2 xT ¸ CT3 rather than only xT 3 xT ¸ CT3 .
Model [EQ 7-2] is equivalent to the proposition that random walks in the rates-of-returns,
which mean that the best prediction of tomorrow’s observation is today’s observation. It is therefore
a permanent earnings model.
A different model is [EQ 7-3] that describes a market with actors who are limited rational
and where they gradually learn. The risk-adjusted residual accounting rates-of-returns gradually regress towards zero over more than one year. Because Chapter 6 reports CT 0 , I apply the results
from the pooled regression model (with spherical disturbances) for the gradual learning process
119
since this is the regression model that Dechow, et al. (1999), Gregory, et al. (2005), and McCrae &
Nilsson (2001) use. Thus, it is easier to compare and contrast my results with previous research. See
Table 7-3 (p. 127) for the intercepts and slopes that I use in this model.
The extreme case of discovery occurs when it is complete after one year. This occurs with
model [EQ 7-4], where the best prediction of next year’s and the future years’ risk-adjusted residual
accounting rates-of-returns is zero. That is, this is a transitory earnings model: a firm discovers and
acts on ignorance in a year, which alerts its peers who start to act. The action eliminates the arbitrage
opportunity within the following year. This prediction model is based on my dynamic fixed-effect
(with spherical AR(1)-disturbances) panel regression model, and since heterogeneity is swept away
from the model through the intercept, the intercept is biased and useless for predictions. Thus, I fix
it to zero.
Model [EQ 7.5] is a special case of [EQ 7-3] since it fixes both the intercept and the slope to
the values reported by McCrae & Nilsson (2001, p. 328, Table 2). This allows for the assessment of
the validity of my models not only compared with my data but also compared with other results. If
McCrae & Nilsson’s model is more valid than mine, it should outperform models [EQ 7-3] and
[EQ 7-4].
Next, follows a description on how the out-of-sample method for assessing validity by predictive accuracy is implemented.
7.2.2 The out-of-sample predictive method
The external validity of the theory of Homo comperiens is tested by making predictions with
[EQ 7-3] and [EQ 7-4] on holdout samples. The forecasts are compared with the outcomes through
forecast errors. Similar predictions are also made using the random walk model, [EQ 7-2] and
McCrae & Nilsson’s (2001) model [EQ 7.5]. The resulting forecast errors from model [EQ 7-2]—
[EQ 7.5] are compared using the criteria from subsection 7.2.3. Subsection 7.2.2.1 discusses the method used to make the predictions.
There are several methods to perform tests of predictive ability on holdout samples (see, e.g.,
Tashman, 2000 for a discussion of alternatives). I validate the results using a fixed-size rollingwindow forecasting method.
7.2.2.1
Fixed-size rolling-window forecasts
The validation method uses the period from 1978 to 1994, which is divided into fit periods and test
periods. The test periods are the holdout samples on which predictions are made. The fit periods are
the periods on which the predictive models are calibrated. A fit period directly precedes the test period and the last observation in the fit period is the forecast origin. Predictions are made for the holdout sample from the forecast origin.
120
A rolling-window prediction occurs when the forecast origin is gradually updated and new
forecasts are made on the updated forecast origin. A benefit with a rolling window compared with
its alternative (i.e. the fixed window) is that the number of forecasts increases significantly. A rollingwindow forecast provides T ¸ T 1
¸ 21 predictions, where T is the length of the test period
(Tashman, 2000, p. 439). A fixed window only provides T forecasts, one per forecast length. I apply
the rolling-window method to increase the number of predictions.
The predictions can either be updated using the existing calibrated model when the forecast
origin rolls forward or they can be predicted anew from a recalibrated model (Tashman, 2000, p.
440). If the model is recalibrated, the model is re-estimated on the fit period. Recalibrations are
used when the fit period changes. Figure 7-1 illustrates two versions of recalibration, namely the
fixed-origin and the fixed-size fit period forecasting.
Set # Fixed-origin fit period prediction
1
2
3
Fit period
Fixed-size fit period prediction
Test period
Figure 7-1: The principal difference between having a fixed-origin fit period and having a
fixed-size fit period in rolling-window forecasts.
When the forecast origin rolls forward, another year of variables becomes available on to
which the model can be fitted. Suppose that the fit period’s origin is fixed (thus, the fit period is of a
variable size), it implies that another year of variables is added to the fit period as the forecast origin
rolls forward. The fit period’s length therefore grows as the forecast origin rolls forward. Another
option is to have a fixed-size fit period and to discard the oldest observations as a new year of observations becomes available (Figure 7-1).
Having a fixed-origin fit period means that the relative weights of the years change as new
years are added to the fit period. This also implies that any already existing outliers or other aberrations in the variable stay in the fit period and where new ones are gradually added to the fit period.
This further contaminates the fit period and adversely affects the reliability of the recalibrated model.
Having a fixed-size fit period allows the oldest observations to be discarded. This means that
outliers and other anomalies are gradually removed from the fit period while the most current information is simultaneously kept in the fit period. A fixed-size fit period also ascertains that the relative weights of the years in the fit period are constant. I use the fixed-size fit period method.
Because Homo comperiens discovers, a market evolves as time passes and old information is
not as important as new information. Removing the oldest observations from the fit period using a
fixed-size fit period is therefore reasonable.
121
There cannot be any discovery using the random walk assumption since it implies that the
actors’ knowledge already spans the objective state set. Thus, the length of the fit period does not
matter for model [EQ 7-2] as long as it is long enough to provide a reasonable number of observations in the fit period.
7.2.2.2
The forecast length
The total period covers 16 years, which is divided into fit and test periods. The panel regressions
from subsection 6.4.1 are fitted on periods of four years; the output from the estimations (see section 6.4.2) serves as inputs into the prediction models, which means that the fit periods in the validation procedure are four years long.
A cursory look at the descriptive data indicates, as noted in subsection L.4.1 (p. 229), a strong
dynamic process. When the process is strong, there is no need to predict far-off into the future. The
forecast length is limited to four years, and thus both the fit and test periods are four years long.
Having a four-year test period provides prediction of the most important periods and therefore captures market dynamics.
However, forecasting four years and having a holdout sample of four years implies that there
is only one prediction for a single firm’s forecast at year T 4 . This reduces the assessment accuracy for the relatively long-term forecasts. Tashman (2000, p. 440) uses a minimum number of three
maximum length forecasts in the Tashman example. I assume that at least three maximum length
forecasts per firm are needed for reasonable forecast accuracy.
Setting the holdout sample’s length to six years means that for each firm there will be at least
three T 4 forecasts. The relationship between the period of the holdout length (HL), the maximum forecast length (FL), and the minimum number of forecasts at maximum forecast length is
(MIN): HL FL MIN 1 (Tashman, 2000, p. 440).
The relation between the fit periods and the holdout samples in the data is found in Table
7-1.
122
Panel #
1
2
3
4
5
6
7
8
9
10
11
12
The fit periods and their corresponding holdout samples
Year 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
Fit origin
Fit period
Forecast origin
Forecast period
Figure 7-2: Fit periods and test periods for the fixed-size rolling-window validation.
Holdout samples #8 to #12 do not meet the criteria of having a forecast length of four years
and a minimum of three forecasts per firm since the holdout period is reduced. The reduction is
because the last available year of empirical data for tests is 1994. Figure 7-2 provides a graphical
summary of fit periods and holdout samples.
Table 7-1 shows the forecast length, the minimum number of forecasts, and how they are adjusted to allow for external validation using holdout samples #8 to #12.
Panel # Forecast origin FL Min HL Panel # Forecast origin FL Min HL
1
1982
4
3
6
7
1988
4
3
6
2
1983
4
3
6
8
1989
3
3
5
3
1984
4
3
6
9
1990
2
3
4
4
1985
4
3
6
10
1991
1
3
3
5
1986
4
3
6
11
1992
1
2
2
6
1987
4
3
6
12
1993
1
1
1
Table 7-1: A summary of the relationships between holdout sample length, forecast length,
and the minimum required predictions per firm at maximum forecast length.
The minimum number of forecasts at maximum forecast length is kept at three for the holdout samples with forecast origins up to 1991; the forecast length is decreased for holdout samples
#8 to #10. For holdout samples #11 and #12, the forecast length is only a year. Thus, the minimum
number of forecasts at maximum forecast length is reduced to accommodate the data that is available for validation.
The reduction of the minimum forecast per firm reduces the reliability since aberrations are
likely to have greater impact on the results. However, it should be noted that the number of firms
meeting the criteria increases as the lengths of the holdout period are reduced, which reduces the
effect of aberrations in the short-window holdout samples.
123
7.2.2.3
Outliers
Outliers are present in both the fit and test periods. The fit periods are rid of outliers using the method discussed in subsection L.4.2 because the regression estimates from the tests of the hypotheses
are inputs into the prediction models.
Outliers in the holdout samples affect the reliability of the external validity tests using predictive accuracy, too. The influence of the outliers is reduced by using robust forecast error statistics
and robust hypothesis tests (see subsection 7.2.3 for more information on the robust forecast error
statistic that I use).
7.2.3 The pooling of forecast errors and the forecast error statistic
Assessing predictive accuracy using a single time series with a fixed window method is a rather
straightforward exercise. In such a setting focus can be on choosing an appropriate forecast error
statistic. If the prediction is for a single time series but with a rolling window, there will be multiple
forecasts for the firm (cf. subsection 7.2.2.2). In this case attention is needed to also focus on how
the forecast errors are aggregated a cross the predictions. I face forecasts on multiple firms using
rolling-window prediction.
To focus the analysis some notation is introduced. In this section a firm is denoted i where
M is the set of firms. A holdout sample is symbolized by n, where N is the total number of available
holdout samples. See Table 7-2 for a description of the data matrix of available forecast errors and
an overview of possible forecast error summary statistics. P-1 signifies panel one, i.e. a firm’s holdout sample one.
The forecast error data matrix for two firms
Firm i
Firm j
Summary
P-1 P-2 P-N P-1 P-2 P-N measure
T+1
ei11 ei12 ei1N ej11 ej12 ej1N
T+1
T+2
ei21 ei22 ei2N ej21 ej22 ej2N
T+2
T+3
ei31 ei32 ei3N ej31 ej32 ej3N
T+3
T+H
eiH1 eiH2 eiHN ejH1 ejH2 ejHN
T+H
per t-s i1 i2 iN j1 j2 jN
M H
i
j
per firm
Table 7-2: The data matrix of forecast errors (e) with N predictions per firm having forecast horizon H with M firms.
An important choice is whether to measure the forecast error statistic over the whole forecast length, H, for a firm’s panel time series
œ
in
\ei1n , ", eiHn ^ , or if the forecast error statistic
should be measured across time series per forecast length, i.e.
œ œ
n ‰N
i ‰M
\ei11, ", eM 1N ^ . It is also
possible to measure the forecast error statistic per holdout sample and forecast length: e.g.,
œ
i ‰M
\ei1n , ", eM 1n ^ , but then there is only one prediction per firm and forecast length, as well as
the additional problem of how to interpret that error statistic.
124
Measuring the forecast error for each time series is not useful since it mixes the forecast error
for one-year predictions with the two-year forecast errors, and so on. The interpretation of such a
measure does not permit a distinction between short- and long-term predictive accuracy. I measure
across the time series per forecast length since such a procedure does not mix short-term predictions with long-term predictions.
Measuring across the time series requires attention to which forecast error statistic is used.
Armstrong & Collopy (1992), Fildes (1992), Hyndman & Koehler (2005), and Tashman (2000) discuss this topic.
When the forecast errors are summarized across the times series, Armstrong & Collopy
(1992, p. 70), Fildes (1992, p. 85), Hyndman & Koehler (2005, p. 16), and Tashman (2000, p. 445)
point out that scale dependent measures, such as the mean square error (MSE) or the mean absolute
error (MAE), should be avoided. Ahlburg (1992, p. 99) notes that there is a consensus in the research community that unit free forecast error statistics should be used when comparing forecast
methods. The other cited authors argue similarly.
According to Tashman (2000, p. 445), a better measure than scale dependent measures is a
scale independent measure such as the median absolute percentage error (MdAPE). MdAPE is robust and can withstand skewed data. However, the MdAPE is not preferable when the time series
has different volatility (Tashman 2000, p. 445).
When volatility differs across the time series, Tashman (2000, p. 445) asserts that relative
measurement errors are preferable. Tashman maintains that the median relative absolute error
(MdRAE) is useful as a summary measure under such premises, or that the geometric mean relative
absolute error (GMRAE) is useful. Armstrong & Collopy (1992, p. 71) prefer the MdRAE and
GMRAE. Fildes calls for a statistic similar to the GMRAE.
The data in the holdout samples are contaminated by outliers, which mean that the single
time series has different volatility. Since this is the case and since the researchers seem to be almost
indifferent between choosing MdRAE or GMRAE, I decided to use the MdRAE statistic in that it is
computationally simpler than the GMRAE. The MdRAE-statistic is measured as:
emhn Omhn Fmhn
*
RAEmhn emhn ¸ emhn
[EQ 7-6]
1
[EQ 7-7]
MdRAEh median \RAE1h 1, ", RAEMhN ^
[EQ 7-8]
where Omhn is the acronym for the observation at time T+h for firm m in holdout sample n.
F is the acronym for the forecasted value, e is generic for the forecast error, and e* is the forecast
error for the benchmark model. MdRAEh is the median relative absolute error across all holdout
samples for forecast length h.
125
When MdRAE<100 percent, the alternative prediction model is more accurate than the
benchmark model. I evaluate the significance of the MdRAE statistic using a one-sided robust t test
that uses the biweight scale estimate setting its constant to nine. This is equivalent to the ‘best’ location estimate method discussed in Appendix I (p. 211).
7.3 Results from the predictions
Popper (1959) sees theories as nets cast to catch ‘the world’. Section 6.4.2 reports the results from
hypothesis tests that fit econometric models to panels. The fit statistics indicates that the theory of
Homo comperiens on which the model rests seems capable of rationalizing and explaining ‘the
world’. However, does the theory of Homo comperiens master ‘the world’ too? Is it such a valid
description of how ‘the world’ works that the model can predict ‘the world’?
This section reports the results from the fix-sized rolling-window forecasts where the
theory’s predictive ability is tested against the predictive ability of the general equilibrium theory.
Homo comperiens predicts that risk-adjusted RROE and risk-adjusted RRNOA regress towards
zero. This adjustment process can be so fast that it is complete after one period (i.e. transitory), or it
can be slower (semi-transitory). A no-arbitrage theory predicts that the risk-adjusted RROE and the
risk-adjusted RRNOA should be randomly walking, which is thus the test’s benchmark model. I call
it the permanent earnings model.
The predictive ability is measured using MdRAE statistic. The MdRAE-statistic is formed as
the median of the ratio of the alternative forecast models’ absolute forecast errors and the benchmark model’s absolute forecast errors. This section reports the results for the following statistics:
(i) The MdRAE when the transitory earnings model [EQ 7-4] is the alternative forecasting model and
where the benchmark model is the permanent earnings model [EQ 7-2].
(ii) The MdRAE when the semi-transitory earnings model [EQ 7-3] is the alternative forecasting model
and where the permanent earnings model is the benchmark model.
(iii) The MdRAE when the alternative forecasting model is McCrae & Nilsson’s (2001) model [EQ 7.5]
and where the benchmark model is the permanent earnings model.
I use the permanent earnings model as the benchmark model with which the transitory earnings and the semi-transitory earnings models are compared. This is similar to the formal hypothesis
tests whose results are reported in Chapter 6, since the null hypotheses in that chapter are based on
the random-walk model, which, in turn, is an offspring of the perfectly rational choice.
Because my results in subsection 6.4.2 differ from those of McCrae & Nilsson (2001), and
therefore need to assess the methods against each other, I perform double-sided paired t tests to
assess if the results significantly differ between the models. The tests’ null hypothesis is that the difference is zero and the alternative hypothesis is that they are non-zero. Giner & Iñiguez (2006) also
use paired t tests to discriminate between forecasting models.
Proposition 3-2 (p. 59) argues when actors discover this implies C 1 , and if the learning is
so fast that the arbitrage opportunity disappears within a period after discovery, it follows that
126
C 0 . The opposite to C 0 is random walk, i.e. C 1 , which only occurs when the actors do
not discover. Assuming C 1 implies a perfectly rational choice since all actors already face the
standard state-partition-model and thus there are no more discoveries.
The first test places the transitory earnings model against the permanent earnings model and
therefore tests if the actors discover at a very fast rate such that C 0 serves as a reasonable approximation as opposed to no discovery in the form of C 1 .
The second comparison places the semi-transitory earnings model against the permanent
earnings model and assesses if the discovery in the form of C 0,1
is a better approximation of
the actors’ behavior rather than no discovery, which would imply C 1 .
The loadings for C can possibly come from subsection 6.4.2, but they are non-significantly
different from zero and cannot be used for forecasting in model [EQ 7-3] since it requires the loadings to be strictly positive and less than one. Instead, the semi-transitory earnings model uses
C from the pooled regression model assuming spherical errors since that is most likely the model
that Dechow, et al. (1999), Gregory, et al. (2005), and McCrae & Nilsson (2001) use. These parameter estimates are presented in Table 7-3.
RRNOA
RROE
Parameter estimates based on the pooled regression model with spherical disturbances
Fit origin
Variable Field
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
INTERCEPT
0.030 0.030 0.026 0.023 0.022 0.022 0.017 0.016 0.013 0.015 0.021
STDE
0.009 0.008 0.006 0.006 0.005 0.005 0.004 0.004 0.005 0.006 0.007
TVALUE_0
-113.80 -125.05 -161.78 -175.66 -187.94 -208.71 -238.23 -222.69 -215.06 -166.22 -149.14
PVALUE_0
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.0% 0.0% 0.00%
SLOPE
0.279 0.191 0.222 0.168 0.169 0.133 0.074 0.100 0.113 0.128 0.223
STDE
0.029 0.024 0.020 0.018 0.018 0.017 0.017 0.021 0.020 0.026 0.023
TVALUE_1
-25.28 -33.81 -38.56 -45.88 -46.24 -50.99 -55.38 -43.09 -43.84 -33.94 -33.23
PVALUE_1
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
TVALUE_0
9.80
7.99 11.00
9.29
9.42
7.83
4.42
4.78
5.58
5.00
9.53
PVALUE_0
0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
INTERCEPT
0.003 0.006 0.008 0.009 0.011 0.010 0.007 0.005 0.002 0.003 0.004
STDE
0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.003 0.003
TVALUE_0
1.04
1.79
3.12
3.52
4.46
4.31
3.11
2.40
0.92
1.01
1.17
PVALUE_0
29.9% 7.34% 0.18% 0.04% 0.00% 0.00% 0.19%
1.6% 35.9% 31.5% 24.1%
SLOPE
0.307 0.244 0.261 0.179 0.200 0.195 0.145 0.212 0.177 0.211 0.282
STDE
0.029 0.027 0.022 0.019 0.019 0.018 0.017 0.022 0.021 0.026 0.024
TVALUE_1
-23.94 -28.20 -34.33 -42.72 -42.12 -44.20 -49.60 -36.39 -39.20 -29.89 -30.34
PVALUE_1
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
TVALUE_0
10.62
9.09 12.13
9.33 10.50 10.68
8.40
9.80
8.40
7.99 11.94
PVALUE_0
0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
1989
0.033
0.007
-133.83
0.00%
0.262
0.023
-32.30
0.00%
11.45
0.0%
0.008
0.004
2.23
2.60%
0.321
0.022
-30.39
0.00%
14.36
0.0%
1990
0.033
0.008
-125.17
0.00%
0.311
0.022
-30.94
0.00%
13.98
0.0%
0.010
0.004
2.73
0.6%
0.350
0.021
-30.34
0.00%
16.362
0.0%
Table 7-3: The parameter estimates from the pooled regression model for risk-adjusted residual rates-of-returns.
If the prediction tests show that MdRAE is significantly less than 100 percent for both comparison (i) and (ii), the permanent earnings model is rejected in favor of the alternative forecast
models proposed by Proposition 3-2.
127
Section 6.4.2 consistently reports that C is close to zero and formal tests fail to reject that it is
non-zero, i.e. the transitory earnings model dominates over the semi-transitory earnings model.
However, Chapter 6 notes that the dynamic fixed model may be affected by the “Nickell effect”.
That is, the parameter estimates may be biased and hence the formal tests may give misleading results. By performing separate predictions based on the estimates from the dynamic fixed model (i.e.
the transitory earnings model) and from the pooled regression model, I also evaluate the validity of
using the dynamic fixed-effect model.
7.3.1 Results from using the risk-adjusted RROE
Table 7-4 presents the MdRAE statistic for forecast lengths (FL) of one year up to four
years. The MdRAE-statistic is measured according to [EQ 7-8]. FM is the alternative forecast model.
BM is the benchmark model and FL is the forecast length. Table 7-4 also reports the number of
forecasts (NOBS), the test statistics t- and p-value. The tests’ null hypotheses are MdRAE=100 percent and the alternative hypotheses are MdRAE<100 percent.
MdRAE for risk-adjusted RROE (one-sided t-test)
Transitory
Semi-transitory
McCrae & Nilsson
FM
Permanent
Permanent
Permanent
BM
FL NOBS MdRAE T-value P-value MdRAE T-value P-value MdRAE T-value P-value
1
11,185
84.7%
-19.8
0.0%
83.7%
-24.0
0.0%
84.1%
-35.7
0.0%
2
9,574
79.3%
-28.3
0.0%
80.0%
-27.5
0.0%
80.2%
-33.4
0.0%
3
8,087
75.9%
-32.9
0.0%
77.3%
-30.6
0.0%
76.7%
-34.9
0.0%
4
6,704
76.4%
-30.5
0.0%
77.5%
-28.9
0.0%
77.0%
-30.6
0.0%
Table 7-4: The MdRAE-statistic for all holdout samples using the risk-adjusted RROE.
The results in Table 7-4 show that the transitory earnings model, the semi-transitory earnings
model, and McCrae & Nilsson’s (2001) model all dominate over the permanent earnings model at all
forecast lengths since the aggregate MdRAE statistic is significantly less than 100 percent for all
models at all forecast lengths.
These results are all significant at the 0.0 percent significance level for all forecast lengths using a one-sided robust significance test.
It is clear from Table 7-4 that the transitory earnings model and the semi-transitory earnings
model fair less well for the one-year forecasts than for longer forecasts, which is a result similar to
the findings reported from the goodness-of-fit tests.
The goodness-of-fit tests’ results in section N.5 cannot rule out that the risk-adjusted RNOA
follows a random-walk process between two consecutive years. The results in Table 7-4 indicate that
the process does not meet the conjectures of a permanent earning model using risk-adjusted RROE
since its MdRAE statistic is significantly less than 100 percent for the one-year forecasts.
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For the longer forecasts, the relative absolute forecast errors from the transitory earnings
model and from the semi-transitory earnings model are 23—24 percent lower than the relative absolute forecasts errors from the permanent earnings model. This is a considerable improvement.
McCrae & Nilsson’s (2001) model performs similarly in the forecasts and I use the paired t
test to compare and contrast this model to the other models. I also use this test to discriminate between the transitory earnings model and the semi-transitory earnings model.
M1
M2
FL NOBS
1
11,185
2
9,574
3
8,087
4
6,704
Difference in MdRAE for risk-adjusted RROE (Paired two-sided t-test)
Transitory
Transitory
Semi-Transitory
Semi-Transitory
McCrae & Nilsson
McCrae & Nilsson
DIFF T-value P-value DIFF T-value P-value DIFF T-value P-value
0.38%
1.5 13.0% -1.05%
-2.0
4.1% -2.20%
-5.4
0.0%
-1.03%
-5.7
0.0% -0.90%
-2.9
0.3% -0.46%
-1.3 19.1%
-1.25%
-6.9
0.0% -0.90%
-4.5
0.0% -0.36%
-1.2 24.5%
-1.55%
-7.8
0.0% -0.49%
-2.8
0.5%
0.17%
0.5 62.5%
Table 7-5: The results from paired t tests used to discriminate between the transitory earnings model, the semi-transitory earnings models, and McCrae & Nilsson’s (2001) model.
Table 7-5 shows the results from the paired robust t test having as the null hypothesis that
the differences are zero and with the alternative hypothesis that they are non-zero.
Table 7-5 shows that the semi-transitory earnings model is not significantly more accurate
than the transitory earnings model in the one-year forecasts. For the forecasts longer than one year,
however, the transitory earnings model yields significantly less forecast errors than the semitransitory earnings model.
In the paired t test McCrae & Nilsson’s (2001) model indicates having significantly (at the
five percent threshold) larger RAEs than the transitory earnings model in the one-year forecast.
However, this result is contradicted by the point estimates in Table 7-4, although the difference is
small in Table 7-4. It should also be noted that the difference is significant at a 4.1 percent level,
which is rather close to the cut-off level and therefore I judge that result rather weak. Thus, I am
inclined to conclude that McCrae & Nilsson’s model and the transitory earnings model perform
similarly in the one-year predictions.
For the forecasts more than one year into the future, McCrae & Nilsson’s model performs
significantly less well than the transitory earnings model having significance levels less than or equal
to 0.5 percent, indicating rather strong results.
The semi-transitory earnings model is not significantly more accurate than McCrae & Nilsson’s (2001) model for forecast lengths more than one year. Indeed, the two models are almost identical in the longer forecasts.
Despite that my estimated models have zero slope coefficients (in the dynamic fixed-effect
model), or close to zero (in the pooled regression model), and consequently, are far from those reported by Dechow, et al. (1999), Meyers (1999), McCrae & Nilsson (2001), Callen & Morel (2001),
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Gregory, et al. (2005), and Giner & Iñiguez (2006), I must conclude that my models have greater
predictive accuracy. This conclusion is based on the above results.
These results imply that the results from section 6.4.2 maintain, i.e. the C 0 is not only a
statistically significant result but also a valid description of the process that guides the risk-adjusted
residual rates-of-returns. The results also imply that the semi-transitory earnings model, using the
regression parameter estimates from Table 7-3, is inferior to the transitory earnings model in all but
the one-year forecasts where it performs comparably with the semi-transitory earnings model.
McCrae & Nilsson’s model is inferior to the transitory earnings model for all forecast lengths.
The fact that the results from subsection 6.4.2.1 (p. 110) are asserted be the results presented
above indicate that those results are robust and thus not a function of spurious events.
7.3.2 Results from using the risk-adjusted RRNOA
The previous subsection shows how the transitory earnings model significantly outperforms the
permanent earnings model, the semi-transitory earnings model, and McCrae & Nilsson’s (2001)
model in almost all circumstances when risk-adjusted RROE is used as the assessment variable. This
section reports the same tests using the risk-adjusted RRNOA as the assessment variable.
MdRAE for risk-adjusted RRNOA (one-sided t-test)
Transitory
Semi-transitory
McCrae & Nilsson
FM
Permanent
Permanent
Permanent
BM
FL NOBS MdRAE T-value P-value MdRAE T-value P-value MdRAE T-value P-value
1
11,176
87.7%
-15.3
0.0%
85.1%
-22.1
0.0%
84.9%
-32.1
0.0%
2
9,568
82.3%
-23.6
0.0%
82.1%
-24.5
0.0%
81.9%
-29.2
0.0%
3
8,082
78.0%
-28.9
0.0%
78.6%
-28.1
0.0%
79.1%
-29.7
0.0%
4
6,701
79.1%
-26.2
0.0%
79.9%
-24.9
0.0%
80.5%
-24.6
0.0%
Table 7-6: The MdRAE statistic for all holdout samples using the risk-adjusted RRNOA.
The results from subsection 6.3.2.3 (p. 106) and subsection 6.4.2.2 (p. 112) show that riskadjusted RRNOA behaves as risk-adjusted RROE in the tests of the hypotheses on the panel regression estimates.
Table 7-6 reports the MdRAE statistics for the risk-adjusted RRNOA. The results from
these predictions are similar to those from the risk-adjusted RROE. That is, the transitory model,
the semi-transitory earnings model, and McCrae & Nilsson’s model are significantly more accurate
than the permanent earnings model. All results are significant at the 0.0 percent significance level for
all years.
The RAEs from the all these models are for the four-year forecasts of risk-adjusted RRNOA
and are about 20 percent less than the RAEs from the permanent earnings model (i.e. from randomwalk predictions).
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The results in Table 7-6 show that the forecasting models proposed by the theory of Homo
comperiens are superior to the permanent earnings model and thus that the results presented in subsection 6.4.2.2 are not spurious. The results from the paired t tests are presented in Table 7-7.
Difference in MdRAE for risk-adjusted RRNOA (Paired two-sided t-test)
Transitory
Transitory
Semi-Transitory
M1
Semi-Transitory
McCrae & Nilsson
McCrae & Nilsson
M2
FL NOBS DIFF T-value P-value DIFF T-value P-value DIFF T-value P-value
1
11,176
2.43%
8.5
0.0%
0.24%
0.4 67.5% -2.43%
-6.0
0.0%
2
9,568
0.08%
0.6 52.5% -0.87%
-2.4
1.7% -1.28%
-3.3
0.1%
3
8,082 -0.25%
-2.2
2.7% -1.80%
-5.9
0.0% -1.69%
-4.4
0.0%
4
6,701 -0.34%
-2.8
0.6% -2.22%
-6.9
0.0% -2.15%
-5.0
0.0%
Table 7-7: The results from paired t tests used to discriminate between the transitory earnings model, the semi-transitory earnings model, and McCrae & Nilsson’s (2001) model.
The results reported in Table 7-7 are somewhat different to the results reported in Table
7-5. Table 7-5 reveals no significant difference between the transitory earnings model and the semitransitory earnings model for the one-year forecasts. The table further shows that the transitory
earnings model is superior for forecast longer than two years.
Table 7-7 shows that the semi-transitory earnings model is significantly more accurate than
the transitory earnings model at the one-year forecasts, that the two models are not significantly
different at two year forecasts, and that three- and four-year forecasts by the transitory earnings
model are superior to the forecasts by the semi-transitory earnings model.
Table 7-5 shows that the transitory earnings model is significantly (though weakly) more accurate than McCrae & Nilsson’s (2001) model at one-year forecasts. The difference disappears in
Table 7-7 and there is no significant difference between them for that forecast length. For two-year
and longer forecasts, the results reported in Table 7-7 show that the transitory earnings model is
superior to McCrae & Nilsson’s (2001) model, which is similar to the conclusions based on Table
7-5. That is, the transitory earnings model is significantly more accurate than McCrae &Nilsson’s
(2001) model.
The semi-transitory model outperforms McCrae & Nilsson’s model for all forecast lengths
when the forecasts are based on risk-adjusted RRNOA.
When considering the results reported in Table 7-5 and Table 7-7 , my conclusion is that the
slope coefficient is perhaps not zero but positive (as my theory also proposes), yet significantly less
than one.
Furthermore, the fact that I have different results for the two variables risk-adjusted RROE
and risk-adjusted RRNOA indicate that the firm’s financial activities reduce the residual profitability
faster than it would have otherwise. This is perhaps an indication that the financial activities yield
negative risk-adjusted rates-of-returns. However, more studies are needed to determine if this hypothesis holds, which is not within the scope of this study.
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It is difficult to discriminate between the semi-transitory earnings model and McCrae & Nilsson’s model since the former is significantly better than McCrae & Nilsson’s model in five out of
eight tests and McCrae & Nilsson’s model is better than the semi-transitory earnings model in the
remaining three tests.
Taking into account both the results presented in Table 7-5 and in Table 7-7 , I am confident that my findings are robust. I believe this indicates that the pooled regression method applied
by Dechow, et al. (1999), McCrae & Nilsson (2001), Callen & Morel (2001), Gregory, et al. (2005),
and Giner & Iñiguez (2006) should be avoided when fitting Ohlson’s (1995) and Feltham & Ohlson’s (1995) model to data. At the very least, I expect that the choice of which panel regression
model is selected should be based on formal specification tests.
7.3.3 Conclusions from the external validation
Section 7.3 focuses on investigating whether the theory of Homo comperiens not only can rational-
ize and explain ‘the world,’ but if it can also master it. That is, to study whether the theory has predictive ability over and above the random walk hypothesis. This assessment builds on Proposition 32 and the results from section 6.4 (p. 108).
The section uses the MdRAE to assess the predictive accuracy of the models. I measure the
statistic across all firms and holdout samples.
The results show that the transitory earnings model and the semi-transitory earnings model
are significantly more accurate in predictions than the permanent earnings model. The results are
robust and the forecast accuracy using MdRAE is significant at the 0.0 percent significance level.
The results thus show that Proposition 3-2 has considerably greater predictive accuracy than the
random walk prediction.
The MdRAE statistics for the one-year forecasts indicates an improvement of approximately
12—16 percent when Proposition 3-2 is evaluated against the permanent earnings prediction model.
These results are also significant at the 0.0 percent significance level.
The MdRAE statistics at the four-year forecast length show that my models yield an improvement from 19-24 percent when compared with the permanent earnings model.
I also show inconsistent results between the transitory earnings model and the semitransitory earnings model. Of eight paired t tests, five show that the transitory earnings model yields
lower RAEs, one test shows that the semi-transitory earnings model yields lower RAEs, and two
tests fail to reject the null hypothesis of no difference. There is a bias for the transitory earnings
model and thus I suggest that the slope coefficient is very close to zero, yet positive. The fact that I
fail to reject the hypothesis of zero slope coefficient in Chapter 6 may be due to the Nickell bias. If
that is the case, it nevertheless implies that its effect is non-material in my research since it does not
affect my conclusions.
132
I also make predictions using McCrae & Nilsson’s (2001) model since it reports rather different slope coefficients than what I find. McCrae & Nilsson’s model is also significantly more accurate
as a forecasting model than the permanent earnings model for risk-adjusted residual accounting rates
of returns.
At the same time, I find that McCrae & Nilsson’s model is significantly worse at making predictions than my transitory earnings model. The results are weaker when comparing my semitransitory earnings model with McCrae & Nilsson’s model since the tests reveal that the semitransitory earnings model significantly outperforms McCrae & Nilsson’s model in five out of eight
tests while there is no significant difference in the remaining three tests. McCrae & Nilsson’s model
never outperforms my models.
The findings in this chapter thus show the external validity of the theory of Homo comperiens and the appropriateness of use of dynamic fixed-effect panel regressions. This implies that the
results reported in section 6.4.2 cannot be easily dismissed by reference to such factors as spurious
results or bad specifications.
Indeed, despite a battery of attempts to falsify Proposition 3-2 posed by the theory of Homo
comperiens, the proposition nevertheless manages to prevail.
7.4 Summary
Chapter 6 and Appendix N reject the null hypotheses in favor of the alternative hypotheses posed
by the theory of Homo comperiens. The null hypotheses are in all but one test (risk-adjusted
RRNOA in Appendix N for t 2 ) rejected. However, it is possible to reject the hypotheses without
them being false; to determine if the results are valid it must be possible to create reproducible effects on other sets of empirical observations. That is, it is necessary to assess the theory’s external
validity.
Chapter 7 assesses the external validity of the theory of Homo comperiens by testing its predictive accuracy using a fixed-size rolling-window out-of-sample forecasting method. More specifically, Proposition 3-2 is validated using this method. The predictive accuracy of Proposition 3-2 is
tested against the predictive accuracy of the random walk hypothesis using the MdRAE statistic.
The theory of Homo comperiens’ predictive accuracy for the one-year forecasts is from12—
14 percent better than the random walk predictions. The improvement increases as the forecasts
length increases up to the forecast horizon at four years. At the four-year forecast length, the errors
of the theory of Homo comperiens are 19 to 24 percent less than those of the random walk model.
All these results are significant at the 0.0 percent significance level.
The results further show that McCrae & Nilsson’s model, which is similar to mine, is inferior
to my transitory earnings model since its predictive accuracy is significantly worse in seven out of
133
eight paired t tests (in the remaining test no difference was observed between models). When I consider the performance of McCrae & Nilsson’s model as compared with the semi-transitory earnings
model, I find that my model is significantly more accurate in five out of eight tests, with no significant differences in the remaining three tests.
The chapter also shows that in five out of eight paired t tests the fixed-effect regression
model is superior to the pooled regression model. The pooled regression model is superior to the
fixed-effect regression model in one test, and the remaining two tests the models perform equally
well. Although the results are not unidirectional, it appears as though the fixed-effect model is preferable. I expect, however, that the future use of models similar to those in this chapter will use specification tests to discriminate between the final choice of models. Some of the inconclusiveness in
this chapter may stem from a Nickell effect. Thus, it may be of interest to explore other panel regression models that use the dynamics from lagged models in an unbiased fashion.
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CHAPTER 8—CONCLUDING DISCUSSION
8.1 Introduction
This chapter summarizes the study’s theoretical and empirical findings, directions for future research, and the implications for the role of accounting in our society.
8.2 Research problems and the research design
Kothari (2001, p. 208) observes that evidence against market efficiency has mounted. Lee (2001, p.
234) writes:
“My thesis is that a naïve view of market efficiency, in which price is assumed to equal fundamental value,
is an inadequate conceptual starting point for future market-related research. In my mind, it is an over
simplification that fails to capture the richness of market pricing dynamics and the process of price discovery. Prices do not adjust to fundamental value instantly by fiat. Price convergence toward fundamental value is better characterized as a process, which is accomplished through the interplay between noise traders
and information arbitrageurs. This process requires time and effort, and is only achieved at substantial cost
to society.”
Kothari (2001, p. 208) writes that “…advocates of market inefficiency should propose robust
hypotheses and empirical tests to differentiate their behavioral-finance theories from the efficient
market hypothesis that does not rely on investor irrationality”. He further argues (p. 191) that there
is a need for a theory of market inefficiency.
In a similar view Lee (2001) reasons that we should assume that the market price and the intrinsic value are two distinct measures. Lee (2001, p. 251) also writes “…we should study how,
when, and why price becomes efficient (and why at other times it fails to do so)”.
This thesis is a response to Kothari and Lee’s calls for a theory of market inefficiency that
sees the market price and the intrinsic value as two distinct measures.
Rather than following the current tradition in behavior economics of (Kahneman 2003, p.
1469) “…retaining the basic architecture of the rational model, adding conjectures about cognitive
limitations designed to account for specific anomalies,” this thesis aims at developing a general
theory of market inefficiency that has a potential to be widely applied. I call it the theory of Homo
comperiens.
I do not start to develop the theory from a sheet of blank paper. There already exist several
important pieces of knowledge in the research community (over and above the standard models in
economics) that I synthesize into this theory. Particularly important pieces of existing knowledge
come from the work of Hayek (1936, 1945), Kirzner (1973), and Simon (1955, 1956). Of less importance, but still significant are Congleton (2001), who continues in the tradition of Hayek and Kirzner, and game theoretical research from Dekel, Lipman &Rustichini (1998), Modica & Rustichini
135
(1994), and Modica & Rustichini (1999), all of whom contribute in one way or another to the way
that I structure the problem.
Yet, despite the inspiration from the research described above, no one has structured a comprehensive limited rational choice theory in the same (or similar) way as I do here. Furthermore,
there is no one that has brought similar theoretical models into empirical financial economics or
market-based accounting research and attempted to empirically test them.
I empirically test theory using tests of hypotheses on a database with accounting data from
the Swedish manufacturing industry. The present thesis uses accounting data from 1978 to 1994
(approximately 22,000 firm-year observations), which is as far as I know by far the most comprehensive Swedish accounting database applied to this type of research. The external validity of my
findings is tested in out-of-sample tests having up to approximately 11,200 predictions.
8.3 The theory of Homo comperiens
Standard research in economics, finance, and market-based accounting research builds largely on the
conjecture of the perfect rational choice. This means that two conjectures are invoked. They are the
completeness conjecture and the transitivity conjecture. A third conjecture, the non-satiation conjecture, is often invoked to enable the researcher to draw sharper inferences.
On top of these main conjectures are a host of auxiliary conjectures levied onto the perfectly
rational choice, such as continuous preferences, state-independent preferences, homogenous preferences, and rational expectations. None of the auxiliary conjectures is normally critical and are used
to enable tractable solutions for specific problems.
The perfect rational choice that is derived in this way creates a no-arbitrage market. The perfect rational choice allows for gradual dissemination of information into the market where the subjects respond to the new information and adjust the prices accordingly using Bayesian learning.
Bayesian learning is modeled within the framework of the standard state-space-and-partition model.
A crux with the standard state-space-and-partition model is that it requires the subjects to
identify everything that they do not know (Dekel, Lipman & Rustichini 1998, p. 164; Rubinstein
1998, p. 47; Samuelson 2004, p. 372, 398). This means that the subjects cannot be unaware of one or
more states in a standard state-space-and-partition model. This is known as, e.g., the axiom of
awareness (Samuelson 2004, p. 372). In a multi-subject situation the standard state-space-andpartition model means that the other subjects’ consumption and investment plans become part of
the focal subjects’ state set (e.g., Samuelson 2004, p. 388), and therefore it follows that the standard
state-space-and-partition model’s axiom of awareness requires each subject to have a complete understanding of all other subjects’ plans for choices, i.e. perfect knowledge.
136
Dekel, Lipman, & Rustichini (1998) show that the standard state-space-and-partition model
cannot cope with the subject’s unawareness of some state. I build on this fact and develop a theory
of inefficient market (i.e. an arbitrage market theory) that forces the subjects to make limited rational
choices in the sense that the choices are made on both strict subsets of the actions available and on
strict subsets of the states that may occur. This is the first main trait that is particular to the theory
of Homo comperiens.
I also make an auxiliary conjecture that we have atomistic competition so that I can reduce
the problem that is dealt with in this thesis.
By replacing the perfect rational choice with a limited rational choice, the market description
is fundamentally changed. It is no longer possible to think of the market as a no-arbitrage market.
Rather, the market is in a non-random state of flux, where there are innumerable arbitrage opportunities. Thus, the market price and the intrinsic value are two distinct measures. It is also not possible to argue that the subject holds rational expectation and that price is randomly walking.
I create the market disequilibrium without having to resort to the conjectures about nonatomistic competition. Nor do I have to conjecture a non-rational choice process (as is done in behavioral finance or bounded rationality models in game theory).
Since the subjects have incomplete knowledge because of the strict subset conjecture, there
is an opportunity for the subjects to revise their price expectations using not only Bayesian learning.
I allow the subjects to also learn about actions and states that they previously were ignorant of. This
is what I refer to as discovery. The discovery of states that the subjects were previously ignorant of
falls outside of Bayesian learning since the prior probability for a previously ignorant state is zero,
and consequently, the posterior probability is also zero. Bayesian learning does not encapsulate the
possibility of discovery of previous actions that the subjects previously were ignorant of.
The ability to learn through discovery is the theory of Homo comperiens’ second central
trait. Endowing the subjects with the capacity to discover induces a price process, much like that
called for by Lee (2001), in which the market prices regress towards the intrinsic value.
The theory of Homo comperiens is built upon the following central definitions:
Definition 2-4: Definition of limited rationality: A subject that has a rational preference relation, i.e. a
preference relation that is complete and transitive on the subjective action set (Definition 2-3) is a limited
rational subject.
Definition 2-8: Definition of limited rationality in the uncertain choice. In addition to Definition 2-4, a
subject exhibits limited rationality when the subject has a rational preference relation on uncertain consequences that are limited because of limited knowledge of states (Definition 2-6).
137
Definition 2-9: Definition of learning as discovery. Discovery takes place when the subject that acts according to Definition 2-4 and Definition 2-8 and that faces the next choice in a sequence of choices expands his or her subjective state set and/or the subjective action set. Discovery takes place because of the
subject’s experience from previous choices: Formally, learning as discovery means that the previous subjective state and/or action sets are strict subsets to the current subjective state set and/or action sets.
With symbols, learning as discovery is defined as SKt 1 ‡ SKt , AKt 1 ‡ AKt AKt 1 ‡ AKt , or when both
situations occur and this is because discovery make certain that I At 1 ‡ I At and I St 1 ‡ I St .
Definition 2-4 and Definition 2-8 rest on separate definitions of the subjective action and
state set that are:
Definition 2-3: Definition of the subjective action set. The subjective action is defined as AK A8 4 I A .
Definition 2-7: Definition of the subjective state set. Let the subjective state set be SK S8 4 I S .
And the subjective action and state sets depend on the definitions of the ignorance sets.
Definition 2-1: Definition of ignorance of actions: Let the subject be unaware of at least one action in the
objective action set, i.e. the subject’s ignorance set is nonempty, I A Š  , and a strict subset to the objective action set, I A ‡ A8 .
Definition 2-5: Let the subject be unaware of at least one state in the objective state set, i.e., the subject’s
ignorance set is nonempty, I S Š  , and a strict subset to the objective action set, I S ‡ S8 .
The ignorance sets are also used to define limited knowledge: The limited knowledge definitions are:
Definition 2-2: Definition of limited knowledge of actions. A subject’s knowledge of alternative actions
is limited when the subject has a nonempty ignorance set according to Definition 2-1.
Definition 2-6: Definition of limited knowledge of states. A subject’s knowledge of potential states is
limited when the subject has a nonempty ignorance set of states according to Definition 2-5.
With this structure on the subjects’ choice, it is possible to explain choice as if they maximize
their subjective expected utility. That is,
Proposition 2-3: When the subject has a preference relation on the subjective consequence sets, which
are complete, transitive, continuous, state uniform, independent, and that follow the Archimedean assumption, it is possible to express the subject’s choice as if he or she makes his or her choice based on an
action’s subjective expected utility: EK 0 ¢¡U K c1, !cS ; QK 1, ! QKS ¯±° œ
s ‰SK
QKs ¸ uK cs , where cs ‰ C Ks ,
and QKs ‰ 1K .
The difference between subjective expected utility and von Neumann and Morgenstern’s expected utility resides in different state probabilities and different Bernoulli utilities. In the theory of
Homo comperiens they are referred to as subjective state probabilities and subjective Bernoulli utilities.
138
The subjective state probability differs from the objective state probability because of the limited state set; the subjective Bernoulli utilities differ from the objective Bernoulli utilities because
of erroneous specification of the supremum and the infimum consequences, an error that is due to
the limited action set. All erroneous choices can therefore be traced back to my introduction of limited knowledge as the ignorance of actions and states, which can be thought of as an unawareness
conjecture.
The price discovery process is covered by the following propositions.
Definition 2-9: Definition of learning as discovery. Discovery takes place when the subject that acts according to Definition 2-4 and Definition 2-8 and that faces the next choice in a sequence of choices expands his or her subjective state set and/or the subjective action set. Discovery takes place because of the
subject’s experience from previous choices: Formally, learning as discovery means that the previous subjective state and/or action sets are strict subsets to the current subjective state set and/or action sets.
With symbols, learning as discovery is defined as SKt 1 ‡ SKt , AKt 1 ‡ AKt , or when both situations occur and this is because discovery make certain that I At 1 ‡ I At and I St 1 ‡ I St .
Proposition 3-1: Learning through discovery (Definition 2-9) ascertains that lim AK x A8 and
t ld
lim SK x S8 since the ignorance sets decrease. This implies that the subjective price approaches the
t ld
objective price as t goes to infinity. That is lim t 1 pKt x t 1 pt .
t ld
Proposition 3-2: Suppose that the Pareto optimal equilibrium price is fixed, which is reasonable since the
objective action and state sets are assumed to be fixed and since inflation is not conjectured. Then, with
Proposition 3-1 in mind, I propose that price convergence can be described as follows: Let the subjective
price be a function of the objective price p and a fraction of the previous period’s discrepancy between
the subjective price and the objective price. That is,
K
t 1 pt
pC¸
t 2 ptK1 p
Ft
where C ‰ < 0,1
and where Ft is a white noise disturbance.
When the theory of Homo comperiens is applied onto firms, it renders propositions on what
a firm’s market price is. From the Homo comperiens propositions, I derive the following propositions on how the risk-adjusted subjective expected residual rates-of-returns behave.
Proposition 4-6: In a market that meets the conjectures of the theory of Homo comperiens (Proposition
2-4), and with unbiased accounting, there exists non-zero risk-adjusted subjective expected RROE and
RRNOA because of arbitrage opportunities. That is, &*K 0 < t 1RROEt > &K 0 <net arbitrage rate of returnt > v 0 ,
and &*K 0 < t 1RRNOAt > &K 0 <operating arbitrage rate of returnt > v 0 .
Proposition 4-5: In a subjectively certain market that meets the assumptions of Homo comperiens
(Proposition 2-4, Proposition 3-2), with unbiased accounting, the subjective expected RROE and
RRNOA regress until, in the limit, they are zero. That is, lim &K 0 < t 1RROEt >
0 , and
t ld
lim &K 0 < t 1RRNOAt >
0 .
t ld
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Proposition 4-7: In a market that meets the conjectures of the theory of Homo comperiens (Proposition
2-4, Proposition 3-2) and with unbiased accounting the limit values of risk-adjusted subjective expected
RROE and RRNOA are zero. That is: lim &*K 0 < t 1RROEt > 0 , and lim &*K 0 < t 1RRNOAt > 0 .
t ld
t ld
8.4 Summary of the hypotheses tests
I subject the theory of Homo comperiens to a large number of attempts to falsify it. Proposition 4-6
and Proposition 4-7 are exposed to the hypotheses tests. The tests are based on ex post proxies for
the risk-adjusted subjective expected residual rates-of-returns. These proxies are:
*
t 1 RROEt
*
t 1 RRNOAt
where
*
t 1 RROEt
t 1 ROEt
t 1 RNOAt
t 1 ROEtI
t 1 RNOAtI
is the ex post risk-adjusted residual return on equity and
*
t 1 RRNOAt
is
the ex post risk-adjusted residual return on net operating assets.
Proposition 4-6 proposes the existence of an arbitrage market while Proposition 4-7 proposes that subjects in the market discover previously unknown action and states such that price converges towards the no-arbitrage price.
8.4.1 Does an arbitrage market exist?
The risk-adjusted residual return on equity and the risk-adjusted residual return on net operating
assets should be, according to Proposition 4-6, non-zero for at least one firm. This notion is tested
against the conjecture of no-arbitrage, i.e. zero risk-adjusted residual return on equity and zero riskadjusted residual return on net operating assets for all firms.
The t tests reject the null hypotheses of zero risk-adjusted residual return on equity in favor
of the alternative hypothesis posed by Proposition 4-6. It finds that in 15,216 double-sided t tests of
22,200 tests the variable is significantly different from zero at the one percent significance level.
The t tests reject the null hypothesis of zero risk-adjusted residual return on net operating assets in favor of the alternative hypothesis posed by Proposition 4-6. It finds that in 15,179 doublesided t tests of 22,193 tests the variable is significantly different from zero at the one percent significance level.
The double-sided t tests apply a robust confidence interval method that uses the biweight location and scale estimates as well as an alternative robust method in which the best possible location
estimate is applied together with the biweight scale estimate. The results from the two test methods
are nearly identical.
Proposition 4-6 is also tested using goodness-of-fit tests in which the alternative hypotheses
state that there is serial dependency in the disturbances. This is posed against the null hypotheses of
no serial dependency in the disturbances. The hypotheses tests for t 2 corroborate the findings
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above and reject the null hypotheses at the 0.0 percent significance level. The hypotheses tests at
t 2 cannot reject the null hypotheses; however, it is argued that the tests’ failure to reject the null
hypotheses is due to too many bins in the study. The hypotheses tests at t 2 use 56 bins, which
is far more than what is used in other research on which accounting rates-of-returns are classified
into bins.
8.4.2 Is discovery part of human action?
Proposition 4-6 ascertains that the market has arbitrage opportunities and this allows for
Proposition 4-7. Proposition 4-7 argues that there is a price process in which prices are not independent. This dependency is a direct effect of the discovery trait as assumed by the theory of Homo
comperiens.
Proposition 4-7 is evaluated on 13 panels of risk-adjusted residual return on equity and 13
panels having risk-adjusted residual return on net operating assets. This means that there are 26 hypotheses tests that assess Proposition 4-7. In all of these hypotheses tests the null hypothesis of random walking risk-adjusted residual accounting rates-of-returns is rejected in favor of its alternative
hypothesis of regressing risk-adjusted residual accounting rates-of-returns at the 0.0 percent significance level.
The panel regression hypotheses tests reveal that the learning trait is so strong that it appears
as if a firm’s risk-adjusted residual accounting rates-of-returns diminish within (or at least almost
within) a year after discovery. This implies that the arbitrage opportunities are temporary. Transitory
arbitrage opportunities mean that it is almost impossible to attain a sustainable competitive advantage. Attaining a sustainable competitive advantage is probably more by luck than by design.
Six alternative operationalizations of the accounting rates-of-returns that act as inputs into
risk-adjusted residual accounting rates-of-returns are also considered. This means that an additional
78 hypotheses tests are evaluated at the 0.0 percent significance level to determine whether the results are sensitive to the operationalization of the risk-adjusted residual accounting rates-of-returns.
None of these 78 hypotheses tests reveal conflicting results to those of the original 26 hypotheses
tests, which implies robustness to the operationalization of accounting rates-of-returns.
The results from the hypotheses tests reported in Chapter 6 classify observations outside of
six standard deviations as outliers and remove them from the analysis. This operationalization may
adversely affect the results and an alternative operationalization of outliers is also tested, one in
which I classify all observations outside of four standard deviations as outliers. The conclusions do
not change because of this change.
Three alternative panel regression models are considered when evaluating Proposition 4-7.
These models are the pooled regression model, the random effect model, and the fixed-effect model. Three specification tests carried out on all 26 panels show that the fixed-effect model is the best
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panel regression model to be fitted on the data sets. The fixed-effect model is used to evaluate the
hypotheses based on Proposition 4-7.
Specification tests also show significant panel heteroscedasticity in all panels. This is incorporated into the panel regression model by allowing for a covariance structure known as panelcorrected standard errors (Beck & Katz 1995). The covariance structures are also corrected for firstorder serially correlated disturbances.
8.5 The external validity of the theory of Homo comperiens
In performing hypotheses tests there is the risk for Type I errors, i.e. the risk of rejecting the null
hypotheses when they are true. It is therefore necessary to assess the external validity of the theory
of Homo comperiens through predictions.
I test the theory’s external validity by testing its predictive accuracy using a fixed-size rollingwindow out-of-sample forecasting method. The theory’s predictive ability is tested against the random-walk model’s predictive accuracy over forecasts up to four years into the future.
The research design that I implement is similar to what Kothari (2001, p. 191) proposes. Kothari uses Bernard & Thomas (1990) as an example of how tests of market inefficiency should be
carried out. Bernard & Thomas specify stock-price behavior under a random-walk earnings expectation model as well as under another sophisticated earnings expectation model.
When forecast errors are summarized across a times series and where volatility differs, the
forecasters (e.g., Tashman 2000) prefer the MdRAE statistic or another similar statistic when evaluating the predictive accuracy. I use the MdRAE statistic to evaluate the theory’s external validity.
The external validity of the theory in the short run (defined here as one year) is assessed using approximately 11,187 and 11,176 predictions depending on the tested variable. The four-year
forecasts use approximately 6,704 and 6,701 predictions depending on the tested variable.
In the four-year predictions the MdRAE statistic shows that the theory of Homo comperiens
generates relative absolute prediction errors that are 19—24 percent less than the random walk
model. In the one-year predictions the theory of Homo comperiens generates relative absolute prediction errors that are 12—16 percent less than the random walk model. These results are significant
at the 0.0 percent significance level. The two- and three-year predictions exhibit similar results with a
sliding trend from the one-year level to the four-year level. All these results are significant at the 0.0
significance percent level.
This implies that the theory of Homo comperiens has significantly greater predictive accuracy than the random walk model and that I thus validate the other findings of the thesis regarding the
discovery process and the existence of arbitrage-based residual rates-of-returns.
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8.6 Directions for future research
The hypotheses tests and the tests of the external validity of the theory of Homo comperiens confirm my theory. The results are even robust with regard to alternative specifications of operationalizations and test methods. For the most part, the tests are significant at the 0.0 percent level.
However, it is possible to commit a Type II error, i.e. fail to reject an incorrect hypothesis. It
may be that one or more of the choices I have made are incorrect.
For instance, the theory of Homo comperiens is still young and thus lacks an asset-pricing
model. This makes it necessary to use an empirical proxy to remove the risk effect from the variables. I remove both the risk effect and the effect of conservatism by using the industry accounting
rate-of-return. If that method is incorrect, it may adversely affect the reliability of the results in this
thesis.
I believe that it is a significant improvement if an asset-pricing model can be developed using
the theory of Homo comperiens.
Another way to improve the theory of Homo comperiens is to adapt it to include Savage’s
([1954] 1972) subjective utility theory. Another way to improve the theory of Homo comperiens is
to allow for imperfect recall, but how this can be done is still an open question.
I also believe that if the theory of Homo comperiens can withstand repeated attempts of falsification it can be attributed a more important status. Such tests should follow at least four avenues.
(i) Testable hypotheses of market prices should be posed and tested against random walk propositions. Such a hypothesis can, e.g., try to connect the firm’s market price (assuming no growth) to
current industry profitability. This could then be posed against the null hypothesis of the market
price being connected to the firm’s own current profitability.
(ii) Better panel regression models that, e.g., consider the Nickell bias.
(iii) Exploring other hypotheses based on accounting data. Obvious improvements are based on the
hypotheses in section N.1. In these tests the alternative hypotheses state that corr Ft 1, Ft v 0 , but
stronger tests are, e.g., where the alternative hypotheses are corr Ft 1, Ft 0 . Indeed, the present
thesis finds support for corr Ft 1, Ft 0.5 , and this can also be tested.
(iv) Using other statistical methods. Other tests than the goodness-of-fit-test that directly targets the
implied correlation is also an interesting avenue to pursue.
All these improvements are outside the scope of this thesis but will be evaluated in the near
future.
My research also questions the use of the pooled panel regression model in favor of the
fixed-effect panel regression model. This, in conjunction with the fact that the within-sample predictions are used for validation, calls for replication studies of Dechow et al. (1999), Gregory, et al.
(2005), McCrae & Nilsson (2001) using their databases that perform a specification test to single out
the relevant panel regression model and that use out-of-sample predictions. I believe that such research will show results that are substantially different than what we now take for granted.
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8.7 The implications for the role of accounting in society
It is assumed that an efficient market ascertains that there is no role for accounting data in the society since the market price always equals the intrinsic value (e.g., Beaver 2002, p. 458; Lundholm 1995,
p. 761). One may then wonder why we observe a demand for accounting data in our society. To
answer this question we need to turn to agency theory and argue that managers have private information that owners do not have. However, I take another approach in this thesis where I question
the efficient market hypothesis altogether.
If the theory of Homo comperiens can function as a first approximation of how people
make choices, we have an inefficient market. Based on to this future research can introduce, e.g.,
asymmetric information.
With the existence of an inefficient market, there exists an inherent demand for accounting
data since it is fundamental in distributing information about a firm’s profitability, which is a necessary condition for learning by discovery. That is, accounting data are needed to facilitate the discovery process that determines that the market prices regress to the intrinsic values. With no accounting
data available, we can expect that this learning process is hampered and will work at a slower speed.
Thus, I expect that such a situation will induce considerable societal costs. A practical example of
what might happen is when we consider the Kreuger collapse that probably would not have happened if we would have had consolidated accounting back then.
Another aspect of accounting data pertains to IFRS’ current introduction of fair value valuation at the expense of historical cost accounting. If the market is inefficient, the fair values (i.e. the
market prices) will be different from the intrinsic values. This means that the market exhibits price
bubbles that inflate and explode. Indeed, the theory of Homo comperiens suggests that there will be
almost an innumerable amount of such bubbles (both positive and negative). The theory also suggests that those bubbles disappear as people discover and act on them. If the balance sheet valuation
is dominated by fair value valuation, we can expect to see large and fast changes in the valuation of
assets and liabilities. I therefore am concerned that the introduction of fair value valuation will increase a firm’s bankruptcy risk.
Related to this fact is the important role that accounting data plays. Central for accounting
data is its forecast relevance. With conservative accounting, we (normally) only allow slow changes
in the valuation of the assets and liabilities. Slow changes are probably a good thing if we have price
bubbles that inflate and explode since the conservatism allows the accounting data to exist relatively
unharmed of market price bubblesand therefore I believe that conservative accounting has greater
forecast relevance than fair value accounting. Therefore, since an inefficient market that meets the
assumptions of the theory of Homo comperiens demands accounting data that has forecast relevance, I am concerned with the current trend of introducing fair value valuation in accounting.
144
Another effect of my findings pertains to how we ought to account for purchased goodwill.
With the introduction of IFRS 3, we have completely abandoned the amortization of goodwill in
favor of impairment tests. This signals the end of a long process in which purchased goodwill in
Sweden was amortized within five years, which then increased to 10 years and finally up to 20 years.
My findings show that this is a dangerous trend. If my parameter estimations are correct, we should
immediately expense purchased goodwill.
However, if we also believe that industries can exhibit residual income, we might use Meyers’
(1999) results to infer the economic life of purchased goodwill. Interpreting Meyers’ results, purchased goodwill implies that we can expect its economic life to be three to four years. Thus, Meyer’s
results indicate that goodwill should, on average, be amortized within three to four years.
Alternatively, if we choose to go by the results from Dechow, Hutton, & Sloan (1999),
McCrae & Nilsson (2001), Callen & Morel (2001), Gregory, Saleh, & Tucker (2005), and Giner &
Iñiguez (2006), the purchased goodwill should be depreciated within five to seven years.
Additionally, all the cited research, including my own, indicates that the value of purchased
decreases degressively and therefore purchased goodwill should be amortized faster in the beginning
than in the end (at least 50 percent should be amortized within the first year). This is very different
from today’s accounting rule for purchased goodwill.
Returning to accounting research as a subset of the society, I wish to point to the accounting
anomaly that is known as post-earnings announcement drift. Research on post-earnings announcement drift has difficulty explaining why such drift occurs.
The theory of Homo comperiens may be able to provide a clue for the post-earnings announcement drift research since the theory suggests that people gradually discover. Gradual discovery is not consistent with random walk, but it is in accordance with a drift in the prices in the direction of discovery towards the intrinsic value. Using accounting data, my findings indicate that the
process is finished within a year after discovery, but the post-earnings announcement literature (Kothari 2001, p. 193-196) suggests that the drift continues up to a year after the event. It may be that
the drift pattern in the post-earnings announcement drift research can be explained by the proposed
theory of limited rational choice.
UPPSALA, July 10, 2007.
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APPENDIX A—PERFECT RATIONALITY AND THE INTRINSIC
VALUE OF THE FIRM IN AN OBJECTIVE CERTAIN CHOICE
General equilibrium models of the firm’s intrinsic value
A.1 Introduction
There exist many different models for valuing firms. Every microeconomic-based model is based on
restrictive assumptions. This appendix derives two accounting-based microeconomic valuation
models that allow for non-constant rates-of-returns. A discussion on the role and association of
economy and accounting rates-of-returns is also part of this appendix.
This appendix’s purpose is to stress the connection between the axioms of the perfect rational choice and the firm’s intrinsic value, as well as to establish a common language for this thesis.
The focus of the analysis is on an individual. The assumption here is that the preferences are homogenous and therefore possible to consider a representative individual for the whole economy. This is
not restrictive in this appendix since I assume that theory of the perfect rational choice is applicable
and thus all individuals are omniscient.
His or her objective opportunity set (and its components the objective budget set and the
objective production set, and the objective prices) are all objective as opposed to where they are the
subjective counterparts (as in Appendix B). The difference between objective and subjective is elaborated in Chapter 2 and Chapter 3 and where focus is on limited knowledge.
A reader well versed in economics should have no problem following the discussion in sections A.2—A.7 and can read them in a cursory manner to become familiar with the symbol language
and definitions that this thesis applies.
Subsection A.8.1can be skipped if the reader is familiar with how net intrinsic values rules
and the dividend valuation models are descendants of optimization problems.
Subsection A.8.3 presents the accounting-based valuation models used in this thesis.
The accounting-based valuation models that use certain non-constant rates-of-returns have
not been previously published. Thus, they present a new development in the field of accountingbased firm valuation models. Ohlson (1995) and Feltham & Ohlson (1995) use certain constant
rates-of-returns to arrive at accounting-based valuation models while Feltham & Ohlson (1999) use
stochastic rates-of-returns to arrive at accounting-based valuation models. My models provide a
middle ground between these two extremes.
The first accounting-based valuation models (see subsection A.8.3.1) presents the intrinsic
valuate of the firm as a function of comprehensive net income, and the second model (subsection
A.8.3.2) presents the intrinsic valuate of the firm as a function of comprehensive operating income.
147
The latter model uses the value additivity idea that Modigliani & Miller (1958) propose. Having two
valuation models serves the purpose of allowing the theory of present thesis to develop propositions
on firms with and without financial effects.
Before closing the appendix, subsection A.8.4 is presented, which derives a theoretically consistent return on equity and a theoretically consistent return on net operating assets. These are then
operationalized in the chapters and appendices in this thesis.
A.2 A point of departure
The present analysis is based on an individual’s choice among desired objects, which in this analysis
are portfolios of current and future goods for consumption. A portfolio of consumption should be
thought of as the set of goods that is consumed at a particular point in time. Current consumption
means the portfolio of all goods available for consumption today. For example, an individual may at
present time consume a certain number of apples and oranges. It is these quantities of apples and
oranges that constitute his or her current portfolio of consumption.
The subject has preferences that order the available consumption alternatives. All the available alternatives form his or her objective opportunity set, X \10 q !q \ A0 q \11 q !q \ A1 , where
\ A0 is the objective current consumption set of good A , and \ A1 is good A ’s objective future con-
sumption set.
The set is also abbreviated X \ L0 q \ L1 , which implies that his or her objective opportunity
set can be seen as two portfolios: One portfolio of current goods for consumption and another
portfolio for the consumption of future goods. To avoid cumbersome notation the time subscripts
are sometimes deleted when necessary. Note that the objective set is not restricted a priori in any
way except that it must be in the real commodity set since there are no limits to his or her knowledge. Theoretically, the consumption set is therefore unlimited is at this point. Restrictions follow as
the analysis proceeds but limiting the consumption set with limited knowledge is done in Appendix
B.
His or her behavior is set forth in a certain environment, where he or she chooses among
combinations of quantities of current and future consumption. Current consumption is certain.
A.3 Choice of consumption over time in objective certainty
This thesis’ basic choice-theoretic structure is introduced in this section and the structure is referred
to as the perfect rational choice 20. It involves choosing one action among a set of alternative actions.
20 The Latin form the perfect rational choice has been used for a very long time in the meaning of a rational selfinterested individual. It has been traced back to at least Pareto (1906) by Persky (1995).
148
The choice of an action in this appendix is made knowing the exact consequence of each
permissible action. That is, the state set has only one element, or, if it has more than one element,
the consequences are constant between each state.
It is necessary to build a model that guarantees that there is only one solution to the choice
problem facing the subject since he or she can only choose one action among several. The appendix
uses mathematical optimization to guarantee the solution’s uniqueness.
The choice problem has tree bricks to build on: the domain, the function, and the codomain. With use of the function, the domain is mapped onto the co-domain. The domain consists
of choice variables, which are the portfolios of current and future consumption. This is called the
objective opportunity set, which is in the spirit of Fisher (1930).
The function is a real function that specifies the relationship that maps the objective opportunity set into the co-domain, U : X l \ . The co-domain, which lies on the real line, is the set of
possible utilities. This can be amended and the utility can, e.g., be made to only cover a portion of
the real line such as <0,1> 21. This means that the function is the objective utility function and since
the analysis in the appendix focuses on an equilibrium-setting meeting the assumptions of the perfect rational choice, it is the objective utility function. Rather, Appendix B makes use of the subjective objective utility function.
The objective opportunity set changes its properties depending on the situation. There is always the overarching objective opportunity set, which is called the objective consumption set. This
latter set covers the real commodity set. However, there is also an objective opportunity set when
pure exchange is considered and yet another set when production is available. More will be said
about this as the analysis develops.
It is not enough to only establish the components of the choice problem to guarantee an objective optimal solution. The components must be endowed with specific properties.
To guarantee a unique solution it is necessary for the objective opportunity set to be strictly
convex, or the objective function must be strictly quasi-concave, or both (e.g., Gravelle & Rees
1998). The objective opportunity set is convex in this analysis and it is thus necessary to endow the
objective function with properties that make certain that it is strictly quasi-concave.
The choice variables are defined at the beginning of the analysis. Any individual must choose
between different objective portfolios of quantities of a finite number of current goods A ‰ L ,
c0 c10 , !, cA 0 ˆ L \ L , and objective portfolios of quantities of a finite number of future
21
A closed interval uses the following notation <¸> , whereas an open interval is designated ¸
.
149
c10 c11 ¬­
ž
goods, c1 c11, !, cA1 ˆ L \ L . The focus is on the objective set, C c0 , c1 žžž # # ­­­­ 22, that
žc c ­
žŸ
A0
­
A1 ®
the subject chooses. The objective consumption set must be attainable, i.e. within his or her objective opportunity set, C ‰ X .
These relations are the basic building blocks from which the analysis proceeds. The next step
is to create the objective function. It is necessary to establish a preference order among the various
sets that the subject chooses among to create the objective function.
A.4 His or her preference relation and the objective utility function in objective
certainty
A relation, ; , on the objective opportunity set is defined as a preference relation if it is asymmetric,
º C`C
(Kreps 1988). It is
ˆºC
ˆ ` C , and negatively transitive, i.e. C ` C
ˆ and C
ˆ `C
i.e. C ; C
assumed that an individual possess such a strict preference relationship on the objective opportunity
set, but for the purpose of this paper a weak preference relation is also defined.
A weak preference relationship \ on the objective opportunity set is a relation in which the
ˆ `CºC\C
ˆ . When C ` C
ˆ , and C
ˆ `CºCC
ˆ , which is
strict relationship is absent, i.e. C
called indifference (Kreps 1988). This means that the subject can always say if he or she prefers one
set to the other, or if he or she is indifferent. To always be able to choose between two alternatives
is a prerequisite for a unique solution to the choice problem.
ˆ , and Ĉ \ C for all permissible conSince his or her preference satisfies C ‰ X , C \ C
sumption pairs, it is complete: The subject has an understanding of all the choice opportunities
available, makes pair-wise comparisons of them all, and expresses what the subject prefers over the
other, or if the subject is indifferent between them.
Not only is his or her preference relation complete but it is also impossible to face the subject with any sequence of pair-wise choices and find inconsistent behavior. That is, it is not possible
and also C [ C
. Faced with this pair-wise comparison,
ˆ , Ĉ \ C
to find a behavior such as C \ C
. The ability to act in this manner is known as the transitivity assumption
the subject exhibits C \ C
(Kreps 1988).
22 This text makes use of both vector and matrix algebra. The reader should bear in mind that a vector is equivalent to a
column matrix. Standard matrix notation is used in the text with bold uppercase letters signifying a matrix, e.g., A .
There is an exception for column matrices. Column matrices are depicted using bold lowercase letters. Thus, we have
the following relationship:
c10 ­¬
ž ­
c0 c10, !, cA 0 žžž # ­­­ . The inner product of two vectors, S ¸ c , can also be written in matrix notation, S5 ¸ c , where
žžŸcA 0 ­­®
ST denotes the transpose of column matrix S .
150
Facing a choice between any two sets of consumption, the subject will always choose the set
that holds more consumption. Consider two potential object sets of consumption, C = c0 , c1 ,
ˆ = ˆc , ˆc , where any or both of the following two relationships hold c \ ˆc , c \ ˆc 23, where
C
0
0
1
1
0 1
any or both of c0 v ˆc0 , and c1 v ˆc1 hold, the subject will always choose objective consumption set
ˆ . This is the strongly monotone assumption (Mas-Colell et al. 1995).
C before Ĉ , C ; C
The assumption of strong monotonicity is also known as the non-satiation assumption (e.g.,
Fama & Miller 1972); it implies that the objective portfolios of current and future consumption are
normal goods: As wealth increases so will consumption. It also ensures that that movement between
sets in the indifference set can only be done by substituting current for future consumption, and
vice-versa. This amounts to a negatively sloped objective indifference curve between objective current and future consumption. The assumption also makes certain that the indifference set can never
be wider than a single point, a set of points, or a curve. If it would be wider (e.g., a band), it would
be possible to find the indifference point also in the preferred and the inferior set, which violates the
transitivity assumption (Gravelle & Rees 1998).
With this preference relation and a fixed objective consumption set CD , it is possible to identify three consumption subsets to the objective opportunity set. The first set is the preferred set,
which contains all available objective consumption sets that are preferred to CD :
X P \C ‰ X : C \ CD ^ ‡ X
[EQ A-1]
The inferior set is the complement set to the preferred set:
‰ X : CD \ C
^ ‡ X
X INF ‰X P \C
[EQ A-2]
It follows that the indifference set equals the intersection between the preferred and the inferior set:
\
^
ˆ ‰X :C
ˆ CD ‡ X
X IND X P ‚ X INF C
[EQ A-3]
With the assumptions of completeness, transitivity, and strong monotonicity, it is possible to
define the indifference set as the intersection between the preferred and the inferior set. This ensures that that the preferences will be continuous (Mas-Colell et al. 1995).
Continuity implies that the preference relation can be represented by a continuous mathematical function that here is called the objective utility function. This means that U : X l \ is established. Continuity also implies that consumption can be divided into however small bits as necessary, i.e. the goods in the economy must be infinitely divisible.
23
The relation c0 \ ˆc0 implies that at least one of the elements is strictly preferred, i.e. cA 0 ; cˆA 0 .
151
With the objective utility function available, it is possible rephrase the preferred set to be the
set that contains all sets that yield higher utility than set CD :
\
^
X P C ‰ X : U C
\ U CD ‡ X
[EQ A-4]
Similarly, the inferior set contains all sets with less utility than CD :
\
^
‰ X : U CD \ U C
‡ X
X INF ‰X P C
[EQ A-5]
The indifference set is then the intersection between the preferred and the not-preferred set.
An equivalent expression would be to state that it contains all sets that yield the same level of objective utility as the fixed set CD . It is known as the objective indifference curve:
\
^
ˆ ‰ X :U C
ˆ U CD ‡ X
X IND X P ‚ X INF C
[EQ A-6]
ˆ U CD can be thought of as all combinations of objective current
The constraint U C
and future consumption that yields an identical level of objective utility. This means that the conˆ c , are the objective indifference curves with which c are
tours of the objective function, U C
various constant levels of utilities. Achieving higher levels of objective utility is equivalent to climb
to higher levels of contour lines.
Despite continuity, it may still not be possible to differentiate the function, which is necessary for the solution of the choice problem. It is therefore assumed that the objective utility function
is differentiable to any necessary degree.
The preference relation is also assumed to exhibit strict convexity. Form an objective consumption set, C , to be a linear combination of any two objective consumption sets that the subject
ˆ , where B ‰ < 0,1> . That is, C B ¸ C 1 B
¸ C
ˆ . The new objective
is indifferent between, C C
ˆ . Strict convexity
consumption set is then always preferred to any of the original two: C ; C C
rules out the possibility that the new combined objective consumption set could be indifferent to
the initial two sets (Mas-Colell et al. 1995).
The solution could yield a set of objective consumption sets among which the consumer
cannot choose if only a convexity assumption is invoked. This is not in line with the intention of
having a unique solution. It is therefore necessary to impose strict convexity, which leads to a solution in which the consumer can only choose one set. Strict convexity implies that the objective utility function will be strictly quasi-concave (Gravelle & Rees 1998).
A convex objective indifference curve is the same as diminishing an objective marginal rate
of substitution between current and future consumption (Mas-Colell et al. 1995). Convexity guarantees that the subject will never give up all current consumption for future consumption, or the other
way around. It is ultimately a matter of survival: the perfect rational choice demands increasing
152
compensation for each unit of consumption forfeited until, in the limit, the subject demands an infinite compensation for sacrificing consumption. It also implies that the subject has a basic inclination
for diversification. The subject always prefers a combination of the two objective consumption sets
rather than only one of those (Mas-Colell et al. 1995).
The strongly monotone assumption translates directly into the objective utility function in
the sense that it will also be strongly monotone. The increasing function makes it possible to analyze
the choice problem as if the subject is a utility maximizer, i.e. the subjects appear to be maximizing
the value of their objective utility function over their objective opportunity set.
A.5 His or her objective opportunity set in objective certainty
It was possible from a behavioral perspective to divide the objective opportunity set into three subsets: the preferred, the indifferent, and the inferior set. This operation has nothing to do with what
elements the objective opportunity set contain. The choice is constrained to be among the objective
consumption sets available within the objective opportunity set.
It is the objective opportunity set that is in focus in this subsection. It can be divided into
two subsets, namely the objective opportunity set under pure exchange and the objective opportunity set under pure production. The objective opportunity set is at this point not limited except to the
commodity set, i.e. X \L0 q \ L1 .
Convexity of the objective opportunity set has already been mentioned as a necessary requirement to achieve a mathematically unique solution to the choice problem. This is not the only
property an opportunity must possess for it to be useful. The objective opportunity set must have
four properties (Gravelle & Rees 1992). It must be:
(i) Non-empty. I.e. it must contain at least one objective consumption set: otherwise, there would be
nothing to optimize and the problem would be trivial.
(ii) Closed. All points on the set’s boundary are elements of the set.
(iii) Bounded. The objective opportunity set must be limited.
(iv) Convex.
An individual must consume at least some good (e.g., oxygen), both today and tomorrow or
the subject will die. It could be argued that an individual can have non-positive consumption in the
presence of a government that provides social security since the government would step in and help
the subject if necessary. This problem is ignored and it is assumed that the subject must at least consume non-negative amounts of goods both in the present and in the future.
Setting the constraint on consumption to be non-negative permits the boundary elements of
current and future consumption to be part of the solution. This is one step in the direction of assuring a closed objective opportunity set. The objective opportunity set can now be expressed as
X \ L q \ L \C ‰ \ L q \ L : c0 p 0, c1 p 0^ ‡ X .
153
The objective opportunity set is still open since the subject can and will consume infinite
amounts of consumption. This is due to the non-satiation assumption. The objective opportunity set
must be closed and the closure must be bounded.
The closure is achieved with the introduction of further constraints on his or her choice. The
final closure looks different depending on whether the subject is only limited by exchange opportunities or whether the subject is also limited by productive opportunities. The two closures are called
the opportunity set in a pure exchange economy and the opportunity set in a pure production economy. These are considered next.
A.5.1 The objective opportunity set in a pure exchange economy
In this section the objective opportunity set for the subject in a pure exchange economy is consi-
dered. The pure exchange economy has a spot economy and a futures economy. In the spot economy all goods in the commodity set are traded for immediate consumption. Claims to all future consumption commodities, available in the future commodity set, are traded in the futures economy,
which is open at present. The spot economy exists both in the present and in the future, which
means that the future spot economy opens when the future becomes the present. The claims from
the previous futures economy are cleared when the future spot economy opens.
There are two basic types of objective price available in the economy: the objective price paid
today for commodities that are consumed today, i.e. the objective spot price, and the objective price
paid today for goods that are consumed tomorrow, i.e. the objective futures price. The objective
price vector for current consumption is 0 p0 0 p10 , !, 0 pA 0 and the objective current price vector
for future consumption is 0 p1 0 p11, !, 0 pA1 . Analogous to the objective current spot price vector is the objective future price vector 1 p1 1 p11, !, 1 pA1 . All objective prices are assumed to be
on the real line, strictly positive, and finite, i.e. 0 0 pA 0 , 0 pA1 d ‡ \ .
The objective price 0 pA 0 is the objective price paid today for consumption of commodity A
delivered today. It is the objective spot price for a particular good. Equivalently is the objective price
0 p A1
, the objective price paid today for commodity A delivered in the future. That is, it is an objec-
tive futures price. The first good is set to be the numerarie in this analysis and its objective spot
prices are defined to be one, i.e. 0 p10 1 , and 1 p11 1 .
It is necessary to make certain that the subject can consume at least one objective consumption set to avoid a trivial solution to the choice problem. In other case, the objective opportunity set
would be empty. A non-empty objective opportunity set is achieved by endowing the subject with
strictly positive wealth at the same time as the objective prices are finite and the goods are infinitely
dividable.
154
Wealth is defined as the quantities of commodities that the subject already has when entering
the choice situation. Some of his or her objective wealth exists today and some is allocated to the
future. That is, the subject has an objective current wealth vector X0 X10 , !, XA 0 and an objective future wealth vector X1 X11, !, XA1 The subject is limited to consume less than what his or her wealth is. His or her constraint is
today 0 pA 0 ¸ cA 0 b 0 pA 0 ¸ X A 0 , A ‰ L . The subject can decrease his or her current consumption by
purchasing a claim for s1 units of an asset to be delivered in the future. When the subject buys
s1 units he or she saves. As the future spot economy is opened, the claims are cleared. At the same
time as the subject buys a claim for future consumption, someone else is selling the claim for the
asset and that person is borrowing. An individual saves when s1 0 and borrows when s1 0 .
The restrictions on consumption today and tomorrow follow these definitions:
0 p0
¸ c0 b 0 S0 ¸ X 0 0 p1 ¸ s1
[EQ A-7]
¸ c1 b 1 p1 ¸ X1 s1 [EQ A-8]
1 p1
It is possible to substitute [EQ A-8] into [EQ A-7]. The objective budget restriction on today’s consumption then becomes:
0 p0
¸ c0 0 p1 ¸ c1 b 0 p0 ¸ X 0 0 p1 ¸ X1
[EQ A-9]
His or her non-empty, closed, bounded, and convex objective opportunity set can be expressed given these assumptions. It is his or her objective budget set:
B \C ‰ X : 0 p0 ¸ c0 0 p1 ¸ c1 b 0 p0 ¸ X 0 0 p1 ¸ X1 ^ ˆ X [EQ A-10]
Together with a strictly quasi-concave objective utility function, the objective budget set
guarantees that there is a unique and non-trivial solution to his or her choice problem. The next step
is the introduction of production and the consideration of the objective opportunity set available
through the transactions with nature.
A.5.2 The objective opportunity set in a pure production economy
Production mitigates the problem when no exchange possibilities are available that enables the
transfer of current consumption into the future. It is assumed that production takes time: It makes
use of current goods in the production of future goods. Production shifts current goods into future
goods, a process that is irreversible.
In the pure exchange problem his or her consumption was restricted to be less than or equal
to his or her objective wealth while at the same time non-negative. It is possible for his or her to
increase his or her objective wealth by investing in production.
The objective opportunity set in a production economy must also be non-empty, closed,
bounded, and convex to guarantee the existence of a unique solution to the consumer’s choice prob155
lem (Gravelle & Rees 1998). The consumer once again faces the real commodity set \ L0 q \ L1 . In
the pure exchange situation the objective opportunity set was restricted to be a subset of the real
commodity set that was bounded from below with the assumption of consumption being nonnegative and from above with the wealth restriction. When only production is available, the objective opportunity set is called the objective production set and is denoted , which is a mnemonic
for dividends.
The objective production set consists of all attainable objective production sets. An objective
production set is a combination of the objective vectors of goods used in production. If a vector is
negative, it is used as an input whereas a positive vector indicates output.
The objective production set is denoted D d 0 , d1 and the objective current production
vector is denoted d 0 d10 , !, d A 0 \d A 0 ‰ \ L : d A 0 b 0^ . Being negative, it signifies that the current goods are used as input into the production. The objective future production vector is
d1 d11, !, d A1 \d A1 ‰ \ L : d A1 p 0^ . Since the objective future production vector is positive,
the goods are outputs. In summary, this means that the objective production set can be expressed as
\D ‰ \ L q \ L : d 0 b 0, d1 p 0^ ‡ \ L0 q \ L1 .
The firm uses a transformation technology to shift current goods into future goods, which
can be expressed as a function: g : \ L l \ L . The objective production function can also be expressed as g d1, d 0 b  , where it is understood that the input vector is negative.
Let da0 d0 4 \d10D ^ . For any fixed level of the current numerarie, d10D , we have the objective

¬

¬
transformation function g žžd1, da0 d10D ­­ b  . If g žžd1, da0 d10D ­­  . This means that the firm could
Ÿ
®
Ÿ
®
produce more output without adding more input and that it is output inefficient. With

¬
D ­
g žžd1, da0 d10
 , it is not possible to produce more with the given input and the firm is output
Ÿ
®­

¬
efficient. Every objective production set that satisfies g žžd1, da0 d10D ­­  lies on the objective transŸ
®
formation frontier. When the objective transformation function has been defined for a firm, it is
possible to describe the objective production set as:
£
²

¦
D ¬
­­ b ¦
¤D ‰ \ L q \ : g žžd1, da0 d10
»
Ÿ
®
¦
¦
¦
¦
¥
¼
[EQ A-11]
where, d0 \d A 0 ‰ \ L : d A 0 b 0^ , da0 d0 4 \d10D ^ , and d1 \d A 0 ‰ \ L : d A 0 p 0^
The defined objective production set implies that the firm could keep inserting current goods
and obtain ever more future goods. This possibility must be restricted with the assumption that the
156
objective production set exhibits strict convexity. Strict convexity implies that if an objective production set D is formed as a linear combination of two output efficient sets D and D̂ , i.e.
ˆ , where C < 0,1> , the new objective production set will always be output
D C ¸ D 1 C ¸ D
inefficient and hence not be on the objective transformation frontier (Mas-Colell et al. 1995). An
objective transformation frontier that exhibits decreasing returns to scale corresponds to the assumption of strict convexity (Mas-Colell et al. 1995). This is the same as saying that the objective
marginal rate of transformation between current and future goods decreases.
With the assumptions above the objective production set is closed. It is bounded in so far
that it is possible to produce on to the objective transformation frontier.
It is now possible to study his or her choice since the objective function, the objective opportunity set in a pure exchange environment, and the objective opportunity set in a pure production environment have been defined. His or her choice follows next.
A.6 His or her optimization problems in objective certainty
The key building blocks are in place that guarantee the uniqueness to his or her choice-problem. The
subject acts as if the subject maximizes his or her strictly quasi-concave objective utility function
over the available objective opportunities. The available objective opportunities are constrained by
non-negative consumption, the exchange opportunities, and by the production opportunities. Corner solution where the subject would consume zero amounts of current or future consumptions is
unlikely. The non-negativity constraints are ignored and the focus is on interior solutions to the optimization problem.
Optimization is first studied in a pure exchange situation. This is followed by the situation
where the subject faces both exchange and productive opportunities.
A.6.1 Optimization in a pure exchange economy
It has been derived that the subject behaves as if he or she maximizes the objective function subject
to a constraint. The objective function is called the objective utility function and the compact and
convex set B \C ‰ % : 0 p0 ¸ c0 0 p1 ¸ c1 b 0 p0 ¸ X 0 0 p1 ¸ X1 ^ ˆ X is the constraint in a pure
exchange economy.
Since the subject is non-satiated, the subject always consumes as much as possible. This
means that the subject never consumes less than what his or her wealth permits his or her, i.e. the
subject never accepts 0 p0 ¸ c0 0 p1 ¸ c1 b 0 p0 ¸ X 0 0 p1 ¸ X1 . The weak inequality in the objective
budget constraint is therefore replaced with equality 0 p0 ¸ c0 0 p1 ¸ c1 0 p0 ¸ X 0 0 p1 ¸ X1 . The
objective budget set then becomes the objective budget hyperplane:
B a \C ‰ X : 0 p0 ¸ c0 0 p1 ¸ c1 0 p0 ¸ X 0 0 p1 ¸ X1 ^ ˆ B
[EQ A-12]
157
The objective budget hyperplane implies that the subjects choose their his or her consumption pattern so that the intrinsic value of his or hertheir consumption is equal to their intrinsic value
of wealth.
The exact choice of set depends on his or her preferences. The subject chooses the set that
gives most objective utility, i.e. the set that lies on the highest possible objective indifference curve.
The highest attainable objective indifference curve is the objective indifference curve X IND tangent
to his or her objective budget hyperplane B a , and his or herhis or her optimal objective consumption set is C* B a ‚V´X IND .
There can only be one unique optimal objective consumption set since B a is compact and
convex and since X IND is strictly convex. The optimal objective consumption set is found solving
the problem:
max U C
subject to
[EQ A-13]
c
0 p0
¸ c0 0 p1 ¸ c1 0 p0 ¸ X 0 0 p1 ¸ X1 0
Lagrange’s method is used to solve the problem and Lagrange’s equation based on the objective function. Its constraint is:
max $ U C
M ¸ < 0 p0 ¸ c0 0 p1 ¸ c1 0 p0 ¸ X 0 0 p1 ¸ X1 >
[EQ A-14]
c,M
The partial derivative of Lagrange’s equation with respect to current consumption is:
‹$ c0 ‹U c0 M ¸ 0 p0 0 ,
[EQ A-15]
 s$
 sU C
sU C
¬­
s$ ¬­
­­ , and where ‹U c0 žž
­.
, ",
, ",
­
žŸ sc10
ž
scA 0 ®
scA 0 ®­­
Ÿ sc10
where ‹$ c0 žžž
For future consumption the partial derivative is:
‹$ c1 ‹U c1 M ¸ 0 p1 0 ,
[EQ A-16]
 s$
 sU C
sU C
¬­
s$ ­¬
­ , and where ‹U c0 žž
­.
, ",
, ",
žŸ sc11
žŸ sc11
scA1 ­­®
scA1 ®­­
where ‹$ c1 žžž
The study of the partial derivative with respect to the numerarie good, whose objective spot
price is defined to be 1, in equation [EQ A-15] yields the solution for Lagrange’s multiplier:
sU C
sL
M ¸ 0 S10 M
sc10
sc10
[EQ A-17]
Dividing equation [EQ A-15] with equation [EQ A-16] gives:
0 p1
0 p0
‹U c1 ‹U c0 [EQ A-18]
The partial derivative with respect to the numerarie in the future gives the solution for the
objective futures price of the numerarie good:
158
sU C
sc11
0 p11 sU C
sc10
[EQ A-19]
Equation [EQ A-19] says that the objective price paid today for a claim to a unit of the numerarie good to be delivered tomorrow equals the objective marginal rate of substitution between
the numerarie tomorrow and the numerarie at present. That is, it is the objective marginal rate of
substitution between saving and consuming.
It is also possible to study objective spot prices between different commodities in the same
period. In the case of [EQ A-19] the relative objective prices are between the goods equal to the
objective marginal rate of substitution between the commodities:
sU C
sU C
S
s
c
S
sc A 1
0 A0
A0
, 1 A1 s
C
s
U
U
C
S
S
0 m0
1 m1
scm 0
scm 1
[EQ A-20]
The partial derivative of Lagrange’s equation with respect to Lagrange’s multiplier gives the
constraint that must be satisfied.
‹$ M 0 p0 ¸ c0 0 p1 ¸ c1 0 p0 ¸ X 0 0 p1 ¸ X1 0
[EQ A-21]
 s$ ¬­
­.
Ÿ sM ®­
where ‹$ M žžž
The solution must satisfy the constraint in equation [EQ A-21] and the optimal consumption
points then become:

¬
p
p
c*0 žžX 0 0 1 ¸ X1 ­­­ 0 1 ¸ c1
­
žŸ
p
p
® 0 0
0 0
[EQ A-22]

¬
p
p
c1* žžX0 ¸ 0 0 X1 ­­­ 0 0 ¸ c*0
­
žŸ
p
® 0 p1
0 1
[EQ A-23]
Due to equation [EQ A-18], it is possible to reformulate the optimal consumption points to
be expressed as functions of the marginal rates of substitution between future and current consumption:

‹U c1 ­¬ ‹U c1 *
c*0 žžžX0 ¸ X1 ­­ ¸c
­® ‹U c0 1
‹U c0 Ÿž
[EQ A-24]

‹U c0 ­¬ ‹U c0 *
c1* žžžX 0 ¸
X1 ­­ ¸c
­® ‹U c1 0
žŸ
‹U c1 [EQ A-25]
From above ([EQ A-18] and [EQ A-22] to [EQ A-25]), it is possible to conclude that the
subject who is a utility maximizer, given an objective budget constraint, chooses the optimal objec-
159
tive consumption set. And the optimal objective consumption set is at the tangency point where the
strictly convex objective indifference curve meets the convex objective budget restriction.
At the tangency point is his or her objective marginal rate of substitution between a future
and a current good equal to the current intrinsic value for a unit of the numerarie, adjusted for the
relative objective price of the focal good between the future and the present.
A.6.2 Optimization in an exchange and production economy
The subject is not only limited by his or her economy exchange opportunities but also limited by the
productive opportunities. This amounts to a joint optimization problem, where the subject must
choose an optimal consumption level and at the same time choose an optimal investment level.
In the pure exchange situation the subject was restricted to consume less than his or her exogenous given objective wealth. The exogenous objective wealth is no longer an absolute restriction
when production is available. With production available, his or her wealth can change by engaging in
exchange with nature.
The subject is assumed to buy shares equal to a portion, Rij ,
œ R
j
i i
1 , of the objective
future output from the firm j ‰ J . Replacing X0 with X0 R ¸ d 0 and X1 with X1 R ¸ d1 in the
objective budget restriction [EQ A-9] yields a new objective budget restriction:
0 p0
¸ c0 0 p1 ¸ c1 b 0 p0 ¸ X0 R ¸ d 0 0 p1 ¸ X1 R ¸ d1 [EQ A-26]
The weak inequality is changed to equality with an individual who is always non-satiated, and
the objective budget restriction becomes the objective budget hyperplane:
¦£ C ‰ % : 0 p0 ¸ c0 X0 0 p1 ¸ c1 X1 ¦²¦
B a ¤¦
»ˆB
¦¦ 0 p0 ¸ R ¸ d 0 0 p1 ¸ R ¸ d 1, D ‰ \ L q \ L
¦¦
¥
¼
[EQ A-27]
The expanded objective budget restriction says that the subject chooses an objective consumption set that equates the intrinsic value of consumption with the intrinsic value of the payoffs
from production and with the intrinsic value of exogenous wealth.
The larger the RHS of the objective budget restriction, the more the subject can consume,
i.e. the larger is the LHS. Since the subject is better off with more consumption, he or she will always want to increase the RHS. His or her payoff from the production is within the grasp of his or
her control and could be increased.
Any individual, no matter how he or she prefers to balance his or her consumption between
the present and the future, will always want the firm to maximize its net present value of the payoffs.
With a fixed input numerarie good, d10D , this amounts to maximizing the intrinsic value of the output
factor, i.e. 1 p1 ¸ d1 , which is equal to maximizing the current intrinsic value of the firm.
160
The objective production set has been specified in equation [EQ A-11] to
£
²

¦
D ¬
­ b ¦
¤D ‰ \ L q \ : g žžd1, da0 d10
» , but since the subject wants the firm to maximize its intrin­
Ÿ
®
¦
¦
¦
¦
¥
¼
sic value, this puts an additional constraint on production. Only output efficient production plans,

¬
D ­
g žžd1, da0 d10
­®  , are acceptable by the perfect rational choice since it maximizes the output for a
Ÿ
given input. It means that the optimal objective production set must lie on the objective transformation frontier:
£
²

D ¬
­ ¦»
a ¦¤D ‰ \ L q \ : g žžd1, da0 d10
Ÿ
®­
¥¦¦
¼¦¦
[EQ A-28]
The subject maximizes his or her objective utility function U C
, but in the joint optimization problem it is subject to the two constraints: the new objective budget hyperplane, [EQ A-27],
and the objective transformation frontier, [EQ A-28].
His or her choice is the optimal objective consumption set that lies on the objective budget
line, satisfying C* B a ‚ X IND . The optimal choice of production plan satisfies D a ‚ B a . With
both production and exchange opportunities available, it is not necessary for the optimal objective
production set and the optimal objective consumption sets to be the same and hence C v D will
generally be the case. This is also known as Fisher’s (1930) separation theorem.
To find the intersection between the objective budget hyperplane, the indifference set, and
the objective production set the problem is formulated as a constrained maximization problem:
maxU C
s.t.
c
0 p0
[EQ A-29]
¸ c0 X0 0 p1 ¸ c1 X1 0 p0 ¸ R ¸ d 0 0 p1 ¸ R ¸ d 1 0

D ¬
­ 0
g žžd1, da0 d10
Ÿ
®­
Using Lagrange’s method the constrained maximization problem turned into an unconstrained maximization problem:
¦£¦
¦²¦
¦¦U C
¦¦
¦¦
¦
¯
p ¸ c0 X0 0 p1 ¸ c1 X1 ¦¦¦
¦
°»
max $ max ¦¤M ¸ ¡¡ 0 0
°¦
p ¸ R ¸ d 0 0 p1 ¸ R ¸ d 1
c,d ,M,N
c,d ,M,N ¦
¦¦
¢ 0 0
±¦¦
¦¦
¦¦

¬
D ­
a
¦¦N ¸ g žžŸd1, d 0 d10 ®­
¦¦
¥¦
¼¦
[EQ A-30]
Solving the unconstrained problem gives the following results.
‹$ c0 ‹U c0 M ¸ 0 p0 0
[EQ A-31]
‹$ c1 ‹U c1 M ¸ 0 p1 0
[EQ A-32]
‹$ d 0 M ¸ R ¸ 0 p0 N ¸ R ¸ ‹g d 0 0
[EQ A-33]
161
‹$ d1 M ¸ R ¸ 0 p1 N ¸ R ¸ ‹g d1 0
0 p1
0 p0
‹U c1 ‹U c0 [EQ A-34]
‹g d1 [EQ A-35]
‹g d 0 Equation [EQ A-35] shows that the subject chooses to consume where his or her objective
marginal rate of substitution between current and future consumption equals the objective marginal
rate of transformation between current and future goods. The objective marginal rate of substitution
and the objective marginal rate of transformation intrinsic value equal the objective futures price for
the commodity adjusted for the objective spot price for future consumption.
‹$ M 0 p0 ¸ c0 X0 0 p1 ¸ c1 X1 0 p0 ¸ R ¸ d 0 0 p1 ¸ R ¸ d1 0
[EQ A-36]

D ¬
­0
‹$ N g žžd1, d a0 d10
Ÿ
®­
[EQ A-37]
The choices made by the subject and by the firm are subject to the constraints expressed as
equations [EQ A-36] and [EQ A-37]. With equation [EQ A-35] and [EQ A-36], it is possible to express the optimal consumption that an individual takes to find his or her tangency solution
C* B a ‚ X IND as:
c0 X0 d0 c1 X1 R ¸ d1 0 p1
0 p0
0 p0
0 p1
¸ R ¸ d1 0 p1
0 p0
¸ R ¸ d 0 ¸
¸ X1 c1 0 p0
0 p1
[EQ A-38]
¸ c0 X 0 [EQ A-39]
To specify the tangency solution D a ‚ B a demands further structure on the production
constraint [EQ A-37]. Since the purpose with this appendix is to derive a valuation model, a further
specification is not necessary. This means the production equivalent to [EQ A-38] and [EQ A-39] is
not derived.
The objective price has until now been exogenous to the model. The subject has to choose
an optimal consumption and investment choice for a given objective price structure. The following
section lets the objective price be determined from within the model.
A.7 The competitive equilibrium
The present discussion has focused thus far on a single individual who is described as a perfect rational choice. In the pure exchange situation the subject was engaged in exchange with other individuals who acted in the same manner, without further specifying the circumstances. The same applies to the situation where the subject faces the dual problem of exchange and production.
This section considers the full extent of the problem where there are several individuals and
where several firms are active in the economy. The expansion makes it possible to let the objective
price be established within the model. Previously, the expansion was, together with his or her preferences and the firm’s transformation technology, made from outside the model.
162
The goal of this section is to present a model in which all individuals are satisfied with their
consumption and investment plan and where there are no incentives to alter the resource allocation.
When everyone is satisfied and there are feasible plans, the supply and demand of the commodities
match and the economy is Pareto optimally allocated.
To go from one individual and one firm acting in a economy to consider several individuals
and several firms active in the economy calls for further restrictions. Throughout this thesis it is
assumed that no individual or productive unit in the economy has the ability to materially affect the
prevailing intrinsic values with their transactions. That is, everyone is an objective price taker.
It is also necessary to add constraints that guarantee that the consumption and investment
plans are feasible. These are the market clearing constraints and they look different when comparing
a pure exchange and a production economy.
A.7.1 Market clearing
Market clearing is a constraint that is imposed to avoid consumption patterns that are not feasible.
E.g., it is inconceivable that consumption of fresh water on earth exceeds the total supply of fresh
water on earth. The constraint is sometimes also known as a materials balance constraint (Gravelle
& Rees 1998) or conservation constraint (Hirshleifer 1970).
Before a formalization of the market clearing constraint is made, it is necessary to define total
consumption and total wealth. Let the aggregate current consumption be the sum of all individuals’
current consumption: œ i ci0 . Similarly, the aggregate future consumption is equal to the sum of all
individuals’ future consumption: œ i c1i . The aggregated current and future endowed wealth are
œX
i
i
0
œX
, and
i
i
1
, and the aggregated current and future productions are œ i di0 , and
œd
i
i
1
.
Feasible consumption patterns assume that the aggregate current consumption must be less
than or equal to the sum of all individuals’ endowed current exogenous wealth and production. The
same restriction applies to future consumption and wealth. That is,
œc
i
i
1
b
œ X œ d
i
i
1
i
i
1
œc
i
i
0
b
œX
i
i
0
œd
i
i
0
, and
prohibit unfeasible consumption plans. This means that supply equals
demand.
However, since the subjects in the economy are always non-satiated, they will not exhibit
wasteful behavior. It means that they do not consume less than what is possible because the remaining resources are lost. This shifts the inequalities to equalities and the supply of resources exactly
corresponds to the demands of the resources. The behavior clears the economy and it is symbolized
by:
œc
i
i 0
œX
i
i
0
, and
œc
i
i 1
œX
i
i
1
.
163
A.7.2 Dovetailing consumption and investment choices
Each subject in society is a perfect rational choice. In section A.4 Homo economics’ preference rela-
tions were defined. The most central assumption concerned completeness, which in words was defined as:
The subject has an understanding of all the choice opportunities available, makes pair-wise comparison of
them all, and expresses whom he or she prefers over the other, or if he or she is indifferent between them.
This means that the subject can assess, fully and correctly, all the consumption and investments opportunities that are available for his or her.
If there are as many individuals in society, it means that their objective opportunity set is affected by what others are willing to trade. If no commodities at all are exogenously inserted into the
economy, all the commodities in the economy must be produced, which means that the subject cannot only focus on the consumption choice and the related trade but must also consider the investment choice.
The only way for each subject in an economy to be able to fully and correctly assess his or
her objective opportunity set and the related objective production set is to have knowledge of each
other’s preferences, opportunities, and objective production sets, including budgetary constraints;
otherwise, some of his or her consumption/investment plans will be erroneous and thus cannot be
executed as expected. This means that some individuals will not be satisfied with the current allocation of goods in the economy and thus will have incentive to change behavior given another chance.
When the plans are erroneous, the economy does not clear and there is no match between the
supply and demand of commodities.
When the economy clears, there are perfectly dovetailing consumption and investment patterns in society. That is, each subject’s consumption and investment choice fit into each other to
form a compact and harmonious whole.
The completeness assumption from section A.4, together with this section’s assumption on
market clearing, means that the subject no longer can be assumed to abide to.
The subject has an understanding of all the choice opportunities available, makes pair-wise comparisons of
them all, and expresses whom he or she prefers over the other, or if he or she is indifferent between them.
Now every individual must behave as below:
Every individual in society has an understanding of all consumption opportunities, all production opportunities, and all budgetary constraints available for all the subjects in society. Each subject also has knowledge of everyone’s preferences. Based on all the opportunities and constraints, the subjects form their expectations on what the aggregate supply and demand will be that clear the economy and what intrinsic values that are needed to clear the economy. Indigenous to this process is also the subjects’ individual choice
process in which they make up their own consumption and investment plans. When all individuals in society have performed this process, the consumption and investment plans are executed.
This is indeed a very strong assumption. In fact, researchers have tried to avoid it by proposing another process that gives a similar result. Walras ([1874] 1954) devised a strategy that today is
164
known as the tâtonnement process. In this process a mastermind decides tentative objective prices
that are transmitted to the subjects in society, who then hand in their tentative consumption and
investments plans to the mastermind. A new set of tentative objective prices is distributed if the
economy does not clear based on the initial tentative plans. This process continues until an objective
price is found that makes all consumption and investment plans dovetail. The plans are executed
when the economy clears.
With the subjects’ tâtonnement process, they are no longer able by themselves to discover
the feasible consumption and investment patterns in society. There is someone else who is more
rational and smarter who acts as a mastermind that mediates to avoid unfeasible plans. This is at
odds with the assumptions that each subject in society is a rational economic choice maker. Therefore, these types of ad hoc device are non-void. This thesis solely builds on individual choice making
and not on a mastermind.
A.7.3 The market equilibrium
With a dovetailing market, it is possible to focus on the objective price formation process. This
process can be described as an aggregate optimization process in which each subject in society participates. Equilibrium is achieved when the aggregate optimization process has run its course, which
gives a Pareto optimal allocation of resources. This means that it is not possible to choose a different allocation of resources in society that makes an individual strictly better off without making any
other individual worse off.
Recall from section A.4 that each subject has an objective utility function U i , and from section A.6 how this objective utility function is optimized based on the restrictions from the objective
budget set and the objective opportunity set. This can be described on an economy level in which all
individuals choose consumption plans that maximize their utilities given their restraints from the
budget and objective opportunity set. On top of that, the chosen consumption and production plans
must be feasible. The best possible allocation is the Pareto optimal allocation that can be found as
the solution to the following constrained maximization problem:
maxU 1 C
s.t.
[EQ A-40]
c
U i C
p U i C
, 2, !, I s.t.
œc
œc
i
i
0
i
i
1
œ
j
œ X œ d
œ X œ d
i
i
0
i
j
0
, A ‰ L
i
i
1
i
j
1
, A ‰ L
j
j
jD
¡ d1 g d 0a , d10
¡¢
°°±¯ 0 , j ‰ J
This maximization gives rise to the following unconstrained optimization:
165
£
¦
¦
¦
¦
U 1 C
¦
¦
¦
¦
E ¡U i C
U i C
¯°
¦
¢
±
¦
¦
max $ max ¦
ci0 Xi ¤ 0 p0 ¸
i
i 0
c,d ,E,M,N
c,d ,E,M,N ¦
¦
¦
¦
0 p1 ¸
ci Xi ¦
i 1
i 1
¦
¦
 j j j D ¬¯
¦
¦¦N ¸
¡ g žd1 , d 0a d10 ­­°
j ¡ ž
¦
Ÿ
®±°
¢
¦
¥
œ
œ
œ
œ
²
¦
¦
¦
¦
¦
¦
¦
¦
¦
¦ i ‰ I
j ¦
d0 ¦
» , A ‰ L ,
j
¦
¦
¦ j ‰ J
d1j ¦
¦
j
¦
¦
¦
¦¦
¦¦
¼
œ œ œ
[EQ A-41]
‹$ ci0 E ¸ ‹U i c0 0 p0 , i ‰ I , A ‰ L
[EQ A-42]
‹$ c1i E ¸ ‹U i c1 0 p1 , i ‰ I , A ‰ L
[EQ A-43]
‹$ d 0j 0 p0 N ¸ g d 0j 0 , j ‰ J , A ‰ L
[EQ A-44]
‹$ d1j 0 p1 N ¸ g d1j 0 , j ‰ J , A ‰ L
[EQ A-45]
0 p1
0 p0
‹U i c1 ‹U i c0 ‹g d1 [EQ A-46]
‹g d 0 Equation system [EQ A-46] shows how each subject in society has the same objective marginal rate of substitution between current and future consumption in a Pareto optimal equilibrium.
The objective marginal rates of transformation are also equal across firms in the economy in this
situation and they are all equal to the prevailing intrinsic value for current consumption scaled by the
objective current objective price for future consumption.
The fact that each subject in society has the same objective marginal rate of substitution is
conceivable given that conjecture of the theory of the perfect rational choice. The perfect rational
choice posits that each subject has complete knowledge, i.e. that he or she can fully specify his or
her action and the state set. With the additional assumption of materials balance constraint, each
subject must have complete knowledge of every other individual’s action set and state set.
Since each subject in society has the same objective marginal rate of substitution, the assumption of homogenous preferences posited by the assumption of the representative individual in
financial economics is not restrictive.
A.8 The intrinsic value rule for firms in objective certainty
The subjects’ choice when facing both productive and exchange opportunities allowed for the conclusion that they would always be better off with a higher net present payoff from the firm. This
conclusion was reached by studying the expanded objective budget set in subsection A.6.2. With the
previous optimization analysis, it is possible to derive this relationship formally.
166
A.8.1 The intrinsic value rule based on dividends
All analyses hitherto have focused on a one-period model. This subsection elaborates on the intrin-
sic value rule based on net dividends. It continues to use a one-period framework that is expanded
into a multi-period context.
A.8.1.1
The one-period dividend valuation model in objective certainty
It was claimed in [EQ A-30] that subjects maximize their utility given the objective budget restriction and the productive opportunities. This is:
£
²
¦
¦
¦
¦
¦
¦
U C
¦
¦
¦
¦
¦
¦
¯
max $ max ¤¦M ¸ ¡ 0 p0 ¸ c0 0 p1 ¸ c0 0 p0 ¸ d 0 0 p1 ¸ d1a °»¦
c,d ,M,N
c ,d ,M,N ¦
¦
¢
±
¦
¦
¦
¦
¦¦N ¸ g žd , da d D ¬­
¦¦
ž 1 0 10 ®­
¦
¦
Ÿ
¦
¦
¥
¼
[EQ A-47]
The maximization problem can be re-written so it focuses on the two separate choices of
choosing an optimal objective consumption set and choosing the optimal production plan.
max \U C
M ¸ < 0 p0 ¸ c0 0 p1 ¸ c1 >^ c,M
£

¬²
¦ ¯
D ­
¦
max ¤M ¸ ¡ 0 p0 ¸ d 0 0 p1 ¸ d1a ° N ¸ g žžd1, da0 d10
­»
Ÿ
®
d ,M,N ¦
¦
¢
±
¦
¦
¥
¼
[EQ A-48]
The maximization problem can be simplified further by defining H w N ¸ M1 . Focusing on
the production maximization problem, it becomes:
²

¦£ ¯
D ¬
­¦ max ¤M ¸ ¡ 0 p0 ¸ d 0 0 p1 ¸ d1a ° M ¸ H ¸ g žžd1, da0 d10
Ÿ
®­»¦¼¦
d ,M,N ¥
±
¦¦ ¢
£ ²

¬¦
¦
¯
D ­
M ¸ max ¤¡ 0 p0 ¸ d 0 0 p1 ¸ d1a ° H ¸ g žžd1, da0 d10
­®»
Ÿ
d ,H ¥
¦¢
¦
±
¦
¦
¼
[EQ A-49]
The subjects’ choice can now be interpreted as if they first maximize the production equation
[EQ A-49]. This yields the optimal production plan, d0 , d1 , that maximizes the net intrinsic value
of the firm given the production constraint and equilibrium objective prices. Since the initial investment is assumed fixed (see section A.5.2), what remains is choosing the investment plan that gives
the highest attainable intrinsic value (given the restraint that is due to production technology), i.e.
D
max 0 p1 ¸ d1 d10
. Then, with an optimal production plan, the subjects proceed to optimize the
remaining problem, i.e.:
max \U C
M ¸ < 0 p0 ¸ c0 0 p1 ¸ c1 0 p0 ¸ d0 0 p1 ¸ d1 >^
[EQ A-50]
c,d ,M,N
From which the subjects get their optimal consumption plan c0 , c1 .
This analysis further highlights the separation of the firm’s production choice and his or her
consumption choice. Any individual prefers equation [EQ A-49] to be maximized no matter what he
167
or she plans to consume since this increases the maximum attainable level of well being, as expressed by the objective utility function.
Equation [EQ A-49] establishes how investments into a firm are made in a Pareto optimal
setting. For a given level of initial investments (here defined as a fixed portion of the present numerarie) and for Pareto optimal objective current objective prices for future consumption, the investments are made such that they maximize the intrinsic value of the future output.
Since the future output can be traded in the future spot economy at Pareto optimal objective
spot prices, it is possible, without loss of generality, to assume that all future commodities are converted into the future numerarie. This allows us to rewrite [EQ A-49] as:
D
max < 0 p10
¸ d10
0 p11
¸ d11 >
[EQ A-51]
d11
The technological constraint is ignored in [EQ A-51], but it should not be interpreted as if it
is not important. Rather, [EQ A-51] can be interpreted as a maximizing problem given the technological constraints. In everyday language this equation is known as the net intrinsic value rule. It
should also be noted that since the future commodity vectors into the future numerarie, it follows
that conceptually d11 will be the net of all future commodities. In practice this would then be called
the net dividends.
The objective spot prices for the numerarie at present and in the future are defined to be 1 in
section A.5.1. This allows the numerarie commodity to be called capital, and accordingly, from a
firm’s perspective, the input and output in [EQ A-51] are equivalent to the firm’s dividends.
The Pareto optimal objective price of any investment can thus be defined as its intrinsic value of future payoffs. In algebra it becomes:
V10 0 p11
¸ d11
[EQ A-52]
Equation [EQ A-52] is said to show the Pareto optimal objective price of a firm. In this thesis I call this value the firm’s intrinsic value in order to signify that it is the value that the firm should
have if the economy is in a Pareto optimal equilibrium.
The subscript that keeps track of the commodity is hereafter dropped to avoid a too cumbersome notation. The stars indicating the Pareto optimal objective prices are also dropped to simplify
the notation.
A.8.1.2
A multi-period dividend valuation model in objective certainty
The one period intrinsic value can be expanded to cover more than one period. Assume that
[EQ A-52] holds for T 1 , where T 2 . This means that V0 0 p1 ¸ d1, ",VT 1 0 pT ¸ dT . This
also implies that the Pareto optimal allocation holds across all periods.
168
As long as V1 v 0 it follows that [EQ A-52] needs to be modified to incorporate the remaining value at the end of the period. Hence, V0 0 p1 ¸ d1 V1 , ",VT 1 T 1 pT ¸ dT VT . Substituting this expression into the latter gives the multi-period dividend valuation model:
T
V0 œ
0 pt
¸ dt 0 pT ¸VT
[EQ A-53]
t 1
T
Where: 0 pT 0 p1 ¸ 1 p2 ¸ ! ¸ T 1 pT  t 1 pt .
t 1
Equation [EQ A-53] is the multi-period dividend valuation model for a finite period. Before
the multi-period dividend valuation model is expanded to cover infinity, the objective market ratesof-return (MROR) is introduced.
A.8.2 The intrinsic value rule with market rates-of-returns and not objective prices
Up to now, the analysis has only made use of spot and objective future prices. The analysis now
turns the objective futures price 0 S1 into an objective MROR.
Let q 0 be the quantity of the current capital and let q1 be the quantity of the objective future
capital. In order to get q1 units of the capital in the future, the subject will have to forfeit in the
present:
q 0 0 p1 ¸ q1
[EQ A-54]
It is also possible to express the quantity of the objective future capital based on the present
capital plus the change in the capital, i.e.:
q1 q 0 %q0
[EQ A-55]
Substituting [EQ A-55] into [EQ A-54] and rearranging gives:
1 %q0 ¸ q 01 0 S01
[EQ A-56]
Define the MROR as the rate of growth of capital, i.e. 0 r1 %q0 ¸ q 01
. This gives:
1
1 0 r1 0 p01 ” 0 p1 1 0 r1 [EQ A-57]
From [EQ A-57], it is apparent that the objective future objective price for capital is equivalent to the commonly used discount factor in investment appraisal. The MROR is equivalent to the
risk-free rates-of-return since the model used is based on objective certainty.
With the introduction of the MROR, it is also possible to expand [EQ A-53] to infinity and
still have a bounded current intrinsic value. It is assumed that
d
t 1 rt
%Vt 1 ¸Vt11 , t . This implies
¬
that lim žžž t 1 pt ¸Vd ­­­ 0 , and then [EQ A-53] collapses to:
­®
t ld ž
Ÿ
t 1
V0 d
œ
0 pt
¸ dt
[EQ A-58]
t 1
169
d
Where: 0 pd 0 p1 ¸ 1 p2 ¸ ! ¸ d1 pd  t 1 pt , and where
t 1
t 1 pt
1
1 t 1rt .
Equation [EQ A-58] shows the infinite dividend valuation model. It expresses the intrinsic
value of, e.g., a firm as a function of the intrinsic value of future dividends with an infinite time horizon. The model allows for non-constant market rates-of-returns, which in practice is often simplified to constant rates-of-returns (Penman 2004; Beaver 1989).
A.8.3 Multi-period, non-constant rates-of-returns, and the intrinsic value rule based on residual
income
It is possible to define a firm’s intrinsic value as a function of future net dividends based on a Pareto
optimal allocation in society. It is also possible to derive accounting valuation models that are equivalent to the dividend valuation model. This section derives the residual income valuation model
measured on both comprehensive net income and on comprehensive operating income. First, follows the residual income valuation model measured on comprehensive net income and then the
residual income valuation model measured on comprehensive operating income.
A.8.3.1
The residual income valuation model measured on comprehensive net income
The residual income valuation model was originally developed by Preinreich (1936, 1937a, 1937b,
1938), but received scarce attention until 1995 when Ohlson popularized it. Ohlson (1995) developed the model using objective certainty and constant MROR. I present a similar model developed
in objective certainty that instead uses non-constant MROR.
Accounting uses several rules. One such rule is the clean surplus relationship, which states
that any change in the equity account is a function of net transactions with the owners and of comprehensive net income. Algebraically this implies:
%EQt CNI t dt
[EQ A-59]
Where CNI t is the comprehensive net income for a period, %EQt is the change in the equity account between two adjacent periods starting at t 1 , and dt is the period’s net dividends. Substituting [EQ A-59] into [EQ A-58] yields:
V0 0 p1 ¸ CNI 1 %EQ0 0 p1 ¸ 1 p2 CNI 2 %EQ1 "
[EQ A-60]
Defining residual income as the portion of comprehensive net income that deviates from the
expected comprehensive net income
RI t CNI t t 1rt ¸ EQt 1 ,
[EQ A-61]
opens the possibility of re-writing [EQ A-60] as a function of residual income, comprehensive net income, and change in equity. Expected comprehensive net income is the comprehensive
net income expected by the owners at the inception of the period, i.e.
t 1 rt
¸ EQt 1 .
V0 0 p1 ¸ RI 1 0 r1 ¸ EQ0 %EQ0 0 p1 ¸ 1 p2 RI 2 1 r2 ¸ EQ1 %EQ1 "
170
which is simplified to
V0 0 p1 ¸ RI 1 1 0 r1 ¸ EQ0 EQ1 0 p1
[EQ A-62]
¸ 1 p2 RI 2 1 1r2 ¸ EQ1 EQ2 "
Since [EQ A-57] provides the means for translating the objective futures price (discount factor) into MROR, and vice versa, it follows that
t 1 pt
1
1 t 1rt . Substituting this into
[EQ A-62] gives:
V0 0 p1 ¸ RI 1 EQ0 0 p1 ¸ EQ1 0 p1 ¸ 1 p2 ¸ RI 2 0 p1 ¸ EQ1 0 p1 ¸ 1 p2 ¸ EQ2 "
[EQ A-63]
Rearranging and summing [EQ A-63] over a finite period gives:
T
V0 EQ0 œ
0 pt
¸ RI t 0 ST ¸ VT EQT [EQ A-64]
t 1
d
¬
Assuming a mild regulatory condition, 0 rt %EQ0 ¸ EQ0 , implies lim žžž t 1 pt ¸ EQd ­­­ 0
t ld ž
Ÿ
®­
t 1
and it collapses [EQ A-64] into the multi-period residual income valuation model with non-constant
rates-of-returns as the horizon is pushed into infinity:
V0 EQ0 d
œ
0 pt
¸ RI t
[EQ A-65]
t 1
Equation [EQ A-65] is an equivalent expression to [EQ A-58] assuming the clean surplus relationship holds. It shows that the firm’s intrinsic value is a function of the present book value of
equity and of the intrinsic value of future residual income. The clean surplus relationship makes it
possible to solve the dividend conundrum posed by Modigliani & Miller (1958) and analyze a firm’s
value creation rather than the value distribution, which is the object of the study in model
[EQ A-58]. When Vt EQt , value has been created. From model [EQ A-65], it is apparent that this
can only occur when RI t 1 . This implies that value is created only when the residual income is
positive. Conversely, value has been destroyed when Vt EQt , and this can only occur when
RI t 1 .
The model [EQ A-65] shows how the intrinsic value is measured when objective certainty is
present and where the rates-of-returns are non-constant. This is a further development compared
with Ohlson (1995) who discusses this model with constant rates-of-returns.
Feltham & Ohlson (1999) derive the residual income valuation model with stochastic ratesof-returns. This is a more complex case compared with the case where model [EQ A-65] operates.
An important conclusion is nevertheless the same: The normal income is measured as the product
of the one-period objective MROR and the beginning of period book value of equity. This is at odds
with how it is proposed to be measured among practitioners such as Copeland, Koller & Murrin
171
(2000), Damodaran (2001), and Stern & Stewart (1999). It is also at odds with how textbooks teach
it. E.g., Penman (2004) applies a constant rate-of-return rather than a time-varying one-period rateof-return when normal income is estimated.
Since firms are not restricted to finance their activities only through equity it is also useful to
convert [EQ A-58] into a valuation model that also considers Modigliani & Miller’s (1958) value
additivity proposition. This is the residual income valuation model measured on comprehensive operating income.
A.8.3.2
The residual income valuation model measured on comprehensive operating income
Using the fact that that the firm’s intrinsic value can be expressed as a function of the value of the
whole firm and the value of debt (Modigliani & Miller 1958), it is possible to express [EQ A-58] as a
function of the intrinsic values of residual operating income, ROI , and the residual net interest expense, RIE . Feltham & Ohlson (1995) derive at a similar model in objective certainty having constant rates-of-returns.
A theoretical income statement and a balance sheet must be introduced in order to derive
such a model. First, the comprehensive net income is classified into comprehensive operating income, COI and comprehensive net interest expense, CNIE :
CNI t COI t CNIEt
[EQ A-66]
Second, the balance sheet is classified into net operating assets, NOA , net financial liabilities,
NFL , and equity:
EQt NOAt NFLt
[EQ A-67]
With these relationships and with the clean surplus relationship [EQ A-59], it is possible to
convert [EQ A-58] into another accounting valuation model similar to [EQ A-65] but where residual
operating income and residual interest expense are income components rather than residual income.
Using a certain setting having non-constant MROR gives the following valuation model:
V0 NOA0 d
œ
t 1
0 pt

¸ ROI t žžžNFL0 žŸ
d
œ
t 1
0 pt
¬
¸ RIEt ­­­
®­
[EQ A-68]
where
ROI t COI t t 1rt ¸ NOAt 1
[EQ A-69]
RIEt CNIEt t 1rt ¸ NFLt 1
[EQ A-70]
Since the model is placed in a certain setting, the MROR is the same for the net operating assets and the net financial liabilities. Similar models derived from a setting in uncertainty would use
the weighted average cost of capital as MROR for the net operating assets and the after-tax net cost
of debt as MROR for the net financial liabilities (e.g., Lundholm & O’Keefe 2001).
172
See Chapter 5 for a further discussion of classification and operationalization of the components to the balance sheet and income statement.
With the models [EQ A-65] and [EQ A-68], it is possible to define and study accounting
rates-of-returns and their relationships to firm valuation. This is done in the next subsection.
A.8.4 The relationship between market rates-of-returns and accounting rates-of-returns
This section defines the accounting rates-of-returns used in this thesis and discusses how they relate
to the objective MROR. The accounting rates-of-returns are the return on equity and the return on
net operating assets. First follows the return on equity.
A.8.4.1
Return on equity and residual rate-of-return on equity
The most fundamental accounting rate-of-return is the growth rate of the owner’s capital. In accounting the growth of the owner’s capital is known as the return on equity (ROE). This section
defines the ROE and also the residual rate-of-return on equity, which can be used to rewrite
[EQ A-65] into a residual rate-of-return on an equity-based valuation model.
In these studies sometimes the net income is divided by beginning of period equity; other
times by ending of period equity or the average equity is used to measure the return on equity. This
thesis defines return on equity such that it matches the derived valuation models. ROE is thus defined as comprehensive net income divided by beginning of period equity:
t 1 ROEt
CNI t ¸ EQt11
[EQ A-71]
Solving for comprehensive net income in [EQ A-71], substituting this into the clean surplus
definition [EQ A-59], and rearranging gives:
dt EQt 1 t 1 ROEt ¸ EQt 1
[EQ A-72]
Suppose that the firm is just formed. This implies that V0 EQ0 . Moreover, assume that the
firm has no value at the end of the period, i.e. V1 EQ1 0 . These two assumptions can be substituted into [EQ A-72], and that gives:
1
V0 d1 ¸ 1 0 ROE1 [EQ A-73]
Thus, when there is no opening or closing valuation error, the ROE, defined as [EQ A-71],
equals the one-period objective MROR, i.e.
t 1 ROEt
t 1 rt
. This fundamental relationship can be
further utilized.
Define the one-period residual rate-of-return on equity as the difference between the oneperiod return on equity and its corresponding objective MROR. Algebraically this becomes:
t 1 RROEt
t 1 ROEt
t 1rt
[EQ A-74]
Recall that residual income was defined in [EQ A-61]. Substituting [EQ A-74] into
[EQ A-61], rearranging and inserting this result into [EQ A-65] gives a new description of how the
value of a firm may be estimated:
173
V0 EQ0 d
œ
0 pt
¸ t 1 RROEt ¸ EQt 1
[EQ A-75]
t 1
The following section defines return on net operating assets, residual rate-of-return on net
operating assets (RRNOA), and connects them to valuation theory and ROE.
Note that the assumption that there is no opening or closing valuation error for [EQ A-73]
implies that for [EQ A-75] there is no intertemporal valuations errors either. That is, the book values are always equal to the intrinsic values and the depreciation equals the change in net book value
during a given period. This is unbiased accounting, and in such a setting the accounting rate-ofreturn always equals MROR, i.e.
A.8.4.2
t 1 ROEt
t 1 rt
t (e.g., Feltham & Ohlson 1996).
Return on net operating assets and residual rate-of-return on net operating assets
Return on equity is related to valuation theory through [EQ A-65]. With a careful definition of return on net operating assets, it can be tied to valuation theory through [EQ A-68]. ROE and RNOA
can also be tied to each other and that also requires the definition of net borrowing cost (NBC) and
financial leverage (FLEV). The necessary definitions are:
COI t ¸ NOAt11
[EQ A-76]
CNIEt ¸ NFLt 11
[EQ A-77]
NFLt 1 ¸ EQt11
[EQ A-78]
t 1 RNOAt
t 1 NBC t
FLEVt 1 With these definitions ROE, RNOA and NBC are related to each other through the familiar
leverage formula. That is,
t 1 ROEt
t 1 RNOAt
t 1 RNOAt t 1 NBC t ¸ FLEVt 1
[EQ A-79]
Also define RRNOA and residual rate-of-return on net financial liabilities (RRIBL) as:
t 1 RRNOAt
t 1 RNOAt
t 1 RRIBLt
t 1 NBC t
t 1rt
[EQ A-80]
t 1rt
[EQ A-81]
With [EQ A-76] to [EQ A-81] it is possible to rewrite [EQ A-69] and [EQ A-70] as:
ROI t t 1 RRNOAt
¸ NOAt 1
RIEt t 1 RRNFLt
¸ NFLt 1
Substituting these intermediate results into [EQ A-68] gives the following description of how
the value of a firm can be estimated:
V0 EQ0 d
œ
t 1
A.8.4.3
0 pt
¸ t 1 RRNOAt ¸ NOAt 1 d
œ
0 pt
¸ t 1 RRNFLt ¸ NFLt 1
[EQ A-82]
t 1
Residual accounting rates-of-returns and their relationship to no-arbitrage: A discussion
This appendix is devoted to no-arbitrage valuation models. The models [EQ A-75] and [EQ A-65]
are the foundation on which all analyses are related. The rates-of-returns are Pareto optimal when
there is no arbitrage and there exists no incentive for individuals to choose other consumption and
investment patterns since we have zero NPV. This implies that there are no investments in society
174
that yield non-zero residual rates and return when there is no opening and closing valuation error
since this would provide the subjects to choose other consumption patterns.
E.g., assume that one asset yields a positive RRNOA, the residual rate-of-return on equity is
null and there are no valuation errors. This means that the owner of this net operating asset can increase his or her income more than what others can achieve. At the same time, since the residual
rate-of-return on equity is null, some net financial liabilities also have a negative residual rate-ofreturn.
Since we have homogenous beliefs, other investors strive to gain access to the positive residual rate-of-return net operating assets investment in order to be able to increase their consumption.
Likewise there will be a shift away from those investments that yield a negative residual rate-ofreturn on net financial liabilities. The effect will be a rebalancing of the consumption pattern where
some will gain and others lose consumption. Striving for increased consumption is always sought for
because of the non-satiation assumption.
The incentive to shift consumption and investment patterns is at odds with the Pareto optimal definition. Further, the conditions for models [EQ A-58], [EQ A-65], and [EQ A-68] are violated.
At face value, it appears as though the models above only require that the present value of
the sum of future RROE, RRNOA, and RRIBL to be zero when there are no opening or closing
valuation errors. However, this restriction is even more austere than is looks when we also consider
the assumptions under which the models are derived
Lundholm (1995, p. 761) notes: “Homogenous investors value the firm under a no-arbitrage
equilibrium condition; there are no differing intertemporal preferences for consumption, no differing risk preferences and no differing beliefs.” Thus, the implication here is that we have a situation
where all subjects have perfect knowledge. Hence, even though the models seem to allow for temporary residual rates-of-returns as long as they are reversed in future periods (with appropriate compensation for the time value of money), this goes against the assumptions of the models.
If there exists, even in expectation, some future positive residual income for a particular firm,
all subjects hold the same beliefs and thus everyone knows that this firm is expected to be more
profitable than other identical firms at that time. Such a situation cannot be Pareto optimal because
the assumption implies that all other firms also know this and hence they have a propensity to seek
to improve in that they no longer are expected to be maximizing their values.
It is therefore not possible for any firm to be expected to earn any residual rates-of-returns in
a no arbitrage situation with homogenous beliefs when we have no opening and closing valuation
errors.
175
Indeed, this fact is recognized by Lo & Lys (1999). Lo & Lys (1999) argue that the unconditional residual income is zero; for this to happen, a firm cannot earn more than the cost-of-capital.
Both Lundholm (1995) and Beaver (2002) are aware of the effect from assuming homogenous beliefs and no arbitrage. Lundholm (1995) even points out that under such a setting there is not
even any demand for accounting information since there is no demand for financial assets.
Beaver (2002, p. 458) also points out that these assumptions imply that there is “…no endogenous demand for accounting data” in the valuation model.
Ohlson (2003) argues differently to Lo and Lys (1999) but focuses on the technicalities of the
conjectured linear information dynamics. This seems to be off the target since Ohlson does not consider the limitations that the assumptions about homogenous beliefs in no arbitrage impose on the
model.
I have to agree with Ohlson (2003) to the extent that, if we remove the assumption of no
opening or closing valuation error, we have a setting that allows for non-zero residual income.
It is also plausible that accounting rules that create early (late) recognition of revenues and
expenses can create expected residual rates-of-returns that are non-zero for individual periods. But
to develop such an accounting system, which should be different to that in the paragraph above and
thus have no opening or closing valuation error, requires careful consideration. In my view, it is unclear how to form such an accounting system.
A.9 Summary
This appendix derives two accounting-based valuation models that are equivalent to the dividend
valuation model. These two models use certain, but non-constant, rates-of-returns, which separates
them from, e.g., the models by Ohlson (1995), Feltham & Ohlson (1995), and Feltham & Ohlson
(1999). The valuation models are derived from basic assumptions about his or her preference function that meets a Pareto optimal general equilibrium that allows non-constant rates-of-returns.
The models are:
V0 EQ0 d
œ
0 pt
¸ RI t
t 1
V0 NOA0 d
œ
t 1
0 pt

¸ ROI t žžžNFL0 žŸ
d
œ
t 1
0 pt
¬
¸ RIEt ­­­
­®
By defining ROE, and RNOA as:
t 1 ROEt
t 1 RNOAt
CNI t ¸ EQt11
COI t ¸ NOAt11
and by defining RROE and RRNOA as:
t 1 RROEt
t 1 ROEt
t 1rt
176
t 1 RRNOAt
t 1 RNOAt
t 1rt
it instead becomes possible to express the derived valuation models using residual rates-ofreturns. The residual rates-of-returns equivalents to the models above are found as [EQ A-75] and
[EQ A-82] above.
It should be noted that RROE and RRNOA are zero in expectation if the economy meets
the no arbitrage conditions (with homogenous beliefs) and if the accounting is unbiased. Thus, they
can be also thought of as arbitrage profitability.
177
APPENDIX B—HOMO COMPERIENS AND THE MARKET
PRICE OF THE FIRM IN A SUBJECTIVE CERTAIN CHOICE
Disequilibrium models of the firm’s market price
B.1 Introduction
This appendix provides the proof for the Homo comperiens market-pricing models that are used in
the analysis in Chapter 2 and Chapter 3. To reduce complexity the analysis in this appendix is limited
to deriving the market price of the firm in a subjective certain decision.
The subjective certain decision can be described in two ways: (i) The decision occurs when
the subjective state set has only one element; (ii) The decision occurs when the subjective state set
has more than one element but where the consequence is constant in all states.
To stress that case (ii) can be present, or that it may be a false hope to believe that the subjective state set has only one element, Chapter 4 uses a subjective expectations operator, &K 0 <¸> ,
when analyzing the subjective certain decision.
Furthermore, this appendix assumes homogenous preferences such that it is possible to analyze the decision and optimize it for a representative individual. This means that the perceive prices
in this appendix become the market’s prices.
Since the representative individual in this appendix is assumed to behave according to the assumptions of the theory of Homo comperiens, it is not possible here to talk about intrinsic values.
Appendix A focuses on the objective prices and those prices are the intrinsic values.
The appendix derives the market price of firms as functions of
(i)
(ii)
(iii)
(iv)
(v)
subjective expected dividends,
subjective expected residual income,
subjective expected residual operating income,
subjective expected residual ROE, and
subjective expected residual RNOA.
The derivations are analogous to those in Appendix A, but they are more succinct here.
B.2 The subject’s opportunity set
Appendix A finds that an individual’s decision is limited to a budget set that is
B \C ‰ X : 0 p0 ¸ c0 0 p1 ¸ c1 b 0 p0 ¸ X 0 0 p1 ¸ X1 ^ ˆ X . In this appendix the subject’s budget
set is also limiting the decision. To distinguish the budget set in Appendix A from this budget set,
the budget set from Appendix A is the objective budget set and the budget set in this appendix is
the subjective budget set.
179
In Appendix A the subject is also limited by a production set which is
£
²

¦
¦
D ¬
­
¤D ‰ \ L q \ : g žžd1, da0 d10
. Appendix A’s objective production set is the parent to the
­ b »
Ÿ
®
¦
¦
¦
¦
¥
¼
subjective production set, i.e. K ‡ that is used in this appendix.
This means that this appendix uses the subjective budget set:
‡C‰X : p ¸c p ¸c b p ¸X p ¸X ^ˆX
B \C
0 K0
K0
0 K1
K1
0 K0
K0
0 K1
K1
[EQ B-1]
The subjective budget set is assumed to be non-empty, closed, bounded, and convex as the
budget set in Appendix A. The subjective current price vector is 0 pK 0 0 pK 10 , !, 0 pK A 0 and the
subjective current price vector is 0 pK 1 0 pK 11, !, 0 pK A1 . The subjective choice portfolio is
CK cK 0 , cK 1 and it is a strict subset to the objective choice portfolio, i.e. CK ‡ C . The subjec-
tive quantity vector for current consumption is cK 0 cK 10 , !, cK A 0 ‡ \ L and the subjective quantity vector for future consumption is cK 1 cK 11, !, cK A1 ‡ \ L , where A ‰ . The subjective current wealth vector is XK 0 XK 10 , !, XK A 0 and the subjective future wealth vector is
XK 1 XK 11, !, XK A1 .
To separate the analysis from that in Appendix A it is further assumed that because of limited knowledge cK 0 ‡ c0 , cK 1 ‡ c1 . Whether the subjective wealth vectors are subsets to the objective wealth vectors or not is not restrictive and so it is instead assumed that XK 0 ˆ X80 and
XK 1 ˆ X81 .
The first good is set to be the numerarie in this analysis and its subjective spot prices are defined to be one, i.e. 0 SK 10 1 , and 1 SK 11 1 .
The subject is a subjective expected utility maximizer endowed with a strictly positive subjective wealth. This is so at the same time as the subjective prices are finite and the goods are infinitely
dividable. It is also assumed that the subject must at least consume non-negative amounts of goods,
both at the present and in the future.
With the setting above, BK v B and the budget set is artificially restricted. Had the subjects
in the market been completely rational, it would perceive more combinations and the prices in the
market would be different. The subjective budget set is therefore restricted, which leads to inefficient solutions where the subject chooses less than optimal consumption combinations.
This appendix uses the following subjective production set.
£
²

¬
¦
K ¤DK ‡ D ‰ \ L q \ : gK žždK 1, dKa 0 dKD 10 ­­ b »¦
Ÿ
®
¦
¦
¦
¦
¥
¼
[EQ B-2]
180
The subjective production vector is DK dK 0, dK 1 and it is a strict subset to the objective
production set, i.e. DK ‡ D . The subjective current production vector is represented as dK 0 , and
dK' 0 dK 0 4 \dKD 10 ^ . The subjective current production vector is a strict subset to the objective pro-
duction vector, dK 0 ‡ d 0 , and its elements are zero or negative since there is a consumption of
goods in the production process. Similarly, the subjective future production vector is denoted as
dK 1 . It is a strict subset to the objective future production vector, dK 1 ‡ d1 , and the vector’s ele-
ments are either zero or positive, indicating that there is some output from the production process.
B.3 The subject’s optimization problems
The subject behaves in this setting according to Homo comperiens. Thus, the subject acts as though
he or she is striving to maximize his or her strictly quasi-concave subjective utility function over his
or her subjective available opportunities, which are constrained by non-negative consumption, the
subjective exchange opportunities, and the subjective production opportunities.
The setting in this appendix is similar to that in Appendix A but here the subject is limited to
choosing from an inefficient opportunity set. It is bounded when compared with the opportunity set
in Appendix A in that the knowledge is limited.
As in Appendix A, the non-negativity constraints are ignored and focus is on interior solutions to the optimization problem.
The optimization is first studied in a pure exchange situation. Next, follows the situation
where the subject faces both exchange and productive opportunities.
B.3.1 Optimization in a pure exchange economy
The subject is assumed to be a utility maximizer which means that the weak inequality in [EQ B-1] is
replaced by an equality. This means that the subject never chooses to waste resources and therefore
the subjective budget restriction is replaced by the hyperplane:
a \C
‰C ‰ % : p ¸c p ¸c p ¸X p ¸X ^ˆB
0 K0
K0
0 K1
K1
0 K0
K0
0 K1
K1
K
[EQ B-3]
The solution to the optimization problem that will let the subject consume according to the
subjective budget hyperplane while attaining the highest possible indifference curve is obtained from
solving the problem:
max U K CK subject to
cK
0 pK 0
[EQ B-4]
¸ cK 0 0 pK 1 ¸ cK 1 0 pK 0 ¸ X K 0 0 pK 1 ¸ X K 1 0
That is:
M ¸< p ¸ c p ¸ c p ¸ X p ¸ X >
max $ U C
0 K0
K0
0 K1
K1
0 K0
K0
0 K1
K1
c,M
[EQ B-5]
181
Taking the partial derivative of Lagrange’s equation with respect to subjective current consumption gives:
‹$ cK 0 ‹U K cK 0 M ¸ 0 pK 0 0 ,
[EQ B-6]
 sU C  s$
sU K CK ¬­
s$ ¬­
­.
­ , and where ‹U K cK 0 žž K K , ",
, ",
­
ž
­
scK A 0 ®
scK A 0 ®­­
Ÿž scK 10
Ÿž scK 10
where ‹$ cK 0 žžž
For the subjective future consumption the partial derivative is:
‹$ cK 1 ‹U K cK 1 M ¸ 0 pK 1 0 ,
[EQ B-7]
 sU C  s$
sU K CK ­¬
s$ ­¬
­.
­ , and where ‹U cK 0 žž K K , ",
, ",
­
ž
­
žŸ scK 11
sc K A1 ­­®
scK A1 ®
Ÿž scK 11
where ‹$ cK 1 žžž
Dividing equation [EQ B-7] with equation [EQ B-6] gives the subjective marginal rate of
substitution between consumption today and consumption in the future:
0 pK 1
0 pK 0
‹U K cK 1 ‹U K cK 0 [EQ B-8]
The subjective marginal rate of substitution between consumption today and consumption in
the future is almost identical to the objective marginal rate of substitution between consumption
today and consumption in the future, which is found in Appendix A. However, in Appendix A the
prices are the objective prices since the solution is Pareto optimal and the marginal utilities are the
objective marginal utilities. Since the subject is endowed with limited knowledge, the marginal utilities are the subjective marginal utilities and the prices are the subjective prices. The solution would
have been Pareto optimal only if the objective budget set had been used instead of the subjective
budget set.
Using the conjecture that 0 pK 0 1 and taking the partial derivative with respect to the numerarie in the future gives the solution for the subjective futures price of the numerarie good:
sU K CK scK 11
0 p11 sU K CK scK 10
[EQ B-9]
The equation above shows the subjective marginal rate of substitution between saving and
consuming, which is very similar to the objective marginal rate of substitution between saving and
consuming. Again, the difference resides between them in the fact that it is the subjective marginal
utilities that are used in [EQ B-9] and not the objective marginal utilities.
182
B.3.2 Optimization in an exchange and production economy
In addition to being limited by the subject’s market exchange opportunities, this subsection also
limits the subject’s opportunities by the productive set, which this amounts to a joint optimization
problem.
The subject is assumed to buy shares equal to a portion Rij ,
œ R
j
i i
1 , of the subjective
future output from the firm j ‰ J . This means that the subject has XK 0 R ¸ dK 0 of subjective current wealth and has XK 1 R ¸ dK 1 of subjective future wealth in the budget hyperplane:
£ CK : 0 p0 ¸ cK 0 X K 0 0 pK 1 ¸ cK 1 X K 1 ²
¦
¦
¦ˆB
Ba ¦
¤
»
K
¦¦ 0 pK 0 ¸ R ¸ d K 0 0 pK 1 ¸ R ¸ d K 1, DK ‡ D ‰ \ L q \ L ¦¦
¥
¼
[EQ B-10]
Since DK ‡ D , we have a situation where there are more efficient combinations that can either produce more outputs given a certain input, or produce the same outputs with less inputs, or a
combination thereof. The efficient transformation frontier is put to use in Appendix A, but here the
firm is only producing at its subjective transformation frontier. The use of an inefficient transformation frontier is an effect of the limited knowledge. The transformation frontier is here:
£
²

¬
¦
¦
K ¤DK ‡ D ‰ \ L q \ : gK žždK 1, dKa 0 dKD 10 ­­ »
Ÿ
®
¦
¦
¦
¦
¥
¼
[EQ B-11]
To find the intersection between the budget hyperplane, the indifference set, and the production set is formulated as a constrained maximization problem:
maxU K CK s.t.
cK
0
0S
[EQ B-12]
0 0 pK 1 ¸ cK 1 X K 1 0 pK 0 ¸ R ¸ d K 0 0 pK 1 ¸ R ¸ d K 1 0
¸ c0 X

¬
gK žždK 1, dKa 0 dKD 10 ­­ 
Ÿ
®
This can be expressed using Lagrange’s method as the following unconstrained maximization
problem:
£
²
¦
¦
¦
¦
¦
¦
U K CK ¦
¦
¦
¦
¦
max $ max ¤M ¸ ¢ 0 pK 0 ¸ cK 0 X K 0 0 pK 1 ¸ cK 1 X K 1 0 pK 0 ¸ R ¸ d K 0 0 pK 1 ¸ R ¸ d K 1 ±¯»¦ [EQ B-13]
cK ,dK ,M,N
cK ,dK ,M,N ¦
¦
¦¦
¦

¦
D ¬
a
­
¦¦¦N ¸ gK žŸždK 1, dK 0 dK 10 ®­
¦¦¦
¥
¼
Solving the unconstrained problem gives the following results.
‹$ cK 0 ‹U K cK 0 M ¸ 0 pK 0 0
[EQ B-14]
‹$ cK 1 ‹U K cK 1 M ¸ 0 pK 1 0
[EQ B-15]
‹$ dK 0 M ¸ R ¸ 0 pK 0 N ¸ R ¸ ‹gK dK 0 0
[EQ B-16]
‹$ dK 1 M ¸ R ¸ 0 pK 1 N ¸ R ¸ ‹gK dK 1 0
[EQ B-17]
183
0 pK 1
0 pK 0
‹U cK 1 ‹U cK 0 ‹gK dK 1 ‹gK dK 0 [EQ B-18]
Equation [EQ B-18] shows that the subject chooses to consume where his or her subjective
marginal rate of substitution between current and future consumption equals the subjective marginal
rate of transformation between current and future goods. The subjective marginal rate of substitution and the subjective marginal rate of transformation equal the subjective price for future consumption adjusted for the subjective price for current consumption.
B.4 The market price and the subjective dividends
This subsection elaborates on the market price based on dividends in a one-period model that is
expanded into a multi-period setting.
B.4.1 The one-period subjective dividend market-pricing model
Subsection B.3.2 discusses optimization for an individual that maximizes his or her subjective ex-
pected utility given the subjective budget restriction and the subjective productive opportunities.
That is:
£
²
¦
¦
¦
¦
¦
¦
U K CK ¦
¦
¦
¦
¦
max $ max ¤M ¸ ¢ 0 pK 0 ¸ cK 0 X K 0 0 pK 1 ¸ cK 1 X K 1 0 pK 0 ¸ R ¸ d K 0 0 pK 1 ¸ R ¸ d K 1 ±¯»¦ [EQ B-13]
cK ,dK ,M,N
cK ,dK ,M,N ¦
¦
¦¦
¦¦

D ¬
a
­
¦¦¦N ¸ gK žŸždK 1, dK 0 dK 10 ®­
¦¦¦
¥
¼
This maximization problem can be expressed as consisting of two choices, namely that of
finding a subjective optimal consumption plan and that of finding a subjective optimal production
plan. Hence:
max \U K CK M ¸ < 0 pK 0 ¸ cK 0 0 pK 1 ¸ cK 1 >^ cK ,M
£

¬²
¦ ¯
max ¤M ¸ ¡ 0 pK 0 ¸ d K 0 0 pK 1 ¸ dKa 1 ° N ¸ gK žždK 1, dKa 0 dKD 10 ­­¦
Ÿ
®»
¦
¢
±
¦
¼
[EQ B-19]
dK ,M,N ¦
¦
¥
Defining H N ¸ M1 and by focusing on the subjective production maximization problem, it
becomes:
£ ¯
M ¸ max ¦¤¡ 0 pK 0 ¸ d K 0 0 pK 1 ¸ dKa 1 ° H ¸ gK
dK , H ¥
¦¢
±
¦

¬²
žždK 1, dKa 0 dKD 10 ­­¦»
Ÿ
®¼
¦
¦
[EQ B-20]
The subject’s choice can now be interpreted as if he or she first maximizes the subjective
production equation [EQ B-20]. This yields the subjective optimal production plan, dK 0 , dK 1 , that
maximizes the market value of the firm given the production constraint and equilibrium prices.
Since the initial investment is assumed fixed, what remains is choosing the investment plan that
gives the highest attainable market price, i.e. max 0 pK 1 ¸ dK 1 dKD 10 . Then, with a subjective optimal
production plan, the subject proceeds to optimize the remaining problem, i.e.:
184
max \U K CK M ¸ < 0 pK 0 ¸ cK 0 0 pK 1 ¸ cK 1 0 pK 0 ¸ dK 0 0 pK 1 ¸ dK 1 >^
[EQ B-21]
cK ,dK ,M,N
From which the subject gets his or her subjective optimal consumption plan c0 , c1 .
Equation [EQ B-20] establishes how investments into a firm are made in a Homo comperiens setting. For a given level of initial investments (here defined as a fixed portion of the present
numerarie) and for subjective optimal current prices for future consumption, the investments are
made such that they maximize the market price of the subjective future output.
As in Appendix A, I assume that all future commodities are converted into the future numerarie. This allows me to rewrite [EQ B-20] as:
max < 0 pK 10 ¸ dKD 10 0 pK 11 ¸ dK 11 >
[EQ B-22]
dK 11
Since the initial investment level is assumed constant it is possible to focus [EQ B-22] further. The market price of any investment is thus according to the theory of Homo comperiens:
P10 0 pK 11 ¸ &K 0 <dK 11 >
[EQ B-23]
The equation above is the one-period subjective dividend market-pricing model. It is similar
to [EQ A-52]. The difference focuses on the fact that (i) the futures price used in the equation above
is the subjective futures price of money and not the objective futures price of money and (ii) the
dividend considered is the subjective dividend and not the objective dividend.
Compared to [EQ A-52] these differences can appear very small at first glance, but are in fact
large. The subjective prices are different from the objective prices because we have (1) limited knowledge of the attainable consumption portfolios, (2) limited knowledge of the attainable production
technology that can be put to use, and (3) limited knowledge of how to best use the existing production technology. Consequently, despite their apparent similarity, there is a stormy ocean of ignorance
separating the two equations.
The subscript that keeps track of the commodity is dropped to simplify matters.
B.4.2 A multi-period subjective dividend market-pricing model
The one period market price can be expanded to cover more than one period. Assume that
[EQ B-23] holds for T 1 where T 2 . This means that PK 0 0 pK 1 ¸ dK 1, ", PKT 1 0 pKT ¸ dKT .
When PK 1 v 0 it follows that [EQ B-23] must be modified to fit in the remaining price at
the end of the period. Hence, PK 0 0 pK 1 ¸ dK 1 PK 1 , ", PKT 1 T 1 pKT ¸ dKT PKT . Substituting this expression into the latter gives the multi-period subjective dividend market-pricing model:
T
PK 0 œ
0 pKt
¸ dKt 0 pKT ¸ PKT
[EQ B-24]
t 1
T
Where 0 pKT 0 pK 1 ¸ 1 pK 2 ¸ ! ¸ T 1 pKT  t 1 pKt .
t 1
185
Equation [EQ B-24] is the multi-period dividend market-pricing model for a finite period.
This is the Homo comperiens equivalent to [EQ A-58].
Before the multi-period dividend market-pricing model is expanded to cover infinity, the
market rate-of-return is introduced.
B.4.3 An infinite subjective dividend market-pricing model with the subjective market rate-ofreturn
Let q 0 be the quantity of the current capital and let qK 1 be the quantity of the subjective future capi-
tal. To get qK 1 units of the capital in the future the subject has to forfeit at present:
q 0 0 pK 1 ¸ qK 1
[EQ B-25]
It is also possible to express the subjective quantity of the future capital based on the present
capital plus the change in the capital, i.e.:
qK 1 q 0 %qK 0
[EQ B-26]
Substituting [EQ B-25] into [EQ B-26] and rearranging gives:
1 %qK 0 ¸ q 01 0 pK10
[EQ B-27]
Define the subjective MROR as the subjective rate of growth of capital, i.e.
0 rK 1
%qK 0 ¸ q 01 . This gives:
1
1 0 rK 1 0 pK10 ” 0 pK 1 1 0 rK 1 Assume that
t 1 rKt
[EQ B-28]
d
%PKt 1 ¸ PKt11 , t . This implies that lim žžž
t ld ž
Ÿ t 1

t 1 SKt
¬
¸ PK d ­­­ 0 , and so
­®
we have the infinite subjective dividend market-pricing model with the subjective market rate-ofreturn:
PK 0 d
œ
0 pKt
¸ &K 0 <dKt >
[EQ B-29]
t 1
d
Where 0 pK d 0 pK 1 ¸ 1 pK 2 ¸ ! ¸ d1 pK d  t 1 pKt , and where
t 1
t 1 pKt
1 t 1rKt .
t
To further highlight that this is only a subjective certain decision, i.e. that the expectations of
certainty may be incorrect because of limited knowledge, the subjective expectations operator,
&K 0 <¸> , is added.
The infinite subjective dividend market-pricing model with the subjective market rate-ofreturn is the Homo comperiens equivalent to the equilibrium model in [EQ A-53].
B.5 The market price based on subjective residual income
This section derives the residual income market-pricing model measured on both comprehensive net
income and comprehensive operating income.
186
B.5.1 The residual net income market-pricing model
Assume the clean surplus relationship:
%EQt CNI t dKt
[EQ B-30]
Where CNI t is the comprehensive net income for a period, %EQt is the change in the equity account between two adjacent periods starting at t 1 , and dt is the period’s net dividends. Substituting [EQ B-30] into [EQ B-29] yields:
PK 0 0 pK 1 ¸ CNI K 1 %EQ0 0 pK 1 ¸ 1 pK 2 CNI K 2 %EQ1 "
[EQ B-31]
Defining the subjective residual income as the portion of comprehensive net income that deviates from the subjective expected comprehensive net income
&K 0 <RI Kt > &K 0 <CNI Kt > &K 0 < t 1rKt > ¸ EQt 1 ,
[EQ B-32]
Substituting [EQ B-32] into [EQ B-31] and simplifying gives:
PK 0 0 pK 1 ¸ RI K 1 1 0 rK 1 ¸ EQ0 EQ1 0 pK 1
[EQ B-33]
¸ 1 pK 2 RI 2 1 1rK 2 ¸ EQ1 EQ2 "
Replacing the subjective futures price with the equivalent expression of subjective MROR,
substituting this into [EQ B-33], rearranging and simplifying gives:
T
PK 0 EQ0 œ
0 pKt
¸ RI Kt 0 pKT ¸ PKT EQT [EQ B-34]
t 1
d
¬
Adding the assumption 0 rKt %EQ0 ¸ EQ0 implies lim žžž t 1 pKt ¸ EQd ­­­ 0 . This as­®
t ld ž
Ÿ
t 1
sumption collapses [EQ B-34] into the multi-period subjective residual net income market-pricing
model with non-constant subjective rates-of-returns as the horizon is pushed into infinity:
PK 0 EQ0 d
œ
0 pKt
¸ &K 0 <RI t >
[EQ B-35]
t 1
The multi-period subjective residual net income market-pricing model is the Homo comperiens equivalent to [EQ A-58].
Since firms are not restricted to finance their activities only through equity, it is also useful to
convert [EQ B-35] into a market-pricing model that considers Modigliani & Miller’s (1958) value
additivity proposition. This is the residual income market-pricing model measured on comprehensive operating income.
B.5.2 The residual operating income market-pricing model
Classify the comprehensive net income into comprehensive operating income, COI , and compre-
hensive net interest expense, CNIE :
CNI t COI t CNIEt
[EQ A-66]
187
Classify the balance sheet into net operating assets, NOA , net financial liabilities, NetIBL ,
and equity:
EQt NOAt NFLt
[EQ A-67]
By substituting [EQ B-30], [EQ A-66], and [EQ A-67] into [EQ B-29], I get the subjective
residual income market-pricing model measured on comprehensive operating income:
PK 0 NOA0 d
œ
0 pKt
t 1

¸ &K 0 <ROI Kt > žžžNetIBL0 žŸ
d
œ
0 pKt
t 1
¬
¸ &K 0 <RIEt >­­­
®­
[EQ B-36]
where
&K 0 <ROI t > &K 0 <COI t > &K 0 < t 1rKt > ¸ NOAt 1
[EQ B-37]
&K 0 <RIEt > &K 0 <CNIEt > &K 0 < t 1rKt > ¸ NetIBLt 1
[EQ B-38]
Since the model is placed in a subjective certain decision, the subjective MROR is the same
for both the net operating assets as for the net financial liabilities.
Similar models derived for a setting in uncertainty would use the weighted average subjective
cost of capital as MROR for the net operating assets and the subjective after-tax net cost of debt as
MROR for the net financial liabilities.
See Chapter 5 for further discussion of classification and operationalization of the components to the balance sheet and to the income statement.
Model [EQ B-36] is the Homo comperiens equivalent to model [EQ A-68].
B.6 The market price based on accounting rates-of-returns
This section converts [EQ B-35] and [EQ B-36] into market pricing models that use accounting
rates-of-returns rather than accounting income.
Define subjective return on equity as:
t 1 ROE Kt
CNI Kt ¸ EQt11
[EQ B-39]
Define the one-period subjective residual rate-of-return on equity as the difference between
the one-period subjective return on equity and its corresponding subjective market rate-of-return:
t 1 RROE Kt
t 1 ROE Kt
t 1rKt
[EQ B-40]
Substituting [EQ B-39] and [EQ B-40] into [EQ B-35] gives the multi-period subjective residual return on equity market-pricing model with non-constant rates-of-returns:
PK 0 EQ0 d
œ
0 pKt
¸ &K 0 <RROEKt > ¸ EQt 1
[EQ B-41]
t 1
Define subjective return on net operating assets as:
t 1 RNOAKt
COI Kt ¸ NOAt11
[EQ B-42]
188
Define the one-period subjective residual rate-of-return on net operating assets as the difference between the one-period subjective return on net operating assets and its corresponding subjective market rate-of-return:
t 1 RRNOAKt
t 1 RNOAKt
t 1rKt
[EQ B-43]
Define the one-period subjective residual rate-of-return on net financial liabilities, RRIBL, as:
t 1 RRNBC Kt
t 1 NBC t
t 1rKt
[EQ B-44]
Substituting [EQ B-43] and [EQ B-44] into [EQ B-36] gives the multi-period subjective residual return on the net operating asset market-pricing model with non-constant subjective rates-ofreturns:
PK 0 EQ0 d
œ
0 pKt
¸ t 1 RRNOAKt ¸ NOAt 1 t 1
d
œ
0 pKt
¸ t 1 RRNBC Kt ¸ NFLt 1
[EQ B-45]
t 1
B.7 Summary
This appendix derives market-pricing models for a market meeting the assumptions in the theory of
Homo comperiens.
It finds that it is possible to describe individual decision-making in a subjective certain decision as though the subjects are choosing its subjective optimal consumption bundle such that its
subjective marginal rate of substitution between future and current consumption equals the ratio
between the subjective futures price vector and the subjective current price vector. That is:
0 pK 1
0 pK 0
‹U K cK 1 ‹U K cK 0 It also finds that the firm chooses its production such that its subjective marginal rate of
transformation between current and future goods equals the marginal rate of substitution between
future and current consumption.
Assuming homogenous preferences opens the door for describing the market price of the
firm in a Homo comperiens setting as:
PK 0 d
œ
0 pKt
¸ &K 0 <dKt >
t 1
Where
t 1 pKt
1 t 1rKt and where
t
t 1 rKt
is the one-period market rate-of-return. The
subjective MROR is in the subjective certain setting equal to the market’s risk-free rate of return.
Defining subjective return on equity, ROE, and the subjective return on net operating-assets,
RNOA, as:
t 1 ROE Kt
t 1 RNOAKt
CNI Kt ¸ EQt11
COI Kt ¸ NOAt11
189
and by defining the residual rate-of-return on equity, RROE, the subjective residual rate-ofreturn on net operating assets, RRNOA, and the subjective residual rate-of-return on net financial
liabilities, RRIBL as:
t 1 RROE Kt
t 1 ROE Kt
t 1 RRNOAKt
t 1 RNOAKt
t 1 RRNBC Kt
t 1 NBC t
t 1rKt
t 1rKt
t 1rKt
it becomes possible to express the derived market-pricing models using residual rates-ofreturns. (Note that subjective MROR is the same for all definitions since this is a subjective certain
decision.)
The multi-period subjective residual return on equity market-pricing model with nonconstant rates-of-returns is:
PK 0 EQ0 d
œ
0 pKt
¸ &K 0 <RROEKt > ¸ EQt 1
t 1
The multi-period subjective residual return on net operating asset market-pricing model with
non-constant subjective rates-of-returns is:
PK 0 EQ0 d
œ
t 1
0 pKt
¸ t 1 RRNOAKt ¸ NOAt 1 d
œ
0 pKt
¸ t 1 RRNBC Kt ¸ NFLt 1
t 1
190
APPENDIX C—PROOF OF PROPOSITION 2-3
Appendix C is the proof of the existence of subjective expected utility in a limited rational choice
and mimics the proof of von Neumann-Morgenstern’s expected utility function in a perfect rational
choice (e.g., Huang & Litzenberger 1988, for a derivation of the vNM utility function).
C.1 Structuring the problem
Assume that the subject has state-independent utility function, i.e. the subject values a consequence
uniformly no matter in which state it occurs: ua c ub c a, b ‰ SK . State-independent utility
makes it possible to form the union of all the state-dependent consequence sets such that it becomes
a total subjective consequence set: C K *s ‰S C s . 24
K
Since the subjective state consequence sets are strict subsets to their objective sets because of
limited knowledge, it is possible to expect total subjective consequence set to be bounded from
above and below. However, when generalizing the concept of the subjective consequence set, it
follows from Proposition 2-1 (p. 32) that the total subjective consequence set can become unbounded unless there are further restrictions from the state set. Since the theory of Homo comperiens also restricts the subjective state set to be a strict subset to its objective set, this set is also
bounded and therefore the total subjective consequence set also becomes bounded.
Since the total subjective consequence set is bounded, it has a upper bound, z , and a lower
bound, z . 25
I assume that all the intermediate consequences between the upper and lower bounds can be
measured as a weighted average of the two bounds. This means that the subject is, e.g., indifferent
between consequence g and a weighted average, uK z ¸ z 1 uK z ¸ z , of the supremum and
infimum consequences, where uK z ‰ <0,1> . 26
24 The total subjective consequence set consists of all consequences that the subject knows. The knowledge of possible
consequence is restricted because of the limited knowledge of available alternatives and by the subject’s limited knowledge of the possible states.
25 Baumol (1961) calls these two extreme consequences “eternal bliss” and “damnation.” Mathematics calls these extreme consequences supremum (eternal bliss) and infimum (damnation). Upper bound, eternal bliss, and supremum are
used interchangeably in this appendix. Damnation, lower bound, and infimum are also used interchangeably in this text
For the mathematical definition of a supremum and infimum, as well as the definition of a bounded set, see, e.g.,
Sydsæter (1999).
Note that I focus on the subjective supremum and infimum consequences and not the objective counterparts.
26 In this study, a consequence, which is a function of two other consequences, is called a complex consequence.
191
The symbol uK ¸
is the subjective unique mass assigned by the subject to the upper bound
consequence in order to have indifference between consequence g and the complex consequence.
This type of mass is interpreted in financial economics as a probability in a lottery where the two
potential consequences are the upper and lower bound, but where only the objective mass is considered (Huang & Litzenberger, 1988).
The possibility to have g uK z ¸ z 1 uK z ¸ z rests on the existence of a preference
relation that is complete, transitive, continuous, state-uniform, independent, and which follows the
Archimedean conjecture. For a proof in a perfect rational choice, see, e.g., Kreps (1988).
The completeness, transitivity, continuity, and the state-uniform conjectures have already
been assumed in Chapter 2. To these I add the independence and the Archimedean conjectures.
These are presented below.
The independence conjecture asserts that for all consequences z , z, z ‰ C K , there exists some
uK z ‰ 0,1> , such that z ; z º uK z ¸ z 1 uK z ¸ z ; uK z ¸ z 1 uK z ¸ z .
Similarly, the Archimedean conjecture asserts that for all consequences z , z, z ‰ C K , and
uK z , uK z a
‰ < 0,1> , z ; z ; z º uK z ¸ z 1 uK z ¸ z ; z ; uK z a
¸ z 1 uK z a
¸ z .
The definition of the independence conjecture and the Archimedean conjecture is found in many
financial economics books (e.g., Huang & Litzenberger 1988), although here I apply them in a limited rational choice.
The independence conjecture determines that the subject’s preference towards the complex
consequence uK z ¸ z 1 uK z ¸ z and the complex consequence uK z ¸ z 1 uK z ¸ z
depends solely on how he or she feels about z and z , given that this is the only thing that differs
between the two complex consequences. Consequence 1 uK z ¸ z is irrelevant in the choice
between the two consequences because it is part of both complex consequences.
The Archimedean conjecture is best exemplified using a gamble. Suppose z is eternal bliss, z
is just managing to go around, and z is a gruesome death. Then, if the complex consequence
uK z ¸ z 1 uK z ¸ z is a lottery, there will be an uK z ‰ <0,1> (most likely close to 1) where
the subject exhibits a preference such as uK z ¸ z 1 uK z ¸ z ; z .
Armed with this structure, I present the derivation of subjective expected utility in a limited
rational choice.
C.2 Derivation
Since every consequence can be described as weighted averages of the supremum and infimum consequences, all state consequences for an uncertain choice can be described using the same argu-
192
ments. Suppose that an action e has three state-dependent consequences denoted p, h, j. Assume for
now that the subject is only aware of the two state-dependent consequences p and h. These consequences can, with the additional conjectures of continuous state-uniform preferences that are independent and that follow the Archimedean conjecture, be described as:
p uK z ¸ z 1 uK z ¸ z , and h uK z a
¸ z 1 uK z a
¸ z , where uK z , uK z a
‰ < 0,1> .
Chapter 2 defines states such that it allows probabilities to be assigned to each state. Since
the occurrence of a state is beyond the control of the subject, it is also not possible for the subject to
affect the probability for a state to occur. The probability-on-states view is useful in the above example. Choice alternative e has the following consequence p, h; QKp , QKh . Since only two consequences can ensue, it can be expressed more succinctly as p, h; QKp . Replacing p with
uK z ¸ z 1 uK z ¸ z and h with uK z a
¸ z 1 uK z a
¸ z gives the following complex con-
sequence uK z ¸ z 1 uK z ¸ z , uK z a
¸ z 1 uK z a
¸ z ; QKp . This means that
p, h; QKp z , z ; Qp ¸ uK z 1 QKp ¸ uK z a
holds.
Precisely as it is possible to describe consequences p and e in terms of a bundle that is a
weighted average of the supremum and infimum consequences, it is also possible to describe the
uncertain consequence p, h; QKp in terms of a weighted average of the extreme consequences. This
standard bundle is signified by z , z ; EK 0 ¡UK p, h; QKp ¯° , where EK 0 ¡UK p, h; QKp ¯° ‰ <0,1> is the
¢
±
¢
±
subjective mass assigned at present to the supremum consequence necessary for p, h; QKp z , z ; E
K0
U p, h; Q ¯ .
Kp °±
¡¢ K
The existence of the standard bundle means the following relations exist
p, h; QKp z , z ; EK 0 ¢¡UK p, h; QKp ¯±° z , z ; QKp ¸ uK z 1 QKp ¸ uK z a
, and from this relation it follows that EK 0 ¡UK p, h; QKp ¯° Qp ¸ uK z 1 QKp ¸ uK z a
.
¢
±
The subjective expected utility function is cardinal with range <0,1> . uK z and uK z a
are
utilities with the same range but on sure-thing consequences. This kind of utility is also known as a
Bernoulli utility (Mas-Colell et al. 1995) in the perfect rational choice. Here I call it subjective Bernoulli utility since it is formed, with limited knowledge on supremum and infimum consequences
that stem from the subjective consequence set.
uK z is from now on denoted uK p and u z a
is denoted uK h . They are the real values
of the function uK : C K l at p and h, where C K ‡ C 8 .
193
The subjective expected-utility function can be expanded to cover more than two states.
When it covers all states in the general description of the state space, it can be written as
EK 0 ¢UK c1, !cS ; QK 1, ! QKS ¯± œ
s ‰SK
QKs ¸ uK cs , where c ‰ C K , and QKs ‰ 1K .
C.3 Discussion
The difference between the subjective expected-utility of an action and the objective expected-utility
of the action rests on (i) the subjective state probability and (ii) the subjective Bernoulli utility.
The subjective states are mutually exclusive and form an exhaustive state set. However, the
subject fails to appreciate all the states because of limited knowledge. The subject thus infers that
each state has a subjective probability, QKs . Proposition 2-2 (p. 35) argues that at least one subjective
state probability must be different to the objective state probability when the subjective state set is a
strict subset of the objective state set. It therefore follows that the subject’s limited rational choice is
erroneous when compared with the perfect rational choice. This is due to limited knowledge.
The supremum and the infimum consequences in the perfect rational choice are based on the
objective consequence set. The subjective consequence set is a strict subset of the objective consequence set and thus the subjective supremum and the infimum consequences are probably different
from the objective supremum and the infimum consequences. This means that the subjective Bernoulli utilities change when we go from a perfect rational choice to a limited rational choice; again,
this is due to limited knowledge.
In conclusion, both the subjective Bernoulli utilities and the subjective expected utilities retain the range <0,1> in the limited rational choice. However, since the subject only knows of a subset
of the objective state set, it is reasonable to expect to see subjective Bernoulli utilities differ from the
objective Bernoulli utilities, as well as a difference between the subjective expected utility and the
objective expected utility. The difference between the subjective expected utility and the objective
expected utility is due to different Bernoulli utilities and different state probabilities and both of
these differences are due to limited knowledge (Definition 2-2, p. 29, and Definition 2-6, p. 33).
194
APPENDIX D—OPERATIONALIZATION OF GROUP
CONTRIBUTION AND OF UNTAXED RESERVE
77NAME 80NAME 85NAME 91NAME 94NAME 95NAME
Group contribution
Contribution from group companies, net
Shareholders' contribution
SPECB4
SPECB6
SPECB6
SPECB7
SPECC6
SPECC7
SPECC5
SPECC1
SPECC2
SPECC3
SPECC1
SPECC2
SPECC3
Appropriations
Change of tax allocation reserve
Change of tax equalization reserve
Change of investment reserve
Dissolving inventory reserve and profit equalization reserve
Transfer to tax equalization reserve
Transfer to transitional reserve
Change of inventory reserve
SPECB1
Change of profit equalization reserve
Transfer to investment reserve
SPECB2
Accelerated depreciation, excl. investment reserve SPECB3
Reversal of accelerated depreciation for sold fixed assets
Other changes in the untaxed reserve
SPECB5
SPECB1
SPECB2
SPECB3
SPECB1
SPECB2
SPECB3
SPECB4
SPECB5
SPECB7
SPECB1
SPECB2
SPECB3
SPECB4
SPECB5
SPECB7
SPECB4
SPECB5
SPECB6
SPECB8
SPECC4
SPECC5
SPECC8
SPECC4
BAL40
BAL41
BAL41
BAL40
BAL32
Untaxed reserve
Total untaxed reserve
Inventory reserve
Accumulated accelerated depreciation
Investment reserve, et cetera
Other untaxed reserves
BAL35
BAL36
BAL37
BAL38
Total untaxed reserve for the period 1977 to 1979 is sometimes not equal to the sum of its components, and an analyzis shows
that it is the total untaxed reserve calculation that is incorrect and the components are correct.
From 1995 is the data collection method changed so that the firm’s group contribution and shareholders’ contribution is
aggregated with the appropriation called “other changes in the untaxed reserve.” To get an estimation of firm’s group
contributions and shareholders’ contributions during 1995 to 1996 is the following method applied.
To get an estimation of firms’ group contributions and shareholders’ contributions during 1995 to 1996 is the ratio between the
group contributions and shareholders’ contributions, and the sum of the group contributions, shareholders’ contributions, and
other changes in the untaxed reserve studied for 1994. The ratio is defined as
(SPECC6+SPECC7)/(SPECC5+SPECC6+SPECC7).
In the full sample of 1511 firms, only two percent (30 firms) reported other changes in the untaxed reserve. Of these firms, 16
reports a ratio between 0.98-1.02, three firms have a ratio higher than 1.02, and 11 firms reports a ratio lower than 0.98.
A total of 780 firms (of 1511) had a sum of group contributions and shareholders’ contributions other than zero for 1994. Of
these firms, the relation was evaluated to 1.0 for 758 firms, the maximum was 1.6, and the minimum was -1.3. This means that
of those firms that has group contributions, or shareholders’ contributions, the vast majority reports no “other changes in the
untaxed reserve.”
Based on these findings is all of other changes in the untaxed reserve for 1995 to 1996 classified as group
contribution/shareholders’ contribution.
195
APPENDIX E—TRACING FIRMS
E.1 Introduction
This appendix supplies a description of the method used for following firms across the empirical
data’s period and for finding the opening balance sheet for the firms.
The financial data set supplied by SCB consists of a table for each year between 1977 and
1996 with financial data for all active27 limited companies (firms) involved in the Swedish manufacturing industry. In these tables are firms the individual elements and they are identified using their
civic registration numbers (Organisationsnummer in Swedish).
Year No. Year No. Year No. Year No.
1977 893 1982 1,689 1987 1,859 1992 1,586
1978 947 1983 1,706 1988 1,907 1993 1,446
1979 1,643 1984 1,738 1989 1,961 1994 1,511
1980 1,644 1985 1,781 1990 1,889 1995 1,801
1981 1,663 1986 1,836 1991 1,869 1996 1,882
Table E-1: The total number of limited companies (firms) in the empirical data.
SCB also supplied tables for each year with information on local units. A local unit is according to SCB’s definition the same as each address, building or group of buildings where the enterprise
carries out economic activity. The local unit is identified in the tables using a unique local unit identification number. To each local unit identification number is a firm’s civic registration number attached. This means that the local units are unique, and to each local unit is only one civic registration
number attached. An active firm has at least one local unit. 28
E.2 Tracing firms and identifying each firm’s opening balance sheet
In the financial tables are, among other things, the firms’ current income statement and the closing
balance sheet supplied.
To be able to calculate rates-of-returns must the opening balance sheet be identified and
therefore must at least two consecutive balance sheets be identified for a particular firm. The change
in the equity account is also analyzed. This requires at least two consecutive balance sheets to be
identified for a particular firm. When the hypotheses have been posed and are tested is pooled timeseries analysis applied to increase the sample size, and this requires that more than two consecutive
27 SCB defines an active firm as a firm that is registered as employer, it is registered for VAT, and it has a certificate for
business tax.
28 An active firm can also have additional local units when the following criteria are met: (i) there are some activity, (ii)
there is a place where activity is going on, (iii) the activity is ongoing, and (iv) it has employees
197
balance sheets can be identified for a particular firm. Because of these reasons is the following method used to identify firm across time.
A firm’s civic registration number may exist in a certain year but can appear to have disappeared in the year that follows. The can be interpreted several ways: (i) The firm may continue to
exist but has changed civic registration number, (ii) the firms has closed its operations without selling off its production structure, (iii) the firm has merged with another firm. Or (iv) the firm has
spun-off all of its production structure to another firms, that may be already existing or where they
are newly incepted with the purpose of taking over parts of the old production structure.
Since the purpose is to find consecutive balance sheets are scenario (iii) and (iv) analyzed
with the purpose of tracing if any firm can be classified as a surviving firm.
It is also possible that firms only merges parts of its operations with another firm, or it may
just spin-off parts of its operations. It is also conceivable that a firm also appears as a seller and buyer of production structure within a financial year. Also these partial transactions are analyzed with
the purpose of tracing if any firm can be classified as a surviving firm.
Whether a firm is classified as a survivor depends on the change in the firms production
structure is deemed significant. The firm’s production structure is in this research operationalized as
the local units attached to the firm.
A merger is defined as follows. First are the information on local units used to identify those
local units that exist in two consecutive years. Those local units are used to identify the civic registration number for the two years. Then are the number of civic registration number in the preceding
year calculated based on each new civic registration number. This procedure provides information
where new firms have purchased at least one local unit during the year from another firm.
A complete merger is defined as those mergers where all of the old civic registration numbers (having one or more local units attached to it) is completely subsumed by a new civic registration number. The new civic registration number may have been part of the set of old civic registration numbers participating in the merger, but this is not a requirement. It is conceivable that the new
firm changes its civic registration number at the time of the merger. Partial mergers are all those
mergers not fulfilling the conditions of a complete merger.
When there is a complete merger between two firms, the size of them can be used as a signal
on the structural change. Size can be measured using e.g., market prices, book values of assets, book
values of equity, or sales.
In this thesis, market prices are considered disequilibrium prices and hence not good descriptors of the firm’s size of its production structure. Book values are subjected to conservativism and
are not good descriptors of the firm’s size. The sales revenue indicates the firm’s market power on
its customers, but is silent on the firm’s productions structure. Since the focus is on the structural
198
stability is also sales a bad descriptors of the firm’s size of its production structure. This thesis used
value added (calculated before depreciation) as a descriptor on the firm’s size of its production structure.
The second issue that must be addressed in survival classification is when the change is significant. This thesis makes an analogy to FAR no. 3 that states that a material difference exists between the book value and market price of an asset when it is greater than 20 percent. Thus is a
change in the firm’s production structure, operationalized as value added, greater than 20 percent,
classified as a significant structural change.
When there is a complete merger, is the firms’ value added from the year preceding the merger used for estimating the structural change. If a firm has at least 80 percent of the combined value
added, it is classified as a survivor, and is deemed structurally stable. This implies that that firm’s
closing balance sheet, preceding the merger, is used as the opening balance sheet after the merger. In
essence, this means that this firm is treated as if there had been no merger. Those firms that do not
satisfy the threshold value are treated as if they close their operations at the time of the merger.
When the complete merger implies that all merging firms are structurally instable, all of them
are treated as if they close their operations at the time of the merger. Since the merger is complete,
the sum of the merging firms’ opening balance sheets can function as the opening balance sheet for
the new firm. By also using these firms’ income statements for the year preceding the merger and
that year’s opening balance sheet the change in rate-of-returns can be analyzed already from the
merging year.
Partial mergers imply that only some of the production structure is sold to another firm. The
purchasing firm may or may not have existed before the financial year when the purchase of takes
place.
When the firm did not exist in the previous year, i.e., when the new civic registration number
did not exist in the previous year, it is classified as structurally instable. When the purchasing firm
existed in the preceding year is its change in real value added 29 between the two consecutive years
used for measuring structural stability. When the change in the real value added is less than or equal
to 20 percent it is treated as a structurally stable firm. A structurally stable firm participating in a
partial merger is treated identically as a structurally stable firm participating in a complete merger.
A spin-off is defined as follows. Again, the local units are used to identify the civic registration number for the two years. The number of civic registration numbers in the new year is calculated based on each old civic registration number. This procedure provides information on old firms
that have sold at least one local unit during the year to another firm.
29 The nominal value added is deflated using the production price index on SIC-code 38 (SNI62) published by SCB. This
ensures that industry-specific inflation does not affect the reliability of the method.
199
A complete spin-off is defined as a spin-off where all of the new civic registration numbers
can be completely related to an old civic registration number. The new civic registration number
may have been part of the set of old civic registration numbers participating in the merger, but this
is not a requirement. No other old civic registration number is allowed among the new civic registration number in the complete spin-off. This assures that the set all new civic registration numbers,
for a particular spin-off, has an identical production set as that of the old civic registration number
that spun-off the units. Partial spin-offs are all those sales of local units that do not fulfill the conditions of a complete spin-off.
The evaluation of the structural stability in the complete spin-off is similar to that in a complete merger. In this research is the value added of each new civic registration number, for a given
spin-off, compared with the sum of the new civic registration numbers’ value added. If a civic registration number has a ratio of at least 80 percent it is evaluated as structurally stable. When this occurs, it is treated identically to a structurally stable complete merger.
A partial spin-off is evaluated similarly to a partial merger. Only a firm that sold part of its
local units and that continued to exist is evaluated in this research as a potentially structurally stable
firm. Any partial spin-off is treated as structurally instable. The structural stability is evaluated using
the change in the real value added, and any change greater than 20 percent implies a structural instable spin-off. A structural stable partial spin-off is treated in the same manner as a structurally stable
complete merger.
Sometimes a firm both sells and buys local units in a given financial year. This implies that it
appear as both a merger and a spin-off. When this happens is again the change in real value added
used as a measure of the structural stability, but since it has made at least two transactions is the
threshold value decreased to 10 percent. Any composite change in the real value added less than or
equal to 10 percent is classified as a structural stable change.
With the procedure above can most of the firms be analyzed. Those firms that are not considered in the analysis above are compared on their civic registration numbers and names. Where the
new civic registration number is identical to an old civic registration number it is classified as a structurally stable firm. That firm that cannot be matched on the civic registration number is compared
based on the firm’s name. Firms having identical names over two consecutive years are also classified as structurally stable firms.
All civic registration numbers that exists in the data set for the new year and that have not
been covered in the analysis above, are classified as completely new firms that lacks an opening balance before the focal year.
The table on the next page provides a summary of the number of structurally stable firm and
structurally instable firms.
200
Number of firms in the sample
Structurally stable firms
of which competely stable firms
of which complete mergers
of which partial mergers
of which complete spin-offs
of which partial spin-offs
of which composite activity
of which matching civic registration no.
of which matching firm name
Structurally instable firms
of which complete mergers
of which partial mergers
of which complete spin-offs
of which partial spin-offs
Total number of firms
1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990
805 859 1,496 1,505 1,534 1,506 1,540 1,587 1,621 1,638 1,668 1,723 1,629 1,639
796
1
0
0
0
0
8
0
845 1,483 1,486 1,518 1,482 1,511 1,558 1,592 1,620
1
1
2
0
2
2
4
3
4
0
0
0
0
0
0
0
0
0
2
2
2
3
2
3
2
2
0
2
0
6
2
2
3
4
0
1
1
0
1
0
0
1
1
2
0
8
10
6
7
15
17
13
18
10
0
0
2
4
3
3
5
4
3
1,646 1,692 1,609 1,626
2
4
2
3
0
0
0
0
6
7
4
5
3
2
2
1
1
1
1
0
7
12
10
2
3
5
1
2
88
88
147
139
129
183
166
151
160
198
191
184
332
250
4
2
0
2
4
8
2
4
6
0
1
1
2
10
1
1
2
2
4
0
12
2
4
0
9
4
2
3
6
2
1
1
10
2
3
3
22
4
2
3
11
8
9
4
16
2
5
0
26
2
6
1
13
6
4
2
893
947 1,643 1,644 1,663 1,689 1,706 1,738 1,781 1,836 1,859 1,907 1,961 1,889
Note that the analysis on which this table rests, focuses on the structural stability/instability for the next following year. That means that the
complete mergers for year 1995 should be interpreted as if there was three firms in 1995 that merged in 1996 with other firms, but where
enough to be classified as structurally stable, i.e., as survivors in the mergers.
Table E-2: A summary of the number of structurally stable and structurally instable firms
for the empirical data
E.3 Finding usable firm-year observations
The table summarizing the effect of the preceding sections method of tracing firms does not suffice
for economic analysis. Some firms have been classified as non-response by SCB have their data imputed. Erikson (2003) reports on the procedure used by SCB on non-response firms.
Non-response firms are according to Erikson firms that did not file an income declaration,
firms that filed their income declaration too late and was not in the database at the time of delivery
to SCB, firms having filed income declaration but is still missing from the database, and the firm
may no longer exist but data is still needed. The last point stems from erroneous definition of the
population of active firms.
SCB uses an all or nothing method for imputation. This means that either is the firm’s data
used or it is not used at all. It implies that when some data is still missing after manual editing, and
the firm is classified as non-response, it has all of its data imputed. The imputation uses either of
two methods. SCB can use the firm’s previous period’s financial data and then imputes it into the
current year. Or SCB uses the average values for the industry and size class as a source in the imputation. The size class is based on average number of employees.
None-response firms have imputed industry average values or imputed one-year old financial
data instead of their true values. Making comparison over time for an individual firm, such as calculating its rate-of-return on equity, gives incorrect values for the non-response firms due to the imputation. The structurally stable firm-year observations from the previous section are tainted by nonresponse firms and are cleansed using the method described below. The remaining firm-years are
classified as usable firm-year observations, and on them can economic analysis can be performed.
There is no a prioi way to identify non-response firms. In this research are two avenues pursued to identify non-response firms. First is non-response firms identified that has had its data im-
201
puted by the industry average. Then is non-response firms identified that have had its data imputed
by the previous year’s financial data.
Non-response firms that uses imputed industry data is identified by finding those firms, for a
given year, that have an identical string of variables. When more than one firm has identical average
number of employees, value added, net income, total assets, total untaxed reserve, and total equity,
are they classified as imputed firms. It is argued that it is virtually impossible for more than one firm
to have so many identical variables.
This method finds the industry average values for those firms where SCB has used the industry average more than once. It fails to detect those situations where the string of variables has been
imputed only once.
The table below reports the number of identified non-response firms per year that uses industry averages.
Year No. Year No. Year No. Year No.
1977 158 1982 100 1987 76 1992 53
1978 100 1983 93 1988 105 1993 28
1979 90 1984 74 1989 110 1994
8
1980 40 1985 80 1990 96 1995 80
1981 35 1986 73 1991 91 1996 15
Table E-3: The number of imputed firm in the data set using industry averages.
Given the analysis in this and the preceding section is the number of firm-year observations
reduced from being totally 33,251 to 26,246 firm-years.
Non-response firms that uses imputed previous year’s financial data is identified as those
firms that have two consecutive years of identical average number of employees, value added, net
income, total assets, total untaxed reserve, and total equity. This method uses the same string of
variables as that is used to identify imputed industry data.
Year No. Year No. Year No. Year No.
1978
0 1983 17 1988 123 1993
6
1979
5 1984 16 1989 104 1994
7
1980
0 1985
0 1990 102 1995
8
1981 117 1986 73 1991 123 1996 68
1982 103 1987 89 1992 43
Table E-4: The number of imputed firm in the data set using previous year’s financial data.
Cleaning the data set from the imputed firm-year observations in the table above reduces the
number of usable observations to 25,245. The table below summarizes the effects of the tracing and
cleansing process.
202
Total number of firm-year observations 1977-1996
Potentially usable firm-year observations (1978-1996)
Structurally stable (or structurally instable w complete merger)
Usable firm-year observations
33,251
32,358
27,864
25,245
A usable firm-year is a firm’s complete set of usable financial data for a
particular year where the firm has a preceding year of usable financial data.
For the financial data to be usable must two criteria be satisfied. (i) The
firm must be classified as either structurally stable or where it is structurally
instable must there be a complete merger. A structurally instable complete
merger allows the merging firms’ financial data to be merged for the
preceding year. This creates a structurally stable opening balance sheet for
the merged firm. (ii) No financial data appears to have been imputed by
SCB.
Table E-5: Summary of number of firm-year observations.
The firm-year observations can be matched to form time-series of financial data for each
firm. The length of each time series depends on the structural stability of each firm and of any imputation of the firm’s financial data. The table below reports the number of usable times-series for
various lengths of the time-series.
Yrs A
B
C
D
Yrs A
B
C
D
1 876 876 3,971 25,245 11 105 1,155 883 13,283
2 499 998 3,095 24,369 12 109 1,308 778 12,128
3 308 924 2,596 23,371 13 111 1,443 669 10,820
4 289 1,156 2,288 22,447 14 68 952 558 9,377
5 238 1,190 1,999 21,291 15 73 1,095 490 8,425
6 236 1,416 1,761 20,101 16 90 1,440 417 7,330
7 183 1,281 1,525 18,685 17 132 2,244 327 5,890
8 161 1,288 1,342 17,404 18 59 1,062 195 3,646
9 147 1,323 1,181 16,116 19 136 2,584 136 2,584
10 151 1,510 1,034 14,793
Table E-6: The time-series of structurally stable non-imputed firms.
The table above should be interpreted as follows. Column A reports the number of firms
that have only a given number of years of structurally stability and that are not affected by imputation. In this case, for example, 499 firms have two years of structurally stable non-imputed data.
These firms use 998 firm-years observations (column B) of the usable set’s 25,245 firm-year observations.
Column C reports the accumulated number of available time-series: There are 3,095 unique
time-series of firms that has at least two years of structurally stable non-imputed data. Column D
reports the accumulated number of usable firm-year observations. A pure cross-sectional analysis on
203
the data set employs 25,245 firm-year observations, where a pooled time-series analysis over five
years employs 21,291 firms-year observations (and 1,999 unique time-series).
204
BAL5, BAL6
BAL1, BAL12
BAL4, BAL7
BAL15, BAL16
BAL3
BAL2, BAL14
BAL24, BAL25
BAL29
BAL23, BAL27, BAL28
BAL32
BAL31, BAL33
BAL40
BAL41
BAL42
BAL43
Rest of BAL39
Tax rate*BAL39
BAL26
BAL9, BAL10
BAL8
BAL17
BAL20
BAL19
BAL18
BAL13
77NAME
BAL5, BAL6
BAL1, BAL12
BAL4, BAL7
BAL15, BAL16
BAL3
BAL2, BAL14
BAL24, BAL25
BAL29
BAL23, BAL27, BAL28
BAL32
BAL31, BAL33
BAL41
BAL42
BAL43
BAL44
Rest of BAL40
Tax rate*BAL40
BAL26
BAL9, BAL10
BAL8
BAL17
BAL20
BAL19
BAL18
BAL13
80NAME
BAL5, BAL6
BAL1, BAL12
BAL4, BAL7
BAL15, BAL16
BAL3
BAL2, BAL14
BAL24, BAL25
BAL29
BAL23, BAL27, BAL28
BAL32
BAL31, BAL33
BAL42
BAL43
BAL44
BAL45
Rest of BAL41
Tax rate*BAL41
BAL26
BAL9, BAL10
BAL8
BAL17
BAL20
BAL19
BAL18
BAL13
85NAME
BAL6
BAL1, BAL12
BAL4, BAL5 BAL7
BAL15, BAL16
BAL3
BAL2, BAL14
BAL25
BAL29
BAL23, BAL24, BAL27, BAL28
BAL32
BAL31, BAL33
BAL42
BAL43
BAL44
BAL45
Rest of BAL41
Tax rate*BAL41
BAL26
BAL9, BAL10
BAL8
BAL17
BAL20
BAL19
BAL18
BAL13
91NAME
BAL6
BAL1, BAL12
BAL4, BAL5 BAL7
BAL15, BAL16
BAL3
BAL2, BAL14
BAL25
BAL29
BAL23, BAL24, BAL27, BAL28
BAL32
BAL31, BAL33
BAL41
BAL42
BAL43
BAL44
Rest of BAL40
Tax rate*BAL40
BAL26
BAL9, BAL10
BAL8
BAL17
BAL20
BAL19
BAL18
BAL13
94NAME
BAL4
BAL1
BAL6
BAL10
BAL3
BAL2, Rest of BAL9
BAL18
BAL22
BAL20, BAL21
BAL24
BAL25
EGKAP1
EGKAP2
EGKAP3
EGKAP4
Rest of BAL32
Tax rate*BAL32
BAL19
BAL7
BAL5
BAL11
BAL14, BAL15
BAL13
BAL12
Part of BAL9
95NAME
It is assumed that firms that did not exist in 1994, but that exist later and that fall into category (i), only have shares and participations in group companies. For firms falling into category (ii) during 1995 and 1996, and that did not exist in 1994, it
is assumed that there are no shares and participations in group companies.
In 1994 firms falling into category (i) have a median ratio of 99.5 percent, indicating that virtually all shares and participations can be ascribed to holdings of group firms. Furthermore, 93 percent of the firms report shares and participations in
group companies. Category (ii) has a median ratio of 0 percent for the same year, and 70 percent of the firms report no shares and participations in group companies.
Firms that did not exist in 1994 are analyzed based on two cases: (i) the firm report dividends from group companies, (ii) the firm report no dividends from group companies.
For 1995 and 1996, the shares and participations in group companies are aggregated with shares and participations in other companies. This thesis split, according to the analysis below, the sum of shares and participations into the two
components to maintain comparability across all periods.
The data from 1994 is used for identifying firms that should have ownership in group companies. For those firms that exist from 1994 through 1995 and 1996, is the 1994-ratio between shares and participations in group companies and shares
and participations in group companies aggregated with shares and participations in other companies [BAL13/(BAL13+BAL14)] assumed to persist through the following years.
Accounts receivables
Cash and bank balances
Other current receivables
Other long-term receivables
Bonds and other securities
Shares and participations in other firms
Financial assets (FA)
Accounts payable
Advance payments from customers
Other current liabilites
Pension liabilities
Other long term liabilities
Financial liabilities (FL)
EQUITY (EQ)
Share capital
Restricted reserves
Retained earnings
Reported net income
Equity proportion of the untaxed reserve
NET FINANCIAL LIABILITIES (NFL)
Deferred tax proportion of the untaxed reserve
Provision for taxes
Operating liabilities (OL)
Inventories and advance payments
Prepaid expenses and accrued income
Intangible assets
Land and buildings
Plant and equipments
Construction in process and advance payments for tangible assets
Shares and participations in group companies
Operating assets (OA)
NET OPERATING ASSETS (NOA)
APPENDIX F—OPERATIONALIZATION OF THE BALANCE
SHEET
205
UTR(t)-UTR(t-1)+APR(t)
GAIN*
ACC*
[Tax rate(t-1)-Tax rate(t)]*UTR(t-1)
-(RES8+RES9-RES10) (RES10+RES11+RES12-RES13)
Sum of below
-Tax rate*GS
-Tax rate*IAC
-Tax rate*[UTR(t)-UTR(t-1)+APR(t)]
-Tax rate*ERROI
Unaccounted changes in UTR
GAIN*
ACC*
Gain or loss due changing tax rate
Summation errors in OI (ERROI)
Tax on peripheral operating income
Tax on government subsidies (TGS)
Tax on items affecting comparability (TIAC)
Tax on unaccounted changes in UTR
Tax on ERROI (TERROI)
RFRET(t)*Accounts receivable(t-1)
RFRET(t)*Accounts receivable(t-1)
Sum of below
SPECA3, SPECA4
-Tax rate*GS
-Tax rate*IAC
-Tax rate*[UTR(t)-UTR(t-1)+APR(t)]
-Tax rate*ERROI
RFRET(t)*Accounts receivable(t-1)
Sum of below
SPECA3, SPECA4
-Tax rate*GS
-Tax rate*IAC
-Tax rate*[UTR(t)-UTR(t-1)+APR(t)]
-Tax rate*ERROI
Sum of below
-(RES1+RES2+RES4-RES5) (RES8+RES9-RES10) (RES10+RES11+RES12-RES13)
-(RES1+RES2+RES4-RES5) (RES8+RES9-RES10) (RES10+RES11+RES12-RES13)
Sum of below
UTR(t)-UTR(t-1)+APR(t)
GAIN*/(1-Tax rate)
ACC*/(1-Tax rate)
[Tax rate(t-1)-Tax rate(t)]*UTR(t-1)
SPECA1
BIDRAG1+BIDRAG2
RES9-BIDRAG2
Sum of below
RES12
Tax rate*APR(t)
-TGS
-TIAC
-TSERROI
-TCCMI
-TPCMI
Sum of below
-BAS4
RES4
VA-RES1
+RFRET(t)*Accounts payable (t-1)
+RFRET(t)*Pension liabilites (t-1)
Sum of below
RES1
-RFRET(t)*Accounts receivable(t-1)
+RFRET(t)*Adv. paym. fr cust (t-1)
Sum of below
85NAME
UTR(t)-UTR(t-1)+APR(t)
GAIN*/(1-Tax rate)
ACC*/(1-Tax rate)
[Tax rate(t-1)-Tax rate(t)]*UTR(t-1)
SPECA1
BIDRAG1+BIDRAG2
RES9-BIDRAG2
Sum of below
RES12
Tax rate*APR(t)
-TGS
-TIAC
-TSERROI
-TCCMI
-TPCMI
Sum of below
-BAS4
RES4
VA-RES1
+RFRET(t)*Accounts payable (t-1)
+RFRET(t)*Pension liabilites (t-1)
Sum of below
RES1
-RFRET(t)*Accounts receivable(t-1)
+RFRET(t)*Adv. paym. fr cust (t-1)
Sum of below
80NAME
RFRET(t)*Accounts receivable(t-1)
Sum of below
SPECA3, SPECA4
-Tax rate*GS
-Tax rate*IAC
-Tax rate*[UTR(t)-UTR(t-1)+APR(t)]
-Tax rate*ERROI
Sum of below
-(RES1+RES2+RES4-RES5) (RES8+RES9-RES10) (RES10+RES11+RES12-RES13)
UTR(t)-UTR(t-1)+APR(t)
GAIN*/(1-Tax rate)
ACC*/(1-Tax rate)
[Tax rate(t-1)-Tax rate(t)]*UTR(t-1)
SPECA1
BIDRAG
RES9
Sum of below
RES12
Tax rate*APR(t)
-TGS
-TIAC
-TSERROI
-TCCMI
-TPCMI
Sum of below
-BAS4
RES4
VA-RES1
+RFRET(t)*Accounts payable (t-1)
+RFRET(t)*Pension liabilites (t-1)
Sum of below
RES1
-RFRET(t)*Accounts receivable(t-1)
+RFRET(t)*Adv. paym. fr cust (t-1)
Sum of below
91NAME
Supporting variable
Value added (VA)
RES3+BAS4-BIDRAG1
RES3+BAS4-BIDRAG1
SPECA7
-(RES5+RES6+RES7-RES8)
-Tax rate*(FXRD+SERR)
RES7-(SPECA5+SPECA6)
-(RES5+RES6+RES7-RES8)
-Tax rate*(FXRD+SERR)
Exchange rate difference (FXRD)
Summation errors in income (ERRFI)
Tax on peripheral CFI (TPCFI)
RES3+BAS4-BIDRAG1
SPECA7
-(RES5+RES6+RES7-RES8)
-Tax rate*(FXRD+SERR)
-Tax rate*(IR+IE+ODIV)
SPECA2
SPECA2
-Tax rate*(IR+IE+ODIV)
SPECA2
-Tax rate*(IR+IE+ODIV)
-RFRET(t)*Pension liabilites (t-1)
-RFRET(t)*Adv. paym. fr cust (t-1)
-RFRET(t)*Pension liabilites (t-1)
-RFRET(t)*Adv. paym. fr cust (t-1)
Other dividends (ODIV)
-RFRET(t)*Pension liabilites (t-1)
-RFRET(t)*Adv. paym. fr cust (t-1)
Tax on core CFI (TCCFI)
-Implicit interest expense on PL
-Implicit interest expense on APL
RES3+BAS4-BIDRAG
SPECA7
-(RES5+RES6+RES7-RES8)
-Tax rate*(FXRD+SERR)
-Tax rate*(IR+IE+ODIV)
SPECA2
-RFRET(t)*Pension liabilites (t-1)
-RFRET(t)*Adv. paym. fr cust (t-1)
UTR(t)-UTR(t-1)+APR(t)
GAIN*/(1-Tax rate)
ACC*/(1-Tax rate)
[Tax rate(t-1)-Tax rate(t)]*UTR(t-1)
SPECB1
SPECA3
RES10+SPECA1+SPECA2
Sum of below
RES12
Tax rate*APR(t)
-TGS
-TIAC
-TSERROI
-TCCMI
-TPCMI
Sum of below
-BAS4
RES4
VA-RES1
+RFRET(t)*Accounts payable (t-1)
+RFRET(t)*Pension liabilites (t-1)
Sum of below
RES1
-RFRET(t)*Accounts receivable(t-1)
+RFRET(t)*Adv. paym. fr cust (t-1)
Sum of below
95NAME
RFRET(t)*Accounts receivable(t-1)
Sum of below
SPECB3, SPECB4, SPECB8
-Tax rate*GS
-Tax rate*IAC
-Tax rate*[UTR(t)-UTR(t-1)+APR(t)]
-Tax rate*ERROI
Sum of below
RES3+BAS4-SPECA1-SPECA2-SPECA4
SPECB7
-(RES5+RES6+RES7-RES8)
-Tax rate*(FXRD+SERR)
-Tax rate*(IR+IE+ODIV)
SPECB2
-RFRET(t)*Pension liabilites (t-1)
-RFRET(t)*Adv. paym. fr cust (t-1)
RES3+BAS4-SPECA1-SPECA2-SPECA3
SPECB5, SPECB6
-(RES5+RES6+RES7+RES8-RES9)
-Tax rate*(FXRD+SERR)
-Tax rate*(IR+IE+ODIV)
SPECB2
-RFRET(t)*Accounts payable (t-1)
-RFRET(t)*Pension liabilites (t-1)
-RFRET(t)*Adv. paym. fr cust (t-1)
Sum of below
SPECB4
RFRET(t)*Accounts receivable(t-1)
Sum of below
SPECB3
-Tax rate*GS
-Tax rate*IAC
-Tax rate*[UTR(t)-UTR(t-1)+APR(t)]
-Tax rate*ERROI
Sum of below
-(RES1+RES2+RES4-RES5) -(RES8+RES9-RES10) - -(RES1+RES2+RES4-RES5) -(RES9+RES10(RES10+RES11+RES12-RES13)
RES11) -(RES11+RES12+RES13-RES14)
UTR(t)-UTR(t-1)+APR(t)
GAIN*/(1-Tax rate)
ACC*/(1-Tax rate)
[Tax rate(t-1)-Tax rate(t)]*UTR(t-1)
SPECB1
SPECA4
RES9+SPECA1+SPECA2
Sum of below
RES12
Tax rate*APR(t)
-TGS
-TIAC
-TSERROI
-TCCMI
-TPCMI
Sum of below
-BAS4
RES4
VA-RES1
+RFRET(t)*Accounts payable (t-1)
+RFRET(t)*Pension liabilites (t-1)
Sum of below
RES1
-RFRET(t)*Accounts receivable(t-1)
+RFRET(t)*Adv. paym. fr cust (t-1)
Sum of below
94NAME
Adjusted
interestbefore
expense
(IE) and where government subsidies
Sum oftobelow
Sumtheofdata
below
Sumsubsidies
of below
Sum
of below
Sum of
oftotal
below
Value
added is calculated
depreciation
operating expenses are excluded. From 1991 does
not supply separate information on government
to operating expenses and on non-recurring
subsidies.
Analyzing the data for 1990 reveals that 85 percent
subsidies where
classified
as government
subsidies to operating expenses. Only 12 percent
of the firms
received any government subsidies to operating
expenses
and only 7 percent of the firms receivedSPECA5,
non-recurringSPECA6
subsidies. For the period 1991-1994 are allSPECA5,
government SPECA6
subsidies classified as government subsidiesSPECB5,
to operatingSPECB6
expenses, and are
Interest
expense
SPECA5,
SPECA6
SPECA5,
SPECA6
excluded from value added. For 1994 and forward are items such as capital gains and losses, and write-downs on fixed assets also included in the firm's operating income. In earlier periods they were treated as extra ordinary gains and losses. They are excluded from calculating value added for 1994 to maintain comparability with
interest
expense
on AP capital gains and losses, and
-RFRET(t)*Accounts
payable
(t-1)
payable
(t-1)
(t-1)
-RFRET(t)*Accounts
(t-1) (UTR) is found
-RFRET(t)*Accounts
earlier-Implicit
periods. 1995
and 1996
are subsidies,
write-downs on fixed assets
already
classified as items -RFRET(t)*Accounts
affecting comparability, and
hence they
do not affect the -RFRET(t)*Accounts
calculation of value added.payable
The operationalization
of appropriations
(APR) and the payable
untaxed reserve
in a separate appendix. payable (t-1)
+Implicit interest revenue on AR
Sum of below
SPECA3, SPECA4
SPECA1
BIDRAG1
RES9
Sum of below
Dividends from the group
Government subsidies (GS)
Items affecting comparability (IAC)
Dirty-surplus accounting
Comprehensive net interest expense
Adjusted interest revenue (IR)
Interest revenue
Sum of below
RES12
Tax rate*APR(t)
-TGS
-TIAC
-TERROI
-TCCMI
-TPCMI
Labor cost
Depreciation
Reported tax
Deferred tax
Tax on government subsidies
Tax on items affecting comparability
Tax on ERROI
Tax on core CFI
Tax on peripheral CFI
-BAS4
RES4
Cost of material
+Implicit interest expense on AP
+Implicit interest expense on PL
Tax on core operating income
Sum of below
VA-RES1
+RFRET(t)*Accounts payable (t-1)
+RFRET(t)*Pension liabilites (t-1)
Adjusted cost of material
Sum of below
RES1
-RFRET(t)*Accounts receivable(t-1)
+RFRET(t)*Adv. paym. fr cust (t-1)
Sales
-Implicit interest revenue on AR
+Implicit interest expense on APL
77NAME
Adjusted sales
Comprehensive operating income
APPENDIX G—OPERATIONALIZATION OF THE INCOME
STATEMENT
207
Swedish description
Redovisningsår
Organisationsnummer
Företagsnamn
Industriklassificering, 1969
Industriklassificering, 1992
Antal anställda
Löner
Arbetskraftskostnader, totalt
Förädlingsvärde
Omsättning
Rörelsens kostnader
Resultat före avskrivningar (Se spec. A)
Avskrivningar
Resultat efter avskrivningar
Jämförelsestörande poster (Se spec A)
Finansiella intäkter (Se spec. B)
Finansiella kostnader (Se spec. B)
Resultat efter finansnetto
Extraordinärt netto
Resultat före bokslutsdispositioner och skatt
Bokslutsdispositioner (Se spec. C)
Skatt (Se spec. C)
Redovisat årsresultat
Föreslagen utdelning
Nyemission inkl. överkurs
Fondemission mot uppskrivning av anläggningstillgångar
Statliga och kommunala bidrag
Bidrag till rörelsekostnader
Extraordinära bidrag
Realisationsvinst/förlust
Nedskrivning av aktier o materiella AT samt omstrukt. kostn.
Nedskrivning av AT
Kursdifferenser, netto
Statliga och kommunala bidrag
Utdelning från koncernföretag
Utdelning från övriga
Ränteintäkter m. m.
Räntekostnader m. m.
Valutakursvinster
Valutakursförluster
Räntor från koncernföretag
Övriga ränteintäkter
Räntor till koncernföretag
Övriga räntekostnader
Valutakursdifferenser, netto
Övriga finansiella poster, netto
Förändring av periodiseringsfond
Förändring av skatteutjämningsreserver m. m.
Förändring av investeringsfonder m. m.
Förändring av lagerreserv
Upplösning av lagerreserv och resultatutjämningsfond
Avsättning till skatteutjämningsreserv
Avsättning till uppskovsbelopp
Förändring av resultatutjämningsfond
Avsättning till investeringsfonder
Avskrivningar utöver plan, exkl. investeringsfonder
Återföring av överavskrivningar för sålda anläggningstillgångar
Koncernbidrag, netto
Aktieägartillskott, netto
Övriga bokslutsdispositioner
Vinstdelningsskatt
Övriga skatter
Kassa och bank
Aktier och andelar
Obligationer m. m.
Likvida medel hos koncernföretag
English description
Financial year
Identification number
Company name
Standard industry classification code, 1969
Standard industry classification code, 1992
Number of employees
Salaries
Labor expenses total
Value added
Sales revenue
Operating expenses
Operating income before depreciation (See spec. A)
Depreciation according to plan
Operating income
Items affecting comparability
Financial revenue (See spec. B)
Financial expenses (See spec. B)
Income after financial items
Non-recurring items
Income before changes in untaxed reserves and taxes
Changes in untaxed reserves (See Spec. C)
Reported tax (See spec. C)
Net income
Proposed dividend
New common stock issue, including agio
Bonus issue
Government and municipal subsidies
Subsidies to operating expenses
Non-recurring subsidies
Capital gain/loss
Write-down of shares, material FA, and restructuring costs
Write-down of fixed assets
Exchange rate difference, net
Government and municipal subsidies
Dividends from group companies
Dividends from other companies
Interest income
Interest expense
Exchange rate gain
Exchange rate loss
Interest revenue from group companies
Other interest revenue
Interest expense paid to group companies
Other interest expense
Exchange rate difference, net
Other financial items, net
Change of tax allocation reserve
Change of tax equalization reserve
Change of investment reserve
Change of inventory reserve
Dissolving inventory reserve and profit equalization reserve
Transfer to tax equalization reserve
Transfer to transitional reserve
Change of profit equalization reserve
Transfer to investment reserve
Accelerated depreciation, excluding investment reserve
Reversal of accelerated depreciation for sold fixed assets
Contribution from group companies, net
Shareholders' contribution
Other changes in the untaxed reserve
Profit sharing tax
Other taxes
Cash and bank
Shares and participation
Bonds and other securities
Liquid assets held by group companies
AR
ORGNR
NAMN
SNI69
BAS2
BAS3
BAS4
BAS5
RES1
RES2
RES3
RES4
RES5
RES6
RES7
RES8
RES9
RES10
RES11
RES12
RES13
UTD1
UTD2
UTD3
BIDRAG1
SPECA1
SPECA2
SPECA3
SPECA4
SPECA5
SPECA6
SPECB1
SPECB2
SPECB3
SPECB4
SPECB5
BAL1
BAL2
BAL3
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
BAL1
BAL2
BAL3
SPECB7
SPECB2
SPECB3
SPECB4
SPECB5
SPECB6
N
E
E
N
E
E
SPECB1
SPECA3
SPECA4
SPECA5
SPECA6
SPECA7
E
N
N
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
BIDRAG1
BIDRAG2
SPECA1
SPECA2
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
RES6
RES7
RES8
RES9
RES10
RES11
RES12
RES13
UTD1
UTD2
UTD3
BAS2
BAS3
BAS4
BAS5
RES1
RES2
RES3
RES4
RES5
AR
ORGNR
NAMN
SNI69
E
E
E
E
E
N
E
E
E
E
E
E
E
E
E
E
E
E
E
D
N
N
E
E
E
E
E
E
E
E
E
E
E
E
E
SPECB7
SPECB8
SPECB9
BAL1
BAL2
BAL3
SPECB2
SPECB3
SPECB4
SPECB5
SPECB6
SPECB1
SPECA3
SPECA4
SPECA5
SPECA6
SPECA7
SPECA1
SPECA2
BIDRAG1
BIDRAG2
RES6
RES7
RES8
RES9
RES10
RES11
RES12
RES13
UTD1
UTD2
UTD3
BAS2
BAS3
BAS4
BAS5
RES1
RES2
RES3
RES4
RES5
AR
ORGNR
NAMN
SNI69
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
D
N
E
E
E
E
E
E
E
E
E
SPECB7
SPECB8
SPECB9
BAL1
BAL2
BAL3
SPECB2
SPECB3
SPECB4
SPECB5
SPECB6
SPECB1
SPECA3
SPECA4
SPECA5
SPECA6
SPECA7
SPECA1
SPECA2
BIDRAG1
BIDRAG2
E
D
D
E
E
E
N
D
N
N
N
D
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
N
D
D
E
E
E
E
E
E
E
E
E
E
SNI92
BAS2
BAS3
BAS4
BAS5
RES1
RES2
RES3
RES4
RES5
RES6
RES7
RES8
RES9
RES10
RES11
RES12
RES13
UTD1
UTD2
UTD3
E
E
E
AR
ORGNR
NAMN
BAL1
BAL2
BAL3
BAL4
SPECB8
SPECB4
SPECB5
SPECB6
SPECB7
SPECB1
SPECB2
SPECB3
SPECA3
SPECA4
SPECA5
SPECA6
SPECA7
SPECA1
SPECA2
RES6
RES7
RES8
RES9
RES10
RES11
RES12
RES13
UTD1
UTD2
UTD3
BIDRAG
SNI92
BAS2
BAS3
BAS4
BAS5
RES1
RES2
RES3
RES4
RES5
AR
ORGNR
NAMN
E
E
E
E
D
E
E
E
N
E
D
D
D
BAL1
BAL2
BAL3
BAL4
SPECC4
SPECC5
SPECC6
SPECC7
SPECC8
SPECB3
SPECB4
SPECB5
SPECB6
SPECB7
SPECB8
SPECC1
SPECC2
SPECC3
SPECA3
SPECA4
SPECB1
SPECB2
N
N
E
E
E
E
E
E
E
N
N
N
N
SPECA1
SPECA2
RES6
RES7
RES8
RES9
RES10
RES11
RES12
RES13
UTD1
UTD2
UTD3
SNI92
BAS2
BAS3
BAS4
BAS5
RES1
RES2
RES3
RES4
RES5
AR
ORGNR
NAMN
N
N
E
E
E
E
E
E
E
E
E
E
E
D
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
D
E
D
D
D
E
E
D
N
D
E
E
E
N
N
N
N
D
D
D
D
D
D
E
E
E
E
E
E
E
E
E
E
E
E
E
N
E
E
E
E
E
E
E
E
D
D
D
E
E
E
BAL1
BAL2
BAL3
SPECC5
SPECC4
SPECC1
SPECC2
SPECC3
SPECA3
SPECB1
SPECB2
SPECB3
SPECB4
SPECB5
SPECB6
SPECA2
SPECA1
SNI92
BAS2
BAS3
BAS4
BAS5
RES1
RES2
RES3
RES4
RES5
RES6
RES7
RES8
RES9
RES10
RES11
RES12
RES13
RES14
AR
ORGNR
NAMN
77STATUS 77NAME 80STATUS 80NAME 85STATUS 85NAME 90STATUS 90NAME 91STATUS 91NAME 94STATUS 94NAME 95STATUS 95NAME
APPENDIX H—FIELDS IN THE DATABASE
209
APPENDIX I—THE INDUSTRY-SPECIFIC ACCOUNTING
RATES-OF-RETURNS
I.1 Introduction
It is not apparent how an industry’s ex post accounting rates-of-returns should be estimated. At least
two problems are pertinent when considering the industry profitability. These include the measurement problem and the classification problem. Both issues are addressed in this appendix. First, the
measuring problem is discussed in subsection I.2, and second, the classification of the industry is
discussed.
I.2 Estimation of the industry year’s ex post accounting rates-of-returns
A common method to estimate an industry year’s accounting rates-of-returns is to assume that the
distribution of the accounting rates-of-returns is Gaussian (Normal). See, e.g., McDonald & Morris
(1984) with respect to how this can be done. The assumption that the distribution of the accounting
rates-of-returns is Gaussian is often not explicit in published research since no discussion is made on
this topic. The tacit assumption of normality shows itself in the choice of location measure since the
arithmetic average is applied when estimating the distribution’s location. Only the location (center)
of a theoretical Gaussian distribution can be measured using the arithmetic average.
Empirical distributions of accounting ratios are not Gaussian for at least two possible reasons: (i) The ratio’s limit value is infinite when the denominator approaches zero and (ii) errors in
the raw data create outliers.
Suppose that the theoretical distribution of the accounting rates-of-returns is Gaussian, but
the empirical distribution is affected by factors (i) and (ii) above. The arithmetic mean is in such a
case no longer a valid location estimator since outliers contaminate the Gaussian distributed data
and another robust location estimate such as the median is needed.
Given the uncertainty about the empirical distributional characteristics of the accounting
rates-of-returns because outliers affect the data because of factors (i) and (ii), it is necessary to apply
a robust location estimate. Since the accounting rates-of-returns must be estimated per industry-year,
the industry-years have to rely on a relatively small number of accounting rates-of-returns. It is
therefore necessary to estimate the industry-year’s accounting rates-of-returns using a location estimate that is robust even in small distributions.
The current subsection uses Rosenberger & Gasko (1983) and Goodall (1983) to determine
robust location estimates. Rosenberger & Gasko (1983) and Goodall (1983) show that the choice of
211
robust location estimate varies across empirical distributions and across sample sizes, making it necessary to asses the empirical distribution of the accounting rates-of-returns for each industry-year.
Rosenberger and Gasko argue that the thickness of the distribution’s tails can be used to classify the
empirical distribution.
To asses the tail thickness Rosenberger & Gasko (1983, p. 322) use a tail-weight index. The
tail-weight index measures the empirical distribution’s ratio between the 99th and 75th percentile from
the median. This ratio is standardized against an equivalent ratio of a Gaussian distribution’s, which
sums to 3.457 to create the tail weight index:
 F 1 0.99
F 1 0.5
¬­
­ ¸ 3.4571
U F žžž 1
žŸ F 0.75
F 1 0.5
­­®
[EQ I-1]
where F-1is the cumulative empirical distribution function, and F 1 0.99
is the
99 percentile’s accounting rate-of-return for a industry-year. F 1 0.5
is consequently the distribution’s median.
A Gaussian distribution has tail weight index 1.0. Lighter tailed distributions have indices less
than 1.0 and heavier tailed distributions such as e.g., Cauchy, has indices above 1.0. Table I-7 is
adopted from Rosenberger & Gasko (1983, p. 322) and describes tail weights for different types of
empirical distribution.
Tail-weight index
Distribution U(F) Distribution U(F) Distribution U(F)
Uniform
Triangular
Gaussian
0.57 CN(.05;3)
0.86 Logistic
1.00 D-exponential
1.20 CN(.05;10)
1.21 Slash
1.63 Cauchy
3.42
7.85
9.22
Table I-7: Tail-weight indices for different distributions.
In Table I-7 CN(.05;3) is a contaminated Gaussian distribution where 95 percent of the observations come from a Gaussian distribution having one standard deviation while five percent
come from a Gaussian distribution having three standard deviations. D-exponential is a double exponential distribution.
Rosenberger & Gasko test eighth location measures of efficiency on different sample sizes
( n 5, 10, and 20) for the distributions in Table I-7. Goodall (1983) also tests several M-estimators
of location. From Rosenberger & Gasko (1983) and Goodall (1983), a set of robust location measures is chosen for the estimation of the robust industry-year accounting rates-of-returns. The most
efficient estimate of location is chosen per sample size and distribution type.
The location estimates used in the present study to estimate the industry-year’s accounting
rates-of-returns are the arithmetic mean (Mean), the median, trimmed means (TM B ), midmean
(MIDM), broadened mean (BMEAN), Huber’s 1-step M-estimate with c 2Q , and biweight 1-step
212
M-estimate with c 8.8 . Table I-8 provides an overview of which location estimate is employed in
this study per industry size.
Robust location estimator per industry size
Industry size
Empirical distribution
Unique Micro Small SemiSmall
Tail-weight
n=1
1<n<4 4n<8 8n<15
Name
Uniform
(F)<0.71
i=I
Median Median Median
Triangular
0.71(F)<0.93 i=I
Median Median Median
Gaussian
0.93(F)<1.04 i=I
Mean TM10 Huber(2)
1.04(F)<1.1 i=I
Median MIDM TM10
One-out
1.1(F)<1.3
i=I
Median MIDM TM10
1.3(F)<1.5
i=I
Median MIDM TM10
D-exp
1.5(F)<1.8
i=I
Median MIDM BMEAN
One-wild
1.8(F)<5.6
i=I
Median Median BMEAN
Slash
5.6(F)<8
i=I
Median Median Median
Cauchy
(F)8
i=I
Median Median Median
Large
n>14
Median
Median
Huber(2)
Biweight(8.8)
Biweight(8.8)
Biweight(8.8)
BMEAN
BMEAN
BMEAN
BMEAN
Table I-8: Robust estimates for the industry-year’s accounting rates-of-returns per industry size.
The estimators in Table I-8 are per tail-weight and per number of observations per industryyear.
The trimmed mean is calculated following Rosenberger and Gasko (1983, p. 308):
TM B n g
1
¸
xi
n ¸ 1 2B
i g 1
œ
[EQ I-2]
Where g B ¸ n , is 10 percent, n is the number of firms per industry-year, and x i is the
accounting rates-of-returns for a specific firm-year.
The midmean is equivalent to an -trimmed mean where is 25 percent (Rosenberger &
Gasko 1983, p. 311).
The broadened mean is also equivalent to -trimmed mean but having a variable . depends on the number of firms per industry-year and is calculated as (Rosenberger & Gasko 1983, p.
313):

1.5 ­¬
ž.5 ­
žŸ
n ­®
5 b n b 12

2.5 ­¬
ž.5 ­
žŸ
n ­®
n p 13
[EQ I-3]
Note that the limit value of is 50 percent. The trimmed mean is equivalent to the median
when is equal to 50 percent. B 49 percent when n 250 , but is already 45 percent at
n 40 . This means that the trimmed mean asymptotically approaches the median and it is approx-
imately equal to the median already at relatively few observations.
Huber’s 1-step M-estimate and the biweight 1-step M-estimate are used for some empirical
distributions. See Goodall (1983) for a discussion on how to calculate them.
213
An alternative method to the method used in this subsection for assessing the accounting
rates-of-returns for industry-years is also used when the hypotheses in section 6.4 are assessed. See
subsection L.4.2 for more information about the alternative estimation method.
I.3 Classifying the industry
There are considerable problems in defining an industry, but a common practice is to use the standard industry classification system (SIC). The SIC system is a hierarchal classification system in
which the first-digit level signifies the economy at large in a country and the fifth-digit level is the
most narrow industry definition (Statistics Sweden 2006). A firm is assigned to an industry based on
the activity it carries out; a firm can be active in several industries at the same time (Statistics Sweden
2006).
This research has access to each firm-year’s main SIC code at the fourth-digit level. Because
of a shift in the classification system in 1990 (from classification system SNI69 to SNI92), it is not
possible to use a four-digit level industry definition. The most narrow and consistent definition of
the industry across the two classification systems is at the three-digit level.
Classifying the industry at a three-digit level serves several purposes: (i) it is practical despite
the change in the classification system and (ii) it provides enough firm observations to separate the
firm from the industry. Sweden is a rather small market and classifying the industry at a four-digit or
at a five-digit level likely renders several industries having only one firm. This also occurs at the
three-digit level, but this is a minor problem at this level. (iii) It is narrow enough to provide for a
stable industry belonging. Gupta & Huefner (1972) argue that a four-digit level is too narrow since
this is such a narrow industry definition that many firms shift industry on a frequent basis.
At least two drawbacks can be found when having an industry definition at a three-digit level
and not at a more narrow level. (i) The products produced in the industry are not close substitutes,
i.e. the industry is not homogenous. E.g., the industry name for SIC-code 291 is manufacture of
machinery for the production and use of mechanical power, except aircraft, vehicle, and cycle engines, suggesting a relatively heterogeneous industry. Relatively homogenous industry classifications
are found at a four-digit level. E.g., the SIC code 2912 is the manufacture of pumps and compressors. However, one can argue that the industry classification at a three-digit level can also capture
the competitive effect of a broader class of substitute products. (ii) With a relatively heterogeneous
classification of the industry, the production functions may differ and this may transfer to a relatively heterogeneous implementation of the accounting standards. E.g., the depreciation policies may
vary relatively more within an industry classified at a three-digit level than at a four-digit level.
Despite these problems, it is common in research to have the industry classification even at
the two-digit level (cf. Geroski & Jacquemin 1988; Gupta & Huefner 1972).
214
APPENDIX J— HYPOTHESES TESTS USING ALTERNATIVE
OPERATIONALIZATIONS OF INCOME
J.1 Introduction
Return on equity is defined in this thesis as
t 1 RNOAt
t 1 ROEt
CNI t ¸ EQt11 , and as
COI t ¸ NOAt11 . This chapter explores if some misspecification of comprehensive net
income (CNI) and comprehensive operating income (COI) may drive the results. The effects of
three alternative specifications of CNI and the effects of three alternative specifications of COI are
investigated in this appendix.
This means that this appendix changes the operationalization of
*
t 1 RROEt
t 1 ROEt
t 1 ROEtI and
*
t 1 RRNOAt
t 1 RNOAt
t 1 RNOAtI since the meaning
of ROE and RNOA changes.
The changes are then evaluated on new panels using the identical method to that applied in
section 6.4 (p. 108) with associated appendices.
The alternative specifications of CNI are:
1. Basic CNI less dividends from the group.
2. As #2 less government subsidies.
3. As #3 less dirty surplus accounting (see [EQ 5-10])
The alternative specifications of COI are:
4. Basic COI less dividends from the group.
5. As #2 less government subsidies.
6. As #3 less dirty surplus accounting (see [EQ 5-10])
215
J.2 The result from panel regression on alternative specification of CNI
The coefficients of determination for the panels having the basic definition of CNI are found in
Table 6-7; they are, on average, 39 percent. This increases to 49 percent when alternative CNI #1 is
tested and 51 percent when alternative CNI #2 is tested. However, by also removing dirty surplus
accounting from the definition, i.e. using alternative CNI #3, it increases to 52 percent. This shows
that dividends from the group have important effects in the variability of the panels despite that
outliers have been removed. Government subsidies and dirty surplus accounting do not contribute
much to the variability.
RROE_ALT#3
RROE_ALT#2
RROE_ALT#1
Variable Field
ESTIMATES
STDE
TVALUE_1
PVALUE_1
TVALUE_0
PVALUE_0
ESTIMATES
STDE
TVALUE_1
PVALUE_1
TVALUE_0
PVALUE_0
ESTIMATES
STDE
TVALUE_1
PVALUE_1
TVALUE_0
PVALUE_0
1978
-0.028
0.249
-4.12
0.00%
-0.11
91.1%
-0.008
0.249
-4.05
0.00%
-0.03
97.6%
-0.020
0.246
-4.15
0.00%
-0.08
93.4%
1979
-0.058
0.250
-4.23
0.00%
-0.23
81.7%
-0.040
0.251
-4.14
0.00%
-0.16
87.3%
-0.040
0.251
-4.15
0.00%
-0.16
87.4%
1980
-0.063
0.240
-4.44
0.00%
-0.26
79.2%
-0.048
0.236
-4.45
0.00%
-0.21
83.7%
-0.060
0.235
-4.52
0.00%
-0.26
79.7%
1981
-0.083
0.241
-4.49
0.00%
-0.34
73.2%
-0.073
0.239
-4.50
0.00%
-0.31
75.8%
-0.081
0.239
-4.53
0.00%
-0.34
73.5%
1982
-0.013
0.226
-4.49
0.00%
-0.06
95.3%
-0.013
0.220
-4.61
0.00%
-0.06
95.3%
0.002
0.218
-4.57
0.00%
0.01
99.1%
Fit origin
1983 1984 1985
-0.001 -0.013 -0.032
0.216 0.180 0.226
-4.63 -5.64 -4.57
0.00% 0.00% 0.00%
0.00 -0.07 -0.14
99.6% 94.2% 88.8%
0.053 -0.008 0.006
0.221 0.181 0.227
-4.29 -5.57 -4.38
0.00% 0.00% 0.00%
0.24 -0.04 0.03
81.2% 96.7% 97.8%
0.067 -0.004 0.005
0.221 0.181 0.230
-4.22 -5.54 -4.33
0.00% 0.00% 0.00%
0.30 -0.02 0.02
76.2% 98.3% 98.3%
1986
-0.015
0.247
-4.10
0.00%
-0.06
95.2%
0.038
0.233
-4.13
0.00%
0.16
87.0%
0.053
0.234
-4.05
0.00%
0.23
82.2%
1987
-0.018
0.262
-3.88
0.01%
-0.07
94.6%
0.050
0.252
-3.77
0.01%
0.20
84.4%
0.047
0.248
-3.84
0.01%
0.19
85.0%
1988
0.062
0.290
-3.23
0.06%
0.21
83.2%
0.089
0.282
-3.23
0.06%
0.31
75.3%
0.096
0.281
-3.22
0.07%
0.34
73.2%
1989
0.018
0.250
-3.93
0.00%
0.07
94.4%
0.084
0.252
-3.63
0.01%
0.34
73.8%
0.075
0.256
-3.62
0.02%
0.29
76.9%
1990
-0.023
0.257
-3.98
0.00%
-0.09
93.0%
0.032
0.256
-3.79
0.01%
0.13
90.0%
0.036
0.258
-3.73
0.01%
0.14
88.8%
Table J-9: Parameter estimates from the fixed-effects panel regression using the riskadjusted RROE with PCSE and AR(1) errors for alternative operationalizations of CNI.
Table J-9 reports the parameter estimates with t-values and p-values for the alternatively
operationalized variables. The table shows that for all alternative specifications and for all panels, the
conclusions from 6.4.2.1 (p. 110) remain unchanged. That is, the parameter estimates are significantly less than one (which therefore rules out random walk) and not significantly different from zero.
216
J.3 The results from panel regression on alternative specification of COI
The coefficients of determination for the panels having the basic definition of COI are found in
Table 6-9; it is, on average, 43 percent. This does not change materially as alternative COI #and
alternative CNI #2 are tested. However, as in the previous section, by removing group dividends
(alternative COI #1 ), it increases to 53 percent. Again, this is a sign that the group dividends
have important effects in the variability of the panels.
RRNOA_ALT#3 RRNOA_ALT#2 RRNOA_ALT#1
Variable Field
ESTIMATES
STDE
TVALUE_1
PVALUE_1
TVALUE_0
PVALUE_0
ESTIMATES
STDE
TVALUE_1
PVALUE_1
TVALUE_0
PVALUE_0
ESTIMATES
STDE
TVALUE_1
PVALUE_1
TVALUE_0
PVALUE_0
1978
-0.021
0.237
-4.30
0.00%
-0.09
92.9%
-0.071
0.251
-4.27
0.00%
-0.28
77.8%
0.018
0.224
-4.39
0.00%
0.08
93.6%
1979
-0.027
0.257
-3.99
0.00%
-0.10
91.7%
-0.127
0.222
-5.08
0.00%
-0.57
56.8%
0.008
0.256
-3.88
0.01%
0.03
97.4%
1980
-0.024
0.255
-4.01
0.00%
-0.09
92.6%
-0.122
0.258
-4.34
0.00%
-0.47
63.8%
0.032
0.258
-3.75
0.01%
0.12
90.2%
1981
-0.085
0.250
-4.35
0.00%
-0.34
73.4%
-0.215
0.245
-4.96
0.00%
-0.88
38.0%
-0.077
0.245
-4.39
0.00%
-0.31
75.3%
1982
-0.010
0.246
-4.11
0.00%
-0.04
96.8%
-0.145
0.252
-4.55
0.00%
-0.58
56.5%
0.009
0.250
-3.96
0.00%
0.04
97.0%
Fit origin
1983 1984 1985
-0.014 -0.008 0.004
0.229 0.204 0.249
-4.43 -4.94 -4.01
0.00% 0.00% 0.00%
-0.06 -0.04 0.01
95.1% 96.9% 98.8%
-0.057 -0.086 -0.157
0.248 0.160 0.239
-4.26 -6.78 -4.85
0.00% 0.00% 0.00%
-0.23 -0.54 -0.66
81.9% 59.1% 51.1%
0.022 0.002 0.041
0.232 0.187 0.248
-4.22 -5.33 -3.87
0.00% 0.00% 0.01%
0.10 0.01 0.17
92.4% 98.9% 86.9%
1986
-0.006
0.239
-4.21
0.00%
-0.02
98.1%
-0.183
0.230
-5.15
0.00%
-0.80
42.6%
0.045
0.239
-4.00
0.00%
0.19
84.9%
1987
0.044
0.253
-3.77
0.01%
0.17
86.3%
-0.161
0.246
-4.73
0.00%
-0.66
51.2%
0.094
0.245
-3.69
0.01%
0.38
70.1%
1988
0.076
0.282
-3.28
0.05%
0.27
78.7%
-0.039
0.309
-3.36
0.04%
-0.13
89.8%
0.126
0.277
-3.15
0.08%
0.46
64.8%
1989
0.032
0.241
-4.03
0.00%
0.13
89.6%
0.005
0.252
-3.95
0.00%
0.02
98.3%
0.077
0.241
-3.82
0.01%
0.32
74.9%
1990
0.026
0.259
-3.76
0.01%
0.10
91.9%
-0.054
0.254
-4.15
0.00%
-0.21
83.3%
0.091
0.264
-3.44
0.03%
0.34
73.2%
Table J-10: Parameter estimates from the fixed-effects panel regression using the riskadjusted RRNOA with PCSE and AR(1) errors for alternative operationalizations of COI.
Table J-10 shows no material changes when compared with the original operationalization
of COI. The table shows that for all alternative specifications and for all panels, the conclusions
from 6.4.2.2 (p. 112) remain unchanged. The parameter estimates are significantly less than one and
not significantly different from zero.
217
APPENDIX K—THE ROBUST T-TEST ASSESSING IF NONZERO RISK-ADJUSTED RESIDUAL ACCOUNTING RATES-OFRETURNS EXISTS
The null hypotheses assume that the risk-adjusted residual return on equity (risk-adjusted RROE),
[EQ 6-8] and the risk-adjusted residual return on net operating assets (risk-adjusted RRNOA),
[EQ 6-4], are zero for all firms. The alternative hypotheses posed by Homo comperiens maintain
that that the risk-adjusted RROE and the risk-adjusted RRNOA are non-zero for at least one firm.
This is tested with a robust double-sided t test.
A t test means that confidence intervals are implicitly estimated. Subsection I.2 discusses how
to measure the industry-year’s accounting rates-of-returns and finds that a robust location estimate is
needed. When estimating a confidence interval, it is not enough with a robust location estimate: the
confidence interval must be robust.
Iglewicz (1983) discusses the robustness of confidence intervals in three empirical distributions (Gaussian, One-wild 30, and Slash). Iglewicz finds that a location estimate based on the wave
estimator slightly dominates a location estimate based on the biweight estimator (93 percent triefficiency compared with 91 triefficiency). These two robust methods completely dominate the usual
way to create confidence intervals using mean and standard deviation, which have only one percent
triefficiency.
However, finding t-values for the biweight estimation method is much easier than for the
wave estimation method. Mosteller & Tukey (1977) suggest that using the t-values from the tdistribution with 0.7 ¸ n-1
degrees of freedom provide a conservative approximation of the cut-off
point when both the location and the scale are estimated using the biweight estimation technique.
Iglewicz (1983) validates Mosteller and Tukey’s approximation. Finding the t-values for the use of
the wave estimation method is not as easy.
This thesis measures robust confidence intervals using two methods. The first method uses
the best possible robust location estimate based on the method discussed in subsection I.2 in conjunction with a biweight scale estimate. This method is subsequently referred to as the Best possible
robust location estimate (BLE). The t-values used for conservative approximation of the cut-off
point for BLE are based on the t-values provided by Gross (1976). The second method uses a biweight estimation of location and a biweight estimation of scale. The cut-off point for the second
30 One-wild in this thesis represents a distribution where 19 observations are from a Gaussian distribution that has one
standard deviation and one observation from a Gaussian distribution that has 100 standard deviations.
219
method is based on Mosteller and Tukey’s suggestion, and is subsequently referred to as the Biweight method (BW).
The biweight estimate of the robust scale estimator (in the research estimated with c 9 ) is
defined as (Iglewicz 1983, p. 416):
n
sbw 1
2
¸¡
¢
4¯
2
œ u 1 xi Median ¸ 1 ui2 °
2
±
i
¡
¢
1
¯
œ u 1 1 ui2 ¸ 1 5 ¸ ui2 ±°
[EQ K-1]
i
1
where ui x i Median ¸ c ¸ MAD , and xi is the accounting rate-of-return for a firmyear in an industry.
The t-test statistic is calculated for the years according to the following equation (follows Iglewicz 1983, p. 416):
1 1
t x it x It ¸ ¡sIt ¸ nIt ¯°
¢
±
where xit is the firm-year accounting rate-of-return, i.e.
dustry-year’s accounting rate-of-return, i.e.
I
t 1 ROEt
and
[EQ K-2]
t 1 ROEt
I
t 1 RNOAt
and
t 1 RNOAt
. xIt is the in-
estimated using method BLE
or BW above. sIt is the scale estimate per industry-year estimated using either method BLE or BW,
and nIt is the number of firms in the industry-year.
The decision rule is thus:
Reject H0 if t t0.7¸n 1
,0.5¸B
where t0.7¸n 1
,0.5¸B is the cut-off point for a t-distribution having 0.7 ¸ n 1
degrees of freedom and with significance level . The hypothesis test uses significance levels of 1, 5, and 10 percent.
220
APPENDIX L—THE PANEL REGRESSION TEST METHOD
L.1 Introduction
This appendix discusses the panel regression method applied for testing the learning hypothesis of
the thesis. The appendix is organized by first discussing the three alternative panel regression models
that are considered. Next, the appendix discusses alternative covariance structures for the fixedeffect model. The appendix also addresses the question of how the panels are formed. This includes
choices of panel length as well as treatment of outliers in the data.
L.2 Three panel regression models
This subsection focuses on panel models for assessing whether learning takes place by focusing on
the factor in [EQ 6-10] and [EQ 6-11].
The null hypotheses are C . 1 and the alternative hypotheses are C 1 . The hypotheses
lend themselves to estimation and statistical tests using panel regression analysis31. The t-test statistics for assessing the hypotheses is measured for the regressions as:
t Cˆ 1
¸ stde 1
[EQ L-1]
The standard error, stde, is the estimated standard deviation for the estimated regression parameter (Newbold 1995).
The decision rule is:
Reject H0 if t tdfe,B
where tdfe,B is the cut-off point for a t-distribution having dfe degrees of freedom and with a
significance level and where Ĉ is the panel regression’s estimated regression parameter. The hypothesis test employs a five percent significance level.
31 The thesis uses SAS 9.1.3 for its statistical analysis. SAS 9.1.3 is weak on panel regression techniques and on specification tests associated to the panel regressions. SAS 9.1.3 has PROC TCSREG and PROC MIXED that can be used for
panel regression but neither is sufficiently versatile to allow for more than cursory panel regression analysis. To compensate for this the panel regression models and all associated specification tests have been hand-written in PROC IML.
Since the programs are hand-written, Appendix L and especially L.3 elaborate more than what would have been necessary if standardized programs had been used.
The written programs are tested in most cases on Grunfeld’s investment data, where the outputs have been compared with the outputs that Green (2003) provides. Accordingly, this determines the programs’ reliability. The drawback
is that this procedure requires the programs to deal with balanced panels.
A balanced panel is a panel in which all cross-sections have a complete set of observations: There are no holes in
the panel. Since the programs are written to handle balanced data, the panels that are used for the panel regressions in
this thesis require that all firms included in a panel must have observations for all the years used in that particular panel.
This greatly reduces the number of cross-sections available for analysis and therefore introduces survival bias. This also
affects the number of years used to set up a panel, as well as how outliers are treated. See section L.4 on page 213 for
further details on this topic.
221
There are several panel regression models available for assessing the regression parameters.
To avoid ex ante affecting the results by choosing an estimation model (e.g., Cubbin & Geroski
1987; Dechow et al. 1999; Fairfield et al. 1996; Finger 1994; Jacobsen 1988; Jacobson & Aaker 1985;
Mueller 1977; Mueller 1990; Ou & Penman 1989b; Penman & Zhang 2002; Waring 1996), I consider
three alternative estimation models. These models are the pooled regression model, the random
effect model, and the fixed-effect model. The estimation models are tested against each other using
a specification test, which allows the most appropriate panel regression model to be used to estimate
the regression parameters.
The pooled regression model assumes no unmodeled heterogeneity between the firms (the
cross sections). That is, all differences between units are accounted for by the difference in the regressors. It also implies that all firms obey the same equation, i.e. have identical behavior. Despite its
widespread use in accounting research, the model is highly restrictive and is thus not considered a
priori to be a likely estimation model for the data in this thesis.
The random effects model assumes that any unmodeled heterogeneity is uncorrelated with
the regressors and that it is a random panel element. That is, the unmodeled heterogeneity randomly
varies across the firms. According to Green (2003, p. 293), the random-effect model is appropriate
if, e.g., the sample of firms is drawn from a much larger population. However, the sample of firms
covers the bulk of the complete Swedish manufacturing industry and hence the random-effect model is not expected a priori to fit the data very well.
The third method assumes that the unmodeled heterogeneity is correlated with the regressors
(Greene 2003). If Homo comperiens is a valid description, unmodeled heterogeneity should be
present in the data; given the alternative hypothesis, it is expected that the heterogeneity will be correlated with the regressors. The fixed model is therefore likely the panel regression model that best
meets the theoretical propositions and hence is most appropriate in this thesis.
If the random- or fixed-effects method is applied, no substantive conclusions can be drawn
from the intercepts in [EQ 6-10] and [EQ 6-11]. This is because they contain firm-specific errors.
The random- and fixed-effects models have the benefit that they provide an unbiased estimation of
(see, e.g., Green (2003, p. 283-374) for a discussion on panel regression methods).
The appropriateness of the pooled regression model, the random-effects model, and the
fixed-effects model depends on the presence and the type of unmodeled heterogeneity. Three specification tests are used in the thesis to choose the most appropriate regression model. Those tests
and their results are discussed in Appendix M (p. 233).
L.3 Alternative covariance structures for the fixed effect method
Alternative covariance structures are needed when the basic assumptions on the disturbance process
are violated. Using different covariance structures affect how regression parameters, standard errors,
222
and fit statistics are calculated. This means that the assumptions of covariance structure can have a
significant effect on the hypotheses tests carried out.
Subsection L.2 assumes that the fixed-effects model a priori best fits the theory of Homo
comperiens. Therefore, to reduce complexity only alternative covariance structures are considered
for the fixed-effects model.
The thesis uses a lagged dependent variable as explanatory variable (as in [EQ 6-10] and
[EQ 6-11]). According to Beck & Katz (2004), this implies that the disturbances are, by design, serially correlated. First-order serially correlated disturbances are considered in the alternative covariance structures.
Because Homo comperiens suggests that firms are heterogeneous, there is no particular reason why disturbances should be homoscedastic. A more likely situation is the presence of panel heteroscedasticity, i.e. each firm’s disturbances have an own, constant, variance. I consider covariance
structures affected by panel heteroscedasticity.
The serially correlated disturbance structure exists by design and thus any applied covariance
structure must deal with serial correlated disturbances. Panel heteroscedasticity, however, is not part
of the structure by design so the test in subsection M.6 (p. 238) is needed to ascertain whether it is
present in the panels.
The data set consists of almost the whole population of incorporated firms within the Swedish manufacturing industry. This means that I expect that the behavior of one firm has an effect on
other firms in the panels, and the panels are therefore likely to be affected by contemporaneous correlated disturbances.
According to Beck & Katz (1995), OLS regression with spherical disturbances is an inefficient method. They propose that the standard errors from the OLS estimation procedure should be
corrected for both panel heteroscedasticity and contemporaneous correlated disturbances. Their
method for correcting the standard errors is known as the panel corrected standard errors (PCSE).
The covariance structure proposed by Beck and Katz is applied on the fixed effect model whenever
the panel heteroscedasticity test indicates that the assumptions of spherical disturbances are violated.
The point of reference when considering covariance structures is the structure having spherical disturbances. Spherical disturbances are covered in this section to provide an overview of the
applied method. First-order serial correlation is added to the spherical disturbances in subsection
L.3.4. Subsection L.3.3 covers the PCSE covariance structure and it is adjusted to allow for firstorder serially correlated disturbances in subsection L.3.5.
Only two of four covariance structures are implemented because serially correlated disturbances exist by construction and the implemented covariance structures are the Spherical AR(1)
covariance structure and the PCSE AR(1) covariance structure. Because the assumptions of spheri223
cal disturbances presume homoscedasticity and because homoscedasticity is not expected to be
present in the data set, a priori, the PCSE AR(1) covariance structure is expected to dominate the
others.
This section begins with a brief subsection that contains this section’s notational structure.
This is followed by a subsection with the spherical disturbances. After the spherical disturbances,
the section having panel corrected standard errors (PCSE) is presented. These two covariance structures come first since they are base cases.
After the base cases, follows the spherical disturbances that are affected by the serial correlation but that is transformed using the Prais-Winsten method. The Prais-Winsten method is also applied to the PCSE covariance structure.
L.3.1 Notational structure
Before the different covariance structures are presented, a common notational system is presented.
Let D in  IT be the selector matrix, i.e. a vector of dummies for the firms (Baltagi 2003). Let y
be the n ¸ T q 1 matrix with the independent observations for the firms. Let X be the n ¸ T q K
matrix of regressors. Finally, let Z <D, X> be the full regressor matrix.
By using these matrices, the fixed-effect model of the present thesis is:
y Z¸ C F
[EQ L-2]
This fixed-effect model is similar to Green’s (2003, p. 287) equation 13-2, and since Z consists of both the dummies and the regressors, it follows that C includes the firm-specific constants.
Another assumption maintained throughout the analysis is that the disturbances are expected to be
zero:
& <F > 0
[EQ L-3]
The general description of the covariance structure is the n q n matrix:
 T1111 ! T1n 1n ¬­
žž
­
‫ٱ‬
& ¡ F F°¯ V T 2 ¸ žž #
%
# ­­­
¢
±
žžT ­
žŸ n 1 n 1 " Tnn nn ®­
[EQ L-4]
The covariance matrix is focused by attributing it with different properties as the analysis
proceeds.
L.3.2 Spherical disturbances
Typical regression analysis assumes as a point of reference the covariance structure with spherical
disturbances. This is also done in this thesis. A spherical disturbance structure exists when the disturbances are white noise disturbances (Greene 2003):
& <F > 0
224
T 2 ¸ 1 !
0 ¬­­
žž
‫¯ ٱ‬
­
2
ž
& ¡
° V T In žž #
%
# ­­
¢ ±
­­
žž
2
" T ¸ 1­­®
žŸ 0
[EQ L-5]
where In is the n q n identity matrix. The variance in this thesis is assumed constant across
firms.
It follows that when the disturbances are spherical; the fixed-effect model estimated with
OLS is the best linear unbiased estimator (BLUE). In this thesis, the regression parameters are estimated as below when the disturbances are spherical:
ˆ Z ‫ ¸ ٱ‬Z
1 ¸ Z ‫ ¸ ٱ‬y
C
[EQ L-6]
The hat-sign identifies estimated matrices.
In the thesis, the fixed-effects panel-regressions model’s fit statistics is the sum of squared
disturbances, the total sum of squares, the coefficient of determination, the mean squared error, the
root mean squared error, and the degrees of freedom (Green 2003):
‫ٱ‬
SSE [EQ L-7]
‫ٱ‬
SST y ¸ M0 ¸ y
[EQ L-8]
SSR SST SSE
R 1 SSE ¸ SST
2
MSE SSE ¸ dfe
[EQ L-9]
1
[EQ L-10]
1
[EQ L-11]
RMSE MSE
[EQ L-12]
dfe n ¸ T n K
[EQ L-13]
‫ٱ‬
where M0 In¸T n ¸ T 1 ¸ i n¸T ¸ i n¸T , in¸T is n ¸ T q 1 matrix of 1’s, and In¸T is an
n ¸ T qT ¸ n identity matrix.
The asymptotic covariance matrix for spherical disturbances in this thesis is calculated as
(note that MSE is a scalar):
1
var ˆ
Z Z
¸ MSE where Xi, j ‰ var ˆ
‫ٱ‬
[EQ L-14]
The thesis collects the standard errors from the asymptotic covariance matrix’s vector diagonal, where the standard errors are the square root of the vector diagonal. Thus, the standard error for the first regression parameter (the constant for the first firm) is:
stde1 X1,1
Next, is the covariance structure when panel heteroscedasticity and contemporaneous correlated disturbances are present.
225
L.3.3 Panel-corrected standard errors (PCSE)
When panel heteroscedasticity and contemporaneous correlated disturbances are present, the spher-
ical V matrix, [EQ L-5], is incorrect. This cascades into incorrect standard errors. Since <Z, y > is not
affected by these problems, ˆ remains unaffected and hence it can still be estimated using [EQ L-6].
The standard errors must be corrected for heteroscedasticity and contemporaneous correlation. This is done in the present thesis with the PCSE estimated V̂ matrix (Beck & Katz 1995):

ˆ 0 0 " 0 ­¬
žž
­
žž 0 ˆ " # ­­­
žž
­
ˆ ž0 0 ˆ  n
ˆ " # ­­­ V
žž
­
žž # # # % # ­­
­
žž
ˆ ­­­
žŸ 0 0 0 " ®
[EQ L-15]
where the estimated contemporaneous covariance matrix is:
 T11
žž T
ˆ žž 21
žž #
žžŸTn 1
T12
T22
#
"
" T1n ¬
" T2n ­­­ ‫
¸ ٱ‬
­
% # ­­ T
" Tnn ­­­®
[EQ L-16]
The elements in the contemporaneous covariance matrix are:
Tij T 1 ¸
œ
T
F
t 1 it
¸ Fjt
[EQ L-17]
Note that if no contemporaneous correlation, Sij 0 , is assumed, the estimated covariance
matrix could be adjusted by calculating the diagonal elements as Tii T 1 ¸ œ t 1 Fit ¸ Fit , and setting
T
the off-diagonal elements to zero, since Tij Tii ¸ T jj ¸ Sij º Tij 0 when Sij 0 . However, contemporaneous correlation is likely to be present in the data set and thus the off-diagonal elements
are allowed to be non-zero.
The thesis applies the PCSE estimated V̂ matrix to adjust the estimated covariance matrix
(Beck & Katz 1995):
1
var ˆ
Z ¸ Z
‫ٱ‬
1
‫ˆ ٱ‬
‫ٱ‬
¸Z ¸ V
¸ Z ¸ Z ¸ Z
[EQ L-18]
The standard errors from [EQ L-18] are found as the square root of the vector diagonal.
This also follows the procedure for spherical disturbances.
Since PCSE only adjusts the standard errors of the estimated regression parameters, the fit
statistics is calculated using [EQ L-7] to [EQ L-13].
L.3.4 Spherical disturbances with first-order serial correlation and the Prais-Winsten
transformation
The estimation of the regression parameters using [EQ L-6] is no longer BLUE when the spherical
disturbances are serially correlated (Greene 2003). There are several methods available to cope with
226
serial correlation; in this thesis, the Prais-Winsten transformation of <Z, y > is applied. The PraisWinsten method is the preferred method by both Green (2003) and Baltagi (2003).
When serial correlation affects the disturbances, it follows that V , [EQ L-4], is affected and
its off-diagonal block are (Greene 2003, p. 326):
 1
S1 S 2 " ST 1 ­¬
žž
­
1
žž S
1 #
#
# ­­­
2
ž
­
Tu
# % #
# ­­­
¸ žž S 2
Tij ¸ ij 2 ž
­
1 S žž #
#
# %
# ­­
­­
žžž T 1
1 ­­®
" " "
žŸS
[EQ L-19]
The serial correlation, S , is assumed constant. More advanced serial correlation structures
can be concocted (e.g., the serial correlation can be assumed firm-specific), however, this is not practical given the limitation of the panel: T is too small for a good estimation of a firm-specific serial
correlation.
The panel is transformed using the Prais-Winsten transformation to remove the first-order
serial correlation. There are several methods to estimate the first-order serial correlation coefficient.
See, e.g., Greene (2003) who discusses one method; however, Baltagi (2003) reports that Greene’s
method performs poorly when T is small. Baltagi’s method is used in this thesis since its panels’ T is
small. Baltagi’s (2003) proposed method to estimate the first-order serial correlation coefficient is:
1
Sˆ Q1 Q2 ¸ Q0 Q1 [EQ L-20]
where Qs ¡ œ i 1 œ t s 1 Fit ¸ Fit s ¯° ¸ <n ¸ T s > . The disturbances originate from the
¢
±
n
1
T
pooled regression model.
Let the Prais-Winsten transformation matrix be (Baltagi 2003):
 1 Sˆ2
žž
žžž Sˆ
C žž 0
žž ¸
žž
žžŸ 0
0
1
Sˆ
¸
¸
¸
¸
0 ¸
1 0
¸
¸
¸ Sˆ
0­­¬
¸ ­­­
­
¸ ­­­
¸ ­­
­
1­­®
[EQ L-21]
Let the block-diagonal augmented Prais-Winsten transformation matrix be (Baltagi 2003):
P* In  C
By premultiplying the <X, y > observations with the block-diagonal augmented Prais-Winsten
transformation matrix, the first-order serial correlation is removed from the observations (Baltagi
2003):
X* C ¸ X , and
[EQ L-22]
y* C ¸ y
227
Z* <D, X* >
The transformed observations are used to estimate the unbiased regression parameters:
1
‫ٱ‬
ˆ* Z* ¸ Z* ‫ٱ‬
¸ Z* ¸ y*
[EQ L-23]
In addition, the fit statistics uses the transformed data to provide unbiased results. The fit
statistics is calculated:
‫ٱ‬
SSE * ¸ [EQ L-24]
‫ٱ‬
SST y* ¸ M0 ¸ y*
[EQ L-25]
SSR SST SSE
[EQ L-26]
R 1 SSE ¸ SST
2
1
[EQ L-27]
2 1
MSE TF2 ¸ 1 Sˆ
[EQ L-28]
RMSE MSE
where
TF2
1
[EQ L-29]
1
SSE ¸ <n ¸ T 1
> , and M In¸T n ¸ T 0
‫ٱ‬
¸ i n¸T ¸ i n¸T . The disturbance va-
riance TF2 is estimated based on Baltagi (2003) and not on Green (2003) since Ŝ is estimated using
Baltagi’s method and not using Greene’s method. The difference lies in that Baltagi uses T 1 ,
where Green uses T.
Assuming AR(1) disturbances are an improvement to the spherical covariance structure for
spherical errors. An even more likely covariance structure is the PCSE with AR(1) disturbances,
which is considered next.
L.3.5 PCSE with first-order serial correlation and the Prais-Winsten transformation
The PCSE covariance structure with first-order serial correlated disturbances is affected in a similar
manner as the covariance structure with spherical disturbances and first-order serial correlation (subsection L.3.4). This means that the PCSE estimated V matrix’s off-diagonal blocks can be described
using [EQ L-19].
Since the serial correlation affects V (the same no matter the two base scenarios), the PraisWinsten transformation can also be applied to the PCSE case. Recall from [EQ L-16]
‫ٱ‬
ˆ ¸ ¸ T 1 . The contemporaneous covariance matrix in this case is:
that: 1
ˆ * *‫ ¸ *
¸ ٱ‬ T ¸ 1 Sˆ2 ¯
¡¢
°±
[EQ L-30]
ˆ in this thesis is:
The 228
 1
S1 S 2 " ST 1 ¬­
žž
­
žž S1
#
# ­­­
1 #
žž 2
­
ˆ ž S
# % #
# ­­­
žž
­­
žž #
#
# %
# ­
­­
žž T 1
"
"
"
S
1
žŸ
®­­
[EQ L-31]
ˆ ˆ
ˆ*  V
*
[EQ L-32]
The V̂ matrix is:
The unbiased regression parameters are estimated using [EQ L-23] but using the PraisWinsten corrected V̂ allows an unbiased adjusted estimated covariance matrix to be expressed as:
1
‫ٱ‬
var ˆ Z* ¸ Z* 1
‫ˆ ٱ‬
‫ٱ‬
¸ Z* ¸ V
* ¸ Z* ¸ Z* ¸ Z* [EQ L-33]
Subsection L.3.3 to subsection L.3.5 considers several more advanced models than the
straightforward fixed-effect model, which occurs with spherical disturbances in subsection L.3.2. By
allowing panel heteroscedasticity and contemporaneous correlation, more robust covariance matrices can be designed. However, it is not certain that those more advanced structures are needed.
The specification test in M.6 (p. 238) ascertains whether panel heteroscedasticity is present in
the disturbances. If the test finds that panel heteroscedasticity is present, then the covariance structure in subsection L.3.5 is applied. If not, the covariance structure in subsection L.3.4 is implemented.
L.4 Formation of panels, the identification, and the treatment of outliers in the
fit periods
This section presents how the panels are created that are used in the panel regressions. All firms in a
panel must have observations for all the panels’ years since the panels must be balanced. The panel
length is therefore an important choice; the choice of panel length is the section’s first topic. The
second topic considers the presence of outliers.
It should be noted that the panel length considered in this section is the fit period’s length,
i.e. the period on which the regressions are estimated. The requirement for balanced panel demands
that a full set of observations exists for the complete fit period and also for the year that precedes
the fit period since the regression equations use a lagged dependent variable (see [EQ 6-10] and
[EQ 6-11]). Therefore, a panel with a four-year period have five years with uninterrupted observations.
L.4.1 The choice of fit period length
One big fit period with 16 years of observations could be used to test the hypotheses, but since the
panel must be balanced, it requires all firms in the fit period to have 16 years of uninterrupted observations. Only very few firms have such a long period of uninterrupted observations available,
229
which therefore shrinks the number of permissible firms substantially. Earlier research (e.g., Albrecht et al. 1977; Holthausen & Larcker 1992; Ou & Penman 1989a, b; Lev 1983) also indicates
that there may be time instabilities that, with a 16-year fit period, adversely affect the reliability of the
regressions estimates.
The choice between long time series versus a large number of firms is a trade-off needed to
be considered as the panels’ lengths are decided. Ideally, a panel’s length is long enough to allow any
dynamics of learning to have impact, but not long enough to allow serious time instabilities to affect
the reliability and validity of the thesis. As panel length increases, the number of firms decreases and
a trade-off between them must determine that there are enough firm-years to be able to achieve
statistical significant results.
The descriptive data in Table L-11shows that it appears as if risk-adjusted RRNOA diminish
rather rapidly. Initially, there are a total of 5,731 time-series reporting significantly positive relative
risk-adjusted RRNOA but there are only 314 time-series consistently reporting significantly positive
relative risk-adjusted RRNOA for six years in a row.
Given that the descriptive data indicate a quick dynamic process, the panels are set up having
a length of four years, which requires five years of uninterrupted observations. Reducing the panel
length from 16 to 4 years increases the number of permissible firms considerably since a panel then
consists of all firms having five years of uninterrupted observations. Reducing panel length from 16
to 4 years also reduces the potential effect of time instabilities and thus there is an increase in the
reliability and validity of the tests.
Sign
POS
NEG
Risk-adjusted RRNOA
Number of observations per prediction
T T+1 T+2 T+3 T+4 T+5
5,731 2,586 1,381
809
500
314
6,218 2,696 1,251
623
330
165
Table L-11: The dynamics of relative risk-adjusted RRNOA measured using number of
observations and the relative risk-adjusted RRNOA.
Nickell (1981) notes that the bias in the regression parameter estimates from a dynamic
fixed-effect model does not disappear as n l d because the asymptotic process depends on large
T and not on large n. There are methods to deal with the bias. One way is to remove the bias by first
taking differences and then applying an instrumental variable estimation method (Green 1993). The
cost for such a method in this thesis is very large since it requires three years of data to perform a
regression for the first year. Green (2003) notes that the Nickell bias is approximately 1 ¸ T 1 , which
means that the bias can be approximately 25 percent with four years of observations. This implies
the need to be careful when drawing far-reaching conclusions from cases where is close to one or
when it is close to zero.
230
Not only regression analysis is performed to asses the theory of Homo comperiens. The results are also validated using an out-of sample method with fixed-size rolling window forecasts
(Chapter 7, p. 117). This validation method requires regressions to be fitted on fit periods. Setting
the panel length to four years allows these panels to be the validations’ fit periods: the estimated
regressions can then work as inputs into the forecasts. Consequently, the choice of panel length is
also subjected to the need to validation.
The observations span from 1978 to 1994 32. This means that, since a panel has four years,
there are 13 panels (one panel per period as depicted in Figure L-1 on which panel regressions are
fitted.
Panel #
1
2
3
4
5
6
7
8
9
10
11
12
13
Panels used in the study
Year 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
Fit origin
Fit period
Figure L-1: The panels with fit periods used to estimate the panel regressions.
Having 13 panels also facilitates detection of significant time inconsistencies. Next, the presence of outliers in the panels is considered.
L.4.2 The presence of outliers in the explanatory variable and in the independent variable
It is clear from subsection 6.2.4 that outliers affect the distributions of the risk-adjusted RROE and
risk-adjusted RRNOA. If the outliers remain in the panels, it renders the regression estimates useless
since the variances are enormous. This means that the estimated regression parameter will be biased
and the corresponding standard error will be so large that it invalidates any statistical tests. The influence of outliers must be reduced before any regression analysis.
Common methods to reduce the influence of outliers are Winsorizing and Trimming of the
distributions before an estimation of location is performed. Two common methods for assessing
robust scale are MAD and the interquartile range. Subsection I.2 discusses another more efficient
method for finding robust estimates of location and scale.
32 The years 1995—1996 are not part of the test since the change in the annual reporting structure from 1995 adversely
affects comparability.
231
Since outlier identification is not concerned with robust confidence intervals, it can focus on
separately identifying efficient robust location estimates and efficient robust scale estimates. The
method used in subsection I.2 is thus not necessary.
Mosteller & Tukey (1977) report that the biweight estimate with c 9 is highly efficient in
large samples and thus that estimate of both the location and the scale are used to identify outliers.
An observation is classified as an outlier if it is farther away from the biweight location estimate than ± 3 biweight standard deviations. This implies that the six standard deviations include
99.99% of all observations in a Gaussian distribution. That is, only the most extreme of the extreme
observations are classified as outliers.
The estimation of robust location and scale is performed per year. Hence, an outlier is identified based on the observation’s distance to its year-specific robust location estimate, and the distance
is compared with the permissible interval implied by the year-specific robust scale and the six sigma
rule.
All firms identified as having at least one outlier are deleted from the panel since the panels
require five years of consecutive data without outliers.
L.5 Summary
This is a technical appendix devoted to discuss the panel regression tests. The appendix considers
three panel regression models. These are the pooled regression model, the random-effect model,
and the fixed-effect model.
Several alternative covariance structures are also considered but the most likely candidate to
the type of data, as well as to the type of econometric model chosen, is the PCSE with AR(1) errors.
This covariance structure is considered in subsection L.3.5.
The formation of panels for the hypotheses tests are, by necessity, restricted to require complete sets of observations because of restrictions in the statistical program used.
A set of 12 panels is used to asses the hypotheses. A robust method using biweight estimates
of location and scale with c=9 is applied to eliminate outliers in the panels.
232
APPENDIX M—PANEL REGRESSION SPECIFICATION TESTS
M.1 Introduction
This appendix presents four specification tests and their results. The first three tests are used to select an appropriate panel regression model while the fourth method is used to asses whether panel
heteroscedasticity is present in the data, which then requires an adaptation of the covariance structure used in the model.
The appendix is structured such that it presents each specification test together with the accompanying results before moving to the next test.
M.2 Specification test plan
The appropriateness of the pooled regression model, the random-effect model, and the fixed-effect
regression model depends on the presence unmodeled heterogeneity and, if it is present, if it is correlated or not with the regressors. To choose the most appropriate of the regression models is therefore a matter of step-wise elimination of them.
The first step is the Breusch-Pagan LM specification test for the presence of random effects.
It test which of the pooled regression and random-effect models that is preferable given the behavior of the disturbances. The second step follows a similar strategy, where the pooled regression
model is poised against the fixed-effect model.
The final step is necessary only when the pooled regression model is rejected in the previous
steps. The third test tests for the presence of correlation between the random firm effects and the
regressors; it poises the random-effect model against the fixed-effect model.
These tests are discussed in this appendix in the same order as above.
M.3 The Breusch-Pagan LM test for presence of random effects
M.3.1 The Breusch-Pagan LM specification test
The Breusch-Pagan Lagrange multiplier test uses the disturbances from the pooled regression mod-
el. With the pooled regression disturbances, the specification test tests the null hypothesis that the
variance for the firm random effect is zero. If the null hypothesis is rejected, there is unmodeled
heterogeneity in the data to such an extent that the random-effect model should replace the pooled
regression model.
The Lagrange multiplier test statistic that the test uses is defined as (Greene 2003):
233

žž
n ¸T
¸ žž
LM ž
2 ¸ T 1
ž
žŸ
œ ¡¢œ
œ ¸œ
n
i 1
n
i 1
T
¯
F
t 1 it °±
T
F2
t 1 it
¬2
­­­
1­­
­­
­®
[EQ M-1]
The decision rule is (Green 2003):
Reject H0 if LM $1,2 B
Where n is the number of firms in the panel, T is the number of years in the panel, $1,2 B is
the cut-off point for a chi-square distribution having one degrees of freedom and with significance
level . In this test a five percent significance level is applied
M.3.2 Results from the Breusch-Pagan LM specification tests
The Breusch-Pagan LM test investigates whether there is any remaining and randomly distributed
unmodeled heterogeneity. If the null hypothesis is rejected, the test has detected such randomly distributed unmodeled heterogeneity. In such a case, the random-effect model is preferable for parameter estimation rather than the pooled regression model. If the null hypothesis is not rejected, the
pooled regression model is the preferable model.
Table M-12 shows the results from the Breusch-Pagan LM test. In the table, LM is the test
statistic, CHIC is the chi-square cut-off point at the five percent significance level having one degree
of freedom.
Table M-12 shows that using the risk-adjusted residual return on equity (risk-adjusted
RROE), the null hypothesis of no unmodeled heterogeneity is rejected for panels with fit origins
1979, 1984, 1989, and 1990.
RRNOA RROE
Variable Field
1978 1979 1980 1981
LM
1.38 8.23 2.16 0.32
CHIC
3.84 3.84 3.84 3.84
PVALUE 24.0% 0.4% 14% 57%
LM
0.02 4.42 2.89 1.37
CHIC
3.84 3.84 3.84 3.84
PVALUE
89% 3.6% 9% 24%
Fit origin
1982 1983 1984 1985
1.00 2.48 9.88 0.52
3.84 3.84 3.84 3.84
32% 11.5% 0.2% 47%
0.38 0.09 18.79 9.16
3.84 3.84 3.84 3.84
54% 77% 0.0% 0.2%
1986
3.69
3.84
5.5%
4.21
3.84
4.0%
1987
1.75
3.84
19%
0.58
3.84
45%
1988
0.26
3.84
61%
0.20
3.84
66%
1989
10.26
3.84
0.1%
8.34
3.84
0.4%
1990
5.41
3.84
2.0%
8.49
3.84
0.4%
Table M-12: The outcome of the Breusch-Pagan LM tests for presence of random effects
using the variables risk-adjusted RROE and risk-adjusted RRNOA.
This means that, according to the specification tests, the pooled regression model is preferable for all panels except those with fit origins 1979, 1984, 1989, and 1990. For the panels having fit
origins 1979, 1984, 1989, and 1990, the random-effect model is the preferred choice according to
the table.
Table M-12 also shows the results using the risk-adjusted residual return on net operating
assets (risk-adjusted RRNOA) variable too; its null hypotheses also fail to be rejected for panels ex-
234
cept those with fit origins 1979, 1984, 1989, and 1990. In addition to these panels, it also fails to
reject the null hypothesis for the panels having 1985 and 1986 as fit origins.
Thus, it appears as though the appropriate model for RROE is on balance not the randomeffect model but for RRNOA it appears as though it is almost even between choosing or not choosing the random-effect model.
The Breusch-Pagan LM test only compares the pooled regression model against the randomeffect model. It is also necessary to compare the pooled regression model with the fixed-effect model. Such a specification tests is discussed in the next subsection.
M.4 The F-test for the presence of firm effects
M.4.1 The F-test specification test
The F-test for firm effects is a specification test in which the null hypothesis presumes that the con-
stant terms are equal across firms. That is, the pooled regression model is applicable to the data. If
the null hypothesis of equal constant terms is rejected, it implies that so much unmodeled heterogeneity exists in the data that the pooled regression model is inferior to the fixed-effect model. The
F-statistic for testing firm effects is defined as (Greene 2003):
F
2
2
RPooled
RFixed
¸ n 1
1
2
1 RFixed
¸ n ¸ T n K 1
[EQ M-2]
The decision rule is (Green 2003):
Reject H0 if F Fn 1,n¸T n K ,B
where Fn 1,n¸T n K ,B is the cut-off point for a F-distribution with significance level having
n 1 numerator degrees of freedom and n ¸ T n K denominator degrees of freedom. In this
2
is the coefficient of determination for the
test, a five percent significance level is applied. RFixed
2
fixed-effect regression model and RPooled
is the coefficient of determination for the pooled regres-
sion.
If neither the Breusch-Pagan LM test for presence of random effects nor the F-test for the
presence of firm effects rejects its null hypothesis, the pooled regression is the preferable model to
use for estimating the regression model. If the Breusch-Pagan LM test for presence of random effects rejects its null hypothesis and the F-test for the presence of firm effects does not, the randomeffect model should be applied for estimating the regression model. If the F-test for the presence of
firm effects rejects its null hypothesis and the Breusch-Pagan LM test for presence of random effects does not, the fixed-effect model should be applied for estimating the regression model.
If both the Breusch-Pagan LM test for presence of random effects and the F-test for the
presence of firm effects reject their respective null hypothesis, the pooled regression is not prefera-
235
ble. A third specification test is therefore needed to discriminate between the random-effect model
and the fixed-effect model. This test is the Hausman test, which is presented in subsection M.5.
M.4.2 Results from the F-tests for the presence of firm effects
The null hypothesis in the F-test assumes that no unmodeled heterogeneity remains in the data and
hence that the intercepts are equal across firms. If the null hypothesis is not rejected, the pooled
regression model is the preferable choice. In this specification test the pooled regression model is
confronting the fixed-effect model, which means that if the null hypothesis is rejected, the fixedeffect model is the preferable regression model.
The results from the test using the risk-adjusted RROE and risk-adjusted RRNOA are presented in Table M-13. The table’s FVALUE is the test statistic and FCRI is the F-distribution cutoff point at the five percent significance level. The cut-off point has NDF numerator degrees of
freedom and DDF denominator degrees of freedom.
RRNOA
RROE
Variable Field
1978 1979 1980
NDF
299
354
635
DDF
899 1,064 1,907
FVALUE
1.92 1.84 1.61
FCRI
1.16 1.15 1.11
PVALUE 0.00% 0.00% 0.00%
NDF
289
353
658
DDF
869 1,061 1,976
FVALUE
1.70 1.85 1.70
FCRI
1.17 1.15 1.11
PVALUE 0.00% 0.00% 0.00%
1981
642
1,928
1.61
1.11
0.00%
639
1,919
1.80
1.11
0.00%
1982
656
1,970
1.35
1.11
0.00%
643
1,931
1.44
1.11
0.00%
Fit origin
1983 1984 1985
669
641
662
2,009 1,925 1,988
1.19 1.52 1.42
1.11 1.11 1.11
0.22% 0.00% 0.00%
634
614
609
1,904 1,844 1,829
1.37 1.71 1.92
1.11 1.11 1.11
0.00% 0.00% 0.00%
1986
616
1,850
1.58
1.11
0.00%
554
1,664
1.88
1.12
0.00%
1987
608
1,826
1.41
1.11
0.00%
578
1,736
1.39
1.12
0.00%
1988
582
1,748
1.40
1.12
0.00%
559
1,679
1.40
1.12
0.00%
1989
574
1,724
1.76
1.12
0.00%
573
1,721
1.80
1.12
0.00%
1990
618
1,856
1.89
1.11
0.00%
626
1,880
2.13
1.11
0.00%
Table M-13: The results of the F-tests for presence of firm effects measured using both
risk-adjusted RROE and risk-adjusted RRNOA.
The table shows that the null hypotheses are rejected in favor of the alternative hypotheses
for all panels and for both variables. The results are so strong that the null hypotheses are rejected
even at the one percent significance level. No significant difference is discernable between the two
variables and thus the results appear robust to the choice of measurement variable.
Using the risk-adjusted RROE, the results in Table M-12 in conjunction with Table M-13
imply that the fixed-effect model should be used rather than any of the pooled regression model and
the random-effect model for all panels except those with fit origins 1979, 1984, 1989, and 1990,. No
Hausman test is needed in order to reach that conclusion. When using the risk-adjusted RROE and
panels with fit origins from 1979, 1984, 1989, and 1990, it is necessary to apply Hausman specification tests to discriminate between the fixed-effect model and the random-effect model.
As Table M-13 shows, the F-tests for the presence of firm effects reject all the null hypotheses at the 0.0 percent significance level when they are tested using the risk-adjusted RRNOA.
When considering Table M-12 too, the fixed-effect model should be employed using the riskadjusted RRNOA for the panels not starting in 1979, 1984, 1985, 1986, 1989, and 1990. The results
236
are strong and consistent enough that no Hausman test is necessary. The results of the Hausman
specification tests nevertheless are presented in subsection M.5.2. The Hausman specification tests
should corroborate the findings above concerning risk-adjusted RRNOA and the findings for riskadjusted RROE.
M.5 The Hausman test for correlation between random firm effects and the
regressors
M.5.1 The Hausman specification test
The Hausman test is a chi-square test that positions the results from the random effect against the
fixed effect. The test’s null hypothesis presumes that there is no correlation between random firm
effects and the regressors. If there is no correlation, the random-effect regression model is preferable (Greene 2003). The fixed-effect regression model is preferable if the null hypothesis is rejected.
To test the hypotheses the estimated covariance matrix is needed and it is defined as (Green
2003):
¯ Var Cˆ
¯
ˆ Var Cˆ
:
¢¡ Fixed ±°
¢¡ Random ±°
[EQ M-3]
Using the estimated covariance matrix, the Wald criterion is defined as (Green 2003):
ˆ 1 ¸ Cˆ
CˆRandom ¯°
W ¡CˆFixed CˆRandom ¯° ¸ :
¢
±
¢¡ Fixed
±
[EQ M-4]
The decision rule is (Green 2003):
Reject H0 if W $2K 1,B
Where $2K 1,B is the cut-off point for a chi-square distribution having K 1 degrees of
freedom and with significance level . A five percent significance level is applied in this specification
test.
The Hausman test also provides an implicit test of Homo comperiens. Homo comperiens
postulates that there should be some firm-specific effect and hence that there should be heterogeneity in the data. Furthermore, it postulates that firm-specific effects are non-random. If the
Hausman test rejects the null hypothesis of random effect in favor of fixed effects, the theory of
Homo comperiens is supported.
This section focuses on finding the most appropriate panel regression model, given the potential existence of heterogeneity. Another important issue concerns the potential existence of heteroscedasticity in the models, which is the topic of subsection M.6.
237
M.5.2 Results from the Hausman tests for correlation between random firm effects and the
regressors
The Hausman test’s null hypothesis assumes that there is no correlation between random firm ef-
fects and the regressors, suggesting that the random-effect model is the preferable estimation model
if the null hypothesis is not rejected.
Table M-14 reports the results from the Hausman tests on all panels using both the riskadjusted RROE and the risk-adjusted RRNOA. W is the Hausman test statistic, CHIC is the chisquare cut-off point.
RRNOA RROE
Variable Field
W
CHIC
PVALUE
W
CHIC
PVALUE
Fit origin
1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990
283
252
484
537
487
422
360
448
463
347
405
419
525
3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
257
278
519
601
506
442
357
519
486
309
365
440
602
3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
Table M-14: The results from the Hausman test for correlation between random firm effects and the regressors when estimated using both the risk-adjusted RROE and the riskadjusted RRNOA.
The results rejects that the random-effect model should be employed for all panels using either the risk-adjusted RROE or the risk-adjusted RRNOA. Therefore, it implies that the fixed-effect
model dominates over the random-effect model. This means that the fixed-effect model is implemented onto all panels as the regression parameters are estimated.
The next subsection presents the results from the tests of panel heteroscedasticity. These
specification tests are conducted using the fixed-effect model since it is the preferred estimation
model based on the analysis above.
M.6 The likelihood test for the presence of panel heteroscedasticity in the fixedeffect model
M.6.1 The likelihood specification test
The likelihood test for panel heteroscedasticity tests the null hypothesis of homoscedasticity against
the alternative hypothesis of panel heteroscedasticity. It tests this by investigating whether the variance of the disturbances is constant across the firms. The test statistic is (Greene 2003):
 ‫­¬ ¸ ٱ‬
­
2 ln L0 ln L1 n ¸ ln¸ žžž
žŸ n ­­®
œ
 ‫ٱ‬
¬¯
¡T ¸ ln¸ žž i ¸ i ­­°
žŸ T ®­­°
i 1 ¡
ž
¢¡
±°
n
[EQ M-5]
As previously, n is the number of firms in the panel and T is the panel length. Since section
L.3 limits itself to consider alternative specifications for a fixed-effect model, is the disturbance
matrix from a fixed-effect regression with spherical disturbances and i is the disturbance matrix
from an individual regression on firm i while assuming spherical disturbances.
The decision rule is (Green 2003):
238
Reject H0 if 2 ln L0 ln L1 Xn21,B
where Xn21,B is the cut-off point for a chi-square distribution having n 1 degrees of freedom and with significance level . A five percent significance level is used in this test.
M.6.2 Results from the tests for panel heteroscedasticity in the fixed-effect model
The fixed-effect model dominates both the pooled regression model and the random-effect model
in the reported specification test, which means that the fixed-effect estimates are used in the hypotheses tests. Running an OLS fixed-effect regression model requires spherical disturbances or else
the standard errors will be biased (see subsection L.3.3, p. 226), which affect the reliability of the
hypotheses tests. The alternative is to allow for panel heteroscedasticity by using a more complex
covariance structure.
Table M-15 reports the results from the specification tests. In the table, LM is the test statistic, CHIC is the cut-off point at the five percent significance level from a chi-square distribution that
has DF degrees of freedom.
RRNOA
RROE
Variable Field
1978 1979 1980
DF
299
354
635
-2(LN0-LN1) 4,154 4,866 8,597
CHIC
340
399
695
PVALUE
0.00% 0.00% 0.00%
DF
289
353
658
-2(LN0-LN1) 5,477 6,585 12,080
CHIC
330
398
719
PVALUE
0.00% 0.00% 0.00%
1981
642
8,747
702
0.00%
639
11,800
699
0.00%
1982
656
9,082
717
0.00%
643
11,958
703
0.00%
Fit origin
1983 1984 1985
669
641
662
9,483 9,821 9,896
730
701
723
0.00% 0.00% 0.00%
634
614
609
11,864 12,065 11,694
694
673
668
0.00% 0.00% 0.00%
1986
616
9,330
675
0.00%
554
10,639
610
0.00%
1987
608
7,948
666
0.00%
578
10,054
635
0.00%
1988
582
7,257
639
0.00%
559
9,195
615
0.00%
1989
574
6,963
631
0.00%
573
9,343
630
0.00%
1990
618
7,358
677
0.00%
626
10,068
685
0.00%
Table M-15: Test for the presence of panel heteroscedasticity using both the risk-adjusted
RROE and the risk-adjusted RRNOA.
The test statistics are extremely large, which leads to the rejection of the null hypothesis of
no panel heteroscedasticity in favor of its alternative of panel heteroscedasticity. This implies that a
covariance structure is needed that allows for panel heteroscedasticity in order to achieve unbiased
standard errors from the panel regressions.
A covariance structure that allows for panel-corrected standard errors (PCSE) (and firstorder correlated disturbances) is applied to the panels with risk-adjusted RROE and to the panels
with risk-adjusted RRNOA. See subsection L.3.5 (p. 228) for a covariance structure having PCSE
and AR(1) disturbances.
M.7 Conclusions from the specification tests
The appendix rejects the pooled regression model as applicable to the accounting data used in this
thesis. The appendix also rejects the random-effect model as applicable to the accounting data. In
the end, the model that perseveres through all specification tests is the fixed-effect model, which
consequently is the applied model in this research.
239
The panel heteroscedasticity specification tests clearly reject the null hypothesis of no panel
heteroscedasticity, which implies that the covariance structure that yields PCSE is implemented as
the regression model.
L.3 concludes that, by design, the estimated regression models are affected by serial correlation. Together with this appendix finding, it means that the preferred regression model on all panels
and for both variables is a fixed-effect model having PCSEs after they are adjusted for first-order
serial correlation. This is equivalent to the covariance model discussed in subsection L.3.5.
It should be noted that using the fixed-effect model with dynamic econometric models, as in
this research, introduces the Nickell bias, which may effect the regression parameter estimation.
Thus, caution is called for when interpreting the results from the hypotheses tests if they are weakly significant or if they are weakly insignificant.
240
APPENDIX N—DOES RANDOM WALK IN THE RISK-ADJUSTED
RESIDUAL ACCOUNTING RATES-OF-RETURNS?
N.1 The hypotheses to be tested
A random-walk process of some variable implies that successive changes of the variable are independent (Fama 1965a). Using probabilities, independence implies that the probability distribution
for the change of the variable at a given period is independent of the sequence of the variable’s
changes from the periods preceding the current time period (Fama 1965a). That is:
x t 1 x t Ft 1 x t 1 Ft Ft 1 " x 0 œ
t
F
i 1 i
Where Ft is a white noise disturbance, which means that it has:
&t ¢ Ft 1 ¯± 0
TF2 T 2
corr Ft 1, Ft 0
Recall the following proposition:
Proposition 4-7: In a market that meets the conjectures of the theory of Homo comperiens (Proposition
2-4, Proposition 3-2) and with unbiased accounting the limit values of risk-adjusted subjective expected
RROE and RRNOA are zero. That is: lim &*K 0 < t 1RROEt > 0 , and lim &*K 0 < t 1RRNOAt > 0 .
t ld
t ld
The process in Proposition 4-7 is a direct contradiction to the definition of a random-walk
process since it implies variable dependency. That is, in Proposition 4-7 it is possible to predict future variables based on the sequence of the variable’s changes from the preceding periods.
The variables in Proposition 4-7 are operationalized as [EQ 6-8] and [EQ 6-9] (p. 98).
This appendix assesses the following two hypotheses (one per variable):
H1A: The theory of Homo comperiens argues that the risk-adjusted subjective expected residual return on equity (RROE) is not randomly walking. Using [EQ 6-8] this can be expressed as:
The serial correlation in t RROEit* 1 *
t 1 RROE it
Ft 1 is not zero, that is:
corr Ft 1, Ft v 0
H0A: The risk-adjusted subjective expected RROE is randomly walking. This can be expressed as:
corr Ft 1, Ft 0 .
241
H1B: The theory of Homo comperiens argues that the risk-adjusted subjective expected residual return on net operating assets (RRNOA) is not randomly walking. Using [EQ 6-9] this can be
expressed as:
The serial correlation in t RRNOAit* 1 *
t 1 RRNOAit
Ft 1 is not zero, that is:
corr Fit 1, Fit v 0
H0A: The risk-adjusted subjective expected RRNOA is randomly walking. This can be expressed as:
corr Fit 1, Fit 0 .
Indeed, an even harsher test could be devised since the proposition implies
corr Ft 1, Ft 0 . This could be tested against the null hypothesis of corr Ft 1, Ft . 0 . Such a test
is not formally carried out since it is thought not to contribute much to the test already reported in
section 6.4 (p. 108).
Nevertheless, the tests reported in this appendix do not have the same strength as those reported in section 6.4. A rejection of the null hypotheses in this appendix does not exclude
corr Ft 1, Ft 0 , but such a rejection does, together with the findings reported in section 6.4, pro-
vide, I argue, strong support for Proposition 4-7.
The appendix is organized such that it first presents the test method followed by the results
from the tests.
N.2 The goodness-of-fit test
The goodness-of-fit test focuses on the independence-dependence difference in the stated hypotheses.
The test is performed by classifying all observations in a period into equal-sized bins. If the
distribution is completely random, as the null hypotheses assume, then the probability for observing
an observation in a certain bin is equal to observing it in any other bin, i.e. the bin-probability is
constant.
Let k ‰ K be a bin and K the total number of bins. The unconditional probability for an observation to be assigned to a bin k ‰ K is Q 1 ¸ K 1 . Let Ok be the number of observations assigned to a bin and let E be the expected number of observations in a bin, which is E n ¸ Q ,
where n is the number of observations for a period. By comparing the difference between the numbers of observations per bin to the expected number of observations per bin, a chi-square test statistic can be measured as (Newbold 1995):
$2 œ
K
k 1
2
Ok E E
[EQ N-1]
242
According to Newbold (1995), the decision rule is:
Reject H0 if $2 $K2 1,B
where $2K 1,B is the cut-off point for a chi-square distribution having K 1 degrees of freedom and with significance level .
The goodness-of-fit test above tests the distributional characteristics of a period and needs to
be extended in order to focus on the independence-dependence since the difference is exacerbated
as a longer perspective is used. The test above is therefore extended to cover more than one period.
N.3 A multi-period goodness-of-fit-test
If the null hypotheses are correct, the observations are serially independent. The independence assumption allows not only the use of unconditional probabilities but also the use of conditional
probabilities. Conditional probabilities make it possible to extend the test into a multi-period setting.
Let the conditional probability for observing the variable from a firm in the same bin for two
consecutive periods be Q2 1 ¸ K 1 . Analogously, the expected number of variables that are ob2
served in the same bin for two consecutive periods is E2 n2 ¸ Q2 , where n2 is the number of complete time series of variables for two consecutive periods.
With the conditional probability perspective, it becomes possible to count the number of observations of variables (stemming from the same firm) that are assigned to the same bin for two
consecutive periods and to measure E2. These variables are then used to measure the chi-square test
statistic according to [EQ N-1] and to evaluate it against the decision rule in section N.2.
The multi-period goodness-of-fit tests the ability to discover non-randomness increases as
the number of periods is added.
Newbold (1995) notes that the goodness-of-fit test works well for samples in which the expected number of observations per bin is greater than five. Having E>5 severely limits the possibility to extend the test into the future: The required sample size increases dramatically since the conditional probability decreases fast. For example, assume there are five bins, which implies an unconditional probability of 20 percent (this requires n to be 25). Assume now that you wish the test to assess the independency in five periods. The conditional probability that the variable from a firm remains in the same bin is then only 0.25 =0.032 percent and n must therefore be at least 15,625.
The multi-period goodness-of-fit test is designed so that it chooses the maximum number of
bins that meets the criteria of having E>5. The exact number of feasible bins is a function of the
minimum number of expected observations, the conditional probability for the forecast length, and
the number of firms. It is calculated as shown below:
243
bins 1
1
t 1
Q1
Et ¸ nt1 [EQ N-2]
For t 4 the number of bins must be greater than or equal:
E 4 5 º bins 1
1
41
Q1
5 ¸ n41 N.4 Test method
The first test uses a two-year conditional probability and thus uses only a firm time series having two
complete years of observations. The second test uses a three-year conditional probability and thus
uses only a firm time series having three complete years of observations. This continues up to the
fourth test, which uses a firm time series having five complete years of observations.
The formation of the set of time series for the first test is done using a rolling-window method that starts in year 1978 and collects all time series having observations in 1978 and 1979. The
window then rolls forward to 1979, and all time series having observations in 1979 and in 1980 are
collected and added to those previously found. The process so continues to the horizon year 1993,
which collects all time series having observations in 1993 and in 1994 and adds them to all other
time series.
The time series are apportioned into the initial period’s , t 1 , equal-sized bins based on the
ranking of the variable (see below). From this, the observations are counted that remain in the same
bin for the following years. The observations are compared with the expectations and a chi-square
statistic is calculated on the differences following [EQ N-1].
Since the time series are apportioned into initial equal-sized bins, it follows that the product
of the number of bins and the observations per bin must equal the total available time series. If this
is not true are time series deleted so that the condition is fulfilled. The time series are deleted from
the center of the distribution.
Because the time series in a set originates from different years, there is a chance that their levels will differ, which can affect the reliability of the test while it presumes that they all come from
the same distribution. To make the risk-adjusted residual accounting rates-of-returns comparable
between different years, this test normalizes them per year. This is a method used elsewhere (Mueller
(1977).
The variables used in the tests, [EQ 6-8] and [EQ 6-9], are normalized against their industryyear’s profitability ratio. The industry year’s profitability ratio is measured according to I.2 (p. 211).
The relative ratios are defined as:
*
t 1 rel-RROE it
*
t 1 rel-RRNOAit
*
t 1 RROEit
¸ t 1 ROEIt1
*
t 1 RRNOAit
¸ t 1 RNOAIt1
[EQ N-3]
[EQ N-4]
244
N.5 Results from the multi-period goodness-of-fit tests
The goodness-of-fit test ascertains the assumption in Proposition 4-7 that the risk-adjusted residual
accounting rates-of-returns are dependent on their sequence of changes against the null hypotheses
of random walks in the variables. The tests are performed using conditional probabilities to capture
the dynamics in the process.
The section is organized where descriptive outputs from the test are discussed followed by
the formal outcome of the hypotheses tests.
N.5.1 Descriptive outputs from the tests
The goodness-of-fit tests are preformed using the relative risk-adjusted RROE and the relative risk-
adjusted RRNOA for two-year 33, three-year, four-year, and five-year conditional probabilities. All
ratios are relative ratios based on the definitions [EQ N-3] and [EQ N-4].
The number of bins is chosen so that maximum permissible number of bins is applied while
keeping the expected number of observations per bin greater than five. The two-year conditional
probability tests apply 56 bins and the unconditional probabilities are Q1 561 1.79% , while the
two-year conditional probabilities are Q2 561 0.0319% . For the three-year tests, 12 bins are
2
used. Six bins are used for the four-year tests and four bins are used for the five-year tests.
t=2
1.79%
Probablility table
t=3
t=4
0.59%
0.46%
t=5
0.10%
Table N-16: The conditional probabilities
Since the test method requires that the firm’s time series are evenly apportioned into the
first-year bins, it follows that some time series are deleted to ascertain equal-sized bins. The table
below provides information of how many time series that are deleted. The time series are deleted
from the center of the distributions. While this is an arbitrary choice, it is not likely to have a material affect on the results since the number of deleted time series is small in relation to the total time
series available for analysis. See Table N-18 for information on total number of available time series.
Number of deleted cpl firm time-series
Variable (relative)
t=2
t=3
t=4
RROE
N/A
6
2
RRNOA
8
6
1
t=5
2
0
Table N-17: Number of deleted complete firm times-series.
33
No goodness-of-fit test is performed using the risk-adjusted RROE with a two-year conditional probability since the
ranking procedure in SAS gives equal ranking to identical RROE. This poses a problem since they are assigned to bins
on their rankings.
The amount of work deemed to solve this problem does not stand in proportion to the gain from performing this
test when considering that three two-year conditional probability goodness-of-fit tests are performed and that three
other goodness-of-fit tests are performed using the risk-adjusted RROE. Fifteen goodness-of-fit tests are performed
compared with potentially 16 tests.
245
At most eight complete time series are deleted. Deleting nine time series has a negligible effect since the statistical test uses many observations after deletion of the nine time series. The number of complete time series that I use after the nine time series are deleted is presented in Table
N-18.
Number of cpl firm time-series available for GoF-tests
Variable (relative)
t=2
t=3
t=4
t=5
RROE
N/A
13,208
10,938
8,972
RRNOA
15,272
12,506
10,224
8,312
Table N-18: Number of used complete firm time series that is available for the goodnessof-fit tests. These time series are the time series available after the trimming explicated in
Table N-17.
Below are three tables (Table N-19—Table N-21) that show the number of observations per
bin and variable for t 5 , t 4 , and t 3 . No such information is provided for t 2 since that
implies information on 56 bins. It is considered to cause too much clutter in the table.
Table N-19 shows that of 8,972 time series with risk-adjusted RROE, only 218 manage to be
ranked into the same bin for five consecutive years. Still, that is much more than what was expected
since only 35 time series were expected to be consistently ranked into the same bin for all five years.
Similar results appear for the other three variables.
No of obs and expectations per bin for t=5
rel-RROE
rel-RRNOA
Bin
Obs
Exp
Obs
Exp
1
64
8.76
130
8.12
2
40
8.76
21
8.12
3
48
8.76
51
8.12
4
66
8.76
76
8.12
218
35.0
278
32.5
Table N-19: Number of empirical observations (Obs) and the expected number of observations (Exp) per bin for t=5.
Another result from Table N-19 is that bin #1 and bin #4 have more persistent time series
than the other bins. From this casual analysis, it appears as if the variables are non-independent.
It also appears as if risk-adjusted residual accounting rates-of-returns measured before financial activities (risk-adjusted RRNOA) are more persistent than when measured after financial activities (risk-adjusted RROE).
246
No of obs and expectations per bin for t=4
rel-RROE
rel-RRNOA
Bin
Obs
Exp
Obs
Exp
1
59
8.44
113
7.89
2
34
8.44
20
7.89
3
27
8.44
11
7.89
4
27
8.44
34
7.89
5
40
8.44
37
7.89
6
75
8.44
86
7.89
262
50.6
301
47.3
Table N-20: Number of empirical observations and the expected number of observations
per bin for t=4.
For t 4 , six bins are used, which is an improvement when compared with t 5 . It is
possible to use more bins in the shorter period since it has more of complete firm time series. The
results interpretable from Table N-20 are comparable with those from Table N-19, and indicate that
the variables are dependent.
Much more observations remain in their bins than expected if they were truly random and if
they are independently distributed. Again, the start and end (bin #1 and #6) are those bins that have
the most persistent time series.
No of obs and expectations per bin for t=3
rel-RROE
rel-RRNOA
Bin
Obs
Exp
Obs
Exp
1
36
6.01
67
5.69
2
17
6.01
26
5.69
3
15
6.01
18
5.69
4
19
6.01
9
5.69
5
14
6.01
12
5.69
6
22
6.01
7
5.69
7
13
6.01
13
5.69
8
10
6.01
13
5.69
9
23
6.01
21
5.69
10
29
6.01
20
5.69
11
15
6.01
12
5.69
12
22
6.01
20
5.69
13
59
6.01
49
5.69
294
78.2
287
74.0
Table N-21: Number of empirical observations and the expected number of observations
per bin for t=3.
Table N-21 reports the results from t 3 . These results are consistent with those reported
in Table N-19 and Table N-20. Table N-21 shows that the observed persistence is much greater
than what should be the case with independent variables.
For t 3 , it appears as though risk-adjusted RRNOA is less independent than risk-adjusted
RROE. This effect is almost nullified at t 3 since the aggregate difference between the two variables is small. An ocular investigation thus indicates that even though some firms manage to report
relatively stable risk-adjusted RRNOA, this does not carry through to risk-adjusted RROE. Thus, it
appears that adding the financial effects remove apparent stability from the firm’s operations.
247
N.5.2 Results from the hypotheses tests
Subsection N.5.1 shows that it appears as though the variables are serially dependent, which sup-
ports Proposition 4-7. A causal ocular analysis therefore rejects the null hypotheses of random walk
in favor of the alternative hypotheses of non-random walk.
This subsection provides the results from the formal hypotheses tests performed on t 2 to
t 5 . The outcomes are presented in descending order since the tests with a high t are more valid
than the tests with a low t.
Summary statistics, t=5
Field
rel-RROE rel-RRNOA
DFE
3
3
CHIC
20.9
30.2
PVALUE
0.01%
0.00%
Table N-22: Summary statistics for the goodness-of-fit tests where t=5.
Table N-22 shows the results from the goodness-of-fit tests, where t 5 . DFE is the degrees of freedom, CHIC is the chi-square statistics as defined in [EQ N-1], and the PVALUE is the
p-values.
The causal ocular analysis from the previous subsection is supported by the statistical test
having t 5 . The test rejects the null hypotheses of independent variables in favor of the alternative hypotheses of dependent variables. The result meets the cut-off point of five percent and the
results are even significant at the 0.0 percent level.
Summary statistics, t=4
Field
rel-RROE rel-RRNOA
DFE
5
5
CHIC
25.0
32.2
PVALUE
0.01%
0.00%
Table N-23: Summary statistics for the goodness-of-fit tests where t=4.
The table above shows the goodness-of-fit tests with t 4 . Also at t 4 the hypotheses
tests reject the null hypotheses of independency in favor of the alternative hypotheses of dependency. These results are significant at the 0.0 percent level.
Summary statistics, t=3
Field
rel-RROE rel-RRNOA
DFE
12
12
CHIC
35.9
37.4
PVALUE
0.03%
0.02%
Table N-24: Summary statistics for the goodness-of-fit tests where t=3.
At t 3 , (see Table N-24) the goodness-of-fit tests are also rejects the null hypotheses of
independency in favor of the alternative hypotheses of dependency. These results are significant at
the 0.0 percent level.
248
Summary statistics, t=2
Field
rel-RROE rel-RRNOA
DFE
N/A
55
CHIC
N/A
39.5
PVALUE N/A
93.07%
Table N-25: Summary statistics for the goodness-of-fit tests where t=2.
The hypotheses tests that investigate the behavior of the variables between two consecutive
periods, i.e. t 2 , fail to reject the null hypotheses of independence in favor of the alternative hypotheses of dependence.
It appears as if the process between two consecutive periods is a random-walk process.
When a longer perspective is applied, the random-walk process gives way for a non-random process.
That is, from a short-run perspective it appears as if the assumption of random walk cannot be rejected, but as the perspective is prolonged, the variables become serially dependent.
The result in this section is similar to findings on tests of market efficiency. Kothari (2001)
reports that in short-window event studies there are hardly no abnormal returns (thus, random walk
works), whereas the long-window event-studies show the possibility to earn abnormal returns, which
implies that the process is not randomly walking.
N.6 Conclusions from the multi-period goodness-of-fit tests
Both the descriptive data and the goodness-of-fit tests that investigate the alternative hypotheses
based on Proposition 4-7 reject the null hypotheses of independent distributed variables in all multiperiod tests, except for t 2 , which favors the alternative hypotheses.
The results can be interpreted in many ways. The number of bins is 56 for t 2 . Having extremely many bins makes it almost impossible to retain the same bin assignment over time since an
extremely small change in the variable mandates a change of the assigned bin. I believe that this may
drive the results for t 2 , especially considering the consistent and strong rejections of the null
hypotheses for t 2 , where the number of bins is no more than 13. Indeed, when researchers (e.g.,
Mueller 1977; Penman 1991) use a bin structure to analyze the behavior of accounting rates-ofreturns, they do not use more than 20 bins.
However, the results of t 2 are more affected by survival bias than for t 2 . This may
also drive the results in the direction of dependency. On the other hand, the number of bins is not
drastically different between t 2 and t 3 , which makes me reluctant to assign too much importance to a survival bias effect.
I therefore find that the most likely difference between results from the hypotheses tests for
t 2 compared with the hypotheses tests for t 2 is due to an excessive use of bins.
The general conclusion is therefore that the goodness-of-fit tests find consistent and strong
support for Proposition 4-7 since the null hypotheses of independence is rejected in favor of the
249
alternative hypothesis of dependence. That is, randomness does not walk in residual accounting
rates-of-returns.
250
ACKNOWLEDGEMENTS
This thesis marks the end of a long journey that started in 1997. During all these years I have managed to do many more things than just working on my thesis. Most importantly I met and married
Maria and we have had our bellowed daughter Nadine.
Stoically Maria has stayed at my side seeing the gradual process in which I have nurtured and
developed my ideas into this thesis. I am eternally grateful for this.
Nadine, being little more than two years has only been in on this ride for a brief time, but she
constantly reminds me of what learning is all about. Being this remarkable daughter of mine she is a
constant light in my life. I do not see how I could have written my thesis without my family supporting me. Thank you!
There are many more people that I wish to thank. Especially I wish to thank Jan-Erik Gröjer
for providing me support and feedback even during his most difficult times. Then I have to thank
Dag Smith for helping me in reviewing all those accounting equations and for our debates. The
same accounts for Ingemund Hägg who with his analytical skills has helped me in developing my
ideas by giving me important comments on my work during critical periods. I must not forget Mats
Åkerblom since he strongly challenged some of my earliest ideas during my second advanced seminar. After this seminar I sat down and did a lot of soul searching, which greatly changed the focus of
the thesis. And finally (I know that I am forgetting people) I wish to thank my former roommates
Mattias Hamberg and Jiri Novak who I have discussed my ideas with over the years.
251
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25
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26
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Universitatis Upsaliensis, Studia Oeconomiae Negotiorum nr. 17.
27
Joachimsson, Robert, 1984, Utlandsägda dotterbolag i Sverige. En analys av
koncerninterna transaktionsmönster och finansiella samband. Stockholm:
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28
Kallinikos, Jannis, 1984, Control and Influence Relationships in Multinational
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30
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31
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32
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33
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35
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Relationships. A Longitudinal Study of Exchange of Resources, Control and
Conflicts. Uppsala: Department of Business Studies.
36
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37
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företagsekonomiämnets tidiga utveckling vid Handelshögskolan i Stockholm.
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38
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Department of Business Studies
39
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40
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41
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Social Sciences nr 21.
42
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Department of Business Studies.
43
Hultbom, Christina, 1991, Intern handel. Köpar/säljarrelationer inom stora
företag. Uppsala: Företagsekonomiska institutionen.
44
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inriktning och utfall. Uppsala: Företagsekonomiska institutionen.
45
Levinson, Klas, 1991, Medbestämmande i strategiska beslutsprocesser. Facklig
medverkan och inflytande i koncerner. Uppsala: Företagsekonomiska
institutionen.
46
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Development in Distant Industrial Networks. Uppsala: Department of Business
Studies
47
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inom de till Landsorganisationen anslutna förbunden. Stockholm: Carlssons
Bokförlag.
48
Henders, Barbara, 1992, Marketing Newsprint in the UK Analyzing Positions in
Industrial Networks. Uppsala: Department of Business Studies.
49
Lampou, Konstantin, 1992, Vårt företag. En empirisk undersökning av några
organisatoriska självuppfattningar och identiteter. Uppsala: Företagsekonomiska
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50
Jungerhem, Sven, 1992, Banker i fusion. Uppsala: Företagsekonomiska
institutionen.
51
Didner, Henrik, 1993, Utländskt ägande av svenska aktier. Uppsala: Företagsekonomiska institutionen.
52
Abraha, Desalegn, 1994, Establishment Processes in an Underdeveloped Country. The Case of Swedish Firms in Kenya. Uppsala: Department of Business
Studies.
53
Holm, Ulf, 1994, Internationalization of the Second Degree. Uppsala:
Department of Business Studies.
54
Eriksson, Kent, 1994, The Inter-relatedness of Environment Technology and
Structure A Study of Differentiation and Integration in Banking. Uppsala:
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55
Marquardt, Rolf, 1994, Banketableringar i främmande länder. Uppsala:
Företagsekonomiska institutionen.
56
Awuah, Gabriel B., 1994, The Presence of Multinational Companies (MNCs) in
Ghana A Study of the Impact of the Interaction between an MNC and Three
Indigenous Companies. Uppsala: Department of Business Studies.
57
Hasselbladh, Hans, 1995, Lokala byråkratiseringsprocesser, institutioner,
tolkning och handling. Uppsala: Företagsekonomiska institutionen.
58
Eriksson, Carin B., 1995, Föreställningar och värderingar i en organisation
under förändring - en studie av identitetsuppfattningar inom konsumentkooperationen. Uppsala: Företagsekonomiska institutionen.
59
Jonsson, Tor, 1995, Value Creation in Mergers and Acquisitions: A Study of
Swedish Domestic and Foreign Takeovers. Uppsala: Department of Business
Studies.
60
Furusten, Staffan, 1995, The Managerial Discourse - A Study of the Creation and
Diffusion of Popular Management Knowledge. Uppsala: Department of Business
Studies.
61
Pahlberg, Cecilia, 1996, Subsidiary - Headquarters Relationships
International Business Networks. Uppsala: Department of Business Studies.
62
Sjöberg, Ulf, 1996, The Process of Product Quality - Change Influences and
Sources - A Case from the Paper and Paper-Related Industries. Uppsala:
Department of Business Studies.
in
63
Lind, Johnny, 1996, Ekonomistyrning och verksamhet i utveckling - Ekonomiska
rapporters utformning och användning när verksamheten flödesorienteras.
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64
Havila, Virpi, 1996, International Business-Relationships Triads - A Study of the
Changing Role of the Intermediating Actor. Uppsala: Department of Business
Studies.
65
Blankenburg Holm, Desirée, 1996, Business Network Connections and
International Business Relationships. Uppsala: Department of Business Studies.
66
Andersson, Ulf, 1997, Subsidiary Network Embeddedness. Integration, Control
and Influence in the Multinational Corporation. Uppsala: Department of
Business Studies.
67
Sanner, Leif, 1997, Trust Between Entrepreneurs and External Actors. Sensemaking in Organising New Business Ventures. Uppsala: Department of Business
Studies.
68
Thilenius, Peter, 1997, Subsidiary Network Context in International Firms.
Uppsala: Department of Business Studies.
69
Tunisini, Annalisa, 1997, The Dissolution of Channels and Hierarchies - An
Inquiry into the Changing Customer Relationships and Organization of the
Computer Corporations. Uppsala: Department of Business Studies.
70
Majkgård, Anders, 1998, Experiential Knowledge in the Internationalization
Process of Service Firms. Uppsala: Department of Business Studies.
71
Hjalmarsson, Dan, 1998, Programteori för statlig företagsservice. Uppsala:
Företagsekonomiska institutionen.
72
Avotie, Leena, 1998, Chefer ur ett genuskulturellt perspektiv. Uppsala:
Företagsekonomiska institutionen.
73
Arnesson, Leif,
institutionen.
74
Dahlqvist, Jonas, 1998, Knowledge Use in Business Exchange – Acting and
Thinking Business Actors. Uppsala: Department of Business Studies.
75
Jonsson, Eskil, 1998, Narrow Management. The Quest for Unity in Diversity.
Uppsala: Department of Business Studies.
76
Greve, Jan, 1999, Ekonomisystem
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77
Roxenhall, Tommy, 1999, Affärskontraktets
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78
Blomgren, Maria, 1999, Pengarna eller livet? Uppsala: Företagsekonomiska
institutionen.
79
Bäckström, Henrik, 1999, Den krattade manegen: Svensk arbetsorganisatorisk
utveckling under tre decennier. Uppsala: Företagsekonomiska institutionen
1998,
Chefsrörlighet.
Uppsala:
och
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affärsstrategier.
användning.
Uppsala:
Uppsala:
80
Hamberg, Mattias, 2000, Risk, Uncertainty & Profitability. An Accounting-Based
Study of Industrial Firms’ Financial Performance. Uppsala: Department of
Business Studies.
81
Sandberg, Eva, 2000, Organiseringens dynamik – Strukturskapande processer i
ett telematikföretag. Uppsala: Företagsekonomiska institutionen.
82
Nordin, Dan, 2000, Två studier av styrning i kunskapsintensiva organisationer.
Uppsala: Företagsekonomiska institutionen.
83
Wedin, Torkel, 2001, Networks and Demand. The Use of Electricity in an
Industrial Process. Uppsala: Department of Business Studies.
84
Lagerström, Katarina, 2001, Transnational Projects within Multinational
Corporations. Uppsala: Department of Business Studies.
85
Markgren, Bertil, 2001, Är närhet en geografisk fråga? Företags affärsverksamhet och geografi – En studie av beroenden mellan företag och
lokaliseringens betydelse. Uppsala: Företagsekonomiska institutionen.
86
Carlsson, Leif, 2001, Framväxten av en intern redovisning i Sverige –
1900-1945. Uppsala: Företagsekonomiska institutionen.
87
Silver, Lars, 2001, Credit Risk Assessment in Different Contexts – The Influence
of Local Networks for Bank Financing of SMEs. Uppsala: Department of
Business Studies.
88
Choi, Soon-Gwon, 2001, Knowledge Translation in the Internationalization of
Firms. Uppsala: Department of Business Studies.
89
Johanson, Martin, 2001, Searching the Known, Discovering the Unknown. The
Russian Transition from Plan to Market as Network Change Processes. Uppsala:
Department of Business Studies.
90
Hohenthal, Jukka, 2001, The Emergence of International Business Relationships.
Experience and performance in the internationalization process of SMEs.
Uppsala: Department of Business Studies.
91
Gidhagen, Mikael, 2002, Critical Business Episodes. The Criticality of Damage
Adjustment Processes in Insurance Relationships. Uppsala: Department of
Business Studies.
92
Löfmarck Vaghult, Anna, 2002, The Quest for Stability. A Network Approach to
Business Relationship Endurance in Professional Services. Uppsala: Department
of Business Studies.
93
Grünberg, Jaan, 2002, Problematic Departures. CEO Exits in Large Swedish
Publicly Traded Corporations. Uppsala: Department of Business Studies.
94
Gerdin, Jonas, 2002, Ekonomisystems utformning inom produktionsavdelningar:
En tvärsnittsstudie. Uppsala: Företagsekonomiska institutionen.
95
Berggren, Björn, 2002, Vigilant Associates – Financiers Contribution to the
Growth of SMEs. Uppsala: Department of Business Studies.
96
Elbe, Jörgen, 2002, Utveckling av turistdestinationer genom samarbete.
Uppsala: Företagsekonomiska institutionen.
97
Andersson, Maria, 2003, Creating and Sharing Subsidiary Knowledge within
Multinational Corporations. Uppsala: Department of Business Studies.
98
Waks, Caroline, 2003, Arbetsorganisering och professionella gränsdragningar.
Sjukgymnasters samarbete och arbetets mångfald. Uppsala: Företagsekonomiska
institutionen.
99
Bengtson, Anna, 2003, Framing Technological Development in a Concrete Context – the Use of Wood in the Swedish Construction Industry. Uppsala:
Department of Business Studies.
100 Bäcklund, Jonas, 2003, Arguing for Relevance – Global and Local Knowledge
Claims in Management Consulting. Uppsala: Department of Business Studies.
101 Levay, Charlotta, 2003, Medicinsk specialisering och läkares ledarskap: En
longitudinell studie i professionell kollegialitet och konkurrens. Uppsala:
Företagsekonomiska institutionen.
102 Lindholm, Cecilia, 2003, Ansvarighet och redovisning i nätverk. En longitudinell
studie om synliggörande och osynliggörande i offentlig verksamhet. Uppsala:
Företagsekonomiska institutionen.
103 Svensson, Birgitta, 2003, Redovisningsinformation för bedömning av små och
medelstora företags kreditvärdighet. Uppsala: Företagsekonomiska institutionen.
104 Lindstrand, Angelika, 2003, The Usefulness of Network Experiential Knowledge
in the Internationalization Process. Uppsala: Department of Business Studies.
105 Baraldi, Enrico, 2003, When Information Technology Faces Resource
Interaction. Using IT Tools to Handle Products at IKEA and Edsbyn. Uppsala:
Department of Business Studies.
106 Prenkert, Frans, 2004, On Business Exchange Activity. Activity Systems and
Business Networks. Uppsala: Department of Business Studies.
107 Abrahamsson, Gun & Helin, Sven, 2004, Problemlösningsarbete på låg
organisatorisk nivå. Två studier om implementering respektive konkretisering av
idéer om kundorderstyrd tillverkning. Uppsala: Företagsekonomiska institutionen.
108 Wedlin, Linda, 2004, Playing the Ranking Game: Field formation and boundarywork in European management education. Uppsala: Department of Business
Studies.
109 Hedmo, Tina, 2004, Rule-making in the Transnational Space. The Development
of European Accreditation of Management Education. Uppsala: Department of
Business Studies.
110 Holmström, Christine, 2004, In search of MNC competitive advantage: The role
of foreign subsidiaries as creators and disseminators of knowledge. Uppsala:
Department of Business Studies.
111 Ciabuschi, Francesco, 2004, On the Innovative MNC. Leveraging Innovations
and the Role of IT Systems. Uppsala: Department of Business Studies.
112 Ståhl, Benjamin, 2004, Innovation and Evolution in the Multinational Enterprise.
Uppsala: Department of Business Studies.
113 Latifi, Mohammad, 2004, Multinational Companies and Host Partnership in
Rural Development. A Network Perspective on the Lamco Case. Uppsala:
Department of Business Studies.
114 Lindbergh, Jessica, 2005, Overcoming Cultural Ignorance: Institutional
Knowledge Development in the Internationalizing Firm. Uppsala: Department of
Business Studies.
115 Spencer, Robert, 2005, Strategic Management of Customer Relationships. A
Network Perspective on Key Account Management, Uppsala: Department of
Business Studies.
116 Neu, Elizabeth, 2006, Lönesättning i praktiken. En studie av chefers
handlingsutrymme, Uppsala: Företagsekonomiska institutionen.
117 Gebert Persson, Sabine, 2006, Crash-Landing in a Turbulent Transition Market.
A Legitimating Activity? Uppsala: Department of Business Studies.
118 Persson, Magnus, 2006, Unpacking the Flow - Knowledge Transfer in MNCs.
Uppsala: Department of Business Studies.
119 Frimanson, Lars, 2006, Management Accounting and Business Relationships
from a Supplier Perspective. Uppsala: Department of Business Studies.
120 Ström, Niklas, 2006, Essays on Information Disclosure. Content, Consequence
and Relevance, Uppsala: Department of Business Studies.
121 Grafström, Maria, 2006, The Development of Swedish Business Journalism.
Historical Roots of an Organisational Field, Uppsala: Department of Business
Studies.
122 Flöstrand, Per, 2006, Valuation Relevance. The Use of Information and Choice of
Method in Equity Valuation, Uppsala: Department of Business Studies.
123 Windell, Karolina, 2006, Corporate Social Responsibility under Construction.
Ideas, Translations, and Institutional Change, Uppsala: Department of Business
Studies.
124 Wictorin, Bo, 2007, Är kluster lönsamma? En undersökning av platsens
betydelse för företags produktivitet, Uppsala: Företagsekonomiska institutionen.
125 Johed, Gustav, 2007, Accounting, Stock Markets and Everyday Life, Uppsala:
Department of Business Studies.
126 Maaninen-Olsson, Eva, 2007, Projekt i tid och rum – Kunskapsintegrering
mellan projektet och dess historiska och organisatoriska kontext, Uppsala:
Företagsekonomiska institutionen.
127 Scherdin, Mikael, 2007, The Invisible Foot. Survival of new art ideas in the
swedish art arena – An autoethnographic study of nontvtvstation, Uppsala:
Department of Business Studies.
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