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Open space amenities, land uses, and property values in Tucson:

U sing a geographic information system to improve hedonic models

Shultz, Steven Dennis, Ph.D.

The University of Arizona, 1993

V·M·I

300 N. Zccb Rd.

Ann Arbor, MI48106

Open Space Amenities, Land Uses, and Property Values in

Tucson: Using a Geographic Information System to Improve

Hedonic Models by steven Dennis Shultz

A Dissertation Submitted to the Faculty of the

School of Renewable Natural Resources

In Partial Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY

WITH A MAJOR IN RENEWABLE NATURAL RESOURCES STUDIES

In the Graduate College

THE UNIVERSITY OF ARIZONA

1 9 9 3

THE UNIVERSITY OF ARIZONA

GRADUATE COLLEGE

2

As

members of the Final

Ex~ination

Committee, we certify that we have read the dissertation prepared

by~S~t~e~v~e~n_D~._S~h~u~l~t~z~

entitled

Open Space Amenities, Land Uses, and Property Values in Tucson:

Using a Geographic Information System to Improve Hedonic Models

and recommend that it be accepted as fulfilling the dissertation

requirement for the Degree of Doctor of Philosophy

--------------~~~--------------------

William E. Shaw

,\. \...r

Phillip D. GueJ;?n

12/18/92

Date

12/18/92

Date

12/18/92

Date

12/18/92

Date

Date

Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final ccpy of the dissertation to the

Graduate College.

I

hereby certify that I have read this dissertation prepared under my direction and recommend that it be

acce~ted

as fulfilling the dissertation

12/18/92

Date

David A. King

3

STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the

University of Arizona and is deposited in the University

Library to be made available to borrowers under rules of the

Library.

Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

Table of Contents:

List of Tables

List of Figures

..........................................

5

.........................................

7

Abstract

................................................

9

Chapter 1: Introduction

An Introduction to the Research Problem . . . . . . . . . . . . . . . 10

Hedonic Valuation Method Theory . . . . . . . . . . . . . . . . . . . . . . . 13

Potential Problems Associated with the HVM . . . . . . . . . . . . 19

Objectives. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . .. 27

4

Chapter 2: Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

The Tucson Urban Area and Past HVM Studies . . . . . . . . . . . . . 30

Specification of the Benchmark Model . . . . . . . . . . . . . . . . . . 35

Unit of analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

The Dependent Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Open Space Amenity Variables . . . . . . . . . . . . . . . . . . . . . . . . 39

Land Use Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Structural Housing Variables . . . . . . . . . . . . . . . . . . . . . . . . 44

Neighborhood Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Functional Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48

Alternative Model Specifications . . . . . . . . . . . . . . . . . . . . . 49

Comparing the Benchmark Model with Alternative

Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Chapter 3: Results and Discussion

Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

The Benchmark Mode 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Modell: Rental Housing Values Excluded . . . . . . . . . . . . . . . 78

Model 2: Land Use Variables Omitted . . . . . . . . . . . . . . . . . . . 82

Model 3: Open Space Amenity Variables Omitted . . . . . . . . . 86

Models 4 and 5: Varied Levels of Land Use Aggregation. 90

Models 6,7, and 8: Reduced sample sizes . . . . . . . . . . . . . . 96

Chapter 4: Conclusions and Implications

Summary of the Empirical Results . . . . . . . . . . . . . . . . . . . . . 104

Implications for HVM Researchers . . . . . . . . . . . . . . . . . . . . . 106

Caveats and future Research Needs . . . . . . . . . . . . . . . . . . . . 109

Appendices

A- Variables in King's et al., (1991) HVM Study ...... 112

B- 1990 Census Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

C- City of Tucson Land Use Data . . . . . . . . . . . . . . . . . . . . . . 114

References . . . . . . . . . . . . . . . . . . . . .

It • • • • • • • • • • • • • • • • • • • • • • •

117

5

List of Tables

1. Open Space Amenity and Land Use Variables in Past HVM

Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2. A Summary of the Alternative HVM Specifications . . . . . . . 29

3. Variables Included in the HVM Study . . . . . . . . . . . . . . . . . . 47

4. Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5. Housing Values by Market Segments . . . . . . . . . . . . . . . . . . . . 62

6. Correlations Among Selected Explanatory Variables 63

7. Regression Output: The Benchmark Model . . . . . . . . . . . . . . . 65

8. Benchmark Marginal Implicit Prices and Elasticities 68

9. Regression Output: Modell (Rental Values Excluded) 79

10. Marginal Implicit Prices and Elasticities of the

Benchmark and Modell (Rental Values Excluded) . . . . . . 81

11. Regression Output: Model 2 (No Land Use Variables) ... 83

12. Standard Errors of Coefficients: Benchmark and Model

2 (Land Use Variables Omitted) . . . . . . . . . . . . . . . . , _ .... 84

13. Marginal Implicit Prices: Benchmark and Model 2 (Land

Use Variables Omitted) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

14. Housing Value Elasticities: Benchmark and Model 2

(Land Use Variables Omitted) . . . . . . . . . . . . . . . . . . . . . . . . 85

15. Regression Output: Model 3 (No Open Space Amenity

Variables Omitted) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

16. Standard Errors: Benchmark

&

Model 3 (Open Space

Amenity Variables Omitted) . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

17. Marginal Implicit Prices: Benchmark

&

Model 3 (Open

Space Amenity Variables Omitted) . . . . . . . . . . . . . . . . . . . . 88

6

List of Tables (Continued)

18. Housing Value Elasticities: Benchmark & Model 3

(Open Space Amenity Variables Omitted) . . . . . . . . . . . . . . . . 89

19. Regression Output: Model 4 (Land Use Data Aggregated at the Block Level of Census Geography) . . . . . . . . . . . . . . 91

20. Regression Output: Model 5 (Land Use Data Aggregated at the Tract Level of Census Geography) . . . . . . . . . . . . . . 92

21. Standard Errors of Coefficients for Alternative Land

Use Aggregations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 93

22. Marginal Implicit Prices for Alternative Land Use

Aggregations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94

23. Housing Value Elasticities for Alternative Land Use

Aggregations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94

24. Regression Output: Model 6 (n=3000)

25. Regression Output: Model 7 (n=1500)

97

98

26. Regression Output: Model 8 (n=500) . . . . . . . . . . . . . . . . . . . 99

27. Standard Errors of the Coefficients: The Benchmark

(n=6277), Model 6 (n=3000), Model 7 (n=1500), and

Model 8 (n=500)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

28. Marginal Implicit Prices and Elasticities: The

Benchmark (n=6277) and Model 6 (3000) . . . . . . . . . . . . . . 102

7

List of Figures

1. The Tucson Urban Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2. Geographic Distribution of 6277 Residential Census

Block Centroids in Tucson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3. Natural Resource Areas, Parks, and Golf Courses in

Tucson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4. River/Wash Habitat Classifications in the Tucson Urban

Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5. Housing Market Segments in the Tucson Urban Area •..... 46

6. Centroid Locations of the Sample of 3000 Census Blocks. 51

7. Centroid Locations of the Sample of 1500 Census Blocks. 52

8. Centroid Locations of the Sample of 500 Census Blocks .. 53

9. Non-Residential Land Uses by Market Segments . . . . . . . . . . 60

10. Housing Densities by Market Segments . . . . . . . . . . . . . . . . . 61

11. Housing Value Function for Single-Family Density ..... 70

12. Housing Value Function for Multiple-Family Density 70

13. Housing Value Function for Industrial Land Uses ....... 71

14. Housing Value Function for Commercial Land Uses ....... 71

15. Housing Value Function for Vacant Lands . . . . . . . . . . . . . . . 72

16. Housing Value Function for Natural Resource Areas 73

17. Housing Value Function for Undeveloped Parks . . . . . . . . . 73

18. Housing Value Function for Regional/District Parks .... 74

19. Housing Value Function for Neighborhood Parks ........ 74

20. Housing Value Function for Public Golf Courses ....... 75

8

List of Figures (Continued)

Page

21. Housing Value Function for Private Golf Courses ...... 75

22. Housing Value Function for Class I Rivers/Washes ...... 76

23. Housing Value Function for Class II Rivers/Washes ..... 76

9

Abstract

The Hedonic Valuation Method (HVM) was used to estimate the relationship between housing values, open space amenities, and non-residential land uses in the Tucson Urban Area. Using a

Geographic Information System, it was possible to estimate a

Benchmark Model that incorporated a wide range of open space amenity and land use variables and a complete enumeration of census blocks. Eight alternative model specifications were estimated with: rental values excluded, fewer open space and land use variables, land use data aggregated at different levels of census geography, and incrementally smaller sample sizes.

Statistical and economic comparisons between the

Benchmark and al ternati ve models included: R2 values, standard errors, F-tests, and the magnitude and stability of both marginal implicit prices and housing value elasticities.

Results indicate that the exclusion of open space amenity variables, the use of different levels of census geography to aggregate land use data, and the use of samp~es of census blocks, all have the potential to reduce the quality of HVM estimates.

10

Chapter 1: Introduction

An Introduction to the Research Problem

Many urban communities are attempting to preserve and/or increase the supply of open space amenities and nonresidential land uses within their jurisdictional boundaries.

Open space amenities include parks, natural open spaces, wildlife corridors, and riparian habitat. Non-residential land uses in urban areas consist of industrial and commercial activities as well as vacant lands.

There are often significant costs involved in the provision or removal of such open space amenities and nonresidential land uses. However, the corresponding benefits associated with such amenity and land use changes are often not known. This lack of information may result in the inefficient and inequitable allocation of public resources.

The hedonic valuation method (HVM), offers an approach to estimate the economic value of different types of open space amenities and land use activities. The HVM uses the relationship between the prices and the characteristics of a market good to estimate both the marginal and total values of those characteristics. When housing value is the market good and the dependent variable in an HVM regression equation, i t is possible to estimate both the individual and combined effects that open space amenity and non-residential land use

11 variables have on housing values.

Unfortunately, the effectiveness of the HVM in valuing open space amenities and non-residential land uses, may be limited by both data inadequacies and model specification errors. These include: the exclusion of rental housing values from the dependent variable, the omission of relevant explanatory variables, the aggregation of land use data at inappropriate levels of census geography, and the use of samples of census blocks in lieu of an entire population.

The purpose of this dissertation is to determine whether the above data inadequacies and specification errors effect the robustness of HVM estimates of open space amenity and nonresidential land uses. This is accomplished with the use of a geographic information system

(GIS)1 and the incorporation of block level 1990 census data and a wide variety of open space amenity and land use variables in the specification a

Benchmark HVM Model. This benchmark Model is then compared to alternative model specifications containing: only self-owned housing values, fewer explanatory variables, land use data aggregated at different levels of census geography, and the use of incrementally smaller sample sizes of census blocks.

Two primary benefits will result from this research.

1A GIS is a computer based system that can integrate, manipulate, analyze, and display a wide variety of spatially referenced topological and attribute data such as natural resource and socio-demographic data.

12

First, the results of this research can potentially provide an indication of the reliability of many past HVM research studies which: excluded rental housing values, incorporated relatively few explanatory variables, adopted highly aggregated units of analysis, and/or used small sample sizes.

Second, this research will establish whether GIS technology which allows the use of more comprehensive and detailed secondary data sources, can improve the accuracy of HVM estimate of open space amenities and non-residential land uses.

13

Hedonic Valuation Method Theory

The hedonic valuation method (HVM) uses the relationship between the prices and characteristics of a market good to estimate the value of particular characteristics associated with that good. The technique is based upon the household production model of consumer behavior. This theory assumes that individuals make consumption choices among combinations of goods and services in order to maximize their utility subject to budget constraints and the profit maximizing behavior of sellers in the marketplace (Rosen, 1974).

When the HVM is used to value characteristics such as open space amenities and land uses, housing and/or property values are typically the market good adopted.

The first stage of the HVM involves estimating implicit prices of bundled attributes associated with differentiated produ~ts.

The method is based upon the assumption that a market good has identifiable objective characteristics which influence buyers consumption choices (Rosen, 1974).

First stage HVM estimates are obtained from a regression model where the value of a market good (such as housing) is the dependent variables and the characteristics of the market good (housing characteristics) are the explanatory variables.

Such a hedonic regression is often referred to as an implicit price function and is summarized by equation 1.

14

Where

Ph

Xs

Xn

Xr

= housing prices

= structural housing characteristics

= neighborhood characteristics

= resource characteristics

Structural characteristics include measures such as area of living space, lot size, number of bedrooms and bathrooms, age, and type of construction. Neighborhood characteristics include a wide variety of quality of life measures (school quality, crime levels, and socio-demographics, etc. , ) .

Resource characteristics refer to parks, opens spaces, natural wilderness areas, non-obtrusive land uses, clean air and water.

The hedonic price function is a joint envelope of supply and demand curves in price and characteristic space representing the locus of points of intersection between buyers' bid functions and sellers' offer functions. As defined by Rosen (1974), the bid function, representing consumers' maximum willingness to pay for a particular characteristic, incorporates a measure of the good's characteristics as well as consumers' income and tastes. The offer function represents the profit maximizing objectives of a seller and hence the minimum unit prices he/she is willing to accept for giving up a bundle of characteristics .

15

The functional form used in estimating the implicit price function is an important consideration (Rosen, 1974; Butler,

1982). A linear form implies that the relationship between resource characteristics and housing prices is constant.

Alternatively, if such a relationship depends on other factors, such as the quantity levels of other amenities and/or the ability of consumers to repackage or arbitrate bundles of a goods' characteristics, then a functional form expressing this assumption should be adopted (Rosen, 1974 and Freeman,

1979).

The most commonly adopted functional forms in HVM studies are the double-log, semi-log, and log-linear forms. Selection of specific functional forms is usually based upon economic theory, goodness of fit, and non-linear statistical testing procedures (Blomquist and Worley, 1981».

As shown by equation 2, the marginal implicit prices

(MIP's) of particular characteristics are obtainea by partially differentiating the estimated hedonic price function

(1), with respect to the resource characteristic of interest.

( 2 ) where: Ph

Xi

=

implicit price function

= ith amenity being valued

the mean values of the quantity of the amenity present, the quantities of other amenities, and the price of the market good.

16

Such MIP estimates are usually calculated by inserting

MIP's measure the effect of a unit change in the quantity of an amenity on the mean price of the market good being studied, ceteris paribus. It is the result of supply and demand forces operating in the housing market, and is the marginal not the mean willingness to pay for an amenity at the existing market equilibrium. Hence, the first stage of the

HVM provides estimates of the value of small changes in the quantity of a characteristic, and therefore indicates the marginal value of the amenity as i t currently exists given the existing quantities of other amenities and the social and economic conditions in the market. As such, the MIP' s of different amenities may be compared with each other.

In order to estimate the total value of particular amenities, their demand functions, and the effect of large changes in the quantity of an amenity, a second stage of the

HVM as proposed by Rosen (1974) must be implemented. The stage involves regressing calculated marginal implicit prices for an amenity (from equation 1), against both the quantities of the amenity that are present and a variety of different exogenous demand and supply shift variables. Second stage HVM estimates are however not a major interest of this present

17 research effort.

An issue very important to the design and implementation of HVM studies is housing market segmentation. The need to account for market segmentation in the context of the HVM, was first recognized by Straszheim (1973) by demonstrating that the housing market in the San Francisco urban area consisted of a set of distinct market segments each with their own hedonic price functions, and that more robust estimates were obtained by accounting for these segments in an HVM regression.

Freeman

(1979) has specified that the following conditions must be met in order for a segmented housing market to exist within a community: 1) Housing consumers in one market segment must face barriers and not participate

"significantly in other market segments due to discrimination, geographical limitations, desires for ethnically homogenous neighborhoods"; and, 2) that there must be differences in the structure of supply and demand for housing in different parts of the housing market. Therefore, market segmentation is considered to exist when the structural characteristics of housing stocks and the socio-demographic characteristics vary throughout the housing market of a particular study area.

The identification of market segments is important to HVM studies for two major reasons: First, by accounting for market segmentation in the first stage of the HVM, the

18 identification of simultaneous demand/supply equations in the second stage is facilitated by the imposed condition that structural demand/supply parameters are identical across market segments even though the hedonic equilibrium points are not (Brown and Rosen, 1982, Dale-Johnson, 1982, and Bajic,

1985). Second, market segmentations are likely represent the spatial effect(s) of the omitted explanatory variables.

Supply and demand characteristics typically used to stratify a housing market include: housing types, densities, and values, property taxes, zoning regulations, and the existence of pre-identified socio-economic , cultural, and historical neighborhoods within a community (Schnare and

Struyk 1976, Dale-Johnson, 1982, Bajic, 1985). The geographic scale of such market segments has ranged from spatially distinct communities (Stull, 1975), to census tracts and block groups (Goodman, 1981 and Li and Brown, 1980), to predesignated and/or historically recognized neighborhood boundaries and real estate markets (Lang and Jones, 1979 and

Micheals and Smith, 1990).

19

Potential Problems Associated with the HVM

Only limited attention has been given to the validity and robustness of HVM estimates (Atkinson and Crocker, 1987, and

Graves et al., 1988). More specifically, questions of whether the robustness of HVM estimates are sensitive to specification biases, the aggregation of land use data at different levels of census geography, and the use of samples of census blocks have not been fully addressed. These potential problems facing the HVM are examined in further detail after a brief review of the prevalent data sources used by HVM studies.

The dependent variable in HVM studies is usually housing and/or land values obtained from property tax assessment records, multiple listing services (MLS), or the self-reported home values and monthly rental payments contained in the

Census of Population and Housing conducted every ten years.

Limitations associated with each of these measures and data sources are: assessed housing values not reporting actual market values, MLS data that is proprietary and exclusive of rental properties, and finally, census data which is out of date and/or reported only at highly aggregated levels.

2

Advantages of the Census as a source of housing value

2

The three smallest levels of Census geography reported by the census are the block, block group, and tract. Census blocks usually represent a city block in urban areas (SMSA's), while block groups consist of approximately 10 census blocks, and census tracts consist of approximately 10 block groups.

20 data for HVM studies include: it's consistency and accuracy,

3 it's accessibility, and the fact that i t incorporates both self-owned home values and the value of rental payments.

Independent variables representing structural housing characteristics also may be obtained from assessor, MLS, and census data sources. Assessor and MLS sources usually contain the most detailed and comprehensive listing of: numbers and types of household rooms, sizes of lots and houses, the inclusion of fireplaces and pools, and the age of housing units. Alternatively

I

the Census provides much less detail on the structural characteristics of a homes. For example, at the block level of census geography, only the total number of rooms in a household unit, and the number and type of existing structures (single family, apartments, or trailers) are reported. At the block group and tract levels, some additional information is provided on the existence and general quality of plumbing and kitchen facilities, telephones, water/sewage systems, and the age of housing units.

Neighborhood and socio-demographic variables used to identify market segments and to estimate second stage demand and supply functions are most often obtained from the census,

3Errors associated with owner estimates of housing values reported by the census have been determined to be insignificant when reasonably large sample sizes are utilized.

(Kain and Quigley, (1972).

21 local governments, and household surveys.

Resource characteristics may be obtained from tabular and map records kept by various local government agencies responsible for the management of specific natural resources.

However, many of these natural resource variables are difficult to obtain and/or quantify and are therefore omitted from many HVM models.

The exclusion of monthly rental payments from the dependent variable that is intended to represent all housing values. This is a form of specification bias and evidence of i t has been found to exist by Linemann (1980) who determined that environmental amenities influenced self-owned home values differently than rental values.

In most cases, the justification for excluding rental values from HVM models was that available data sources have not contained detailed information pertaining to rental values. However, i t is now easier to incorporate rental values into the dependent variable by using the 1990 census which reports both self-reported monthly rental payments and home values down to the block level of analysis.

Specification bias is most often associated with the ofllission of relevant explanatory variables from an

HVM

regression model. This results in the coefficients of the explanatory variables that have been included in the model, being biased and inefficient. Such a bias is likely to

22 result in invalid t-statistics and artificially low

R2 values

(Johnson et al., 1984). The existence of specification bias has been demonstrated through the comparison of the

R2 values, coefficients, and standard errors of benchmark models containing a wide range of variables to alternative model specifications with selected explanatory variables omitted

(Butler, 1982, and McMillen and Mcdonald, 1989).

A review of the literature (Table 1) shows that most HVM studies include only a few open space amenity variables in their model specifications. Similarly, in a critique of the

HVM, Freeman (1979) has noted that:

"overall the selection of explanatory variables [in HVM experiments], seems to be almost haphazard. Convenience and data availability appear to be the major determinants of this part of model specification. Virtually all of the studies reviewed can be criticized on one or another aspect of their model specification. The variety of model specifications raises some questions about the extent to which results are sensitive to the choice of explanatory variables" (pg. 169).

As Freeman (1979) suggests, the likely reason for not specifying a full range of explanatory variables is the difficulty in obtaining, manipulating, and integrating such data into HVM study designs. Other reasons may include the potential of multi-collinearity between similar resource characteristics, and the fact that many researchers are simply interested in empirical estimates (i.e. MIP's) for one or two focus variables.

23

Table 1: Open Space Amenity and Land Use Variables Included in Past HVM Studies.

Author and Year Location

Coughlin & Kawashima 1973 Philad.

Reuter 1973 Pittsburg

Stull 1975

Correll et aI., 1978

Boston

Boulder

Nelson 1978

Diamond, 1980

Judd, 1980

Li and Brown, 1980

McMillian et aI., 1980

Blomquist & Worley, 1981

Cao and Cory, 1981

Palmquist, 1982

Allen et aI., 1986

Graves et aI., 1988

Des Rosiers, 1990

Micheals & Smith, 1990

King et aI., 1991.

Kohlhase, 1991

Palmquist, 1992.

Variables Specified

Parks of varying sizes (-)

Alternative land uses (?)

Alternative land uses (+/ -)

A 1,383 acre greenbelt (+)

Wash DC Air Pollution, Noise (-)

Chicago Air Pollution( -), a Lake(+), H ills (I +)

CharI. SC Alternative land uses (+/ -)

Boston Housing Density( -), Scenic Views( +),

Air & Noise Pollution( -), Rivers( +),

Highways( -), Conservation and recreation areas(+/ -), Alternative land uses(+/ -)

Edmonton Noise (-)

Spring.IL A lake(+), Parks(+), Highways(-)

Tucson

Seattle

Mass..

S. Calif.

Quebec

Boston

Noise(?), Alternative land uses (+/ -)

Highway Noise (-)

8 Urban parks (-)

Air Pol.( -), Beaches(+), Scenic

Views(+)

Parks(+), Highways( -)

Toxic Waste Sites (-)

Tucson Resource areas(+), Parks( -), Golf

Courses(+), Wildlife Habitats(+)

Toxic Waste Sites( -) Houston

WA State Parks(+), Trees(+), Rec. Areas(+)

Roads( -)

+/-/?

In

Icate pOSItive, housing values

24

The limited availability of data for explanatory variables is· closely related to the issue of data manipulation. More specifically, detailed information about specific natural resource based amenities such as air and water pollution, land uses, and the location of parks, and natural areas have not been readily available in formats that allow such data to be easily integrated with housing values.

Such data integration requires that different data sources cover the same geographical area and be at the same scale and resolution. Automated (computer based) methodologies for analyzing large volumes of integrated data also must exist. For example, in HVM studies i t is necessary to measure the distances between amenities and housing locations. This is a complex and time consuming task especially when several amenity variables are included in a study.

With the recent introduction of TIGER

4

, and the availability of reasonably priced GIS software packages, i t is now relatively easy to integrate spatially referenced natural

4TIGER (a topologically integrated geographic encoding and referencing system) is an extensive national digital map database created by the census bureau to assist with their enumeration and data dissemination efforts beginning with the

1990 census. It includes features (roads, railroads, rivers, etc), address ranges and zip codes (in urban areas only), all census statistical areas, and political or administrative boundaries for the whole country.

25 resource, housing, and census data. Many government agencies responsible for natural resource management, have begun using

GIS technology to collect, standardize, manipulate, and display natural resource, public infrastructure, and housing value data (Shultz and Regan, 1990, and Thrall, 1991).

Land use data may be aggregated at various levels of geography including census blocks, block groups, and tracts.

It has been demonstrated that aggregating land use data by census block groups provides more robust HVM estimates (higher

R2 values, and larger numbers of statistically significant coefficients) than HVM estimates based on census tracts which are larger and contain more heterogenous data (Goodman, 1977).

However, i t has not yet been established whether the.~se of the census block as a unit of analysis (which contains smaller and even more homogenous data), further improves the robustness of HVM estimates.

The rationale for not using the census block as a unit of analysis in HVM studies includes: the suppression of many categories of census data at the block level in order to ensure confidentiality5, and, that until the 1990 census and the development of GIS technology, the spatial analysis of the numerous census blocks was not feasible.

5 The suppression of block level census data for reasons of confidentiality has been relaxed in the 1990 census, especially in urban areas where now virtually all data categories are made available.

26

The relationship(s) between the robustness of HVM estimates and the use of different sample sizes of census has also not been adequately addressed in the literature.

The objective in selecting sample sizes in most cases is to find the right balance between reliable sample estimates and the time and cost constraints of using larger sample sizes

(Kish, 1967). with regards to HVM studies, the costs of a complete enumeration, or even the use large sample sizes of census blocks, has in most cases been restrictively high. However, with the use of GIS technology, i t is now significantly easier and cheaper to quantify the spatial relationships between amenity variables and large numbers of geographically referenced census blocks.

The issue of alternative sizes and HVM estimates is relevant for two reasons. First, knowledge of how different sample sizes impact HVM estimates can shed light on the reliability of past HVM studies that have used samples of varying sizes. Second, such information will be useful to future HVM studies of large areas with numerous census blocks, and/or to those requiring the collection of detailed block level data that is not readily available in a GIS data format.

In such cases, even with the use of a GIS, time, money, and computing limitations are likely to require the use of a sample rather than a population of census blocks.

27

Objectives

The purpose of this dissertation is to determine the effects of model specification errors and various data inadequacies on the quality of HVM estimates dealing with open space amenities and non-residential land uses.

More specifically, the objectives of this study are to determine whether the robustness and quality of HVM estimates are reduced by:

1) Excluding rental values from the dependant variable.

2) Omitting open space amenity and land use variables.

3) Aggregating land use data at varied levels of geography.

4) Using incrementally smaller sample sizes of census blocks.

28

Chapter 2: Methods

To determine whether specification biases, alternative levels of land use aggregation , and the use of samples rather than a population of census blocks effect the robustness of

HVM estimates, the results of a Benchmark Model are compared to those of alternative model specifications.

The Benchmark Model incorporates a variety of open space amenity and land use variables, and utilizes the entire population of residential census blocks within the Tucson

Urban Area (TUA).6 The eight alternative model specifications include: one which excludes renters from the dependent variable, two containing fewer open space amenity and land use variables, two that are based upon varied levels of land use data aggregation, and finally, three fully specified models

(i.e. the benchmark Model), that are based upon incrementally smaller sample sizes. Table 2 contains a summary of these alternative model specifications.

6The Tucson Urban Area is a geographical area adopted by the

Tucson Planning Department for use in their Decennial 'Land

Use Classification Study'. As illustrated in Map 1, this study area extends beyond the Tucson City Limits, but does not incorporate the entire region of eastern Pima County.

29

Model

1

2

3

4

5

6

7

8

Table 2. A Summary of the Alternative Model Specifications

Characteristics (differing from Benchmark)

Rental values excluded from dependent variable

Non-residential land use variables omitted

Open space amenity variables omitted

Land use variables aggregated at block level

Land use variables aggregated at tract level

Sample size of 3000 census blocks

Sample size of 1500 census blocks

Sample size of 500 census blocks

30

The Tucson Urban Area and Past HVM Studies

In order to provide a better understanding of the assumptions and model specifications adopted in this study, an introduction to the study area, and a summary of the results of two previously conducted HVM studies in Tucson (Cao and

Cory, 1981, and King, White and Shaw, 1991) is presented below.

The Tucson Urban Area (TUA) contains almost 500, 000 people, and is surrounded on three sides by publicly owned open spaces that are managed by the Pima County Parks and

Recreation Department, the National Park Service, and the U.S.

Forest Service (Figure 1). The TUA also contains a variety of urban and regional park facilities, as well as four ephemeral rivers, numerous washes, and an abundant variety of wildlife habitat and species. These open space based amenities are commonly cited as major contributors to Tucson's quality of life.

Cao and Cory (1981) used the HVM to estimate the economic tradeoffs associated with alternative and mixed land uses in the TUA. The census tract was the unit of analysis in this study and the dependent variable was the self-reported median value of owner occupied homes from the 1970 Census, at the tract level of geography.

Structural explanatory variables in the study included the median number of household rooms, and the presence of

basements and adequate plumbing facilities.

31

Accessibility variables included distance to the central business district and other employment centers. Public sector variables such as property tax rates and reading achievement tests were used as measures of school quality. Neighborhood variables included ethnic composition, unemployment rates, and noise and crime levels. Land use variables included the proportion of single family, multiple family, commercial, industrial, and institutional land uses occurring in individual census tracts.

A standard first stage hedonic equation is estimated using an ordinary least squares regression. The coefficients on distance to the central business district and other employment centers were statistically insignificant. This is attributed to the city's relatively small size and dispersed employment areas. Other statistically insignificant variables included: property tax rates, plumbing, basements, and crime and noise levels, all of which were excluded from further analysis.

Due to a high degree of multi-collinearity between the percentage of minorities in particular census tracts and other socio-demographic variables, the minority variable was adopted as a proxy variable to represent the others. This variable had a negative coefficient and was statistically significant at the 99% level of confidence.

The remaining variables included in the study also had

Coronado National Forest

IZSZI

179 t1:Jjcr

Rivers a-.d Washes source:

EGIS 1991

Figure 1. The Tucson Urban Area

Saguaro

National

Jlonument

East

w

I\.)

33 statistically significant coefficients. Of particular interest was the finding that the percentage of multiplefamily, industrial, and commercial land uses occurring within the acreage of individual census tracts, did not negatively influence the values of single-family homes. The authors noted that this result may have been influenced by the fact that the units of analysis (census tracts) were characterized by very heterogenous or 'mixed' land use activities. In other words, because the proportions of each land use were all very low (i.e. between 0, 10, 12, 20, and 25 percent), i t appeared as though specific land uses did not have negative effects on property values. The authors pointed out that different results were likely if smaller and more homogeneous units of analysis (such as census blocks or block groups), were used to aggregate the land use data.

King, White, and Shaw (1991), conducted an HVM study in

Tucson to estimate the influence of proximity open space amenities (parks, natural resource areas, and wildlife habitats) on single-family housing values.

The dependent variable was the sale price of homes reported in a multiple listing service database. The explanatory variables in the study were broken down into structural, neighborhood, and open space categories. A more detailed description of all the variables utilized in this study is contained in Appendix A.

34

Five market segments were identified through an examination of ·socio-economic characteristics, and the authors personal knowledge of the TUA. A stratified random sample of

575 homes was drawn from MLS reports of homes sold in the

Tucson area in 1986.

A high degree of multi-collinearity was discovered among the structural and neighborhood variables. The size of homes was therefore used to represent the other structural variables. Also, the age variable represented the stages of

Tucson's urban development, and housing density and distance to employment centers were neighborhood characteristics. the variables representing

A hedonic price equation was estimated using a double, natural log functional form. A one tailed ' t ' test was used to test the significance of the regression coefficients. The major conclusions of this study were that a segmented housing market existed in Tucson, proximity to natural resource based open space areas positively influenced horne values, and that proximity to developed public recreation sites (county and urban park facilities) negatively influenced horne prices.

35

Specification of the Benchmark Model

The first. task of this study is the estimation of the benchmark hedonic price equation based upon a wide range of open space amenity and land use variables. This general specification is represented by:

( 3 ) where: HVAL

Zo

ZL

Zs and,

Zn

= housing values

= open space amenity variables

= land use variables

= structural variables

= neighborhood variables

This Model is based upon the entire population of residential census blocks in the Tucson Urban Area (TUA). A more detailed discussion of the units of analysis (census blocks), the dependent variable, and the range of explanatory variables contained in the Model are discussed below.

unit of Analysis

The unit of analysis in the benchmark (and all the other models) is the census block, which is the smallest geographical unit reported by the Census. Blocks are bounded by visible features such as roads, streams, railroad tracks, and political boundaries. In densely settled urban areas, census blocks are actual city blocks. In less densely settled

36 areas, census blocks tend to be larger and more irregularly shaped.

There are 8590 census blocks within the adopted TUA study boundary. After removing all blocks having less than 25% of their total area associated with residential land uses, and all blocks consisting primarily of institutional and government structures (over 50% of the block area), a total of

6277 census blocks remain.?

The locations (longitude and latitude coordinates) of each block centroid (geographical center) of the 6277 residential census blocks in the study area, were obtained from the 1990 Census file STF-1A and are shown in figure 2.

With the use of an automated GIS command, the euclidean distances between the census block centroids and the other boundaries of all of the open space amenities were measured to the nearest tenth of a mile.

?

These census blocks were deleted from the study because of they did not include any significant levels of housing within their boundaries.

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38

The Dependent Variable.

The dependent variable in the Benchmark Model is the mean value of all residential housing values in individual census blocks.

More specifically, housing value (HVAL) is the weighted mean of: the median value of owner occupied units and the median value of capitalized rental payments both of which were obtained from file STF-1A of the 1990 census. This formula is shown below by equation 4:

(4) HVAL

=

NRU(MEDRENT)

+

NOU(MEDOWN)

NRU

+

NOU

Where: HVAL

NRU

NOU

MEDRENT

MEDOWN

=

Housing values

=

Number of rental units in a block

=

Number of self-owned units in a block

=

Median value of capitalized rental payments

=

Median value of self-owned homes

The capitalized value of rental payments was calculated using equation 5 under the assumption of a 30 year mortgage at

9% interest.

B

(5) Capitalized Rental Value

=

Monthly Rent

*

(1

+

i)" -

1 i(l+i)1l

Where: i and, n

=

0.0075%

=

360 (monthly payments)

BAccording to local real estate brokers, 30 year mortgage contracts at 9% interest annually have been a common practice in

Tucson in the last few years.

39

Open Space Amenity Variables.

The distance to the following open space amenity variables are included in the Benchmark HVM Model: large publicly owned natural resource parks, including the Coronado

National Forest, Tucson Mountain Park, and Saguaro National

Monument East/West (NRAS) ; undeveloped parks are natural desert environments and with limited or no developed facilities (UPKS); regional and district parks containing a variety of different recreational and athletic facilities that are intended to serve inhabitants within a 1 to 3 mile radius neighborhood and/or school parks which are relatively small and serve local populations within a 1 mile radius (NPKS); public and private golf courses (GOLF and

PGOLF); and river/wash habitat classified as being either

Class I or II (HAB1, HAB2)

.10

9

Regional and district parks were combined because of their relative infrequency and the fact that their sizes and facilities were almost identical. The golf course portions of several regional parks were delineated and are represented exclusively by the GOLF variable.

10

Class 1 habitats are prii3tine and important biological areas made up of deciduous riparian woodlands, mesquite bosques, lakes, ponds, wetlands, important movement corridors for wildlife species, and major extensions of large public natural reserves. Class 2 habitats are less critical to specific wildlife species and in most cases less visually attractive to humans. Class II habitat includes major segments of riparian habitat that are isolated by development from protected areas,

Paloverde-saguaro, Sonoran desert, and Ironwood plant communities

(S~law et al., 1986).

40

All distances are measured from census block centroids to the closest boundary of an open space amenity to the nearest tenth of a mile.

From the results of the previous Tucson based HVM study

(King, Shaw, and White, 1991), i t is hypothesized that RDPKS and NPKS are negatively related to housing values while all other open space variables are expected to have a positive influence on housing values. As distance measurements increase as the proximity to an amenity decrease, coefficients with positive signs are interpreted as having a negative relationship with housing value.

Open space amenity data was obtained from the Pima County

Engineering and GIS Department (EGIS).11 Due to the relative small size of many of the neighborhood parks, they are represented simply as point locations. The locations of all the parks represented in the HVM Model are shown in Figure 3.

The habitat classifications for rivers and washes were originally defined and identified by Shaw et al.

(1986).

This information was then updated with 1990 aerial photographs and transferred to a GIS format by the Pima County EGIS department. Figure 4 shows the geographical extent of these habitat classifications.

11

EGIS does not guarantee it's data to be of 'engineering quality'

(i.

e. for use in very detailed engineering and construction projects), but i t is considered to be sufficient for this research.

• a

Coronado National Forest

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Saluaro

Na ional

Jlonument

East

NATP~S llillililililililill

W~

• oo..F

W~S

• source: Shultz 1992. EGIS 1991

Figure 3. Natural Resource Areas, Parks, and Golf Courses in

~ucson e

Coronado National Forest

"\.....

\

-

Saguaro

National

Monument

East

"

~

"~~

~

..

12SZ1

HabiloL II source: Shaw 1986, EGIS 1991

Figure 4. River/Wash Habitat Classifications in the Tucson Urban Area

tf:-

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43

Land Use Variables.

The non-residential land use variables included in the

Benchmark Model are: the percentage of commercial (COM%)

I

industrial (IND%), and vacant (VAC%) land uses occurring in the block group in which a census block is located. These variables were calculated by dividing the acreage associated with industrial, commercial, and vacant land used uses by the total acreage of a block group.

12

It should be noted that the vacant land use variable (VAC%) does not include any of the land area associated with the open space amenities. All of the land use data was obtained from the City of Tucson

Planning Department.

The land use data is a9gregated at the block group level of geography because the variation in industrial, commercial, and vacant land uses occurring at the block level of analysis is very low, and the assumption that housing values are influenced as much by land uses occurring in nearby, adjacent, and/or opposite blocks, as by the land uses in an individual block. Each of the three non-residential land use variables is hypothesized to have a negative relationship with housing value.

12Non-structural and structural industrial land uses were combined into the category IND%, and general commercial development, major office buildings, and shopping center land uses were combined into the category COM%. A more detailed description of this land use data is included in Appendix C.

44

Structural Housing Variables.

Structural housing variables (Zs)' include the number of household rooms per census block (ROOMS), and the density of single family homes in a census block (SFD).

The SFD variable was calculated by dividing the number of single family units in a census block by the total area of the census block that is devoted to single-family uses. This data also was obtained from the City of Tucson Planning

Department.

13

SFD is a proxy for the size of homes/lots within a census tract, and is therefore expected to be negatively related to property values. More specifically, census blocks with low SFD values (large home/lot sizes) are expected to have higher housing values than do otherwise similar blocks with high SFD values (small home/lot sizes).

Conversely, ROOMS is expected to have a positive relationship with housing values.

Neighborhood Variables.

Neighborhood variables are represented by the density of all residential (self-owned and rental) units in a census block (RDEN), and a set of dummy variables representing 12 hypothesized market segments in the TUA (Sl to S12).

13Single-family and single-ranch household unit and land areas categories were combined to the category 'Single-family'.

45

RDEN was calculated by dividing the number of residential units (both self-owned homes and rentals) in a census block, by the total acreage of the block. The acreage used to calculate RDEN did not include any of the area associated with the open space amenities. The number of residential units was obtained from file STF-1A of the census, while the block acreage data was obtained from the City of Tucson Planning

Department.

RDEN is hypothesized to be negatively related with housing value.

The twelve market segments used in the study are portrayed in Figure 5. These market segments are derived from the fifteen economic districts identified by the Drachman

Institute (Worden and DeKok, 1992) on the basis of: historically distinct neighborhoods, physical infrastructure boundaries (roads , political constituencies, and physical features), and the constraint that market segments are comprised of contiguous census tracts.

The Drachman Institute uses these same economic districts to analyze structural changes in the Tucson real estate market.

The fifteen original economic districts were reduced to

12 because only small portions of three of the districts

(Marana-Avra Valley, Oro Valley-Catalina, and SouthEast), were within the study area.

All of the variables incorporated in the specification of the benchmark HVM Model are summarized in Table 3

SlIgtI"fI

Nalml

lIonumm'

Jest

8o.Jlh

Coronado

National

fansl

Norlt-Easl

S(J~fO

National

Monument

lad source: Worden

&

Dekok 1991

,f>. m

Figure S. Housing Market Segments in the Tucson Urban Area

Variable

HVAL

ROOMS

SFD

BPKS

UPKS

RDPKS

NPKS

GOLF

PGOLF

HABI

HAB2

IND%

COM%

VAC%

RDEN

SEG

Table 3. Variables Included in the HVM Study

Description

Self-reported horne values and capitalized monthly rents

Mean number of rooms per household

Single-family homes per acre single-family land

Distance to large undeveloped natural resource parks

Distance to small undeveloped parks

Distance to developed regional parks

Distance to developed neighborhood and schoolyard parks

Distance to public golf courses

Distance to private golf courses

Distance to open spaces designated as class I habitat

Distance to open spaces designated as class II habitat

Percentage of industrial land uses in block groups

Percentage of commercial land uses in block groups

Percentage of vacant lands in block groups

Number of residential units per acre of land

Dummv variable indicatina market searnent a block is in

units

$

#

#/acre

0~10 miles

0.10 miles

0.10 miles

0.10 miles

0.10 miles

0.10 miles

0.10 miles

0.10 miles

%

%

%

#/acre

1/0

~

-...J

48

Functional Form.

The semi-log functional form is adopted for all of the open-space (proximity) variables in order to allow for their expected patterns of decreasing marginal implicit prices.

This is consistent with HVM theory and more specifically, the distance decay functions associated with these types of amenities (Halvorsen and Pollakowski, 1981).

A linear specification is adopted for the remaining explanatory variables that represent categorical, density, and percentage data. Therefore, the following general benchmark

HVM Model is specified:

( 6 )

Y

=

Bo + B· X· + B· I n X·

1 1

J J

Where:

Xi are dummy, density and percentage variables and, Xj are amenity (proximity) variables

While the specific Benchmark Model is:

(7)

HV

=

Bo + B1ROOMS + B2SFD + B3MFD + B4MHD + Bs IND% + B6

COM% + B7 VAC% + Bs InBPKS + B9 InRDPKS + B10 InUPKS

+ B11 InNPKS + B12 InGOLF + B13 InPGOLF + B14 InHAB1

+ B1S InHAB2 + B16Seg1 ... B24Segs

49

Alternative Model Specifications

To determine the effect(s) of excluding rental values from an HVM model, the results of Model

1

(which has the capitalized rental values removed from the dependent variable), are compared with those of the Benchmark Model.

Two results of two alternative model specifications

(Models 2 and 3) are also compared to the Benchmark Model in order to determine the presence and effect of specification bias, or more specifically, how the exclusion of particular explanatory variables changes the robustness of HVM estimates .

. Model 2 is the Benchmark Model with the land use variables

(IND%,COM%, and VAC%) removed. It is expected that omitting these non-residential land use variables will reduce the robustness of the HVM estimates of the remaining open space amenity variables. Model 3 is the Benchmark specification with the open space amenity variables removed. Similarly, i t is expected that the robustness of the HVM estimates of the remaining land use variables are decreased.

The results of two alternative specifications (Models

4 and 5) with land uses variables (IND%, COM%, and VAC%) aggregated at the block and tract levels of census geography, are compared to those of the Benchmark Model aggregated at the block group level.

14

14WJ.' thJ.' n th d

0 f h h blocks, 505 block groups, and 107 census tracts.

627

7 census

50

It should be noted that the overall unit of analysis for all of the alternative model specifications is still the census block. More specifically, the land use variables are defined as the proportion of a particular land use (IND%,

COM%, or VAC%) occurring in the block, block group, or the tract that a particular census block is located in.

Finally, three alternative model specifications are estimated in order to determine the effect (s) of smaller sample sizes on HVM estimates. Models 6, 7, and 8 are the benchmark specification with successively reduced sample sizes of 3000, 1500, and 500 respectively. These smaller sample sizes were obtained by taking random samples of approximately

50%, 25%, and 8.5% in each of the twelve housing market segments. The geographical distribution of the census blocks in each of these three samples are shown in Figures 6, 7, and

8.

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Figure 8. Centroid Locations of the Sample of 500 Census Blocks

U1 w

54

Comparing the Benchmark Model with Alternative Specifications

HVM estimates are defined as being robust if their statistical and economic measures remain stable when the potential specification biases, alternative aggregation levels, and the use of samples of census blocks are imposed on the Benchmark Model (i.e. the specification of alternative models). For the purposes of this study, the robustness of

HVM estimates is evaluated only in reference to the open space amenity, and non-residential land use variables.

Statistical robustness measures that evaluated and compared include: adjusted

R2 values 15, F-tests, the magnitude of change in the standard errors on the coefficients of the explanatory variables, and t-tests determining the statistical significance of particular explanatory variables.

F-tests are also performed in order to determine if the coefficients of the alternative models are significantly different from the corresponding parameters in the Benchmark

Model. The null hypothesis of such an F-test is that the parameters of the Benchmark Model are jointly equal to the corresponding coefficients of alternative specifications. The appropriate F-statistic for comparing the Benchmark Model with

Models 2 and 3 having open space amenity and land use

15Adjusted

R2 values are able to account for the effect of unequal variable numbers and sample sizes in alternative model specifications.

55 variables removed, is:

( 8 )

Where: ESS UR is the sum of error sum of squares of the

Benchmark and the Alternative Model specifications (the

Unrestricted Model) and, ESS R is the error sum of squares resulting from fitting both Models with a common set of coefficients (the

Restricted Model)

The appropriate F-statistic for all of the other alternative model specifications which contain the same number of explanatory variables as the Benchmark Model is:

( 9 )

ESSUR/(N

+

M 2k)

Where: ESS R is the error sum of squares of an Alternative

Model specification (Restricted Model)

ESS UR is the sum of the error sum of squares of the

Benchmark and Alternative Models (Unrestricted Model) k is the number of restrictions and, N

+

M - 2k is the sum of the number of degrees of freedom in the two Models

Economic robustness measures include: a quantitative assessment of the magnitude and change of the equilibrium marginal implicit price estimates (MIP's) for particular open

56 space and land use variables, and a qualitative assessment of elasticities (E yx )' which are used to rank the relative importance that particular explanatory variables have on the dependent variable.

16

For linear variables, MIP' s are obtained from equation 10 which solves the derivative of the estimated implicit price function with respect to the variable in question.

(10)

aP

MIP(X.) = - = B ·

~

aX·

~

~ where:

Ph

X;

B;

=

=

= implicit price function ith amenity being valued the coefficient for the amenity

For the semi-log variables (open space amenities), equation 11 is used to calculate MIP's:

( 11) where:

Ph

X;

B;

= implicit price function

= ith amenity being valued

= the coefficient for the amenity

16

Beta Coefficients for comparing the relative importance of explanatory variables were not adopted because of the fact that Standard Deviations are difficult to interpret with these particular variables.

57

Elasticities

(E~) represent the percentage change in the dependent variable (Y) associated with a one percent change in an explanatory variable (Xi). Such elasticities represent the relative importance of different explanatory variables and because they are unitless, can be ranked, they allow different types of explanatory variables to be ranked in order of their relative influence housing values.

Equation 12 is used to calculate the elasticities of linear variables, while equation 13 is used with semi-log variables. In both cases, the calculations are made at the means of the variables.

(12)

(13)

Where: EYXi

= the housing value elasticity for an amenity

Xi

= the quantity level of an amenity

B; = the coefficient of an amenity

Y

= the mean housing value

X

= the mean level of an amenity

58

Chapter 3: Results and Discussion

Descriptive Statistics

The median value of capitalized rents is $43,415, the median value of self-owned homes is $76,877, and the weighted mean of all housing values is $73,088. The means and standard deviations of housing values and all the explanatory variables

(except for the market segments) are presented in Table 4.

Table 4: Summary Statistics

Variable

HVAL

($)

ROOMS

(#/home)

SFD

(#/SF acre)

IND%

(%/acres)*

COM%

(%/acres)*

VAC%

(%/ acres)*

NRAS

(.10 miles)

Mean S.D.

73088 49064

3.38

3.47

1.46

1.42

16.67

43.28

4.69

2.37

4.82

3.90

17.58

17.62

Quantity Present

59089 acres

3515 IND acres

6382 COM acres

7016 VAC acres

3 areas/74303 acres*

UPKS

(.10 miles)

RDPKS

(.10 miles)

23.29

12.85

12.08

8.14

20 parks/2282 acres

25 Parks/1786 acres

NPKS

PGOLF

(.10 miles)

GOLF

(.10 miles)

(.10 miles)

HABl

(.10 miles)

11.17 12.32

25.89

12.85

17.23

38.97 20.87

8.14

78 Parks**

7 Courses/982 acres

8 Courses/1230 acres

204 miles/23309 acres

HAB2

(.10 miles) 7.36 5.48 563 miles/11720 acres

* A County park, a National Monument, and a National Forest

** NPKS are represented only point locations

59

The Coronado National Forest, the Saguaro National

Monument, and the Tucson Mountain Park (together represented by the variable NRAS), are considerably larger (in terms of total acreage) than any of the other open space amenities in the TUA. However, neighborhood parks (NPKS) occur the most frequently and along with Regional/District parks (RDPKS) are within the closest proximity to residential census blocks.

Class II river/wash habitat (HAB2) traverses a greater distance of the study area than does Class I habitat (HAB1), but the total HAB2 acreage is slightly less than half of the

HAB1 acreage.

Descriptive statistics for the land use variables (IND%,

COM%, VAC%) are also summarized in Table 4 and broken down by market segments in Figure 9. The percentage of vacant land uses (VAC%) are larger than industrial and commercial land uses in all of the market segments, and there are some large discrepancies in the percentage of industrial and commercial land uses among several of the market segments.

Among the structural housing variables, the average number of household rooms in the study area is 3.39 with a standard deviation of 4.69. The number of single-family homes per acre of single family land (which is a proxy for the size of single family lots and homes), has a mean of 3.47 and a standard deviation of 2.37. This variable also is broken down by market segments in Figure 10.

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62

Among the neighborhood variables, the mean residential density of both rental and self-owned units, is 3.79 with a standard deviation of 3.46. As shown by Table 5 and Figure

10, housing values and residential density levels vary considerably throughout the TUA.

Table 5. Housing Values by

Market Segments

Market Segment

1) West

2) Northwest

3) Catal. Foothills

4) Northeast

5) Far East

6) Near East

7) South Tucson

8) Southwest

9 ) South Central

10) North Central

11) University

12) Flowing Wells

Study Area

Blocks

Housing Values

208 $82,051

382

398

264

501

456

1025

379

741

697

617

609

6277

$95,638

$163,313

$141,997

$89,114

$68,110

$41,204

$61,577

$71,687

$59,692

$62,310

$46,506

$73,088

Finally, the correlation coefficients for the explanatory variables are summarized in Table 6. These correlations are generally low with the exception of the relationships between neighborhood parks (NPKS) and most of the other open space amenity variables. This may be due to the fact that the

63 numerous NPKS are in close proximity to many of these other variables. Also, the percentage of vacant lands occurring in census block groups (VAC%) is strongly negatively correlated with large natural resource areas (NRAS) because of the fact that much of the vacant land in the TUA is immediately adjacent to the natural resource areas on the outskirts of the

TUA.

Table 6. Correlations Among Selected Explanatory Variables

-

I

I hvaL rooms sfd Lnras Lupks Lrdpks Lnpks

--------+---------------------------------------------------------------

hvaq 1.0000 rooms: 0.1218 1.0000 sfd: -0.3347 -0.0536 1.0000

Lnras: -0.3265 -0.0832

0.2957 1.0000

Lupks: 0.1728 -0.0476 -0.0109 0.2274 1.0000

Lrdpks: 0.2902 0.0247 -0.2456 -0.3540 -0.0676 1.0000

Lnpks:

0.4873 0.0195 -0.4036 -0.5231 0.1315 0.3354 1.0000

LgoLf:

0.0335 0.0101 -0.0783 -0.3912 -0.2170 0.3502 0.2759

LpgoLf: -0.4522 0.0633 0.2904 0.2701 -0.3342 -0.3006 -0.4514

Lhab1:

-0.3257 -0.0172 0.3155 0.4888 0.1361 -0.1903 -0.4104

Lhab2: -0.2797 -0.0512

0.2636 0.3633 0.1032 -0.1924 -0.3545 indp: -0.1938

0.1411 0.0933 0.0390 -0.1343 -0.1136 -0.1425 comp: -0.0028 -0.0146 0.0074 0.1660

0.0992 -0.0579 -0.0551 vacp: 0.1602 0.1111 -0.2256 -0.4940 -0.2771 0.2508

0.3263 rden: -0.3357 -0.2325

0.0648 0.1723 0.0082 -0.1530 -0.1889

: LgoLf LpgoLf Lhab1 Lhab2 indp comp vacp

--------+---------------------------------------------------------------

LgoL f: 1.0000

LpgoLf: -0.0573

Lhab1: -0.0753

Lhab2: -0.1293 indp: -0.0624 comp: -0.1285 vacp: 0.3432 rden: -0.0881

1.0000

0.3780

0.1218

0.2401

-0.0501

-0.0831

0.0891

1.0000

0.3099

0.0260

0.0437

-0.3365

0.1382

1.0000

0.0171

0.0886

-0.3371

0.1067

1.0000

-0.0588 1.0000

0.1113 -0.1450 1.0000

0.0140 0.0594 -0.1649

64

The Benchmark Model

As shown in Table 7, the R2 and adjusted R2 values for the

Benchmark Model, which represents the entire population of residential census blocks in the TUA, are 0.53 and 0.52 respectively.

Empirically, the F-statistic for this Model is significantly different from zero, meaning that the explanatory variables explain a significant amount of the total variation in housing values. Similarly, all of the

Benchmark Model coefficients are statistically significant at the 100% confidence level except for RDPKS (which is significant at the 90% level), and the South Tucson market segment.

These two variables are insignificant because they do not have a substantial effect in influencing housing values. Therefore, their reported standard errors do not represent sampling error variation, but rather standard deviations around their respective means.

The signs of most of the coefficients are consistent with the a priori hypotheses. Exceptions are class I habitat

(HAB1) and undeveloped parks (UPKS) which are both negatively related to housing values. A possible explanation for HAB1 being negatively related to property values is that self-owned homes located in very close proximity to class I rivers and washes are in a potential flood plain and have a less scenic view than otherwise similar neighboring homes.

6546

1556

5984

16885

4806

17156

111238

75

-2745

10050

20718

77526

58655

12421

Coefficient

828

-1500

-2795

3862

1014

5102

-6297

-10157

1351

-2539

-678

427

Variable

ROOMS

SFSIZE

LNRAS

LUPKS

LROPKS

LNPKS

LGOLF

LPGOLF

LHAB1

LHAB2

INOP

COMP

VACP

ROEN

SEG1

SEG2

SEG3

SEG4

SEG5

SEG6

SEG7

SEG8

SEG9

SEGlO

SEG11

CONSTANT

Table 7. Regression Output: Benchmark Model

5

F

.:stat

= 275.8 (prob.

>

F = 0)

R2 = 052 AR2= 052

Prob

> t

0.00

0.02

0.00

0.04

0.00

0.02

0.00

0.00

0.00

0.00

0.00

0.00

0.01

0.44

0.00

0.03

0.00

0.01

0.00

0.01

0.00

0.00

0.09

0.00

0.00

0.00

0.8

2.0

82

23

82

16.4

-20.6

3.0

7.7

26.0

175

4.8

2.7

T-Stat

8.6

-72

-2.4

4.1

1.7

7.6

-7.6

-11.6

25

-53

-6.9

3.7

22

2679

2977

3356

2577

2467

2031

2959

2071

2076

2090

6795

Std. Error

96

209

1176

879

549

476

99

115

947

592

673

827

34

133

3352

65

66

The marginal implicit price (MIP) and elasticity (E~) estimates of the Benchmark Model are shown in Table 8. MIP's measure the effect that a one unit change in the quantity of an explanatory variable has on housing values. For example, increasing the mean number of rooms per household by one while holding all other variables constant at their means, increases mean housing values by $828. Similarly, if the distance from census blocks centroids to natural resource areas (NRAS) is increased by a tenth of a mile, mean housing values are decreased by $770, while an equivalent change in the distance away from undeveloped parks (UPKS) increases mean housing values by $1,296.

The MIP's are highest among the twelve market segments, followed by the housing density variables (SFD and RDEN) , open space amenities, and non-residential land uses. However, direct comparison of the MIP's of different amenities is of limited relevance as their MIP's may be based upon different units of analysis.

In contrast, elasticities (E yx )' measuring the percentage change in the dependent variable associated with the percentage change in an explanatory variable are unitless and better suited to compare the relative effect(s) and relative importance of individual explanatory variables.

By ranking the magnitude of the elasticities in Table 8, i t is apparent that the neighborhood market segments (S1 to

67

S12) have the greatest relative influence on housing values.

This is a result of the fact that the market segments account for a great deal of the variation in housing values. However, because the specific nature and role of market segments is not the primary methodological focuses of this present research, no further comparisons and/or discussions of market segments will be made.

After the market segments, the variables with the highest relative rankings are: residential density (RDEN), golf courses (PGOLF, and GOLF), and the proxy variable for the size of single family lots and homes (SFD). The remaining open space amenity variables have relative importance rankings between 14 and 21, while the land use variables (IND%, COM%, and VAC%) have the lowest ranks and hence the smallest relative influence on housing values.

Among the open space amenity variables, public and private golf courses (PGOLF and GOLF), natural resource areas

(NRAS) , undeveloped parks (UPKS), and neighborhood parks

(NPKS), have the greatest relative influence on housing values.

68

Table 8. Benchmark Marginal Implicit Prices and Elasticities

Variable (units)

ROOMS (#)

SFD (# SF homes per SF acre)

NRAS (prox. in .10 miles)

UPKS (prox. in .10 miles)

RDPKS (prox. in .10 miles)

NPKS (prox. in .10 miles)

GOLF (Prox. in .10 miles)

PGOLF (prox. in .10 miles)

HAB1 (prox. in .10 miles)

HAB2 (prox. in .10 miles)

IND% (% IND land use in BG)

COM% (% COM land use in BG)

V AC% (% V AC land use in BG)

RDEN (residential density)

Sl (West (1/0»

S2 (NorthWest (1/0»

S3 (Catalina Foothilks (1/0»

S4 (NorthEast (1/0»

S5 (Far East (1/0»

S6 (Near East (1/0»

S7 (South Tucson (1/0»

S8 (SouthWest (1/0»

S9 (South Central (1/0»

S10 (North Central (1/0»

Sl1 (University (1/0»

S12 (Flowing Wells (1/0»'" l e regressIOn equatIOn

EYX

0.038

-0.071

0.038

-0.053

-0.014

-0.070

0.086

0.139

-0.018

0.035

-0.013

0.008

0.017

-0.142

0.049

0.106

0.151

0.085

0.124

0.106

0.025

0.094

0205

0.174

0.167

0.145

427

75

-2,745

121,288

131,956

188,764

169,893

2,092

2,953

-615

1,587

-678

123,659

117,784

112,794

117,222

128,123

116,044

128,394

111,238

MIP($)

828

-1,500

770

-1,296

-463

-2,616

69

Among the land use variables, vacant land uses have a greater relative effect on housing values than do industrial or commercial land uses.

Finally, figures 11 to 21 portray the marginal implicit price functions for each of the explanatory variables in the

Benchmark Model, ceteris paribus. Each of these graphs illustrate the direction of a variable's influence on housing values (i.e. an upward or downward sloping MIP curve), the magnitude of MIP' s, and the underlying functional form of these relationships

(i.

e. constant or decreasing marginal effects). For example, explanatory variables not having a strong influence on housing value are characterized by flat and/or short MIP functions. Conversely, those variables having a large influence on housing values have steep and/or long MIP functions.

70

80000

III

<lJ

:l

<1l

>

01 c:

U;

:l

0

J:

40000

0

0 30 _

Single-FamIly Umts per Acre SF Land

60

Figure 11. Housing Value Function for Single-Family Density

80000

<lJ

:l

';ij

>

01 c:

U;

:l o

J:

40000 o o

30 nesldentlal Un! ts per Acre

60

Figure 12. Housing Value Function for Multiple-Family

Density

90000

Iil

OJ

~

<U

> en

S

U1

;J a

I

70000

"-"'-,,-

"'"

"",-

'.

""~,

'"

50000 o

I

44

r.

Industrlal Land Uses In a BG

BB

Figure 13. Housing Value Function for Industrial Land Uses

71

Iil

OJ

;J

-;;;

> g' 70000

U1

;J a

I

50000 o

%

44

CommercIal Land Uses In a BG

BB

Figure 14. Housing Value Function for Commercial Land Uses

90000 ttl

OJ

"

"'

>

c

U1

"

70000

50000 o

~

I

44

Vacant

Land Uses

In a 8G

I

88

Figure 15. Housing Value Function for Vacant Lands

72

150000

Ifl

<lJ

>

Cl

" j

100000

" - -

----------------

50000 a

50 wlstance to NRAS m .10 mlles

100

Figure 16. Housing Value Function for Natural Resource Areas

73

150000

Ifl

<lJ

"

>

Cl

"

"'

::::

100000

50000 o

50

Dlstance to UPKS In .10 mlles

100

Figu~e

17. Housing Value Function for Undeveloped Parks

74

150000 ttl

'"

';;j

>

0> c:

<11

::l o

:I:

100000

50000 a

50

DIstance to RDPKS In .lD mIles

100

Figure 18. Housing Value Function for Regional/District Parks

150000

'"

';;j

>

0> c:

<11

:l o

:I:

100000-

50000

~------------------'I------------------'I a

50

DIstance to NPKS In .10 mIles

100

Figure 19. Housing Value Function for Neighborhood Parks

150000

If)

'"

';ii

>

Cl

C

<II

:J

:r:

100000

50000 o

50

Distance to GOLF

In

.10 miles

I

100

Figure 20. Housing Value Function for Public Golf Courses

75

150000

!It

'"

'"

>

Cl c:

<Il

:J a

:r:

100000

50000 o

50

Distance to

PGOLF

In .10 mlles

100

Figure 21. Housing Value Function for Private Golf Courses

76

150000

If)

QJ

::> m

>

Cl c

U;

::> a

:x:

100000

50000 a

50

Distance to

HASI in .10 mIles

100

Figure 22. Housing Value Function for Class I Rivers/Washes

150000

III

'"

It!

> 100000

Cl

S en

::> a

I

50000 a

50

DIstance to HAS2 In 10 mIles

100

Figure 23. Housing Value Function for Class II Rivers/Washes

77

The results of this Benchmark Model are very similar to the earlier findings of King et ale (1991). Both studies indicate that natural resource areas (NRAS) , class II river/wash habitats (HAB2), and golf courses (GOLF and PGOLF) have a significant positive relationship with housing value, while other open space amenities as well as residential housing density (RDEN) have a negative relationship with housing value.

Differences between the two Models are minor: HAB1 is insignificant only in King et al., and RDPKS is insignificant

(above the 95% confidence level) in the present study.

Further comparisons are not possible as the two studies are based on different units of analyses and sampling strategies.

The results of the Benchmark HVM Model differ greatly from those of Cao and Cory (1981). This earlier HVM study concluded that non-single family land uses did not negatively influence housing values. In contrast, the present benchmark

HVM Model indicates that industrial land uses (IND%) have a statistically significant negative influence on housing value while commercial and vacant land uses (COM% and VAC%) have statistically significant positive relationships with housing value. These dissimilarities may be attributed to specification biases or the use of census tracts rather than blocks as the unit of analysis. These issues will be examined in further detail with the estimation of alternative models.

78

Model 1: Rental Housing Values Excluded

Model 1 is characterized by the removal of capitalized rental values from the dependent variable (housing values).

It is otherwise identical to the Benchmark specification.

As shown by the regression output in Table 9, Modell has an adjusted R2 value of 0.44 which is quite a bit lower than the adjusted R2 value of Benchmark Model (0.52). However, the

F-statistic in both Models is significantly different from zero. The Benchmark Model therefore does a better job in explaining the variation in housing value yet Model 2 with rental values excluded still explains a significant amount of the total variation in housing values.

This rental value exclusion Model also has two additional variables (NRAS and VAC%) that are statistically insignificant at the 95% confidence level.

The F-statistic used to test the hypothesis that the coefficients of Model 1 are jointly equal to the corresponding parameters of Benchmark Model is 190, which exceeds the critical F-value at the 5% significance level. Therefore, the exclusion of rental values does change the coefficients of the explanatory variables of the Benchmark Model.

79

Table 9. Regression Output: Model 1 (Rental Values Excluded)

Coefficient

444

-991

-2551

2492

1094

5288

-6653

-9859

1842

-3030

-805

418

40

-3045

6658

18689

80819

60586

11220

3295

-42

2128

15563

7555

21483

119088

Variable

ROOMS

SFSIZE

LNRAS

LUPKS

LRDPKS

LNPKS

LGOLF

LPGOLF

LHAB1

LHAB2

INDP

COMP

VACP

RDEN

SEG1

SEG2

SEG3

SEG4

SEG5

SEG6

SEG7

SEG8

SEG9

SEG10

SEG11

CONSTANT

F -Stat = 1995 (prob. > F = 0)

R2 = 0.44 AR2= 0.44

Std. Error T-Stat

114 3.9

247

1389

1119

-4.0

-1.8

2.2

700

795

977

1039

648

562

116

136

40

157

3960

3165

3517

2.8

-5.4

-6.9

3.1

1.6

6.7

-6.8

-95

1.0

-19.4

1.7

5.9

23.0

3965

3044

2915

2399

3496

2447

2452

2470

8027

153

3.7

1.1

0.1

0.6

6.4

3.1

8.7

14.8

Prob

> t

0.00

0.00

0.00

0.26

0.99

054

0.00

0.01

0.00

0.00

032

0.01

0.09

0.00

0.00

0.00

0.07

0.00

0.01

0.00

0.00

0.01

0.03

0.12

0.00

0.00

80

As shown by Table 10, the differences the MIP estimates of Modell differ from those of the Benchmark Model. In fact, three out of ten of the MIP estimates for the open space amenity and land use variables differ by more than 30%. In most cases, the MIP's of the Benchmark Model are smaller than those of Modell. Finally, the elasticity rankings also shown in Table 10, indicate that more than half of the relative importance rankings in the two Models differ.

To summarize, HVM estimates of the open space amenity and land use variables do not remain robust when rental housing values are excluded from the dependent variable representing housing values. This confirms the existence of rental value exclusion bias when the objective of an HVM study is to obtain valuation estimates representing the entire housing market and/or all of the residents within a study area.

Table 10. Marginal Implicit Prices and Elasticities of the

Benchmark and Model 1 (Rental Values Excluded)

Variable MIP

Benchmarl{

MIP Modell Change EYX/Rank

Benchmark

EYX/Rank

Modell

81

NRAS

UPKS

RDPKS

NPKS

GOLF

PGOLF

HABI

HAB2

IND%

COM%

VAC%

770

-1,296

463

-2,616

2,092

2,953

-615

1,587

-678

427

75

701

-836

-500

-2,712

2,210

2,866

-841

1,894

-80

418

40

- 9 %

-35 %

8%

4%

6%

- 3 %

37 %

19 %

19 %

-2%

-47 %

0.038 (5)

-0.053 (4)

-0.014 (9)

-0.070 (3)

0.086 (2)

0.139 (1)

-0.018 (7)

0.035 (6)

-0.013 (10)

0.008 (11)

0.017 (8)

0.035 (5)

-0.034 (6)

-0.015 (9)

-0.072 (3)

0.091 (2)

0.135 (1)

-0.025 (7)

0.042 (4)

-0.016 (8)

0.008 (11)

0.009 (10)

82

Model 2: Land Use Variables Omitted

As shown by the regression results in Table 11, Model 2, of 0.52 which is identical to the Benchmark Model.

The Fstatistic also is significantly different from zero in both

Models.

The F-statistic used for comparing the joint equality of the coefficients of Model 2 to those in the Benchmark Model is

0.28, which does not exceed the critical F-value at the 95% confidence level. Therefore, the exclusion of the land use variables does not result in a significant change in the coefficients of the remaining variables.

Table 12 shows that the differences in the standard errors of individual regression coefficients between the benchmark and Model 2 are very small (all less that 0.1%).

Similarly, there is no difference in the number of the statistically significant variables (at the 95% confidence level) in each of the two Models.

From an economic standpoint, as shown by Table 13, the magnitude of all the MIP's in both the benchmark and Model 2 are very similar. The only variables experiencing any change associated with the exclusion of land use variables are: GOLF

(8%), HAB1 (7%), and UPKS (6%). Finally, Table 14 shows that the elasticities and relative importance rankings of the variables are identical between the two Models.

83

Table 11. Regression Output: Model 2 (No Land Use Variables)

ee

'4 e

AiM

F -Stat = 307.4 (prob. > F = 0)

R2 = 052 AR2= 052

Variable

ROOMS

SFSIZE

LNRAS

LUPKS

LRDPKS

LNPKS

LGOLF

LPGOLF

LHAB1

LHAB2

RDEN

SEG1

SEG2

SEG3

SEG4

SEG5

SEG6

SEG7

SEG8

SEG9

SEG10

SEGll

CONSTANT

Coefficient

771

-1558

-2710

4080

1010

5165

-5817

-10343

1448

-2553

-2747

14381

23412

80181

61706

15162

8609

1433

9454

18597

7542

18265

108633

45

8.8

27.1

18.6

6.0

35

0.7

3.4

9.1

3.7

8.8

16.0

T-Stat

8.1

-7.4

-23

43

1.7

6.7

-7.0

-11.7

2.6

-5.4

-20.6

Std. Error

96

210

1180

951

595

675

827

883

549

476

134

3231

2660

2955

3315

2548

2446

2015

2822

2054

2038

2066

6779

Prob

> t

0.00

0.00

0.02

0.00

0.00

0.00

0.48

0.00

0.00

0.00

0.00

0.00

0.00

0.01

0.00

0.00

0.00

0.09

0.00

0.00

0.00

0.00

0.00

84

Table 12. Standard Errors of the Coefficients: Benchmark and

Model 2 (Land Use Variables Omitted)

Variable Benchmark Model 1 Change

NRAS

UPKS

RDPKS

NPKS

GOLF

PGOLF

HAB1

HAB2

1,176

947

592

673

827

879

549

476

1,180

950

595

675

827

883

549

476

0.1 %

0.1 %

0.1 %

0.1 %

0.0 %

0.1 %

0.0 %

0.0 %

Table 13. Marginal Implicit Prices: Benchmark and Model

2

(Land Use Variables Omitted)

Variable Benchmark Model Model 1

NRA

UPKS

RDPKS

NPKS

GOLF

PGOLF

HAB1

HAB2

770

1,296

463

2,616

2,092

2,953

-

615

1,587

745

-1,369

-461

-2,649

1,933

3,007

-658

1,596

Change

-5%

6%

-0.1%

-0.1%

-8%

2%

7%

0.1%

85

Table 14. Housing Value Elasticities: Benchmark and Model 2

(Land Use Variables Omitted)

Variable

NRAS

UPKS

RDPKS

NPKS

GOLF

PGOLF

HAB1

HAB2

Benchmark Model

EYX and Rank

0.038 ( 5 )

0.053 (4 )

0.014 (8 )

0.070 (3)

0.086 (2 )

0.139 ( 1 )

0.018 (7 )

0.035 ( 6)

Model 2

EYX and Rank

0.037 ( 5 )

0.056 (4)

0.014 ( 8 )

0.071 ( 3 )

0.080 (2)

0.142 ( 1)

0.020 ( 7 )

0.035 ( 6 )

To summarize, the effect of removing non-residential land use variables from the Benchmark Model has a negligible effect on the statistical and economic robustness of open space amenity HVM estimates. Specification bias resulting from the exclusion of land use variables is not apparent.

86

Model 3: Open Space Amenity Variables Omitted

As shown by the regression results in Table 15, omitting the open space amenity variables from the Benchmark Model results in a slightly decreased adjusted

R2 value. The Fstatistic for Model 3 is significantly different from zero meaning that after omitting the open space amenity variables, the remaining explanatory variables still explain significant amount of the variation in housing values. a

The F-statistic used to compare the equality of coefficients of Model 3 with those of the Benchmark Model is

9.19, which exceeds the critical F-value at the 95% confidence level. Therefore, the exclusion of the open space amenity variables results in a significant change in the coefficients of the remaining variables.

87

Table 15. Regression Output: Model

3 (Open Space Amenity

Variables Omitted)

M

F -Stat = 3645 (prob.

>

F = 0)

R2 = 050 AR2= 050

Variable

ROOMS

SFSIZE

INDP

COMP

VACP

RDEN

SEG1

SEG2

SEG3

SEG4

SEG5

SEG6

SEG7

SEG8

SEG9

SEGIO

SEG11

CONSTANT

Coefficient

857

-2186

.(j63

18019

-8571

798

21066

10017

15852

506

114

-2836

19718

35269

99092

74245

33917

66846

Std. Error

98

209

100

118

34

2187

2204

1824

2566

1952

136

3051

2383

2427

2802

1995

2049

1938

65

14.8

40.8

265

155

82

4.7

T-Stat

8.7

-105

.(j.6

43

33

-20.8

03

10.8

5.0

7.7

345

Prob

> t

0.00

0.00

0.00

0.00

0.00

0.00

0.76

0.00

0.00

0.00

0.00

0.01

0.01

0.00

0.00

0.00

0.00

0.00

11IIIIIIII

The differences between the standard errors of the

Benchmark and 3rd Models is minimal (Table 16). Similarly, there are no differences in the number of statistically significant variables in each Model.

88

Table 16. Standard Errors of the Coefficients: Model 3 (Open

Space Amenities Omitted)

Variable

IND%

COM%

VAC%

Benchmark Model 3

99

115

33

100

118

34

Change

1.

0%

3.0%

3.0%

From an economic standpoint, as shown by table 17, the estimates for commercial and vacant land use percentages (COM% and VAC%) change considerably with the exclusion of the open space amenities (by 19% and 52% respectively), while the MIP for the percentage of industrial lands (IND%) remains relatively unchanged. However, the relative elasticity rankings (shown in table 18), are identical among the two

Models

Table 17. Marginal Implicit Prices: Benchmark and Model

3

(Open Space Amenity Variables Omitted)

Variable Benchmark Model

IND%

COM%

VAC%

-678

427

75

Model 2

-

663

506

114

Change

-2%

19%

52%

IND%

COM%

VAC%

Benchmark Model

EYX and Rank

-0.013 (3)

0.008 (4)

0.017 (2)

Model 2

EYX and Rank

0.013 (3)

0.010 (6)

0.026 2)

89

Table 18. Housing Value Elasticities: Benchmark and Model 3

(Open Space Amenity Variables Excluded)

Variable

To summarize, the removal of the open space amenity variables from the Benchmark Model does not effect either the statistical measures or the elasticities and relative importance rankings of the remaining land use variables.

However, the exclusion of these variables significantly change in the coefficients of the remaining explanatory variables.

And, the magnitude of the MIP's for two of the three land use variables do change considerably. Therefore, a limited yet potentially serious amount of specification bias is associated with excluding open space amenity variables from an HVM Model designed to estimate the relationship between housing value and non-residential land uses.

90

Models 4 and 5: Varied Levels of Land Use Aggregation

Model 4 with the three non-residential land use variables

(IND%, COM%, VAC%) aggregated at the block level of census geography has an adjusted

R2 of 0.52 which is identical to the adjusted R

2

,s of Model 5 (with land use variables aggregated at the census tract level of geography), as well as the

Benchmark Model (aggregated at the block group level).

The F-statistics of all three Models are significantly different from zero. Therefore, even with aggregation bias imposed, the explanatory variables still explain a significant amount of the variation in housing values.

The F-statistic use to test the joint equality of the coefficients of Model 4 and the Benchmark Model is 0.27 which does not exceed the F-critical value at the 95% confidence level. The corresponding F-statistic for Model 5 is 0.90 which does not exceed the F-critical value. Therefore, the aggregation of the land use variables by blocks and tracts does not result in a significant change in the coefficients of the Benchmark Model with land use variables aggregated by block groups.

The regression results of Models 4 and 5 (Tables 19 and

20) indicate that there are no substantial differences in the magnitude and standard errors of any of the open space amenity variables in the three HVM Models incorporating different levels of land use data aggregation.

91

Table

19.

Regression Output: Model 4 (Land Use Data Aggregated at the Block Level of Census Geography)

F

-Stat

=

275B

(prob.

>

F = 0)

R2 = 053 AR2= 052

-17472

-10310

-1010

-11577

-1533

128200

-2825

-5682

3523

60091

41484

4858

-11269

Coefficient

867

-1594

-2551

4273

929

5248

-5916

-10343

1384

-2567

-S50

-621

-1.1

RDEN

SEG1

SEG2

SEG3

SEG4

SEG5

SEG6

SEG7

SEG8

SEG9

SEGlO

SEG11

CONSTANT

Variable

ROOMS

SFSIZE

LNRAS

LUPKS

LRDPKS

LNPKS

LGOLF

LPGOLF

LHAB1

LHAB2

INDP

COMP

VACP

3567

2911

3262

3621

2663

2496

2105

3026

2128

2187

188

7207

Std. Error

97

208

1177

948

592

672

136

124

40

136

823

879

547

474

-62

-5.0

-0.1

-20.7

-1.6

12

18.4

115

-1.8

T-Stat

8.9

-7.6

-22

45

1.6

7B

-72

-11.8

25

-5.4

45

-S3

-3.4

-05

-53

-S2

17.8

Prob

> t

0.00

0.00

0.00

0.07

0.00

0.00

0.00

0.64

0.00

0.98

0.00

0.11

023

0.00

0.00

0.00

0.00

0.00

0.00

0.01

0.00

0.00

0.03

0.00

0.12

0.00

92

Table 20. Regression Output: Model 5 (Land Use Data Aggregated at the Tract Level of Census Geography)

@

COMP

VACP

RDEN

SEG1

SEG2

SEG3

SEG4

SEG5

SEG6

SEG7

SEG8

SEG9

SEGlO

SEG11

CONSTANT

Variable

ROOMS

SFSIZE

LNRAS

LUPKS

LRDPKS

LNPKS

LGOLF

LPGOLF

LHABI

LHAB2

INDP

F --Stat = 274.8 (Prob. > F = 0)

R2 = 052 AR2= 052

-02

-20.4

-2.1

0.7

16.7

10.1

-2.1

4.7

-52

-3.1

-02

-52

.fJ5

18.8

T-Stat

8.9

-7.1

-25

3.9

1.9

7.1

-83

-11.6

1.8

-5.4

-7.1

-2.1

Std. Error

96

210

1178

950

595

676

839

883

553

479

150

95

55

134

4245

3066

3478

3944

2818

2542

2568

3849

2156

2281

204

7278

Coefficient

860

-1490

-2937

3702

1108

4820

.fJ967

-10267

976

-2594

-1061

-197

9

-2725

-8805

2095

58212

40006

-5925

-12046

-13352

-11731

412

-11937

-1316

136857

Prob > t

0.00

0.00

0.87

0.00

0.04

0.49

0.00

0.00

0.04

0.00

0.00

0.01

0.85

0.00

0.00

0.00

0.00

0.00

0.08

0.00

0.00

0.04

0.01

0.00

0.06

0.00

93

Regarding land use data aggregation, as the level of aggregation increases (from blocks to block groups to tracts), the standard errors of the HVM estimates change over a range from 7% to 38% (table 21).

The percentage of vacant land variable (VAC%) is statistically significant at the 95% confidence level in the

Benchmark Model (block groups), yet insignificant at the block and tract levels of aggregation. The remaining land use variables (IND%, and COM%) are statistically significant at each level of land use aggregation. As these Models are based upon a complete population of census blocks, the occurrence of insignificant variables are not related to sampling errors but rather, simply indicate that a particular explanatory variable does not have a strong influence on housing values.

Table 21. Standard Errors of Coefficients for Alternative

Land Use Aggregations:

Variable

Change

IND%

COM%

VAC%

Model 4 Model B

(Block} (BGrouE}

136

124

40

99

115

34

Change Model

5

(Tract}

-27%

-7%

-15%

150

95

55

34%

-21%

38%

Table 22 portrays how the

MIP

I s of the land use variables change at extreme rates as aggregation levels change

(from 88% to 760%). Even the signs of MIP values change with

94 alternative aggregation levels: the percentage of commercial land uses (COM%) becomes positive in Model 4, and the percentage of vacant lands (VAC%) becomes positive in both

Model 4 and 5. The only moderate change in Marginal implicit prices associated with alternative aggregation levels, occurs with the percentage of industrial lands (IND%).

Table 22. Marginal Implicit Prices for Alternative Land Use

Aggregations.

Variable Change

IND%

COM%

VAC%

Model 4 Model B

(Block)

(BGrouE}

-849

-620

-1

-678

427

75

Change

Model 5

(Tract)

-20%

168%

760%

-1060

-197

9

56%

146%

-88%

Table 23 shows that the relative importance ran kings of the land use variables are virtually identical at the block level of aggregation, while at the block group level, the ranking order is completely reversed.

Table 23. Housing Value Elasticities for Alternative Land Use

Aggregations:

Variable

IND%

COM%

VAC%

Model 4

(Block)

0.005 ( 1 )

0.004 ( 2 )

0.001 ( 3 )

Model B

(BGrouE)

0.013 (2 )

0.008 ( 3 )

0.117 ( 1 )

Model 5

(Tract}

0.024 ( 1 )

0.019 (2)

0.002 ( 3 )

95

To summarize, the aggregation of land uses at different levels of census geography (blocks, block groups, and tracts) does not appear to significantly change the joint effect of the coefficients in the Benchmark Model. However, the robustness of HVM estimates for the three individual land use variables do seem to be effected by aggregation levels. More specifically, alternative land use data aggregation effected: the size of the standard errors of coefficients, levels of insignificance, the stability of MIP's, and the relative importance rankings of each of these individual land use variables.

Finally, i t should be noted that the most robust and stable HVM estimates of the coefficients of the land use variables occur in the Benchmark Model where the land use data is aggregated at the block group level. This result is clearly influenced by the specific land use and housing value patterns existing in the TUA. Therefore, i t is quite possible that alternative land use aggregation levels may be more appropriate for other study area locations.

96

Models 6, 7, and 8: Reduced Sample Sizes

The robustness of HVM estimates associated with the use of incrementally smaller sample sizes is evaluated by examining changes in the statistical and economic characteristics of Model specifications 6 (n=3000), 7

(n=lS00), and 8 (n=SOO). The regression results for each of these Models is contained in Tables 24, 2S, and 26.

The adjusted

R2 values for each of these three Models are very similar and the F-statistic of each Model is significantly different from zero. Therefore, even with reduced sample sizes, the explanatory variables still explain a significant amount of the variation in housing values.

The F-statistics of Models 6, 7, and 8 are used to test the hypothesis that their coefficients are jointly equal to those of the Benchmark Model. These F-statistics are: 180.2

(Model 6), 238.6 (Model 7), and 244.S (Model 8), all of which exceed the F-critical values at the 9S% confidence level.

Therefore, the use of sample sizes of 3000, lS00, and SOO census blocks results in HVM estimates that are significantly different than those obtained from a Benchmark Model based upon the population of 6277 census blocks.

-

SEG1

SEG2

SEG3

SEG4

SEG5

SEG6

SEG7

SEG8

SEG9

SEG10

SEG11

CONSTANT

Variable

ROOMS

SFSIZE

LNRAS

LUPKS

LRDPKS

LNPKS

LGOLF

LPGOLF

LHAB1

LHAB2

INDP

COMP

VACP

RDEN

-2449

5206

16038

4893

21124

116060

4764

21489

76615

55235

13639

4555

Coefficient

729

-1848

-3568

4422

1145

5138

-6934

-9904

198

-1527

-683

527

110

-2797

Table 24. Regression Output: Model 6 (n=3000)

M

F

~tat

=

130.1 (prob. > F = 0)

R2 = 052 AR2= 052

Std. Error T-Stat

145 5.0

330

1799

1447

869

10lD

1267

1299

-5.6

-2.0

3.1

13

5.1

-55

-7.6

794

733

146

-D3

-2.1

-4.7

3.1 173

50

194

22

-145

1.0

5.4

5041

3969

4423

4926

3794

3628

3021

173

112

3.6

13

0.8

12

4480

3050

3044

3081

10215

53

1.6

6.9

11.4

Prob

> t

0.00

0.00

035

0.00

0.00

0.00

0.00

021

0.42

025

0.00

0.10

0.00

0.00

0.80

0.04

0.00

0.00

0.03

0.00

0.05

0.00

0.19

0.00

0.00

0.00

97

Coefficient

992

-1994

-2477

5572

-343

4984

-6289

-5676

-766

-1."06

-869

625

-26

-2764

13317

28421

73989

70847

14811

7799

3534

14057

20425

4736

16227

96277

Table 25. Regression Output: Model

7

(n=1500) iM" 6H3 d iMM

3 hue" e&

M

F -Stat = 74.5 (Prob.

>

F

=

0)

R2 = 0.56 AR2= 0.55

Va~iable

ROOMS

SFSIZE

LNRAS

LUPKS

LRDPKS

LNPKS

LGOLF

LPGOLF

LHAB1

LHAB2

INDP

COMP

VACP

RDEN

SEGI

SEG2

SEG3

SEG4

SEG5

SEG6

SEG7

SEG8

SEG9

SEGlO

SEG11

CONSTANT

6300

5097

5762

6528

4900

4668

3893

5644

3951

3936

3925

12659

Std. Error

181

445

2276

1784

1123

1279

1558

1730

1038

893

201

217

63

284

Prob

> t

0.00

0.09

0.00

0.00

0.69

0.00

0.00

0.00

0.46

0.00

0.04

0.00

0.00

028

0.0

0.76

0.00

0.00

0.00

0.10

036

0.01

0.00

023

0.00

0.00

5.6

12.8

10.9

3.0

1.7

0.9

2.5

52

12

4.1

7.6

T-Stat

5.5

-4.5

-1.1

3.1

-0.7

-1.7

-43

2.9

-03

3.9

-4.0

-33

-0.4

-9.8

2.1

98

Coefficient

640

-2999

-1938

6330

-206

5787

-4900

-14213

2709

-2285

-1027

175

-116

-2944

17682

13154

60717

52059

16481

5611

8777

13402

21839

5091

23429

98465

Variable

ROOMS

SFSIZE

LogNRAS

LogUPKS

LogRDPKS

LogNPKS

LogGOLF

LogPGOLF

LogHAB1

LogHAB2

INDP

COMP

VACP

RDEN

SEG1

SEG2

SEG3

SEG4

SEG5

SEG6

SEG7

SEG8

SEG9

SEGlO

SEG11

CONSTANT

*HNfWM

M

frMA

F -Stat

=

745 (prob.

>

F = 0)

R2 = 056 AR2= 055

05

12

-53

1.7

15

6.1

-5.0

1.6

-1.7

-3.4

T-Stat

22

-3.9

-0.4

2.0

0.1

2.9

-1.8

5.0

2.0

0.8

15

1.4

35

0.8

3.8

4.1

Std. Error

289

776

4404

3099

2055

2022

344

100

555

10506

8684

9949

10455

2689

2867

1726

1314

299

8124

7422

6066

9444

6287

6322

6233

24377

Prob > t

0.03

0.00

0.66

0.04

0.09

0.13

0.00

0.00

0.08

0.00

0.61

024

0.00

0.92

0.00

0.07

0.00

0.12

0.00

0.42

0.00

0.00

0.04

0.45

0.15

0.16

99

100

As shown by Table 27, the standard errors of the coefficients in Model 6 differ from the standard errors of the

Benchmark Model by between 22% to 49%, with a mean of 46%.

The standard errors of Model 7 differ by an even greater amount (88% to 97%, with a mean of 91%). Finally, the standard errors of Model 8 are very high and extremely different from those of the Benchmark Model (176% to 274% with a mean of 217%).

Correspondingly, the number of statistically significant open space amenity and land use variables (at the 95% confidence level), decreases as sample sizes decrease. The

Benchmark Model has one insignificant variable, Model 6 has two, Model 7 has five, and Model 8 has seven.

The t-values associated with reduced sample sizes are mathematically expected to differ by 70%, 59%, and 28%

(n=3000, 1500, and 500). Still, the frequency of statistically insignificant variables in Models 7 and 8 are still exceptionally high.

Due to the high proportion of statistically insignificant open space amenity and land use variables in Models 7 and 8, these HVM estimates are considered to be unreliable and are dropped from further comparisons involving MIP's and relative elasticity rankings.

Table 27. Standard Errors of the Coefficients: The Benchmark (n=6277), Model 6 (n=3000),

Model 7 (n=1500), and Model 8 (n=500)

Benchmark Model 6 Change B:3

Model 7 Change B:4 Model 8

IND%

COM%

VAC%

NRAS

UPKS

RDPKS

NPKS

GOLF

PGOLF

99

115

34

1,176

947

*592

673

827

879

146

173

50

1,799

1,447

*869

1,010

965

1,267

48 %

50 %

47 %

53 %

53 %

47 %

50 %

17 %

44 %

201

218

*64

*2,276

1,764

*1,122

1,279

1,558

1,730

103 %

90 %

88 %

94 %

88 %

89 %

90 %

88 %

97 %

HAB1

549 794 45 % *1,038 89 %

HAB2

476 733

54 % * 893

* Statistically insignificant at the 95% confidence level

88 %

299

*344

100

*4,404

3,099

*2,055

2,022

*2,689

2,867

* 1,726

*1,314

Change

B:6

202 %

199 %

194 %

274 %

227 %

247 %

200 %

225 %

226 %

214 %

176 %

I-' o

I-'

102

From an economic standpoint, as shown by Table 28, the

MIP's of Model 6 differ from the Benchmark Model on average by

21%, with a range of between 1% and 47%. The MIP's for some of the variables differ by very minor amounts while others including HAB1, HAB2, NRAS, VAC%, and COM%, have MIP's that differ from the population parameters of the Benchmark Model by large amounts.

Table 28. Marginal Implicit Prices and Elasticities: The

Benchmark (n=6277) and Model 6 (n=3000)

IND%

COM%

VAC%

NRAS

UPKS

RDPKS

NPKS

GOLF

Variable

PGOLF

HAB1

Benchmark

MIP

-678

427

75

770

-1,296

... 463

-2,616

2,092

2,953

-615

Model 6

MIP

-683

527

110

980

-1,479

... -528

-2,621

2,311

2,879

... 90 eHG Benchmark

B:6 EYX & Rank

1 % 0.008 (11)

23%

47%

0.017 (9)

0.142 (1)

27%

14%

14%

1%

11 %

0.038 (6)

0.053 (5)

0.014 (10)

0.070 (4)

0.086 (3)

3% 0.139 (2)

Model 6

EYX & Rank

0.010 (10)

0.025 (7)

0.147 (1)

0.049 (6)

0.061 (5)

0.016 (9)

0.070 (4)

0.095 (3)

0.136 (2)

-9% 0.018 (8)

0.003 (11)

HAB2 1,587 942 41 % 0.035 (7) 0.021 (8)

*

Statistically insignificant at the 95% confidence level

103

Finally, Table 28 shows that the elasticities and relative importance rankings of the open space amenity and land use variables of Model 6 differ only slightly from those of the Benchmark Model (two variables differ by 2 rankings, and 3 differ by single rankings).

To summarize, the use of different sample sizes has mixed effects on the robustness of HVM estimates of open space amenities and non-residential land uses. In a multi-variate context, the use of smaller sample sizes results in statistically significant changes in the coefficients of the explanatory variables. From the univariate perspective, Model

6 (based upon a sample size of approximately 50%), resulted in moderate changes in the statistical and economic properties of HVM estimates. More specifically, although the standard errors and MIP's of certain variables did increase, the actual number of statistically significant variables, and the relative importance rankings of those variables did not change very much. However, with approximate sample sizes of 25% and

8.5%, HVM estimates are generally unusable do their high numbers of statistically insignificant variables.

104

Chapter 4: Conclusions and Implications

A Summary of the Empirical Results

Alternative HVM Models with varied specifications of open space amenity and land use variables, adopted units of land use aggregation, and sample sizes, were compared to a

Benchmark Model. This Benchmark Model incorporated the widest range of open space and land use variables, land use data aggregated at the block group level, and a complete population of census blocks. From these comparisons, several important methodological findings related to the robustness and quality of HVM estimates have come forth.

Excluding rental payments from the dependent variable HVM greatly changed the statistical significance and economic measures of both the open space amenity and non-residential land use variables in the Benchmark HVM Model.

Removing non-residential land use variables from the

Benchmark Model had a negligible effect on the statistical and economic robustness of the HVM estimates for the remaining open space amenity variables. Similarly, the removal of the open space amenity variables from the Benchmark Model did not effect the statistical measures or the elasticities measuring the relative importance rankings of the individual land use estimates. However, the exclusion of the open space amenity

105 variables did significantly change the coefficients of. all the explanatory variables evaluated jointly. In addition, the magnitude of the marginal implicit prices (MIP's) for two of the three land use variables also changed considerably when the open space amenity variables were omitted.

The aggregation of non-residential land uses at different levels of census geography (blocks, block groups, and tracts) was found to effect the robustness of HVM estimates in a limited way. The aggregation of the land use data at the block and tract levels of census geography did not significantly change the coefficients of the Benchmark Model

(aggregated by block groups) when the coefficients were evaluated jointly. Sirni.larly, the HVM estimates (MIP' s) of the open space amenity variables were not changed very much.

However, the standard errors, levels of insignificance, MIP's, and the relative importance rankings of the specific land use variables themselves, were all greatly effected by alternative aggregation levels. As expected, the block group level of land use aggregation (i.e. the Benchmark Model) resulted in coefficients with the lowest standard errors.

The use of different sample sizes of census blocks had a varied effect on the robustness of the HVM estimates of open space amenities and non-residential land uses. Samples of

3000, 1500, and 500 census blocks resulted in coefficients

(evaluated jointly) that were significantly different from

106 those of the Benchmark Model which utilized the population of

6277 census blocks. And, while the use of a sample size of approximately 50% (n=3000), did not greatly effect the statistical and economic properties of the HVM estimates for the open space amenity and land use variables, sample sizes of approximately 25% (n=1500) and 8.5% (n=500), greatly increased the standard errors and the numbers of statistically insignificant variables.

Implications for HVM Researchers

HVM estimates of the economic values of open space amenities and non-residential land uses, can assist with the efficient and equitable allocation of public resources.

However, this will not occur if the statistical and/or economic characteristics of such estimates are not accurate and reliable. Therefore, if the underlying relationships between housing values, open space amenities, and nonresidential land uses in the Tucson Urban Area are similar to those of other urban areas, then HVM researchers should carefully consider the results of this research effort.

If the objective of an HVM study is to determine the relationship between open space amenities, non-residential land uses, and all of the housing values within a study area, then rental values should be incorporated into the dependent variable. As demonstrated by this study, open space amenities

107 and non-residential land uses influence self-owned housing values differently than rental housing values. Therefore the results of past HVM studies which have assumed HVM estimates to be similar among self-owned and rental housing are potentially suspect.

Future HVM research efforts can easily avoid this potential bias as Census data (beginning in 1990) contains both housing value and rental payment data down to the block level of geography for most areas of the country. With the use of a GIS, this will enable both self owned and rental housing values to be easily incorporated into the dependent variable of HVM Models.

Regarding specification bias, the results of this study indicate that researchers need not be overly concerned with ~ the omission of land use variables from HVM Models that are concerned primarily with the estimation of open space amenity values. However, when the objective is to obtain HVM estimates for non-residential land uses (industrial, commercial, or vacant land uses), i t is recommended that a full range of open space amenities be incorporated into the specification of an HVM Model.

In the future, the quantity and quality of available open space amenity data is likely to increase with the adoption of

GIS technology by federal, state, and local governments. From this, i t is expected that HVM studies will incorporate more of

108 these variables in their models in order to avoid potential specification biases.

The findings of this research also suggest that HVM researchers should be cautious with regard to the .level of census geography used to aggregate non-residential land use data (blocks, block groups and tracts). More specifically, this research has demonstrated that the magnitude and quality of HVM estimates of non-residential land uses are directly influenced by the adopted level of aggregation. In this study i t was determined tha·t the block group level of census geography resulted in the most robust HVM estimates.

Finally, future HVM research efforts should carefully consider how HVM estimates are affected by the use of samples rather than a population of census blocks. This research indicates that even with a 50% sample size, resulting HVM coefficients (evaluated jointly) may be significantly different from those derived from the use of a population of census blocks. This is in spite of the fact that many of the other statistical properties and economic measures of the 50% sample size HVM Model appeared robust. In such cases, HVM researchers must carefully balance their desire for accurate

HVM estimates with the costs of utilizing a complete enumeration of census blocks.

However, with the use of smaller sample sizes (below

50%), this research indicates that resulting HVM estimates are

109 likely to be extremely unreliable. unstable HVM estimates associated with the use of alternative sample sizes has not been a recognizable issue in the HVM literature because until recently, i t has not been possible to utilize the numerous census blocks as a unit of analysis. However, with the recent advent of GIS technology and 1990 Census, i t is now relatively easy to integrate block level census data with a variety of open space amenity and land use data. The results of this research, indicate that a complete enumeration of census blocks or at least a 50% sample size, should be used in the estimation of the relationships between housing values, open space amenities, and nonresidential land uses. When this is not feasible, extreme caution in the interpretation of HVM estimates is warranted.

Caveats and Future Research Needs

Several caveats and future research needs remain. First, although the Benchmark HVM Model of this study incorporated a wide range of open space amenity and land use variables, other potentially relevant explanatory variables such as the location of toxic waste sites and wildcat dump locations in the TUA were not inc 1 uded . 17 The inclusion of these, and

17This GIS based site location data has been collected by the

Pima County Department of Environmental Quality, but this

Department treats i t as a proprietary data source in spite of the fact that i t was collected with public monies.

110 perhaps other explanatory data sources, could potentially modify the specification bias findings of this research.

Another problem with this study is that detailed structural housing variables such as the age of the homes, number of bathrooms, actual home and lot sizes, and professionally assessed housing values were not utilized.

These variables were not incorporated into the Benchmark Model because the data was not available in a spatially referenced digital format that could be easily integrated with the 6277 census blocks utilized in the study.

18

This omission of detailed structural housing data may be the reason why the King et al., (1991) HVM study which utilized a small sample size of individual homes (n

=600), and did not incorporate any land use variables, had statistically significant results which are very similar to the those of the

Benchmark Model in this study. However, another possibility is that the earlier study had a reduced level of aggregation bias from the use of individual homes as sampling units.

To summarize, future HVM research concerned with these methodological issues, should attempt to incorporate an even wider range of explanatory variables, as well as more detailed structural housing variables into their models. Also, further

18Detailed structural housing data collected by the Pima County

Assessors office is expected to be incorporated within the

County's GIS within the next 2 years.

111 research on the effect(s) of using individual homes rather than census blocks as a unit of analysis is warranted.

Appendices

Appendix A: Variables in King's et al., 1991 HVM Study.

112

structural Variables:

HAREA-- Interior living area (sq. ft.)

LAREA-- Area of Lot (sq. ft.)

Bedrooms--Number of bedrooms

Bathroom--Number of bathrooms

Age--Age of house (Years)

Presence of: (0,1)

FP--Fireplace GH--Guest House GA--Garage

SP--Swimming Pool PA--Patio

Neighborhood Variables:

Distance to Nearest: (miles)

EMP--Employment center

MALL--Regional mall

DEN--Density O=low ( l=high (

>

1 acre per dwelling)

<

1 acre per dwelling)

Open Space Variables:

Distance to nearest: (0.10 miles)

NEIGHPK--Neighborhood park

DISTPK--District Park

REGPK--Regional park

PRIVGOLF--Private golf course

BIG--Tucson Mtn.

Pa~k,

Coronado National Forest, or

Saguaro National Monument (distance in miles only)

HABI--wildlife habitat I

HABII--Wildlife habitat II

OTHOP-- Other Natural Open Space

113

Appendix B: 1990 Census Data

1) Rooms:

The number of whole rooms in both occupied and vacant housing units.

2) Contract Rent:

Monthly rental payment of all occupied housing units that were rented for cash rent and all vacant housing units that were for rent at the time of enumeration. Total aggregates, means, and medians are reported. Rent free units are not included in quartile and median rent calculations.

3) Home Values

Respondent's estimate of how much their property (house and lot, or condominium unit) would sell for in the present (1990) housing market. For vacant units, the most recent 'asking price' of the property was adopted. Total aggregates, means, and medians are reported.

114

Appendix C: City of Tucson Land Use Data

Every 10 years (in conjunction with the census of population and housing), the City of Tucson Planning

Department conducts a land use survey of the city. Aerial photo coverages for the entire city are used to interpret and classifying alternative land use activities at the block level of analysis. The total area of each block as well as the area associated with a particular land use activities in that block are reported. Below is a list of definitions pertaining to selected land use classifications:

1) Single Family (SF)

The combined acreage and total residential units associated with single family and suburban ranch housing.

Single family housing consists of conventional detached structures located on lots less than four acres in size.

Small, detached apartment units, such as apartment courts are considered to be Single family residential units.

Suburban ranch housing consists of detached single family or mobile homes located on land zoned SR, UR, RX-1 (City), GR or

SR (County). In order to qualify for the designation Suburban

Ranch, four or more acres must be visible on the aerial photo as residential use. Acreage which does not appear to be residential, but may be part of the legal lot, is categorized as vacant.

2) Multiple Family (MF)

Consist of either single story common wall units, such as duplexes and row houses, townhouses, condominiums, or multiple story apartments. Hotels and motels are considered to be commercial. University of Arizona dormitories, sororities and fraternities are coded in Miscellaneous Institutions (MI).

115

3) Mobile Home (MH)

Consist of non-recreational mobile homes and/or trailers located on individual parcels of land that approximate single family land use densities or are within mobile home parks.

Note: RV parks are coded in General Commercial (GC).

4) Commercial (CO):

(% of total acreage in a census block)

The combined acreage of Commercial Strip Development, Major

Office Buildings, and Shopping centers.

Commercial strip developments make up the majority of commercial acreage and consist of any retail or service establishments not located within a residential building.

Wholesale establishments along thoroughfares also fall into this category.

Office buildings consist of large office complexes.

Shopping centers consist of groups of commercial establishments that are contained in one unit, provide off street parking, and/or exceed 20,000 square feet of gross building area.

5) Industrial (IND):

(% of total acreage in a census block)

The combined acreage of Industrial structure and Non-Structure facilities.

Industrial structure facilities consist of industrial and manufacturing firms, outdoor storage and salvage operations and industrial parks. The buildings must cover 50% of the lot minus the parking areas in order to be placed in this category.

Industrial non-structure facilities consist of all outdoor storage, salvage operations, and construction yards are included in this category.

6) Vacant Land (VAC):

(% of total acreage in a census block)

Consists of property that does not currently have an

116 established land use upon it. Since "vacant" land is property which has the potential of eventually being developed,· washes, drainageways, and riverbeds are not considered vacant

117

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