Government Corruption and Foreign Direct Investment Under the Threat of Expropriation

Government Corruption and Foreign Direct Investment Under the Threat of Expropriation
Staff Working Paper/Document de travail du personnel 2016-13
Government Corruption and
Foreign Direct Investment Under
the Threat of Expropriation
by Christopher Hajzler and Jonathan Rosborough
Bank of Canada staff working papers provide a forum for staff to publish work-in-progress research independently from the Bank’s Governing
Council. This research may support or challenge prevailing policy orthodoxy. Therefore, the views expressed in this paper are solely those of the
authors and may differ from official Bank of Canada views. No responsibility for them should be attributed to the Bank.
www.bank-banque-canada.ca
Bank of Canada Staff Working Paper 2016-13
March 2016
Government Corruption and Foreign Direct
Investment Under the Threat of Expropriation
by
Christopher Hajzler1 and Jonathan Rosborough2
1International
Economic Analysis Department
Bank of Canada
Ottawa, Ontario, Canada K1A 0G9
and
Centre for Applied Macroeconomic Analysis (CAMA)
Corresponding author: chajzler@bankofcanada.ca
2Department
of Economics
St. Francis Xavier University
jrosboro@stfx.ca
ISSN 1701-9397
2
© 2016 Bank of Canada
Acknowledgements
We are indebted to Jeannine Bailliu, Richard Chisik, Yuriy Gorodnichenko, Timothy
Kam, Oleksiy Kryvtsov, and Ricardo Lagos for helpful advice and workshop discussions.
We also thank participants of the European Economics Association Meetings, the
Association of Public Economic Theory Meetings, the Workshop of the Australasian
Macroeconomics Society, and the Canadian Economics Association Meetings, and
seminar participants at Ryerson University, the Bank of Canada, St. Francis Xavier
University, the University of Canterbury and the University of Otago for constructive
comments.
ii
Abstract
Foreign investment is often constrained by two forms of political risk: expropriation and
corruption. We examine the role of government corruption in foreign direct investment
(FDI) when contracts are not fully transparent and investors face the threat of
expropriation. Using a novel dataset on worldwide expropriations of FDI over the 1990–
2014 period, we find a positive relationship between the extent of foreign investor
protections and the likelihood of expropriation when a country’s government is perceived
to be highly corrupt, but not otherwise. We then develop a theory of dynamic FDI
contracts under imperfect enforcement and contract opacity in which expropriation is a
result of illicit deals made with previous governments. In the model, a host-country
government manages the FDI contract on behalf of the public, which does not directly
observe government type (honest or corrupt). A corrupt type is able to extract rents by
encouraging hidden investments in return for bribes. Opportunities for corrupt deals arise
from the distortions in the optimal contract when the threat of expropriation is binding.
Moreover, a higher likelihood of the government being corrupt increases the public’s
temptation to expropriate FDI, magnifying investor risk. The model predicts that
expropriation is more likely to occur when the share of government take is low and
following allegations of bribes to public officials, and it suggests an alternative channel
through which corruption reduces optimal foreign capital flows.
JEL classification: F23, F21, F34
Bank classification: International topics; Development economics; Economic models
Résumé
Deux formes de risque politique, à savoir l’expropriation et la corruption, constituent
souvent une entrave à l’investissement étranger. Dans le présent article, nous examinons
le rôle de la corruption du gouvernement dans l’investissement direct étranger lorsque les
contrats ne sont pas entièrement transparents et que les investisseurs sont confrontés à la
menace d’une expropriation. Grâce à un nouvel ensemble de données sur les
expropriations liées à l’investissement direct étranger à l’échelle mondiale au cours de la
période 1990-2014, nous mettons en évidence un lien positif entre l’étendue des
protections accordées aux investisseurs étrangers et la probabilité d’expropriation dans le
cas d’un gouvernement perçu comme fortement corrompu, mais cet effet n’est pas
observé lorsque le taux de corruption est faible. Nous élaborons ensuite une théorie des
contrats dynamiques d’investissement direct étranger faisant l’objet d’une application
imparfaite. Par la suite, nous étudions l’opacité des contrats dans le cadre desquels
l’expropriation est le résultat d’affaires illicites conclues avec d’anciens gouvernements.
iii
Dans ce modèle, le gouvernement du pays d’accueil gère le contrat d’investissement
direct étranger pour le compte de la population qui n’est pas en mesure d’observer
directement s’il s’agit d’un gouvernement honnête ou corrompu. Un gouvernement
corrompu peut s’adonner à l’extraction de rentes en encourageant des investissements
cachés en échange de pots-de-vin. Les occasions d’affaires illicites découlent de
distorsions dans le contrat optimal lorsque la menace d’expropriation a une valeur
contraignante. De surcroît, plus la probabilité que le gouvernement soit corrompu est
élevée, plus la population est incitée à exproprier l’investissement direct étranger, ce qui
a pour effet d’accentuer le risque pour les investisseurs. Le modèle prévoit que la
probabilité d’expropriation est plus forte lorsque les intérêts du gouvernement sont
moindres et que des allégations de pots-de-vin pèsent contre des fonctionnaires. Enfin, le
modèle nous porte à croire qu’il existe un autre canal par l’entremise duquel la corruption
réduit le flux optimal de capitaux étrangers.
Classification JEL : F23, F21, F34
Classification de la Banque : Questions internationales; Économie du développement;
Modèles économiques
iv
Non-Technical Summary
Recent efforts to deepen our understanding of barriers to cross-border capital flows to
relatively capital-poor developing countries have found that foreign investment is lower
in countries with relatively weak institutions and poor governance. Two forms of political
risk appear to be especially important in explaining global patterns of foreign direct
investment (FDI): government corruption and expropriation. While these two forms of
political risk are typically studied in isolation, recent disputes between foreign investors
and host-country governments suggest that expropriation risk and corruption are
interrelated. Specifically, several recent cancellations of direct investment contracts have
been justified by national governments as attempts to reverse unfair or “exploitative”
deals signed with investors under a previous government.
This paper examines the link between high-level government corruption, transparency of
foreign investment contracts, and the security of foreign investor property rights.
Specifically, we consider the incentives for corrupt officials to make secret deals with
foreign investors when terms of the contract are not fully transparent to the public, and
we study the consequences for expropriation risk and host-country welfare. Using a novel
dataset on worldwide expropriations of FDI over 1990–2014, we find that expropriation
is more common in industries where host-country governments typically play a direct
role in establishing contracts with foreign investors (such as mining and utilities). We
also document a positive relationship between the strength of foreign investor protections
and the likelihood of expropriation when a country’s government is perceived as being
highly corrupt, but not otherwise.
We then develop a theory of dynamic FDI contracts under imperfect enforcement and
contract opacity that can help explain these facts. In the model, a host-country
government manages the FDI contract on behalf of the public, which does not directly
observe government type (either honest or corrupt). A corrupt type is able to extract rents
by encouraging hidden investments in return for bribes. Opportunities for corrupt deals
arise from the distortions in the optimal foreign investment contract caused by
expropriation risk. Moreover, a higher likelihood of the government being corrupt
increases the public’s temptation to expropriate FDI, magnifying investor risk. In the
model, expropriation occurs as a result of illicit deals made by previous governments that
violate the optimal contract. Consistent with the empirical and anecdotal evidence, the
theory predicts that expropriation is more likely to occur when the share of government
take is low and following allegations of bribes to public officials, and it suggests an
alternative channel through which corruption decreases host-country income.
v
CORRUPTION, FDI AND EXPROPRIATION
1
Introduction
Recent efforts to deepen our understanding of barriers to cross-border capital flows to
relatively capital-poor, developing countries have generally found that foreign investment is lower in countries with relatively weak institutions and poor governance (see,
for example, Alfaro, Kalemli-Ozcan, and Volosovych, 2008; Faria and Mauro, 2009; Papaioannou, 2009; Ju and Wei, 2010; Méon and Sekkat, 2012; Okada, 2013; Reinhardt,
Ricci, and Tressel, 2013). Empirical work that has focused on foreign direct investment
(FDI) in particular—the largest and most stable source of capital inflows to developing
and emerging markets—has emphasized the importance of two prevalent forms of political risk: government corruption (e.g., Wei, 2000; Asiedu, 2006; Hakkala, Norbäck,
and Svaleryd, 2008; Morrissey and Udomkerdmongkol, 2012) and risk of expropriation
(Bénassy-Quéré, Coupet, and Mayer, 2007; Busse and Hefeker, 2007; Asiedu, Jin, and
Nandwa, 2009).1 Although these two forms of political risk are typically studied in isolation, an examination of recent disputes between foreign investors and host-country governments suggests that expropriation risk and corruption may be interrelated. In several
high-profile cases involving the cancellation of direct investment contracts (including the
numerous expropriations in Bolivia, Russia, and Venezuela over the past decade),2 national governments have justified the takings as an attempt to undo the unfair or “exploitative” deals offered to the investor by previous national or local government leaders.
In several cases, accusations of corruption and acceptance of bribes in return for low
tax or royalty payments are explicit.3 This paper examines the link between high-level
government corruption, transparency of foreign investment contracts, and the security of
foreign investor property rights. Specifically, we consider the incentives for corrupt officials to make clandestine deals with foreign investors when terms of the contract are
not fully transparent to the public, and study the consequences for expropriation risk and
host-country welfare.
We assemble a unique dataset on expropriations of FDI across all developing countries worldwide over 1990–2014 to study the relationships between the likelihood of expropriation and commonly used measures of foreign investor property rights protection
and government corruption. We find that the strength of investor protections is associ1
The principal roles of corruption and expropriation risk in the allocation of FDI across emerging markets are also underscored in the IMF Capital Markets Consultative Group’s (2003) foreign investor survey.
The report emphasizes investor concerns over both forms of risk, noting that investors rank quality of
governance second in importance (behind market access) in deciding where to invest.
2
We adopt a relatively narrow definition of expropriation, which is outlined in detail in Section 2.
3
For example, prior to nationalizing Bolivia’s petroleum industry in 2005, the president declared:
Many of these contracts signed by various governments are illegal and unconstitutional. It
is not possible that our natural resources continue to be looted, exploited illegally, and as
the lawyers say, these contracts are legally void and must be adjusted. (Associated Press,
December 21, 2005)
Numerous other examples of expropriation of FDI coinciding with investigations into government corruption are discussed in Section 2.
1
CORRUPTION, FDI AND EXPROPRIATION
ated with a lower propensity to expropriate in countries with higher corruption, but this
association is weak in countries where corruption is low. We then develop a model of expropriation of FDI in the presence of high-level government corruption that is consistent
with these findings, providing a novel channel through which corruption distorts foreign
investment and reduces host-country welfare.
Our theoretical framework builds on the work of Eaton and Gersovitz (1984), Cole
and English (1991), and Thomas and Worrall (1994) in which a host country requires
foreign capital to finance an excludable investment opportunity and the government is
unable to commit to not seizing the investor’s assets. The model environment is closest to Thomas and Worrall (1994), who characterize the optimal, self-enforcing contract
between a host-country government and foreign firm when the government type and contracts are fully transparent. In contrast to their work, however, we assume that the public
observes whether the contracted transfer payments from the investor to the host country
are made but relies upon (possibly misleading) reports from the government in every period concerning the actual value of FDI assets.4 The government official who manages
the contract is assumed to be either honest or dishonest, and the official’s type is not
directly observable by the public. The honest type always implements the contract that
maximizes the ex ante expected welfare of the public, does not accept bribes, and expropriates FDI whenever this is beneficial to the public ex post. In contrast, the dishonest
type only cares about the stream of side payments that can be extracted from the foreign
investor by deviating from the optimal contract.
In this environment, the optimal foreign investment contract features gradualism in
FDI flows, which minimizes the temptation of the host-country citizens to demand that
the government expropriate investor assets and redistribute the gains. Opportunities for
dishonest officials to extract side payments through corrupt deals with foreign investors
depend crucially on this risk-induced distortion in the optimal investment path. However,
there is also a causal link between corruption and expropriation operating in the opposite direction. A higher propensity for corruption in a country, which we model as the
likelihood of a politician being a dishonest type, increases the temptation to expropriate.
The expectation of corruption magnifies the distortions to investment and payments to the
host country under the contract due to expropriation risk, even if no corrupt deals occur
ex ante. Finally, when we allow for the possibility of exogenous government turnover,
corrupt deals increase the likelihood of an expropriation actually occurring. In fact, the
contract the public is able to write with an investor is fully self-enforcing in the absence
of corruption, and expropriation only occurs if a corrupt deal has taken place.
We find that government corruption constrains the optimal contract in several ways.
First, when there are positive start-up costs, corruption constrains the set of contracts
4
We also depart from Thomas and Worrall (1994) in that we consider the related, dual problem of characterizing the contract that maximizes host-country welfare, subject to the investor’s expected discounted
payoffs from date 0 being sufficient to cover the investor’s initial start-up costs, as opposed to analyzing the
optimal contract that maximizes investor returns. However, this does not impact the equilibrium dynamics
of the optimal contract.
2
CORRUPTION, FDI AND EXPROPRIATION
in which foreign investors can profitably participate, resulting in a more limited set of
projects that are ultimately financed. Second, for any given project that is financed, the
potential for corruption decreases contracted investment leading up to the stationary investment stage of the contract (and may even decrease the long-run investment level)
while delaying transfers to the host country. Corrupt deals, when they take place, entail
foreign investment in excess of the official contract. Therefore, corruption decreases FDI
on the extensive margin, but the effect on the intensive margin is ambiguous. However,
a higher likelihood of corruption results in lower transfers to the host country and lower
welfare.5 Moreover, an expropriation is more likely to occur before any contracted transfers to the host country are made and when there is evidence of past corruption. These
features relating to the timing of expropriation provide a rationale for why governments
frequently claim contracts are corrupt, unfair and/or exploitative as a justification for
breaking them.6
Our work is related to recent literature on the distortionary effects of uncertainty in the
form of extortion and/or expropriation by corrupt governments. Phelan (2006) considers
the dynamics of investment an environment where domestic investors update their beliefs
about government type (and whether to elect a new government with a lower ex ante
likelihood of being corrupt) and where the corrupt type optimally chooses when to seize
investor assets. He characterizes a Markov perfect equilibrium in which the opportunistic
type gradually ratchets up the probability of expropriating in a given period as investment
increases and investors become more confident that the government is not corrupt. Bhattacharyya and Hodler (2010) consider random government types (corrupt or honest) in
the context of theft of public revenues. They show that higher resource abundance in the
absence of executive constraints on the government (i.e., when it is more difficult for investors to overthrow a government that is suspected of past corruption) increases theft by
corrupt officials and lowers private investment, resulting in a resource curse. Though neither paper considers foreign investment explicitly, their basic arguments could be carried
to this context as well, suggesting potential channels by which corruption discourages
FDI, as documented by Wei (2000). However, in both papers government corruption and
expropriation (more generically, government theft) are treated as synonymous. Our focus
instead is on how corruption and bribes shape the foreign investment contract on the one
hand, and the implications for the security of these contracts, FDI flows, and host-country
welfare on the other.
5
We follow much of the existing literature by focusing on the welfare impact owing to distortions in
foreign capital flows. However, expropriation risk may affect the value of the project in a number of other
ways, depending on the specific contract setting. Melek (2014) develops a model of non-renewable resource
extraction where the anticipation of expropriation will encourage investors to over-extract the resource,
and estimates large productivity losses in Venezuela’s oil sector leading up to its 1975 nationalization.
Baldursson and Von der Fehr (2015) formally examine the case of a renewable resource in the presence of
initial contracting costs and show that expropriation risk reduces the value of the project through distortions
in the optimal duration of the lease.
6
For evidence that larger gaps between oil revenue shares in favor of the foreign investor increase the
likelihood of expropriation, see Mahdavi (2014).
3
CORRUPTION, FDI AND EXPROPRIATION
Relatively little attention has been given to the endogenous determination of expropriation risk and the incentives for corrupt officials to solicit bribes from foreign investors.
Two important exceptions are Azzimonti and Sarte (2007) and Koessler and LambertMogiliansky (2014). In each of these models, acts of expropriation are treated as distinct
from theft through extortion (i.e., bribes), which enables the authors to consider the effects of bribe-taking on expropriation and vice versa. In Azzimonti and Sarte (2007),
the contracting government during the initial investment phase of the FDI project faces a
trade-off between demanding payments from the investor in proportion to investment (a
tax or a bribe), which distort investment, and the amount of assets that can be expropriated during the production phase, which the government may not be able to appropriate
in the event it is replaced by a new government. The authors show that higher political
turnover results in a higher level of bribes and a lower level of expropriation. In their
model, expropriation occurs with probability one—varying only in the proportion of assets seized—and the value of assets expropriated is negatively related to the extent of
bribes acquired during the investment phase. Building on the work of Myerson (1981),
Koessler and Lambert-Mogiliansky (2014) model government corruption as an auction
between a large number of heterogeneous foreign firms, where bribes paid to the corrupt
official are determined by the reservation price the official requires for a promise to not
expropriate investor assets. The bribe required may differ from asset values, given the
assumptions that the official’s private valuation differs across firms and a political constraint limits the number of firms that can be expropriated. The model predicts that the
likelihood of expropriation increases with the value of firm assets (and decreases with the
value of other firms when the constraint binds), generating a positive association between
expropriation risk and the amount of bribes paid by firms.
The connection between corruption and expropriation risk that we explore is complementary to the mechanisms proposed in these recent theories. Each offers insight
into expropriation as a tool for politicians to generate personal financial or political gain.
However, several recent expropriation cases analyzed in the next section suggest that the
solicitation of bribes and outright expropriation of investor assets are frequently motivated
by a conflicting set of objectives. In the model we develop, corruption and expropriation
risk are endogenously co-determined, as in Azzimonti and Sarte (2007) and Koessler and
Lambert-Mogiliansky (2014); a key difference in our model is that expropriations arise
from the conflicting objectives of corrupt officials and the intended beneficiaries from the
FDI contracts, the host-country public. Our results have direct implications for the timing of expropriation and suggest that allegations of corrupt deals made between public
officials and foreign investors may not simply be a convenient justification for seizing
investor assets. They also lend insight into repeated cycles of nationalization and subsequent privatization in countries with poor contract transparency and extensive histories of
government corruption such as those documented by Gadano (2010) in the Argentinian
oil sector.
The rest of the paper is organized as follows. Section 2 presents empirical evidence
for the effect of weak contract enforcement on risk of expropriation when governments
4
CORRUPTION, FDI AND EXPROPRIATION
are perceived as being relatively corrupt. These relationships are examined formally in
Section 3. Here we introduce contract opacity and exogenous government types (honest
or corrupt) into a standard model of FDI under imperfectly enforceable contracts, and
characterize the optimal contract when the government type is constant but not observable
by the public. This basic framework is then extended in Section 4 to consider the effects
of government turnover, where we consider the effects of political risk corruption on the
likelihood that expropriation occurs. Section 5 concludes.
2
Empirical Facts on Expropriation and Corruption
Political risk has been frequently cited as an important barrier to foreign investment in
developing countries, particularly those forms of risk associated with changes in contract
terms by governments and the threat of expropriation of investor assets. The prevalence
of government corruption in negotiating and managing foreign investor contracts in particular can exacerbate enforcement problems. In her comprehensive analysis of corruption in developing countries, Rose-Ackerman (1999) notes that the demand for bribes by
high-level officials in the procurement of contracts may result in investor concerns over
whether corrupt officials will “stay bought.” Rose-Ackerman proposes two reasons for
this concern. First, corrupt officials may be vulnerable to being replaced by a new government, and the investor may fear that the new regime will not honor the old commitments.
Foreign investors forced to pay bribes in the bidding for contracts may expect that future
governments (possibly at the behest of the host-country electorate) will demand outright
nationalization of investor assets if there is suspicion that the deal was reached under illicit circumstances.7 Second, the willingness of officials to accept bribes in securing the
contract may be viewed as a negative signal that the investor is likely to face extortion and
costly changes in contract terms throughout the life of the contract. This tendency for officials to demand further side-payments from investors that were not agreed to during the
initial contract phase is a form of what is often referred to as “creeping expropriation.”8
The risk to investor property rights implied by the first concern is distinct from the second
in that the former reflects either the attempt of the host-country governments to rescind
corrupt contracts or the time-inconsistency of past deals that offer few current benefits to
the country. The latter stems from a lack of contract transparency and the prevalence of
government corruption itself.
A number of recently publicized cases of expropriation of FDI lend support to the
view that illicit deals between foreign investors and corrupt officials increase contract
vulnerability. In the case of Russia, for example, legislation governing production shar7
See Rose-Ackerman (1999) Chapter 3, pp. 32-35, for a detailed discussion.
The term creeping expropriation has been used more broadly to refer to all adjustments in investor
payments that do not involve a transfer of asset ownership or outright cancellation of contracts, including
changes in official tax and royalty payments conflicting with the provisions of the original contract. However, Rose-Ackerman’s discussion of changes in contract terms in the context of government corruption
focuses on illicit payments.
8
5
CORRUPTION, FDI AND EXPROPRIATION
ing agreements with foreign investors in energy and mining, signed by President Yeltsin
in 1993, was never ratified, and the few foreign investment contracts that were concluded
under Yeltsin, such as the Sakhalin II agreement with Royal Dutch Shell, did not receive legislative approval. These contracts offered internationally non-standard terms
that tended to strongly advantage the foreign investor (Bamberger, 2007). When Shell
refused a bid by the state petroleum company to acquire its stake in Sakhalin II in 2005,
the government forced Shell to transfer the assets to the state by revoking key operational
licences. In Guinea, the government takeover of Brazilian iron mining operations BSGR
in 2013 accompanied allegations that the rights were illegally issued by the country’s
previous dictator in return for bribes. This case culminated in the FBI’s involvement in
an investigation into bribe payments and an indictment against a French national who
worked as an intermediary for BSGR in securing the contested mineral rights.9 Media
reports indicate that the current government is also scrutinizing 18 other contracts signed
by foreign mining firms and previous regimes. Similarly, in 2013, the Kyrgyz government
decided to review the contract of a Canadian mining affiliate because the 2009 agreement
under the former government was deemed to be unconstitutional, resulting in the government acquisition of a 33 per cent stake in the operations (and the subsequent demands for
a 67 per cent equity stake).10
Allegations of corruption by previous contracting officials are also found in the recent wave of expropriations in Latin America. In Bolivia, several mining and petroleum
contracts have been cancelled amidst claims that the contracts cancelled with foreign
investors were either exploitative or corrupt.11 Following the Venezuelan government’s
2010 nationalization of a U.S. and Italian-owned chemical and fertilizer subsidiary, a
former co-owner is serving a four-year sentence in the United States for having bribed
Venezuelan officials.12 Suspicion of corruption in signing foreign investment contracts
also appears to have had broader influence in the decision to nationalize several industries in Venezuela. In a 1999 public speech, Venezuela’s Minster of Foreign Affairs—
under the newly elected Chavez government—claimed that government corruption over
the previous 20 years was responsible for sending an estimated $100 billion abroad owing
to “irregularities” in public works contracts.
While these recent expropriation cases are suggestive of a causal connection between
government graft and the security of foreign investor assets, we formally investigate the
prevalence of this relationship by assembling data on acts of expropriation of FDI world9
The French businessman was apprehended in a U.S. airport in April 2013 on charges of making illegal
payments to the former Guinean president and transferring these payments into the United States.
10
The Kyrgyz government also nationalized a Latvian bank in 2010 after it had been accused of money
laundering on behalf of relatives of the former president.
11
These cases include the seizure of a Canadian company’s mining concessions in 2012 and a Swiss
mining affiliate in 2007 amidst claims that the concessions were fraudulently obtained and that the current
government was simply putting things right.
12
The owners purchased the subsidiary Venoco shortly after the brief coup and imprisonment of the
Venezuelan president, in which the company’s chief executive member is alleged to have played a lead
role.
6
CORRUPTION, FDI AND EXPROPRIATION
wide over 1990–2014, and estimate the impact of corruption and the strength of contract
enforcement on the likelihood of expropriation. Following Kobrin (1984), we measure an
act of expropriation as the forced transfer of FDI assets in a given industry (3-digit SIC
category) and in a given year. The data are collected by systematically scanning a wide
range of international mainstream media outlets and published investment treaty arbitration claims and checking the details against a number of criteria.13 To capture the impacts
of government corruption and foreign investor protections, we adopt the index measures
of corruption and foreign investor contract enforcement published by the PRS Group’s
International Country Risk Guide (ICRG) and commonly considered in the empirical literature on political risk and foreign investment.14
Global expropriations of FDI over 1990–2014 are depicted in Figure 1, broken down
by sector. A total of 162 expropriation acts occurred across 44 countries during this
period, with a relatively large share of takings in resource-based industries (44 per cent),
the bulk of these occurring in mining and petroleum.15 A substantial proportion of takings
has also been in public utilities (11 per cent). The figure shows that expropriation had
been on the rise between 1990 and 2010, but since 2011 the frequency of takings has
declined. (It should be noted that Venezuela alone accounts for almost 25 per cent of
acts during this period, but these dynamic and sectoral patterns look very similar when
Venezuela is excluded.)
The broad set of factors accounting for the global dynamic and sectoral expropriation
patterns is beyond the scope of the present paper; sectoral characteristics relating to the
timing of expropriation are examined in Opp (2012) and Hajzler (2014), whereas national
and international politico-economic pressures have been studied in Li (2009); Asiedu, Jin,
and Nandwa (2009); Chang, Hevia, and Loayza (2010); Koivumaeki (2015); and Tomz
and Wright (2010), among others. (See also Guriev, Kolotilin, and Sonin, 2011; Engel
and Fischer, 2010; Mahdavi, 2014 for analysis of political and economic factors related
13
These data update and extend those assembled by Hajzler (2012) for the 1990–2006 period to cover
2007–2014. Definitions, data collection and coding follow the methodology of Kobrin (1984), who produced the original dataset on expropriations in all developing and emerging markets over the 1960-1979
period. Arguably a more ideal measure of expropriation intensity would be based on the value of assets seized. However, this company information is often confidential or difficult to obtain, whereas the
frequency-based measure used here is conducive to obtaining more complete global coverage of all expropriation. Owing to the growing use of investment dispute resolution through international arbitration
claims, Hajzler (2012) is able to draw on available investor claim information to compare sectoral and time
patterns based on both the reported assets seized and the frequency of acts, and finds that observed patterns are broadly the same. (A detailed discussion of the advantages of this expropriation measure and the
comprehensiveness of country coverage can be found in Kobrin, 1984; Hajzler, 2012.)
14
See, for example, Aguiar, Amador, and Gopinath (2009), Asiedu and Lien (2011), and Li and Resnick
(2003) who consider the ICRG’s contract enforcement, and Arezki and Brückner (2011), Fratzscher and
Imbs (2009), Hakkala, Norbäck, and Svaleryd (2008), Svensson (2005), and Wei (2000) who consider the
effects of ICRG’s government corruption. A description of each indicator is available on the PRS website:
http://www.prsgroup.com/wp-content/uploads/2012/11/icrgmethodology.pdf.
15
Of these, a total of 116 expropriation acts have been documented in our 2007–2014 update. Although
there has been a sharp increase in expropriations since 1990, the frequency of takings remains low compared
with their peak in the late 1960s and early 1970s. (See Kobrin, 1984, for a comparison.)
7
CORRUPTION, FDI AND EXPROPRIATION
Figure 1: Expropriation acts by sector, 1990–2014
25
20
15
10
5
0
Primary
Manufacturing
Services
Total
Source: Hajzler (2012) and authors’ estimates
to the timing of expropriation in mining and petroleum in particular.)16 However, two observations are worth emphasizing here. First, the relative frequency of takings in resource
extraction and utilities industries exceeds the industry shares in developing-country GDP.
These are also industries where government officials typically have a more active role
in allocating concessions and negotiating the terms of foreign investor contracts, and
where opportunities for soliciting bribes are expected to be relatively high. Arezki and
Brückner (2011) and Arezki and Gylfason (2013), for example, present evidence that the
extent of government corruption in a country is positively associated with the level of
resource rents, controlling for a host of other determinants of corruption.17 Second, the
time path of expropriations, particularly in natural resource sectors, broadly tracks global
fluctuations in mineral and energy prices, as has been previously documented in related
literature (Duncan, 2005; Guriev, Kolotilin, and Sonin, 2011; Hajzler, 2012; Mahdavi,
2014).18 This suggests that expropriation is driven, at least in part, by an opportunistic
16
Examining global oil sector nationalizations over the past century, Mahdavi (2014) also considers a
number of external factors influencing contract enforcement, including reliance on exports (which makes
an expropriating country more vulnerable to foreign retaliation) and spillover effects from expropriating
neighbors (capturing the notion that the capacity for foreign retaliation is limited, and less likely when
many nations expropriate).
17
O’Higgins (2006, p.242) also observes that theft tends to be easiest in resource extraction because
contracts are often less transparent to the public and corrupt deals are more difficult to detect. Ades and
Di Tella (1999) argue that corruption in the form of wasteful government spending increases when revenues
from resource extraction are also above average.
18
Higher risk of expropriation associated with the prevalence of sunk costs in resources and mineral price
volatility is also discussed in Nellor (1987), Monaldi (2001), Engel and Fischer (2010).
8
CORRUPTION, FDI AND EXPROPRIATION
Table 1: Comparison of political risk and FDI in developing economies
(1990–2014)
Expropriating Countries
Average Min Max
Investment risk index
Corruption index
Log FDI stock per capita
Log income per capita
5.36
3.65
5.81
8.54
0.68
1.00
0
6.13
11.38
6.00
9.58
10.28
Non-expropriating Countries
Average Min
Max
5.21
3.67
5.21
8.21
0.50
1.00
0
6.14
10.83
5.27
10.83
10.46
Countries
44
92
Sources: Corruption and Investment Risk are calculated from the PRS Group’s ICRG
indexes, which are measured on 0-6 and 0-12 point scales, respectively. For clarity,
values for (6 - Corruption Absent) and (12 - Investment Profile) are presented. Inward
FDI stocks per capita are expressed in (logged) constant 2005 U.S. dollars and obtained
from UNCTAD, while income per capita is in constant PPP dollars from the World Bank.
motive related to the value of investor assets.
Table 1 contains summary statistics relating to income, FDI, and the ICRG country
risk scores among developing countries that have expropriated during the sample period and those that have not. Investment risk is calculated from the ICRG Investment
Profile index (reported on a 12-point scale), which measures the strength of contract
enforcement, the ability to repatriate profits, and the absence of payment delays. The
ICRG corruption index aims to mainly capture high-level government corruption, including nepotism in government, “favor-for-favors,” secret party funding, suspiciously close
ties between politics and business, and excessive patronage, which aligns well with the
type of illicit activity we focus on in this paper.19 The ICRG measures corruption on a
6-point scale, with higher values indicating lower corruption. For clarity, we recalculate
corruption as 6 minus the index value.
A comparison of simple means reveals that expropriating countries exhibit slightly
lower security of contracts, as captured by the higher average investment risk rating.
However, there is little evidence that recently expropriating countries are perceived as
being more corrupt on average. Expropriating countries have higher average stocks of
FDI, which is perhaps not too surprising given that countries with more FDI have more
to potentially expropriate.20 Interestingly, a comparison of income per capita (in constant
international dollars) reveals that expropriating countries are slightly richer on average,
which may reflect the higher FDI. However, the differences in means appear rather small
given the within-group variation. Moreover, other determinants of expropriation may
19
Costs associated with corruption at low levels of public service such as special payments and bribes
connected with import and export licences, filing taxes, police protection, or loans are factored in to the
overall ratings but receive a comparatively small weight.
20
Data are from UNCTAD and converted to constant dollar terms: http://unctad.org/en/
Pages/DIAE/FDI\%20Statistics/Interactive-database.aspx.
9
CORRUPTION, FDI AND EXPROPRIATION
be correlated with corruption and investment risk, potentially clouding the underlying
relationships of interest. To adequately control for these and other determinants of expropriation, we estimate a multivariate statistical model. Importantly, the statistical model
allows us to explicitly consider key interactions between foreign investment contract enforcement and corruption that are implied by our theory.
We regress expropriation acts on both political risk measures and a number of controls
using a negative binomial model with random effects using data averaged over five-year
periods (t = {1990–94, 1995–99, 2000–04, 2005–09, 2010–14}).21 Specifically, we
estimate
Yi,t =β0 + τt + β1 Riski,t + β2 Corrupti,t + β3 F DIi,t−1 + β4 Riskit × Corrupti,t
+ γXi,t + i,t ,
where Yit is the number of expropriation acts in country i and period t, Risk and Corrupt
are the investment risk and government corruption indicators calculated from the ICRG
indexes, F DI is the stock of FDI per capita in constant dollars, and τt is a time dummy. X
is a vector of additional controls: log per capita income (measured in purchasing-power
parity and capturing a country’s relative level of development) and its squared term, a
democratic accountability index, and exports as a share of GDP.22
We include the interaction between investment risk and corruption because we hypothesize that, while weak enforcement of foreign investor contracts is a necessary contributor to a country’s expropriation propensity, the prevalence of corrupt deals is a catalyzing factor. The time dummy controls for exogenous time-varying factors not explicitly modelled, such as global commodity price and asset value movements, as well as
global macroeconomic and financial conditions, which potentially influence the temptation to expropriation in all countries. We include lagged FDI stocks in the model because
countries with little or no FDI likely have little to expropriate even at high levels of
investor risk and corruption. Finally, the level of development and democratic accountability capture a host of other aspects of institutional quality that influence a country’s
propensity to expropriate, and which may also be correlated with FDI and our political
risk measures. Export dependence relates to external contract enforcement; countries
more reliant on international trade are more likely to weigh the benefits of expropriation against the threat of damaging diplomatic and trade ties with the governments of the
original owners of the expropriated assets.23
21
We average the data over five-year intervals both because political risk measures evolve gradually
over time and because large expropriation events involving the takeover of multiple companies often occur
gradually with expropriation acts spanning multiple years.
22
Data used to measure the control variables are from the World Bank’s World Development Indicators,
except for Democratic Accountability, which is from the ICRG.
23
A recent example of the use of trade sanctions in this context is Argentina’s expropriation of assets
belonging to Spain’s largest oil company, Repsol, in 2012. Following the decision, the Spanish government
said it would restrict imports of fuel from Argentina, and the European parliament called for the suspension
of Argentina’s tariff concessions under the generalized system of preferences.
10
CORRUPTION, FDI AND EXPROPRIATION
Table 2: Effects of corruption on expropriation
(1990-2014)
Dependent Variable
# of Expropriation Acts
Investment Risk
Corruption
FDI Stock (t − 1)
(1)
(2)
(3)
0.341**
(0.103)
-0.199
(0.251)
0.351**
(0.125)
-0.570
(0.360)
-1.550**
(0.549)
0.332*
(0.130)
0.217**
(0.082)
-4.873**
(1.245)
0.892
(2.434)
-0.720+
(0.387)
-1.760**
(0.578)
0.153
(0.140)
0.276**
(0.088)
0.038
(0.138)
0.000
(0.014)
-0.916
(3.412)
0.088
(0.206)
3.403
(14.37)
435
89
Yes
435
89
Yes
406
85
Yes
39.53
43.86
58.55
Corruption×Risk
Democratic
Export Share
ln(Income)
ln(Income)2
Constant
N
Countries
Year Dummies
χ2
Standard errors in parentheses. ** p<0.01, * p<0.05, + p<0.1
Given that our dependent variable is a count variable, with most countries having
fewer than five expropriation acts over our sample period, a negative binomial specification is appropriate. (We also check the robustness of all of our estimates in the presence
of country fixed effects and in the context of OLS regressions, and do not find any differences in the signs or statistical significance of the estimates.)24 We first present the results
from a baseline model based on investor risk, corruption, and FDI stocks per capita (without additional controls) and report the model estimates and standard errors in the first
24
These results are available from the authors upon request. However, we limit our discussion to the estimates from the negative binomial random-effects model for a number of reasons. For each set of estimates,
a Hausman test does not to reject the hypothesis that the random effects are uncorrelated with the other
regressors. Moreover, in a fixed-effects model with a count-dependent variable, countries characterized
by expropriation acts that are constant over time (most often these are countries with zero acts over the
entire period) are dropped from the analysis, and estimates based solely on observations with time-varying
expropriation patterns are likely to be imprecise. Finally, given that the dependent variable is truncated at
zero with a large proportion of zero observations, our data violate the OLS distributional assumptions.
11
CORRUPTION, FDI AND EXPROPRIATION
Figure 2: Marginal effects of investment risk on expropriation at different levels of corruption
2
1
0
-1
-2
1
2
3
4
Corrup/on
5
6
Black Line: β̂1 + β̂4 Corrupt based on Model (3). Gray Lines:
95 per cent confidence intervals.
column of Table 2. These results reaffirm the conclusions drawn from examining Table 1.
On their own, investment risk and lagged FDI stocks are positively correlated with expropriation events, but expropriating countries are not, on average, more corrupt. However,
the prevalence of corruption potentially amplifies existing weaknesses in investor contract
enforcement mechanisms. To test this hypothesis, we re-estimate the model interacting
investment risk with corruption, and report the estimates in the second column of the
table (Model (2)). The results support this hypothesis: we find a statistically significant
positive relationship between corruption and expropriation when interacted with investor
risk. Moreover, we find little evidence that investment risk has any effect on expropriation in countries at the lowest level of the corruption scale. In Model (3), we add the
additional control variables. The relationships between the political risk variables and the
likelihood of expropriation are the same as in Model (2), except that the effect of investment risk becomes negative for countries at the low end of the corruption scale (but it is
only marginally significant at the 10 per cent level).
The interaction between investment risk and corruption is summarized in Figure 2,
which plots the estimated marginal effects (and associated 95 per cent confidence interval)
of investment risk at varying levels of corruption, evaluated at the sample means of the
remaining explanatory variables. At levels of corruption below 3.5, which corresponds to
the sample mean, the correlation between investor property protection and the likelihood
of expropriation is insignificant at conventional levels of confidence. Only for aboveaverage corruption levels, by contrast, is the increase in a country’s level of investment
12
CORRUPTION, FDI AND EXPROPRIATION
risk positively and significantly related to its propensity to expropriate.
Taken together, the anecdotal and statistical evidence suggests an important role for
past transgressions by corrupt officials in accounting for observed expropriation patterns.
This finding motivates the theoretical model developed in the next section. It should be
noted, however, that these estimated relationships are also consistent with the extortion
theory of Koessler and Lambert-Mogiliansky (2014). Both mechanisms are potentially
at work in the underlying data, and the insights from this analysis should be viewed as
complementary to theirs.
We model the optimal, self-enforcing “official” contract between the investor and the
host country where, owing to lack of transparency, contracting parties may secretly violate the official terms of this contract. Consistent with our empirical findings, the model
predicts that expropriation occurs as a result of government corruption (i.e., when contract
transparency is low and the incidence of illicit deals is sufficiently likely) when the threat
of expropriation is binding. The model also predicts that opportunities for corrupt officials to make illicit deals depend positively on the degree of exogenous investment risk.
This moves the official contract away from the unconstrained optimum and increases the
likelihood of expropriation, reinforcing the positive interaction between investment risk
and corruption observed in the data.
3
Theoretical Model
3.1
Basic Environment
The basic environment consists of a large number of foreign investors that compete for the
exclusive right to operate a single project in a small open economy. The host country is
unable to finance the project itself.25 For simplicity, it is assumed that there is no foreign
borrowing, so all capital inflows take the form of FDI.26 An investor that is successful
in its bid for the project incurs an initial start-up cost of I0 > 0, and receives the value
of output from time t = 0 onward resulting from capital investment kt ≥ 0 made at the
beginning of each period, equal to pf (kt ), where we assume
f 0 (kt ) > 0,
f 00 (kt ) < 0,
f (0) = 0,
25
and
lim f 0 (kt ) = ∞.
kt →0
This could be because the host country lacks the required capital or the technological knowledge
necessary to carry out the project independent of the foreign investor. Even if technology is the main
contribution of the foreign investor, we assume that the host country is sufficiently cash constrained that it is
unable to transfer the value of investment upfront as collateral in case the investor’s assets are expropriated.
26
Albuquerque (2003) considers both FDI and foreign borrowing in an imperfect contract enforcement
environment, where the value of borrowed capital can be fully appropriated whenever default occurs but
only a fraction of the value of FDI can be appropriated. In our model, if it is relatively costly for the host
country to appropriate FDI due to the specificity of knowledge involved, foreign investment is a superior
form of capital inflows in the presence of expropriation risk, which provides one justification for abstracting
from other types of inflows.
13
CORRUPTION, FDI AND EXPROPRIATION
Output is tradable and p represents the exogenous world price. For simplicity, we assume
that capital fully depreciates at the end of each period. Finally, we assume that there exists
a k ∗ satisfying pf 0 (k ∗ ) = 1. In addition to the capital invested in each period, which is
specified under a contract with the host-country government, the investor is responsible
for making any specified transfers τt ≥ 0 to the government at the end of each period.
Investment is risky. In any period, once the investor invests and output is produced,
the public may not be able to commit to honoring the terms of the contract. Specifically,
the public may demand that the government expropriate the entire value of output and
forgo the contracted transfers. Following Aguiar, Amador, and Gopinath (2009); Cole
and English (1991); Thomas and Worrall (1994) and others, exogenous variation in the
temptation to expropriate is captured by the country’s discount factor. This captures the
degree to which the host-country governments and/or electorate are forward-looking, as
well as institutional determinants of contract enforcement. We also follow this literature
by assuming that, if the contract is changed in a way that leaves the investor worse off
than under the originally agreed terms (including expropriation), the investors punish the
host country by cutting off all future investment.27
Taking into consideration its inability to commit to not expropriating, the public
chooses the dynamic foreign investment contract that maximizes the discounted expected
host-country income generated from the project.28 Although the full terms of this contract are common knowledge to the investors, government officials, and the public, we
assume that capital investments and output from the project are unobserved by the public.
Instead, the government in each period sends a message mt ∈ M ⊂ R+ to the public
(which may or may not be credible) concerning the level of investment. However, we
assume that the public observes when the contracted transfer payments are received (or
not received) into the public funds.
The government manages the foreign investment contract, monitoring investments
and collecting transfers, and can be one of two types—honest or corrupt—where types
differ according to their objective function. While the investor knows the government’s
type at each date t, we assume that the public does not. The objective function of the
honest type is aligned with that of the public, ensuring that the contract desired by the
general public is implemented, does not appropriate any of the transfers under the contract, and always truthfully reports the level of investment each period. The corrupt type,
in contrast, only cares about the amount of side payments it can secretly appropriate by
deviating from the optimal contract and does not necessarily provide truthful reports on
investment. We assume that an incumbent government may be replaced randomly in any
given period by a new government of either type and, in addition, that the public may in27
As discussed in Thomas and Worrall (1994), the model results do not depend qualitatively on this
assumption of a maximum punishment trigger-strategy, but simplify the analysis. What is essential in the
absence of any direct punishment or enforcement mechanism is that there is a credible threat to not invest
for some minimum length of time.
28
Alternatively, we can view the contract as being chosen by an initial-period elected government according to the public’s preferences.
14
CORRUPTION, FDI AND EXPROPRIATION
state a new government whenever it is revealed that the incumbent is a corrupt type. If the
incumbent government is replaced, it is no longer involved in managing the resource contract and a new government takes over, having the same exogenous probability of being
corrupt as the one before it. Note that, because the honest government type only implements the contract chosen by the public and reports the truth, the strategic agents in the
model consist of the foreign investor, the public/electorate, and the corrupt government
official.
In this environment, government corruption takes the form of receiving side-payments
bt > 0 from the investor, which arise from deviations in investment from the level specified under the optimal contract. We assume that corrupt governments do not have the
same incentive as the public to expropriate foreign investment because they are unable to
appropriate any part of an expropriated project. (Expropriations are assumed to be highly
visible events, constraining the ability of corrupt officials to steal any part of expropriated
assets.) Because the investments are not directly observed by the public, violations of
the optimal contract yield potential rents to the parties engaged in the corrupt deals. We
will show that such rents are increasing in the public’s temptation to expropriate (i.e., the
extent to which the public discounts the future).
The timing of the model is as follows: Once an initial contract is offered by the government to an investor, the investor obtains an exclusive right to the project and agrees to
make a sequence of capital investments, as well as public transfers to the host country,
conditional on not being expropriated. At the beginning of each period, the incumbent
government may be of either type. A corrupt government may agree to a level of investment ktd that exceeds the contract level ktc . If kt = ktd , a side payment bt is paid by the firm
to the government. If, instead, the government is an honest type or if ktd is rejected by the
corrupt type, kt = ktc . Before the production process is complete, an election takes place
and the incumbent government is potentially replaced by a new government (its type also
unknown to the public). The government (incumbent or new) observes investment and
sends a message to the public: mt ∈ M ⊂ R+ . Output is produced, and the public
demands that the government either expropriate the full value of output or collect the
contracted transfers τt from the investor and continue to the next period of the contract.
This timing within each period is summarized in Figure 3.
3.2
Public Returns
A contract is a sequence of investment levels and transfers from the investor in the form
of public revenues (conditional on not being expropriated), θ = {ktc , τt }∞
t=0 , given that
the firm has incurred the initial start-up cost I0 . We denote the discounted expected
payoff to the host-country public from remaining in a contract with the foreign investor
from period t onward by Vtc , and the corresponding contracted discounted profits to the
investor as Wtc . If expropriation occurs in any period t, the investor cuts off all future
investments, and there is no public gain to seizing only part of the value of assets in that
period. Therefore, when expropriation occurs, the entire value of output is seized. The
15
CORRUPTION, FDI AND EXPROPRIATION
Figure 3: Model Timing
t−1
t
Investor decides whether to invest
↓
If corrupt, government may accept investment ktd
with private payment bt ; otherwise ktc is invested
↓
Government election occurs
↓
Government sends public message mt ∈ M
↓
Public decides whether or not to expropriate given mt
↓
Investors pay τt to the public if not expropriated;
otherwise contract is terminated from t + 1 onward
t+1
host-country payoff from expropriating all output that is expected by the public, who do
not observe investment directly but form expectations based on the messages they receive,
is Vte (mt ) = Et [pf (kt )|mt ]. (This value may or may not be equal to the actual value of
expropriation, which is known to the government, depending on whether the message mt
is credible.)
We assume that investors, host-country governments, and the public are risk neutral
and discount future returns at the same rate β ∈ (0, 1). Suppose for the moment that, under the optimal contract, expropriation occurs whenever deemed beneficial by the public,
regardless of the government’s type. (We will show that this assumption is consistent with
equilibrium strategies of the agents.) The recursive formulation of the public’s ex post expected payoff under the contract, after having received message mt from the government,
is
Vt (mt ) = max τt + βEt [Vt+1 (mt+1 )|mt ], Vte (mt ) ,
(1)
where expropriation does not occur provided
τt + βEt [Vt+1 (mt+1 )|mt ] ≥ Vte (mt ).
(2)
We are interested in the optimal contract between the firm and host country that maximizes expected public utility from the beginning of each period t, Vtc = Et [Vt (mt )],
conditional on not having expropriated and terminated the contract in the past. Although
an honest-type government implements the contract, the optimal contract must take into
account the potential contract violations that may be carried out by a corrupt type.
We can express Vtc more compactly by defining the set of government reports Dt (θ) ⊂
M (possibly empty) in a given period t for which the public believes with certainty that
16
CORRUPTION, FDI AND EXPROPRIATION
Condition (2) is violated:
Dt (θ) = mt ∈ M
| τt + βEt [Vt+1 (mt+1 )|mt ] < Vte (mt ) .
We use ρt (θ) to denote the public’s belief at the beginning of period t about the likelihood
that they will receive a report mt ∈ Dt (θ). Thus, the ex ante expected payoff in period t to
the public from the contract θ, given that expropriation has not occurred in any previous
period, can be defined recursively as
c
Vtc = sup
1 − ρt τt + βVt+1
+ ρt Et [Vte (mt )|mt ∈ Dt ],
(3)
θ
where the notation signifying the dependence of ρt and Dt on θ has been suppressed for
brevity. We are interested in the characteristics of an official (or “honest”) contract that
maximizes (3) that is feasible and satisfies the participation constraint of the investor,
subject to the probability of expropriation given ρt . The official contract is feasible if
τt ≥ 0
(4)
pf (ktc ) − τt ≥ 0
(5)
and
for all t. The firm is willing to participate in the official contract, provided it offers
expected discounted profits at least equal to the initial start-up cost I0 .
According to the following lemma, under such a contract there would be no expropriation whenever the public receives a report that the contracted amount is invested. This
/ Dt (θ) for any t.
implies that, if θ is an optimal contract, ktc ∈
c
Lemma 3.1. Under the optimal contract {ktc , τt }∞
t=0 , in any t such that mt = kt , Condition (2) is satisfied.
Proof. Consider the case where kt = ktc . By definition, an honest type always ensures the
contracted amount of investment and reports investment truthfully. Suppose that, having
received the report mt = ktc , expropriation was optimal under the contract. Then, for
some report mt 6= ktc , expropriation is not optimal; otherwise the investor would not be
willing to invest in period t. Since ktc is invested, such a report must originate from a
corrupt type, implying that the investor would only ever be willing to invest kt = ktc
under a corrupt regime. But then ktc would not be optimal under the contract.
The next section outlines the expected returns of the foreign investor engaged in an
official contract with the public when the investor may also engage in corrupt contracts
that are not directly observable. Consistency conditions for the recursive formulation of
the contract (or “promise-keeping” constraints) are then established in sections 3.4 and 4,
which characterize the optimal contract when the government type is constant and when
there is stochastic type renewal, respectively.
17
CORRUPTION, FDI AND EXPROPRIATION
3.3
Investor Returns and Corrupt Contracts
In characterizing the optimal contract, it is useful to begin by considering the optimal
responses of the firm under a corrupt regime to a given contract θ. Discounted investor
profits can be expressed recursively as
−kt − bt + 1 − ρt pf (kt ) − τt + βEt Wt+1 .
Wt = sup
{kt ,bt }∞
t=0
If the government is an honest type in period t, the investor and government are committed to the transfers and investment levels set out in the contract. If the government is a
corrupt type, however, it may be profitable for the investor and government to violate the
contract terms by investing ktd > ktc if ktc is below the unconstrained efficient level k ∗ .
We define total rents from investing ktd given ktc as the difference in expected profits that
can be shared between the investor and corrupt government by not honoring ktc (but still
making the contracted transfers to the public):
R kt |ktc = (1 − ρt )pf (kt ) − pf (ktc ) − kt − ktc − ρt βEt Wt+1 .
(6)
The following lemma establishes that, whenever under a corrupt regime the investor’s
optimal responseto a contract is to invest the contracted amount, there is no expropriation
risk and R kt |ktc = 0. This implies that any violation of the contract terms must offer
strictly positive rents.
Lemma 3.2. R kt |ktc = bt = ρt = 0 whenever kt = ktc is an optimal response to a
contract θ.
Proof. If, given the official contract, the optimal response under a corrupt regime is
to invest the contracted amount ktc , the public would always expect kt = ktc . From
Lemma 3.1, expropriation therefore cannot occur in period t, implying ρt = 0. Therefore
R ktc |ktc = 0 and bt = 0.
Next, consider a potential profitable violation of the official contract such that ρt is
independent of kt for any level strictly above ktc . (In Sections
3.4 and 4, this will be the
relevant case to consider.) Clearly, if ktc ≥ k ∗ , R kt |ktc < 0 whenever kt > ktc , there is
no incentive to violate the contract. Then, if ktc < k ∗ , given that violation of the contract
is profitable, optimal investment ktd maximizes period-by-period rents:
(1 − ρt )pf 0 (k̃t ) = 1.
(7)
If R k̃t |ktc > 0, then ktd = k̃t > ktc ; otherwise ktd = ktc . This results in a sequence
∞
{ktd }∞
t=0 for a given contract and a given sequence {ρt }t=0 representing realized investment in every period that an expropriation has not previously occurred. The side payments {bt }∞
t=0 reflect the division of these rents between the corrupt government and the
investor. In the ensuing analysis, any division of rents (if they are positive), including the
Nash bargaining solution, is allowed provided bt > 0.
18
CORRUPTION, FDI AND EXPROPRIATION
The optimal contract maximizes public utility, taking as given this optimal response of
the investor under corrupt regimes. We first consider the optimal contract in the simplest
possible environment with no political turnover and constant government types. In this
environment, government reports about the level of investment are not informative and,
if a non-trivial contract exists, it is self-enforcing. We then extend the analysis to include
political turnover with stochastic type renewal and show that expropriation can occur in
equilibrium as a result of corrupt contract violations.
3.4
Optimal Contract With Constant Government Type
We consider the optimal contract in an environment with no political turnover, where the
type of government is constant throughout the contract but initially unknown to the public.
We restrict our attention to the interesting case where the unconstrained efficient level of
investment in all periods is unattainable owing to the public’s temptation to expropriate.
We proceed by characterizing the optimal contract under the assumption that the government, regardless of its type and the actual investment level, always reports mt = ktc ,
rendering the messages uninformative, and then demonstrate that, in fact, mt = ktc for all
t is an equilibrium. This, along with Lemma 3.1, implies that expropriation never occurs
under a constant government type. We find that the dynamics of the optimal contract are
qualitatively similar to the optimal contract studied by Thomas and Worrall (1994). However, we also find that the mere possibility of corrupt contracts results in lower contracted
investments, particularly at the early stages of the contract, and a lower discounted stream
of transfers to the public.
Suppose that the government is a corrupt type with probability δ and an honest type
with probability 1 − δ. Assuming that mt = ktc for any level of actual investment, then
V̄te = Vte (ktc ) = δpf (ktd ) + (1 − δ)pf (ktc ),
where ktd is defined in Section 3.3 and is fully anticipated by the public, given ktc . The
following lemma establishes the amount of capital that is invested when the government
type is corrupt, ktd , as well as the implied constraints on the optimal contract taking ktd as
given.
Lemma 3.3. If government types are constant, ρt = 0 for all t and a corrupt government
chooses kt = ktd = k ∗ given any ktc . Moreover, the optimal contract satisfies
c
τt + βVt+1
≥ δpf (k ∗ ) + (1 − δ)pf (ktc )
(8)
for all t, taking ktd = k ∗ as given.
Proof. Consider a period under the contract where ktc < k ∗ and suppose that ktd = k̃t >
ktc , where k̃t is implicitly defined by (7) given ρt . Since both government types report
mt = ktc , Condition (2) is satisfied, implying that ρt = 0 and hence ktd = k ∗ . Then
19
CORRUPTION, FDI AND EXPROPRIATION
c
ktc is constrained to satisfy (8), where the left hand equals V̄te and Vt+1
is simply the
t
c
/ D (see Lemma 3.1).
continuation value of the contract given mt = kt ∈
With ρt = 0 and ktd = k ∗ for all corrupt types taken as given by the public, Lemma
3.3 implies that the optimal contract solves
Vtc = sup
θ
c
τt + βVt+1
,
subject to Condition (8) as well as feasibility conditions, the investor’s participation constraint, and a promise-keeping constraint. The latter enables us to solve the dynamic
problem using the recursive definitions given above while treating the continuation profc
its of the investor under the contract, Wt+1
, as a state variable, where
Wtc
=
∞
X
c
β s−t pf (ksc ) − ksc − τs = pf (ktc ) − ktc − τt + βWt+1
.
s=t
That is, in addition to specifying investment and transfers, the contract can be considered
c
a promise in time t of discounted future profits, Wt+1
, such that
c
pf (ktc ) − ktc − τt + βWt+1
≥ Wtc .
(9)
Finally, an investor is willing to participate in the contract under an honest government
regime from any period t onward provided
c
Wt+1
≥0
(10)
W0c ≥ I0 .
(11)
and given initial condition
Features of this dynamic programming problem are very similar to the problem considered in Thomas and Worrall (1994). In particular, owing to the dependence of the
constraint set on the optimum value function itself, and because the concavity of f (·)
on the right hand side of (8) implies the constraint set is not convex, standard contraction mapping arguments cannot be used to establish a unique fixed point for the value
function Vtc = V c (Wt ). However, the authors describe an iterative mapping procedure
starting from the first-best Pareto frontier that converges to the optimum value function.
Lemma 3.4 applies their result in the present context.
Lemma 3.4. There exists a sequence {Ln P ∗ }∞
n=0 defined by operator L : P → P,
where P is the space of continuous, bounded, and concave functions on [0, W̄ ] and W̄ =
(pf (k ∗ ) − k ∗ )/(1 − β) that converges pointwise to the optimum value function V c (W ).
Proof. See the Mathematical Appendix.
Using multipliers µt , ϕt , φt , λt , and βζt on constraints (4), (5), and (8)–(10), the
20
CORRUPTION, FDI AND EXPROPRIATION
first-order conditions corresponding to the dynamic programming problem are
1 − ϕt + µt + φt − λt = 0
: ϕt + λt − φt (1 − δ) pf 0 (ktc ) − λt = 0.
τt :
(12)
ktc
(13)
c
c
, we can summarize the
and Wt+1
Moreover, fully differentiating with respect to Vt+1
c
c
Pareto frontier V (Wt ):
c
∂Vt+1
λt + ζt
=−
.
(14)
c
∂Wt+1
1 + φt
Finally, we have the envelope condition
∂Vtc
= −λt .
∂Wtc
(15)
Taken together, equations (14) and (15) summarize the dynamics of the contract as well
as expected future payoffs for both the public and the investor. Before turning to the dynamics of the optimal contract, the following lemmas establish that the conditions above
describe a global optimum and lay out some other features of the optimal contract that
help simplify the analysis.
Lemma 3.5. V c (Wtc ) is concave, with strict concavity when V c (Wtc ) does not correspond
with the first-best Pareto frontier. Moreover, ∂Vtc /∂Wtc ≤ −1, and (5) never binds.
Proof. See the Mathematical Appendix.
Lemma 3.5 implies that λt ≥ 1 and ϕt = 0 for all t. The following lemma implies
that φt > 0 if and only if ktc is less than the unconstrained efficient level.
Lemma 3.6. For any period t in which ktc < k ∗ , the optimal contract satisfies (8) with
c
= V̄te .
strict equality: τt + βVt+1
Proof. Suppose, toward a contradiction, that for some period t we have both ktc < k ∗ and
c
τt + βVt+1
> V̄te . The latter implies that φt = 0 from complementary slackness and,
since ϕt = 0 and λt > 0 from Lemma 3.5, (13) becomes pf 0 (ktc ) = 1, which would
imply ktc = k ∗ .
The next proposition establishes that the dynamics of the optimal contract, which
features a back-loading of transfers from the investor to the host country, and a gradual increase in contracted investment levels over time (which may or may not reach the
unconstrained efficient level):
Proposition 3.7. Under the optimal contract, ktc is increasing over time and τt = 0 until
ktc reaches stationary value k̂ ≤ k ∗ , after which transfers to the host country are positive.
Proof. See the Mathematical Appendix.
21
CORRUPTION, FDI AND EXPROPRIATION
Assuming a contract characterized by the unconstrained efficient level of investment
in all periods cannot be achieved, the optimal contract is structured to deliver the investor’s minimum expected payoff from the project, W0 = I0 , as quickly as possible
without violating the expropriation constraint. This involves postponing transfers to the
host country until I0 is recovered through investor profits. If, instead, the contract featured a positive transfer on some earlier date, lowering this transfer today (keeping the
contracted investment stream constant) could be offset with an equal (discounted) increase in future transfers. This would satisfy today’s expropriation constraint, allowing
current period investment to remain the same. It would also satisfy promise-keeping,
since a reduction in the investor’s taxes today is offset by an equal (discounted) increase
in future taxes (as all agents discount transfers at the same rate). Note that this otherwise
neutral change in the timing of transfers relaxes the host-country expropriation constraint
in every period up to the time that the offsetting transfer increases are received. But then
higher investment is possible in every one of these future periods such that the expropriation constraint binds. Increasing investment in each of these periods also implies higher
discounted transfers and host-country welfare (given the promise it has kept to the investor), and therefore higher investment today. Contracted investment, in turn, is set at
the maximum level permissible in each period without inducing expropriation, given the
scheduled transfers from the investor to the host country. Because these transfers do not
appear until some date t∗ −1, the discounted payoff to the public arising from the contract
at every date t < t∗ , Vtc , increases at the rate β −1 . Since the expected value of output
(given public beliefs) under the contract must not exceed the discounted expected value
of transfers under the contract, the no-expropriation constraint defines the bounds on the
rate at which contracted investment can increase.
Figure 4 illustrates the Pareto frontier when (i) the efficient level of investment along
the first-best frontier is eventually reached (k̂ = k ∗ ), and (ii) the efficient level of investment cannot be supported as a stationary contract (k̂ < k ∗ ). In turn, the relative position
of the Pareto Frontier depends on, in addition to the production technology, values of β
and δ. (These relationships are described below.) Because the optimal contract (if one
exists) must offer a discounted payoff over the life of the contract at least equal to the
investor’s sunk investement, the position along the frontier where W0 = I0 determines
the discounted payoff to the host country, which reflects the levels of investment along
the transition to the stationary contract as well as the duration of this transition. When I0
is large, a longer period of zero transfers is required for the investor to recoup the initial
investment. All else equal, prolonging transfers lowers the discounted payoff to the host
country, making it more tempting to expropriate for a given level of investment. As a
result, contracted investment levels along the transition to the stationary contract are also
lower, which further reduces the discounted payoff received by the host country.
In the event the government is an honest type, actual investment follows the constrained optimal investment path, and the host-country public receives the entire discounted value of transfers under the contract, less I0 . If, instead, the government is dishonest, the expected income from the project received by the public does not change, but
22
CORRUPTION, FDI AND EXPROPRIATION
Figure 4: Existence of Contracts given I0
V
Pareto Frontier k̂ = k ∗
Pareto Frontier k̂ < k ∗
First-Best Frontier
Π∗
V + W = 1−β
0
I0
W
the realized investment path differs, with kt = k ∗ for all t. This results in economic rents
equal to the shaded region in Figure 5, which are shared between the foreign investor and
the corrupt official.
Whether or not a non-trivial optimal contract exists offering the investor I0 and positive expected return to the host country depends on parameters I0 , β, and δ. Proposition
3.7 demonstrates that a non-trivial optimal contract, if it exists, must converge to a stationary contract period with constant ktc = k̂ ≤ k ∗ . Therefore the existence of a stationary
contract period supporting k̂ > 0 is a necessary, though not sufficient, condition for the
existence of an optimal contract. Proposition 3.8 establishes necessary and sufficient
conditions for a stationary contract period, which depends on parameters β and δ. Having established the conditions for the existence of a stationary contract, we are able to
identify necessary and sufficient conditions for an optimal contract with the features of
Proposition 3.7, conditional on the existence of a stationary contract.
Proposition 3.8. Given δ ≥ 0 and I0 > 0, there exists a continuous relationship β(δ)
such that for any β ≥ β(δ) a stationary contract exists but not otherwise. Moreover, β(δ)
is strictly increasing in δ, is bounded below at β(0) = 0, and bounded above at β(1) = β̄,
where β̄ ∈ (0, 1) is the threshold level of β such that k̂ = k ∗ if and only if β ≥ β̄.
Proof. See the Mathematical Appendix.
According to Proposition 3.8, a non-trivial optimal contract, if it exists, eventually
attains the efficient level of investment for any probability that the government is a corrupt type if the rate of discounting is sufficiently low. Additionally, if the probability that
23
CORRUPTION, FDI AND EXPROPRIATION
Figure 5: Potential rents from corruption
V
First-Best Frontier
Π∗
V + W = 1−β
0
I0
W
the government is a corrupt type is zero, our assumptions on f (·) imply that a stationary
contract exists for any discount factor. For higher levels of impatience and higher corruption levels, there is a monotonic trade-off between patience and the corruption level that
describes the set of possible contracts: as corruption becomes more likely, a higher level
of patience is required in order to support any stationary contract. Intuitively, as the rate
of discount rises above a certain threshold, there is an increasing wedge between the level
of contracted investment that can be supported in the stationary period of the contract
and the efficient level, where the contracted stationary investment level is bounded by the
expropriation constraint. Then, as the level of corruption rises, the public believes it is
more likely that actual investment (under a corrupt type) is the efficient level, and this
necessitates an even lower contracted investment level in order to satisfy the expropriation constraint. However, not all levels of investment can be supported in the stationary
period of the contract. Even when the host country receives all profits from the contract,
when impatience and/or the likelihood of a corrupt contract are sufficiently high, there is
no contracted level of investment low enough to mitigate the temptation to expropriate.
The trade-off between the likelihood of a corrupt type and the discount factor, β(δ), is
illustrated in Figure 6. In the shaded region above β(δ), a stationary contract can be supported in equilibrium. For β ≥ β̄ (the lightly shaded region), a stationary contract always
exists, independent of the level of corruption. As agents become more impatient, however, a stationary contract exists if and only if the likelihood of corruption is sufficiently
low (indicated here by the more darkly shaded region).
Given the existence of a stationary contract, there exists a non-trivial optimal contract that offers both the host country and the investor some positive return from date 0.
24
CORRUPTION, FDI AND EXPROPRIATION
Figure 6: Existence of a stationary contract
β
1
β̄
β(δ)
0
1
δ
However, since the investor requires at least promised payoff I0 in order to participate in
the contract, the set of optimal contracts given I0 is only a subset of possible stationary
contracts. We now examine how this subset of possible contracts is related to parameters
β and δ through I0 .
Proposition 3.9. If a non-trivial stationary contract exists given β and δ, then there
¯ δ) increasing in β and decreasing in δ such that a
is a corresponding threshold I(β,
¯ δ). Moreover, if
non-trivial optimal contract exists from date 0 if and only if I0 ≤ I(β,
c
∗
c
¯
I0 ≤ I(β, δ) then, for any date t in which kt < k , kt is strictly decreasing in δ.
Proof. See the Mathematical Appendix.
Proposition 3.9 implies that anticipated corruption lowers overall investment and hostcountry welfare under the optimal contract in two ways. First, for any optimal contract
that can be supported under δ, β, and I0 , contracted investment in every period along
the transition to the stationary period of the contract is strictly lower as δ is increased
and, unless the efficient frontier is reached, investment also remains low in the stationary
period. Second, the set of initial start-up costs I0 for which an optimal contract exists is
smaller for larger values of δ. That is, for sufficiently high δ, only projects featuring arbitrarily low initial start-up costs I0 will be undertaken by foreign investors. Extending this
intuition to an environment with a large number of simultaneous projects characterized
by different start-up costs, this implies an extensive margin for foreign investment that
decreases as the possibility of corruption increases.
Figure 7 illustrates the impact of corruption on the Pareto frontier and the set of permissible contracts given I0 . As the probability of a corrupt type δ increases, the frontier
25
CORRUPTION, FDI AND EXPROPRIATION
Figure 7: Corruption and the Pareto Frontier
V
Frontier (low δ)
I0
0
Frontier (high δ)
¯ δh ) I(β,
¯ δl )
I(β,
W
shifts downward, but without influencing the stationary contract, in the case that it can
be reached, and is therefore pivoted at k̂. Given I0 , this implies that an optimal contract,
if it exists, will offer the host country lower initial utility V0 , which reflects both lower
investment levels along the transition to the stationary contract and a prolonged transition
with zero transfers. The figure also shows that, if δ is sufficiently high, then an optimal
contract may not exist given I0 , even though an optimal contract would have existed at
lower levels of corruption.
It is worth noting that, although realized foreign investment for a given project under
a corrupt government is unchanged as the likelihood of corruption increases, our results
imply that the expected value of investment and output decrease as the expectation of
corruption increases. Nevertheless, public returns from the project depend only on reported investments over the length of the contract. Therefore, in addition to potential
reductions in host-country welfare owing to lower investment on the extensive margin,
host-country welfare is reduced by lower investment on this intensive margin of any particular contract. Interestingly, a higher probability of corruption will, conditional on the
project being financed, increase the rents obtained through corrupt deals whenever they
occur (as illustrated by Figure 5).
We close the analysis of this section by arguing that, if the government is a corrupt
type, there is no incentive to report anything other than mt = ktc . If the honest type always
implements kt = ktc and reports truthfully, then any report mt 6= ktc reveals to the public
that the government is a corrupt type. The public, knowing that kt = k ∗ , would therefore
26
CORRUPTION, FDI AND EXPROPRIATION
require that the contract satisfy
c
τt + βVt+1
≥ pf (kt∗ )
for all t following such a report in order to not expropriate. Otherwise, the firm would not
invest. However, along the transition to the stationary contract period before the efficient
frontier can be reached, this condition cannot be satisfied. (Otherwise it would always be
possible to attain the efficient level of investment and the expropriation constraint never
binds.) On the other hand, once the efficient frontier is reached (if at all), there is no
longer any incentive for the investor to write a corrupt contract, ktc = ktd = k ∗ is known
by the public, and the above condition is already satisfied under the optimal contract.
Therefore mt = ktc in equilibrium, regardless of government type.
4
Optimal Contract With Political Turnover
We now consider the optimal contract in the presence of exogenous government turnover.
Specifically, we assume that in any period an incumbent government can be replaced by a
new government in one of two ways. First, the public can decide to replace a government
based on beliefs about the government type, taking into account the implications of type
on the expected public returns from the contract, as in Bhattacharyya and Hodler (2010).
Second, the incumbent may be replaced randomly in any period independent of public
beliefs and the optimal contract. This captures the idea that governments are sometimes
replaced by the electorate based on factors outside of the model. As in Phelan (2006), this
results in stochastic government type renewal, and public beliefs about the government
type are conditioned on the actions taken by the government.29
In this environment, equilibrium outcomes will be influenced by the ability of the
government to send credible messages to the public. Specifically, although a corrupt type
will have no incentive to report anything other than mt = ktc , as in the case without
government turnover considered in Section 3.4, the public will receive report mt = ktd
whenever a corrupt type is replaced by an honest type. When ktd 6= ktc and a corrupt
type always reports mt = ktc in equilibrium, the fact that an honest type always reports
truthfully and a corrupt type always reports mt = ktc implies that the message mt = ktd is
credible. Knowing that kt = ktd when mt = ktd the public will, under certain conditions,
find it optimal to expropriate in equilibrium.
Denote the probability that a government is randomly replaced in any given period by
σ. (With probability 1 − σ, the incumbent government remains in power.) Assume for
the moment that a corrupt incumbent government always reports mt = ktc , so that it never
reveals its type. Then, conditional on the incumbent being a corrupt type, the probability
that the public will receive a report mt = ktd is the probability that it is replaced by an
29
As will become clear, information concerning government type will be transmitted to the public only in
the case of exogenous turnover in this set-up, and the ability of the public to overthrow a corrupt government
plays only an indirect role in influencing equilibrium outcomes.
27
CORRUPTION, FDI AND EXPROPRIATION
honest type, σ(1 − δ). In the analysis that follows, we are interested in the probability
the public places on receiving a report mt = ktd in any period for the first time over the
course of the contract. Since the posterior belief that the government is a corrupt type
having only received message mt = ktc up to the current period t is δ, the public believes
that report mt = ktd will be received for the first time with probability σδ(1 − δ). The
following propositions establish that this also equals the probability that expropriation
occurs in equilibrium:
Proposition 4.1. When there is stochastic political turnover, the probability of expropriation occurring in any period t such that ktd 6= ktc is ρ̄ = σδ(1 − δ).
Proof. See the Mathematical Appendix.
In other words, whenever a corrupt contract ktd 6= ktc is profitable, ktd solves pf 0 (kt ) =
−1
1 − ρ̄ , and expropriation occurs with probability ρ̄ = σδ(1 − δ). The contracted level
of investment ktc , in turn, must satisfy
c τt + βEt Vt+1
≥ Et Vte (ktc ) = δpf (ktd ) + (1 − δ)pf (ktc ).
(16)
The corresponding dynamic programming problem maximizes (3) subject to (4), (5),
(9)–(10), and (16), taking the probability of expropriation ρ̄ = σδ(1 − δ) and the corresponding level of investment under the corrupt contract, ktd < k ∗ , as given.
The main features of the optimal contract are very similar to the contract without government turnover in Section 3.4. However, expropriation may occur in equilibrium, and
the likelihood of expropriation is determined by the likelihood of government turnover
and the prevalence of corruption. Features of the optimal contract are summarized in the
following proposition:
Proposition 4.2. Under the optimal contract, ktc is increasing over time, τt = 0, and the
probability of expropriation is ρ̄ until ktc reaches stationary value k̂ ≤ k ∗ , after which
transfers to the host country are positive, and expropriation occurs with positive probability if and only if k̂ < k ∗ .
Proof. See the Mathematical Appendix.
The intuition for the dynamics of the optimal contract is the same as in Section 3.4.
The only substantive difference is a positive probability of expropriation under the optimal contract. By assumption, the first-best frontier is unattainable in the very first period
and ktc < k ∗ over some initial phase of the contract. Because agents are unable to condition the contract on incidents of corruption, the possibility of an honest government
replacing a corrupt one implies that, with positive probability, kt = k ∗ is revealed to
the public with certainty. When ktc < k ∗ , this must violate the expropriation constraint.
Therefore government turnover increases the likelihood of expropriation, but only if there
is positive corruption (δ > 0).
28
CORRUPTION, FDI AND EXPROPRIATION
Given σ, however, the effect of corruption on the likelihood of expropriation reaches
a maximum δ = 0.5. (As δ rises above or below this threshold, it is less likely that
government turnover will result in a change in government type, which is necessary in
the model for generating reports that induce expropriation.) That is, the prevalence of
government graft increases the probability of expropriation whenever the expropriation
constraint binds up to a certain threshold, but this effect is reduced as corruption becomes
ubiquitous. Nevertheless, higher corruption decreases both FDI under the official contract
and host-country welfare over the entire range of δ.
To close the characterization of the equilibrium contract, we verify that these equilibrium strategies are consistent with mt 6= ktc being reported only if an honest type has
succeeded a corrupt type (at a point in the contract that does not correspond to the firstbest Pareto frontier). As in the case of no government turnover considered in Section
3.4, a corrupt type has no incentive to report mt 6= ktc as an incumbent, which would
reveal that it is not an honest type. (Otherwise ktc would have been both invested and
reported.) The reason is that, under a corrupt government, actual investment is ktd = k ∗ ,
and type revelation would result in a violation of the expropriation constraint whenever
ktc < k ∗ and the termination of the contract with the foreign investor for all future dates.
But since this outcome does not increase the corrupt government’s expected future payoff
(and strictly decreases its payoff when future contracted investments are below the unconstrained efficient level), a corrupt incumbent would never choose to report mt 6= ktc .
Given that an honest incumbent also always reports mt = ktc (as the incumbent it ensures
this is what is invested), only a succeeding government reports anything other than ktc .
A newly elected honest government reports mt = ktd 6= ktc only if it replaces a corrupt
type and ktc < k ∗ , and reports mt = ktc otherwise. Therefore, the message kt = ktd must
increase the probability that public beliefs place on kt > ktc . As a result, expropriation
would occur after report mt = ktd = k ∗ independent of government type. But this makes
the corrupt type strictly worse off compared to always reporting mt = ktc , in which case
the public believes that kt = ktc with probability δ and expropriation does not occur.
Therefore mt = ktd credibly reveals that kt = ktd .
5
Conclusions
Although it has been widely conjectured that corruption is harmful for development, the
empirical evidence linking corruption and long-run growth has been controversial (see,
for example, Mauro, 1995; Mo, 2001; Svensson, 2005). This has motivated research that
is more acutely focused on the specific channels through which corruption influences
investment and productivity. Given the perceived importance of foreign capital and technology for developing-country growth, there has been increasing interest in the impact
of corruption on FDI (Wei, 2000; Azzimonti and Sarte, 2007; Bhattacharyya and Hodler,
2010; Delgado, McCloud, and Kumbhakar, 2014; Koessler and Lambert-Mogiliansky,
2014). We contribute to this literature on two fronts. First, in examining expropriations of
29
CORRUPTION, FDI AND EXPROPRIATION
FDI across developing countries over 1990–2014, we provide previously undocumented
evidence for the relationship between government corruption and outright confiscation of
foreign investor assets: weak investor protection increases the likelihood of expropriation
when the government is perceived as sufficiently corrupt. This evidence suggests that,
in addition to the direct disincentives to invest owing to uncertainty in the payment of
costly bribes, a potential repercussion from corruption is a magnification of expropriation
risk. Second, by introducing a lack of contract transparency in a standard model of FDI
with imperfect contract enforcement, we show how expropriation and corrupt deals with
foreign investors arise endogenously and constrain foreign investment.
The theoretical environment we consider departs from much of the existing literature
on corruption and expropriation by treating expropriation and theft from corruption as being motivated by different objectives; furtive deals with foreign investors produce unobserved rents for corrupt officials, whereas outright expropriations are highly visible events
that transfer returns from the investment project from the investor to the public. The key
insight from our analysis is that higher anticipated corruption—captured by the likelihood
that a government is dishonest—decreases FDI under the optimal contract along two margins. On the intensive margin, higher corruption increases the public’s expectation that
the value of foreign assets is above what is specified under the official contract, increasing
the temptation to expropriate for every contracted sequence of investments. This lowers
contracted investment at each date conditional on the project being financed. Second,
as corruption increases, successively larger projects (i.e., projects involving larger initial
start-up costs) can no longer be supported by an optimal contract owing to the higher
risk. Moreover, a binding expropriation constraint under the contract is necessary in our
model for opportunities for corrupt deals to arise, and higher expropriation risk results
in corruption. This endogenous relationship between corruption and expropriation implies a channel through which corruption reduces the host-country benefits from FDI not
previously considered in the literature. Finally, consistent with media reports on several
recent expropriation events, our model predicts that expropriation is more likely to occur when the share of government take from the project is reportedly low and outgoing
governments are accused of making corrupt deals with investors. These findings suggest
that improvements in the security of investor property rights and host-country welfare can
be achieved by increasing transparency in the deals struck between government officials
and foreign investors, and by imposing greater penalties on officials culpable of soliciting
bribe payments.
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34
CORRUPTION, FDI AND EXPROPRIATION
Appendices
A
A.A
Mathematical Appendix
Proof of Lemma 3.4
Consider a decreasing, concave function P ∈ P and define operator L by the following
modified, non-convex dynamic program:
LP (W ) = sup τ + βP (W 0 ),
{τ,k,W 0 }
subject to
µ:
ϕ:
φ:
λ:
βζ :
τ ≥0
pf (k) − τ ≥ 0
τ + βP (W 0 ) ≥ δpf (kt∗ ) + (1 − δ)pf (k)
pf (k) − k − τ + βW 0 ≥ W
W 0 ≥ 0.
(17)
(18)
(19)
(20)
(21)
Moreover, define P ∗ as the unconstrained, first-best Pareto frontier for the problem without constraint (19). Defining Π(k) = pf (k) − k, along the first-best frontier, investment
equals k ∗ , Π∗ = Π(k ∗ ), and {τs∗ }∞
s=t is any sequence of transfers that satisfies the remaining constraints. Given
∞
X
∗
β s−t (Π∗ − τs∗ ) ,
Wt =
s=t
the first-best Pareto frontier is
P ∗ (Wt∗ ) =
∞
X
β s−t τs∗ =
s=t
∞
X
β s−t Π∗ − Wt∗ =
s=t
Π∗
− Wt∗ ,
1−β
with P ∗ (W̄ ) = 0. Given the definition of Wt∗ , it is straightforward to verify that
∗
sup τs∗ + βP ∗ ([Wt+1
) = P ∗ (Wt∗ ).
{τs∗ }∞
s=t
Therefore the solution to the maximization problem without constraint (19) satisfies k =
k ∗ and τ − βW 0 = Π∗ − W , yielding a maximum value Π∗ /(1 − β) − W = P ∗ (W ).
It follows that, taking LP (W ) with constraint (19), starting from the first-best frontier,
P (W 0 ) = P ∗ (W ) for any W ∈ [0, W̄ ], LP ∗ (W ) ≤ P ∗ (W ).
The remainder of the proof follows the induction argument of Thomas and Worrall
n
(1994) showing that, starting from P ∗ (W ), the sequence {Ln P ∗ (W )}∞
n=0 , where L is
35
CORRUPTION, FDI AND EXPROPRIATION
the nth application of
L, converges pointwise
to V c (W ). Assume Ln P ∗ ≤ Ln−1 P ∗ .
Comparing L Ln P ∗ and L Ln−1 P ∗ , constraint (19) implies that the constraint set
for the latter case is at least
as the
given Ln P ∗ ≤ Ln−1 P ∗ . There former,
as large
n ∗
n−1 ∗
n+1 ∗
n ∗
= L P , implying Ln P ∗ is a decreasing
≤ L L P
fore L P = L L P
sequence over a compact set converging to V 0 . For any initial W ∈ [0, W̄ ], consider
the sequence of variables chosen at each application of L, {τ n , k n , W n }∞
n=1 . (19) imn
n−1 ∗
n
e n
n ∗
n+1
plies τ + βL P (W ) ≥ V̄ (k ) ≥ 0 and so L P (W
) ≥ 0 for each n, so in
0
n
0
the limit V (W ) ≥ 0. Since V (W ) satisfies (17)–(21) and offers the host country expected return V 0 (W ), LV 0 (W ) ≥ V 0 (W ). However, Ln−1 P ∗ ≥ Ln P ∗ ≥ . . . ≥ V 0
and hence Ln P ∗ ≥ LV 0 , and taking the limit n → ∞, V 0 (W ) ≥ LV 0 (W ). Therefore V 0 (W ) = LV 0 (W ) is a fixed point of L starting from P ∗ . Since P ∗ ≥ V ,
Ln P ∗ ≥ Ln V c = V c . In the limit we have V 0 ≥ V c . By the definition of V c ,
V 0 = V c.
A.B
Proof of Lemma 3.5
Assume P is a continuous, concave, and bounded function,
and take any W 1 , W 2 ∈
[0, W̄ ] with corresponding contracts τ 1 , k 1 , W 01 and τ 2 , k 2 , W 02 . Next consider
W α = αW 1 + (1 − α)W 2 for α ∈ (0, 1) with associated contract
k α = αk 1 + (1 − α)k 2
W 0α = αW 01 + (1 − α)W 02
τ α = ατ 1 + (1 − α)τ 2 + (1 − δ) pf (k α ) − (αpf (k 1 ) + (1 − α)pf (k 2 )) .
Note that this contract satisfies (17)–(21), and that τ α ≥ ατ 1 + (1 − α)τ 2 with equality
if and only if k 1 = k 2 , because f (·) is strictly concave. Because P is concave:
LP (W α ) = sup τ + βP W 0α
θ
α
≥ τ + βP W 0α
≥ ατ 1 + (1 − α)τ 2 + βP W 0α
≥ ατ 1 + (1 − α)τ 2 + β αP W 01 + (1 − α)P W 02
= αLP W 1 + (1 − α)LP W 2 .
Thus LP (W ) is concave. Consider two cases: (i) P W 01 ) and P W 02 ) correspond with
the first-best Pareto frontier, and (ii) at least one of P W 01 ) and P W 02 ) lies below the
first-best frontier. Because the first-best frontier is linear in W , P (W 0α ) also corresponds
with this frontier for any convex combination W 0α . (See the proof of Lemma 3.4.) This
implies that, in case (i), k 1 = k 2 = k ∗ and k α = k ∗ , and therefore τ α = ατ 1 + (1 − α)τ 2 .
Because supθ τ + βP W 0 = P W 0 , where P ∗ (W 0 ) is the first-best frontier, L maps
weakly concave functions into weakly concave functions provided P (W 0 ) = P ∗ (W ).
36
CORRUPTION, FDI AND EXPROPRIATION
In case (ii), at least one of P W 01 ) and P W 02 ) is below the Pareto frontier, implying at least one of k1 , k 2 is less than k ∗ , hence τ α > ατ 1 + (1 − α)τ 2 . This implies
LP (W α ) > P W 0α , and therefore L maps weakly concave functions into strictly concave functions when P (W 0 ) does not correspond with the first-best frontier. Since V c is
the pointwise limit of Ln P from Lemma 3.4, V c (W ) is itself concave, with strict concavity when V c (W ) does not correspond with the first-best frontier.
Next, to see why ∂Vtc /∂Wtc ≤ −1 for all t, suppose to the contrary that −∂Vtc /∂Wtc =
λt < 1 for some t = t̃. By concavity of V c , if this is true anywhere, it is certainly true at
the minimum value Wtc = 0. Then condition (12) implies that
ϕt̃ = (1 − λt̃ ) + µt̃ + φt̃ > 0,
and by complementary slackness τt̃ = pf (kt̃c ) (µt̃ = 0) and the investor’s profits are negc
ative in period t̃. Constraint (9) then implies Wt̃+1
≥ Wt̃c ≥ 0 (the first inequality is strict
c
whenever kt̃c > 0). If kt̃c = 0, then τt̃ = pf (kt̃c ) = 0 and therefore Wt̃+1
= Wt̃c = 0. But
if a non-trivial contract featuring positive investment in finite time exists from period 0
onward, promising the investor discounted expected return at least equal to I0 ≥ 0 while
satisfying (8) and offering the host country τ0 + βEt [V1c ] > 0, then it is also feasible to
deliver a strictly positive expected return to the host country from any period t̃ onward
given promise Wt̃c = 0 that would require positive investment on some future date. This
c
implies that, if ϕt̃ > 0, τt̃ = pf (kt̃c ) > 0 and hence Wt̃+1
> Wt̃c = 0. Complementary
slackness then implies ζt̃ = 0, and λt̃+1 = (λt̃ + ζt̃ )/(1 + φt̃ ) = λt̃ /(1 + φt̃ ) ≤ λt̃ < 1.
Repeating the argument for period t̃ + 1, it immediately follows that λt̃+n+1 ≤ λt̃+n ≤ 1
for all n > 0. But then τt = pf (ktc ) for all t ≥ t̃, which violates the condition Wt̃c ≥ 0.
Therefore it must be the case that λt ≥ 1 for all t.
Finally, because λt ≥ 1 for all t, whenever ϕt > 0 we must also have φt > 0 (since
µt = 0). Since ϕt > 0 implies τt = pf (ktc ), (8) becomes
c
Vt+1
≥
δ
pf (k ∗ ) − pf (ktc ) ,
β
and if φt > 0, this constraint binds. But if δ > 0, this cannot bind because it is possible to
c
increase ktc and hence also increase τt while holding Wt+1
constant without violating (9).
c
If δ = 0, then the constraint reduces to Vt+1 ≥ 0, which never binds under the condition
τt ≥ 0. Therefore ϕt = 0 and (5) never binds.
37
CORRUPTION, FDI AND EXPROPRIATION
A.C
Proof of Proposition 3.7
From Lemma 3.5, ϕt = 0 and λt = 1 + µt + φt and pf 0 (ktc ) = λt / λt − φt (1 − δ) for
all t. Moreover, Equations (14) and (15) imply
λt+1 =
λt + ζt
.
1 + φt
Consider a stationary contract in which investment is constant, kt = k̂ ≤ k ∗ , and where
c
= 0 binds
λt = λt+1 = λ̂, so that (1 + φ̂)λ̂ = λ̂ + ζ̂. If φ̂ > 0, then ζ̂ > 0 and thus Wt+1
c
∗
c
for all t. In this case, (8) binds (k̂ ≤ k ) and (9) binds for Wt = Wt+1 = 0. This implies
the stationary contract k̂ with τt = τ̂ solves
∞
X
β t−s τ̂ =
t=s
τ̂
= δpf (k ∗ ) + (1 − δ)pf (k̂)
1−β
and
pf (k̂) − k̂ = τ̂ ,
which implies k̂ the solution to
k̂ = βpf (k̂) − δ(1 − β) pf (k ∗ ) − pf (k̂)
for 0 < k̂ ≤ k ∗ . Note that, for sufficiently high values of δ, there does not exist k̂ > 0
that solves this equality, in which case a non-trivial stationary contract does not exist.
(Conditions for existence are considered in Propositions 3.8 and 3.9.) Also note that only
c
if φ̂ = 0 and hence k̂ = k ∗ (Lemma 3.6) is it the case that ζ̂ = 0 (λ̂ = 1) and Wt+1
≥0
never binds in the stationary contract. This corresponds to a contract on the first-best
c
Pareto frontier, where V attains its maximum value, and τt and Wt+1
are not uniquely
determined in any period.
Assuming for the moment that a non-trivial stationary contract exists (k̂ > 0), the
optimal contract converges to this stationary contract period. This follows from λt+1 ≤ λt
for all t. To see why, suppose instead that λt+1 > λt for some t. Then (1+φt )λt < λt +ζt ,
c
c
which implies ζt > 0 and hence Wt+1
binds. This would imply Wtc ≥ Wt+1
= 0 and,
c
c
c
c
c
by the concavity of V , ∂Vt+1 /∂Wt+1 ≥ ∂Vt /∂Wt . But then by the envelope theorem
we have λt+1 ≤ λt , a contradiction. Therefore λt+1 ≤ λt , and since λt ≥ 1 for all t, λt
must converge to some value λ̂ ≥ 1. Assume for the moment that convergence occurs in
finite time in some period t∗ . Then either λt = λ̂ = 1 for all t ≥ t∗ , implying ζ̂ = φ̂ = 0
and Wtc ≥ 0 for t ≥ t∗ (Case 1), or λ̂ > 1, implying ζt = ζ̂ > 0, φt = φ̂ > 0, and
Wtc = 0 for all t ≥ t∗ (Case 2). Case 1 corresponds to the efficient stationary contract,
where kt = k̂ = k ∗ for all t and the first-best Pareto frontier is reached, whereas in Case 2
k̂ ≥ k ∗ . Since W0 ≥ I0 and I0 > 0 by assumption, we know λ1 = λ0 and therefore t∗ = 0
if and only if the first-best frontier can be immediately reached in the initial period of the
38
CORRUPTION, FDI AND EXPROPRIATION
contract. Otherwise t∗ > 0 and there is a positive transition period toward the stationary
c
≥ 0 for all t < t∗ , or else t = t∗ − 1, ζt > 0
contract where either ζt = 0 and Wtc > Wt+1
c
= 0 (but ζt = 0 for t < t∗ − 1). In both cases, λt+1 < λt for all t < t∗ .
and Wtc > Wt+1
We now argue that, if a non-trivial optimal contract exists, t∗ is reached in finite time and
under this contract τt = 0 until period t∗ − 1.
Consider any period t < t∗ along the transition to the stationary contract such that
c
Wtc > Wt+1
. Substituting λt = 1 + µt + φt into the above expression for λt+1 , we have
λt+1 = (1 + φt + µt + ζt )/(1 + φt ). Because λt+1 < λt when t < t∗ , one of the following
sets of conditions must hold:
(i) µt = 0, ζt = 0, and λt+1 = λ̂ = 1;
(ii) µt = 0, ζt > 0 (t = t∗ − 1), and λt+1 = λ̂ > 1;
(iii) µt > 0 and λt+1 > λ̂.
In cases (i) and (ii), the stationary contract is reached in period t + 1 (hence t = t∗ −
1). For all other t < t∗ , µt > 0, implying that τt ≥ 0 strictly binds. The optimal
contract therefore features zero transfers to the host country until the period just before
the stationary contract is reached. Because β ∈ (0, 1), V0 > 0 (if a non-trivial contract
exists) and τt = 0 for t < t∗ − 1 imply t∗ must be finite.
Finally, given λt is strictly decreasing and φt > 0 for all t < t∗ , concavity of V c (Wt )
c
implies Wt is decreasing and Vt is increasing with t < t∗ . Therefore Vt+1
− Vtc > 0 along
the transition to the stationary contract and, given τt = τt−1 = 0 and (8) strictly binds at
t and t − 1, this implies
c
c
β Vt+1
− Vtc = (1 − δ) pf (ktc ) − pf (kt−1
) > 0.
c
Therefore ktc > kt−1
whenever t < t∗ .
A.D
Proof of Proposition 3.8
An optimal contract converging to stationary investment k̂ must satisfy Condition (8) for
all t ≥ t∗ :
V max (β) ≥ δpf (k ∗ ) + (1 − δ)pf (k̂),
where
V max (β) =
∞
X
s=t∗
∗
β s−t τs =
∞
X
pf (k̂) − k̂
∗
β s−t pf (k̂) − k̂ =
.
1
−
β
∗
s=t
It is useful to begin by defining β(δ) as the minimum value of β that supports any particular stationary investment level k̂, given δ:
k̂ + δ pf (k ∗ ) − pf (k̂)
β(k̂) =
,
pf (k̂) + δ pf (k ∗ ) − pf (k̂)
39
CORRUPTION, FDI AND EXPROPRIATION
as well as the minimum value of β that supports k̂ = k ∗ , β̄ = k ∗ /pf (k ∗ ). We are
interested in the relationship β(δ) that defines the value of β below which there is no
k̄ > 0 that can be supported as a stationary contract, given δ. This can be expressed as
β(δ) = inf β(k̂).
k̂∈[0,k∗ ]
Denoting k̂ min (δ) = arg mink̂ β(δ), evaluating the derivative of β(δ) with respect to k̂
reveals that k̂ min (δ) satisfies
∗
δpf
(k
)
+
(1
−
δ)pf
(
k̂)
pf 0 (k̂) =
.
δpf (k ∗ ) + (1 − δ)k̂
Note that, at δ = 0, k̂ min (δ) = 0 solves pf 0 (k̂)k̂ = pf (k̂), implying that β(0) = 0.
Moreover, as δ → 0, k̂ min (δ) approaches zero. If δ = 1, k̂ min (δ) = k ∗ solves pf 0 (k̂) = 1,
and therefore β(1) = β̄.
For δ > 0, k̂ min (δ) > 0. We show that β(δ) is strictly increasing on δ ∈ [0, 1), converging asymptotically to β̄ as δ approaches 1 from below. Moreover k ∗ can be supported
as a stationary contract (if one exists) if and only if β ≥ β̄.
Because β(δ) and k̂ min (δ) are continuous and differentiable in δ, by the envelope theorem we can determine the slope of β(δ) by the slope of β(δ) evaluated at k̂ = k̂ min (δ):
∂β(δ)
pf (k ∗ ) − pf (k̂ min (δ)) pf (k̂ min (δ)) − k̂ min (δ)
∂β(k̂) =
=
≥ 0.
∗ ) + (1 − δ)pf (k̂ min (δ))
∂δ
∂δ min
δpf
(k
k̂=k̂
(δ)
We know from the above that k̂ min (δ) → 0 when δ → 0. This also implies that
∂β(δ)/∂δ → ∞ as δ → 0. Moreover, when δ = 1, k̂ min (δ) = k ∗ and therefore
∂β(δ)/∂δ = 0. Finally, for δ > 0 and k̂ min (δ) < k ∗ , ∂β(δ)/∂δ > 0. Therefore β(0) = 0,
β(1) = β̄, β(δ) is strictly increasing on δ ∈ [0, 1), and converges asymptotically to β̄ as
δ approaches 1.
A.E
Proof of Proposition 3.9
Given that the Pareto frontier V c (W c ) is concave and strictly decreasing in W c (Lemma
3.5), define W max as the maximum value of W c such that V min = V c (W max ) is the
minimum initial promised utility to the host country under an optimal contract. (Evidently
V min > 0 under a non-trivial contract, solving condition (8) with equality given k0c > 0.)
The optimal contract, if one exists, must offer the investor a return W0 ≥ I0 , and therefore
W max represents the threshold level for I0 above which a non-trivial optimal contract
¯ δ) to be this
does not exist. As V c (W c ) depends on β and δ, so does W max . Define I(β,
threshold for start-up costs I0 , given β and δ.
40
CORRUPTION, FDI AND EXPROPRIATION
Under the optimal contract such that (8) binds in the transition to the stationary
contract period, τ0 = 0. Condition (9) at period t = 0 can therefore be rewritten as
W0c = pf (k0c ) − koc + βW1c , while (8) becomes
V0c = βV1c = βV c (W1c ) ≥ δpf (k ∗ ) − (1 − δ)pf (k0c ).
Given W0c and V c (W c ), the optimal contract when (8) binds is summarized by the pair
{k0c , W1 } that solves these two conditions. Therefore, the maximum value for W0c given
V c (W c ) is the solution to
max
c
c
ko ,W1
W0c = pf (k0c ) − k0c + βW1c
subject to βV c (W1c ) − δpf (k ∗ ) − (1 − δ)pf (k0c ) = 0.
Note that the expression for W0c is concave and the constraint is convex given that V c (W c )
is concave. According to the envelope condition, we have
∂W0c
= W1c + γV c (W1c ) > 0
∂δ
∂W0c
= −γ pf (k ∗ ) − pf (k0c ) < 0,
∂β
where γ ≥ 0 is the multiplier on the constraint, and the derivatives are evaluated at the op¯ δ),
timized solution {k0c , W1c }. Recognizing that W0c evaluated at the solution equals I(β,
¯ δ) is strictly increasing in β and strictly decreasing in δ
these conditions show that I(β,
whenever (8) strictly binds (k0c < k ∗ ).
To see that ktc is strictly decreasing in δ whenever ktc < k ∗ consider δ 00 > δ 0 , note that
by the envelope condition, ∂Vt /∂Wt = −φt pf (k ∗ ) − pf (ktc ) < 0 for all t in which (8)
binds. This implies that the Pareto frontier V 00 (W ) corresponding to δ 00 lies strictly below
the frontier V 0 (W ) at δ 0 wherever V 0 (W ) is below the first-best Pareto frontier. Hence,
for any period t of the contract, beginning in period 0, before the first-best frontier is
reached (if at all), we have
00
0
V 00 (Wt+1
) < V 0 (Wt+1
),
0
00
where Wt+1
and Wt+1
correspond to the optimal contract under δ 0 and δ 00 . But this also
00
0
implies that Wt+1 > Wt+1
and, by the promise-keeping constraint, we know that kt00 < kt0 .
c
If this were not the case, then given Vt = βV c (Wt+1
) = δpf (k ∗ ) + (1 − δ)pf (ktc ), and
00
0
00
0
00
00
0
0
δ > δ , kt ≥ kt would imply V (Wt+1 ) > V (Wt+1 ).
A.F
Proof of Proposition 4.1
If following the first report mt = ktd the public does not choose to expropriate under the
contract, investors, knowing that expropriation will not occur and ρt = 0 when ktd 6= ktc ,
41
CORRUPTION, FDI AND EXPROPRIATION
choose ktd = k ∗ . This then implies that the contract satisfies
τt + βEt [Vt+1 (mt+1 )|ktd ] ≥ pf (k ∗ ).
But if the optimal contract satisfies this condition, then ktc = k ∗ is optimal at time t, since
it offers higher investment without increasing the risk of expropriation. Therefore, if expropriation does not occur, it must be the case that ktd = ktc . However, unless ktc = k ∗ , this
is not an equilibrium. Therefore, under a corrupt regime, the probability of expropriation
−1
is ρt = ρ̄ = σδ(1 − δ) for all t such that ktc < k ∗ and ktd solves pf 0 (kt ) = 1 − ρ̄ .
A.G
Proof of Proposition 4.2
Assigning multipliers ϕt , µt , λt , βζt and φt to constraints (4), (5), (9)–(10), and (16) and
recalling that ϕt = 0, the corresponding first-order conditions to the dynamic program
are
λt = (1 − ρ̄) + µt + φt
λt
pf 0 (ktc ) =
λt − (1 − δ)φt
c
∂Vt+1
λt + ζt
=−
,
c
∂Wt+1
(1 − ρ̄) + φt
(22)
(23)
(24)
as well as the envelope condition
∂Vtc
= −λt .
∂Wtc
Substituting λt = 1 − ρ̄ + µt + φt into Condition (24) yields
−
c
∂Vt+1
µt + ζt
=1+
≥ 1.
c
∂Wt+1
1 − ρ̄ + φt
Provided ζt > 0 and the investor is still promised positive future utility, λt+1 > 1 and
µt > 0. Therefore transfers are zero until either the efficient frontier is reached (at which
point the timing of transfers is no longer uniquely determined) or the investor has comc
pletely recovered I0 and Wt+1
= 0. Moreover, as long as λt+1 < λt and the contract is
converging to a stationary contract λt = λt+1 = λ̂, it must be the case that φt > 1 − ρ̄,
which implies ktc < k ∗ . Moreover, ktc is strictly increasing over time along the transition
to the stationary contract following an argument analogous to Proposition 3.7.
In the stationary contract period, λt = λt+1 = λ̂ and λ̂(φ̂ − ρ̄) = ζ̂. Since in the
stationary contract µ̂ = 0 and λ̂ ≥ 1, φ̂ ≥ ρ̄. If φ̂ > ρ̄, then ζ̂ ≥ (φ̂ − ρ̄) and Wt ≥ 0 must
bind. Only if φ̂ = ρ̄ = 0 and the efficient frontier is reached is it the case that ζ̂ = 0 and
this non-negativity constraint never binds in the stationary contract period.
42
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