ESTIMATION OF BLACK AND WHITE HOUSING SERVICES DEMAND ELASTICITIES
IN THE UNITED STATES USING A SIMULTANEOUS MODEL OF TENURE CHOICE
AND HOUSING SERVICES DEMAND
By
DAVID RICHARD WILLIAMS
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
Copyright 1986
by
David Richard Williams
ACKNOWLEDGEMENTS
I would like to thank the members of my dissertation committee, Dr.
Lawrence Kenny (Chairman), Dr. Stephen Cosslett, Dr. David Denslow, Dr. Jerome
Milliman and Dr. Gary Lynne, not only for all their advice and continued
support during the preparation of this dissertation, but also for their
guidance during my years at the University of Florida.
My deepest gratitude goes to my father, late mother, auntie Gwyn, and
uncle Bill for their love and continuous understanding over the years.
I would also like to thank Dr. James Frew, who aroused my interest in
applied econometrics while I was at the University of North Carolina at
Greensboro. Also, I want to thank the staff of the Revenue and Economic
Analysis Unit of the Governor's Office of Florida for their encouragement
during the latter stages of this dissertation. Financial assistance was
provided to me during my doctoral studies by the Elizabeth Tuckerman
Scholarship Foundation, Los Angeles, California.
Last, but by no means least, my thanks to DeLayne Redding for typing this
dissertation.
TABLE OF CONTENTS
ACKNOWLEDGMENTS ...................................
LIST OF TABLES ....................................
ABSTRACT ...........................................
CHAPTERS
I INTRODUCTION ...........................
II REVIEW OF THE LITERATURE ON PREVIOUS
STUDIES ESTIMATING RACIAL HOUSING DEMAND
ELASTICITIES .............................
III IMPROVEMENTS IN THE MEASUREMENT OF
HOUSING VARIABLES ........................
IV THE MODEL ................................
Estimation Technique Theory.............
Specification of the Model and
Construction of Housing Variables.......
V EMPIRICAL RESULTS AND DISCUSSION..........
Notes....................................
VI CONCLUSIONS ..............................
APPENDIX
DATA SOURCES AND DETAILED VARIABLE
DEFINITIONS..............................
BIBLIOGRAPHY ......................................
BIOGRAPHICAL SKETCH...............................
Page
iii
V
viii
1
7
13
20
20
22
42
94
95
99
109
114
LIST OF TABLES
TABLES Page
1 List of Dependent and Independent Variables Used in
the Hedonic Equation Regression Analysis............. 27
2 List of Independent Variables Used in the Permanent
Income Regression Equation Analysis................. 33
3 List of Dependent Variables Used in the Tenure
Choice Regression Equation Analysis................. 36
4 List of Independent Variables Used in the Housing
Services Demand Regression Equation Analysis......... 37
5 1981 Hedonic Equation Regression Coefficients for
AnaheimSanta AnaGarden Grove SMSA ................. 51
6 1981 Hedonic Equation Regression Coefficients for
Boston SMSA........................................ 52
7 1981 Hedonic Equation Regression Coefficients for
Dallas SMSA......................................... 53
8 1981 Hedonic Equation Regression Coefficients for
Detroit SMSA......................................... 54
9 1981 Hedonic Equation Regression Coefficients for
Fort Worth SMSA...................................... 55
10 1981 Hedonic Equation Regression Coefficients for
Madison SMSA......................................... 56
11 1981 Hedonic Equation Regression Coefficients for
MinneapolisSt. Paul SMSA........................... 57
12 1981 Hedonic Equation Regression Coefficients for
Newark SMSA ........................................ 58
13 1981 Hedonic Equation Regression Coefficients for
Orlando SMSA ........................................ 59
14 1981 Hedonic Equation Regression Coefficients for
Phoenix SMSA......................................... 60
15 1981 Hedonic Equation Regression Coefficients for
Pittsburgh SMSA..................................... 61
TABLES Page
16 1981 Hedonic Equation Regression Coefficients for
Spokane SMSA......................................... 62
17 1981 Hedonic Equation Regression Coefficients for
Tacoma SMSA......................................... 63
18 1981 Hedonic Equation Regression Coefficients for
Washington, D.C. SMSA............................... 64
19 1981 Hedonic Equation Regression Coefficients for
Wichita SMSA........................................ 65
20 Significance and Mean Effects of Hedonic Equation
Regression Coefficients using the Pearson PX Test... 66
21 Means of Hedonic Housing Variables (X.'s) used in
the Construction of the Hedonic Housing Services
Price Indices....................................... 67
22 1981 Hedonic Housing Services Price Indices for
Black and White Homeowners in each of the 15 SMSAs.. 71
23 1981 Hedonic Housing Services Price Indices for
Black and White Renters in each of the 15 SMSAs..... 72
24 1981 Price Index for all Goods and Services in each
of the 15 SMSAs ..................................... 73
25 1981 Permanent Income Equation Regression
Coefficients for Grouped Sample..................... 75
26 1981 Probit Equation Regression Coefficients........ 76
27 1981 Housing Services Demand Equation Regression
Coefficients for Homeowners ........................ 82
28 1981 Housing Services Demand Equation Regression
Coefficients for Renters............................ 83
29 1981 Housing Services Demand Equation Regression
Coefficients for White Homeowners by Education
Classification...................................... 84
30 1981 Housing Services Demand Equation Regression
Coefficients for Black Homeowners by Education
Classification...................................... 85
31 1981 Housing Services Demand Equation Regression
Coefficients for White Renters by Education
Classification......................... ............. 86
TABLES Page
32 1981 Housing Services Demand Equation Regression
Coefficients for Black Renters by Education
Classification ...................................... 87
33 Final Price and Income Elasticities of Housing
Services Demand for Black and White Homeowners and
Renters............................................. 88
34 Comparison of Homeowner Housing Services Demand
Equations Using (1) AHS Endogenously Constructed and
(2) BLS Price Indices............................... 91
35 Comparison of Renter Housing Services Demand
Equations Using (1) AHS Endogenously Constructed and
(2) BLS Price Indices............................... 92
36 Comparison of Final Price and Income Elasticities of
Housing Services Demand for Black and White Homeown
ers and Renters Using (1) AHS Endogenously Construct
ed and (2) BLS Price Indices........................ 93
37 Sample Size of Each Tenure/Race Classification by
SMSA............................................... 101
38 Income Tax Brackets, 1981........................... 102
39 City Specific Features Used in the Permanent Income
Regression Equation................................ 103
40 NonHousing and Housing Budgets from the 1981 Bureau
of Labor Statistics Urban Family Budget Survey...... 104
41 Capital Gains Rates in the SMSAs in the Annual Hous
ing Survey......................................... 105
42 NonHousing and Housing Budgets from the 1978 Bureau
of Labor Statistics Urban Family Budget Survey...... 106
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ESTIMATION OF BLACK AND WHITE HOUSING SERVICES DEMAND ELASTICITIES
IN THE UNITED STATES USING A SIMULTANEOUS MODEL OF TENURE CHOICE
AND HOUSING SERVICES DEMAND
By
DAVID RICHARD WILLIAMS
December 1986
Chairman: Dr. L. W. Kenny
Major Department: Economics
This dissertation presents estimates of black and white homeowner
and renter income and price elasticities of housing services demand in
the United States for the year 1981. The econometric model employed in
this analysis takes into account the individual's twofold decision on
(1) the level of housing services to select and (2) whether to own or
rent a housing unit. The data set used in this study is the 1981 SMSA
Annual Housing Survey, the most detailed housing database currently
available.
A measure of permanent income is estimated using an instrumental
variables technique. Endogenously constructed racial housing price
indices are built using hedonic pricing techniques for homeowners and
renters in each of the fifteen Standard Metropolitan Statistical Areas
(SMSAs) in the sample. These income and price terms together with a set
of demographic variables and a variable which captures any simultaneity
between the housing demand and tenure choice decisions are used as
explanatory variables in the final housing demand equations.
The results from these equations show that blacks have higher price
and income elasticities of housing services demand than whites in both
the homeowner and rental markets. The price elasticities are 1.04 and
1.01 for black and white owners, 0.62 and 0.12 for black and white
renters. The income elasticities are 1.42 and 1.30 for black and white
owners, 0.53 and 0.36 for black and white renters. Evidence of
simultaneity is found between the rent and housing consumption
decisions and also between the own and housing consumption decisions.
On examining any changes in price and income elasticities estimates
caused by using price indices (1) constructed endogenously from the
Annual Housing Survey and (2) from the Bureau of Labor Statistics,
differences in the relevant elasticities ranged between two and
fiftyfour percent.
CHAPTER I
INTRODUCTION
The main contribution of this research is that it is the first
paper to use endogenously constructed price indices for black and white
homeowners and renters in housing demand equations. Most housing demand
studies use the timeseries or crosssectional housing price indices
constructed by the Bureau of Labor Statistics (BLS). The timeseries
BLS city housing price indices are inappropriate for use in
crosssectional studies as they do not measure relative differences in
prices or living costs between cities at a point in time. Unfortunately,
Lee and Trost (1978) use these price indices in their housing study.
These indices show how prices change in a particular city over time, not
whether prices are higher in one city than in another. As stated in
U.S. Department of Labor (1984):
The area indices measure the average changes in price for
each area since the base period. They do not measure
differences in the level of prices among cities; that is,
they cannot be used to determine "high living cost" or
"low living cost" cities or regions. (p. 6)
The BLS crosssectional family budget data measure differences in
living costs between cities for a family comprising a 38yearold
employed husband, a wife not employed outside the home, an 8yearold
girl, and a 13yearold boy a typical 4person family. For renter
families, the standard unit is an unfurnished fiveroom apartment in
sound condition with a particular set of neighborhood dwelling
characteristics, such as a complete private bath and a fully equipped
kitchen. For homeowner families, the standard unit is a five or
sixroom, 1 or 12bath house with the same set of neighborhood and
dwelling characteristics as the standard rental unit. Problems with the
BLS family budget are that it not only looks at a very arbitrarily
specified family composition, but also only keeps quality constant in so
far as looking at arbitrarily and vaguely defined sound rental and
homeowner housing units (see Chapter III for a thorough discussion of
this topic). The price and income elasticities of housing services
demand reported in studies using BLS price indices can be directly
compared to the price and income elasticities obtained in this study
which use endogenously constructed price indices.
Several authors, notably Gillingham (1975), Follain, Ozanne, and
Alburger (1979), and Follain and Malpezzi (1979), do construct owner and
rental price indices using hedonic methods, as in my study. However,
they do not incorporate their indices into housing demand analysis, a
logical place for such housing price indices. This study takes the
current state of the art forward by incorporating endogenously
constructed housing price indices, not BLS price indices, in a study of
the demand for housing.
A second contribution of this study is to apply the econometric
technique developed by Lee and Trost (1978) to the best housing data
available, the Annual Housing Survey (AHS). Other papers using the
LeeTrost model, namely Lee and Trost (1978) and Rosen (1979a and
1979b), use the Panel Study of Income Dynamics (PSID) from the
University of Michigan. This data set overrepresents lowincome
households, includes only 2,000 households, and contains few items
concerning housing. The only other paper to use the LeeTrost model,
namely Gillingham and Hagemann (1983), used the Consumer Expenditure
Survey (CES) which, although it contains more households (approximately
23,000) than the PSID, again has insufficient information on shelter.
Housing was not the focus of the PSID or the CES. However, the Annual
Housing Survey, as the name suggests, emphasizes housing. The 1981
Annual Housing Survey (SMSA file), which I use in this study, is a sur
vey of about 75,000 individual housing units across 15 SMSAs. Each
household head was asked approximately 500 questions about his previous
and current housing situation. The Annual Housing Survey is by far the
largest and the most detailed source of housing information currently
available.
Before summarizing housing demand elasticities computed by single
equation methods, that generally use BLS price indices, I will briefly
describe the methodology underlying the single equation estimation
methods.
Prior to Lee and Trost (1978), housing services demand elasticities
(income and price) for grouped and micro data were obtained by
estimating single equations of housing demand for homeowners and renters
separately, taking no account of the tenure choice decision. Before
1978, the typical procedure used to derive estimates of housing demand
elasticities started with the following equation:
log qH = 0 + B1 log y + B2 log PH + B3 log Px + u (11)
where qH = quantity of housing services
y = current income
PH = price index of housing services
PX = price index of all goods (excluding housing
services)
In equation (1), B1 and 82 were the "true" income and price
elasticities of housing services demand, respectively. The demand
equation is homogeneous of degree zero in prices and income, implying
the constraint B1 + B2 + 83 = 0. Adding log pH and subtracting log pX
from both sides of (1) yielded the following equation, estimable with
micro data:
log (eH/PX) = B0 + 10 log (y/PX) + (1 + B2) log (pH/PX) + e (12)
where eH = expenditures on housing services.
A similar procedure was carried out for grouped data (details of
which are discussed in Polinsky and Ellwood (1979)). Equation (12) in
many studies also included demographic variables, so that the housing
demand equation estimated was a slight variation of (12). An excellent
survey of the pre1978 literature by Mayo (1981) found micro housing
demand elasticities to lie in the following ranges: renter and owner
income elasticities of demand, 0.08+0.70 and 0.21+0.71; and renter and
owner price elasticities of demand, 0.17+1.28 and 0.52+0.89.
Lee and Trost (1978) solved the econometric problem posed in Vaughn
(1976): "A method does not yet exist to include both categories (home
owners and renters expenditures) within a single regression equation"
(p. 55).
All pre1978 housing demand studies are limited by not having the
LeeTrost modelling procedure available. Not incorporating a variable
which takes into account the simultaneity between the housing
consumption and tenure choice decisions renders the elasticities
computed from single equation methods biased and inconsistent. Since
Lee and Trost, three more papers have been published, all using micro
data, which allow for simultaneity between the decision whether to own
or rent and how much to spend on housing services.Lee and Trost
estimated income elasticities of demand to be in the ranges 0.55+0.61
for owners and 0.50+0.51 for renters. Rosen (1979a) estimated owners'
elasticities of demand to be 0.76 for income and 0.97 for price.
Gillingham and Hagemann (1983) estimated income elasticities for owners
and renters in the ranges 0.23+0.54 and 0.29+0.74, respectively, and the
price elasticities for owners and renters to be in the ranges
0.27+0.57 and 0.66+1.17, respectively. A similar study carried out
in the United Kingdom by King (1980) estimated the price elasticities of
housing demand for owner occupied, subsidized rental, and furnished
rental housing at 0.52, 0.49, and 0.65, respectively. From these
four studies the evidence seems to be that the income elasticities are
in the ranges 0.25+0.75 and 0.30+0.75 for owners and renters, while the
price elasticities are in the ranges 0.30+1.00 and 0.50+1.20 for
owners and renters, respectively.
Each of the three U.S. studies leaves room for improvement. Lee
and Trost (1978) fail to include the income tax advantages of owning a
home in their price index of housing services for homeowners. Although
Rosen (1979a) and Gillingham and Hagemann (1983) both correct for income
tax effects, Rosen uses for eo (the expenditures on housing services by
homeowners) the market value of the home, while Gillingham and Hagemann
use the respondent's estimate of the rental value of the home net of
utilities. Also Gillingham and Hagemann use current instead of
permanent income and do not include the net imputed rental value of
owning a home in owners' income.
The third major contribution of this study is to fill a void in the
existing housing demand literature. No published papers use Lee and
Trost's simultaneous model of tenure choice and housing services demand
to estimate black and white homeowners and renters' price and income
elasticities of demand for housing services separately. A crux of my
paper is to estimate elasticities for blacks and whites separately.
This study also estimates these elasticities for black and white
homeowners and renters across three major education levels to examine
whether housing demand elasticities vary with educational attainment.
The endogenous construction of racial price indices for owners and
renters in this study also permits me to test for racial price
discrimination with regard to housing across the fifteen SMSAs in my
sample. Although the main questions asked in this thesis are not
related to housing policies, it is possible to use the computed
elasticities to examine whether national housing policies have varying
effects on different racial groups and even across groups with different
education levels in the United States.
In Chapter II the few previous studies on racial housing demand
elasticities are reviewed. Chapter III highlights the deficiencies
of past housing research and the resulting consequences on coefficient
estimation. Chapter IV details the statistical theory behind the
LeeTrost model of simultaneously looking at the decisions of how much
housing services to consume and the tenure choice decision. Also in
this chapter the housing variables used in this analysis are
constructed and the best functional form of the housing demand and other
relevant equations are found. In Chapter V the empirical results are
tabulated and discussed, the conclusions of the thesis are presented in
Chapter VI. Finally, the appendix details the data used from the Annual
Housing Survey and other sources. The appendix also defines all the
housing variables used in the thesis.
CHAPTER II
A REVIEW OF THE LITERATURE ON PREVIOUS STUDIES
ESTIMATING RACIAL HOUSING SERVICES DEMAND ELASTICITIES
Using single equation methods, three papers using micro data have
looked at racial housing demand elasticities. The first, Kain and
Quigley (1975), used a sample of 1,200 individual housing units (owners
and renters) in St. Louis. The best of their numerous specifications
yielded income elasticities of housing demand of 0.28 for white and 0.07
for black owners. Their best equation for renters produced income
elasticities of 0.25 for white and 0.15 for black renters. They assumed
a linear functional form for owner equations and a semilogarithmic form
for renter equations. No price elasticity of housing demand was
computed since all individuals in St. Louis face the same price of
housing; therefore, no price term was included in their demand
equations. When calculating a homeowner's income, they did not take
into account the net imputed rental value of a house. Finally, the
sample had only 72 black owners and 266 black renters.
The second study, Mayo (1977), has its results tabulated below:
White RenterOccupied
Black RenterOccupied
n Tn
y P
Pittsburgh Phoenix Pittsburgh Phoenix
0.52 0.72 0.27 0.55
0.77 0.33 0.38 0.81
Mayo used a stock adjustment model on individual rental data from
the Housing Allowance Demand Experiment (HADE), carried out in
Pittsburgh and Phoenix, to examine the feasibility of a percent of rent
payment scheme. Although the price elasticities (n ) are consistently
more elastic for black renters than for white renters, no pattern
emerges concerning the income elasticities (n ). Mayo's results must be
viewed with caution. First, his equations suffer from a high degree of
collinearity between the income and lagged rental expenditure variables.
Second, the data, from an experiment of limited duration, reflect house
hold reaction to a temporary, not a permanent rental price reduction.
Third, the equations included no demographic variables.
The third paper, Friedman and Weinberg (1982), to use micro data in
order to examine racial housing demand elasticities produced the
following results:
"y np
Pittsburgh Phoenix Pittsburgh Phoenix
White RenterOccupied 0.39 0.43 0.21 0.29
Black RenterOccupied 0.21 0.22 0.20 0.26
Friedman and Weinberg also used data from the Housing Allowance
Demand Experiment (HADE), and consequently their analysis, like Mayo's,
suffers from flaws inherent in using this data, particularly that it is
from a temporary experiment. Unlike Mayo, Friedman and Weinberg did not
use a stock adjustment model but instead a more standard demand equation
approach. Their paper also assumes a semilogarithmic functional form
for the equation, and has no demographic regressors.
Using pre1978 techniques, two papers employing grouped data have
looked at racial housing demand elasticities, de Leeuw (1971) and Vaughn
(1976). The results of the two studies are summarized in the table
below:
All OwnerOccupied
OtherI Head, Owner
Occupied
All RenterOccupied
OtherI Head, Renter
Occupied
de Leeuw, Other = Nonwhite
Vaughn, Other = Black
I have little confidence in the de Leeuw and Vaughn estimates. Both
studies use current instead of permanent income in their demand equa
tions, resulting in a downward bias in their estimates of the permanent
income elasticity of housing demand (Chapter III has a thorough discus
sion of the consequences of this error). The elasticity ranges given by
Vaughn are far too wide for any meaningful comparisons with other
estimates. Also, neither study includes the net imputed rental value of
a home in homeowners' income, or allows for the income tax advantages of
owning a house. In fact, de Leeuw does not even include a price term in
Ti n
ny "p
de Leeuw Vaughn de Leeuw Vaughn
1.34 1.88 0.33+2.70
0.76+2.67 0.63+6.25
0.81+0.99 0.32 0.71+1.47 0.48+2.63
0.79 0.41+0.50 0.97 0.35+2.38
his owner demand equations. Finally, neither study treats blacks and
whites separately.
My study fills a void in the existing racial housing demand
elasticity literature by not only taking into account the omissions and
errors of previous studies, but also by using a simultaneous model of
housing demand and the tenure choice decision. All previous racial
studies have used only single equations of housing demand in their
elasticity estimation.
On examination of the few prior racial housing demand studies,
it is clear that no overall conclusion can be drawn that the price and
income elasticities of housing services demand are higher for blacks
than whites, or vice versa. From a general review of the housing demand
literature it was found that the price and income elasticities of
housing services demand are higher for homeowners than renters. The
price elasticity of housing services demand for homeowners is generally
in the 0.7+1.0 range, while the income elasticity of housing services
demand for homeowners is generally in the 0.8+1.3 range. As stated
above, the same two elasticities are found to be lower in the rental
market.
There are numerous theories (see King and Mieszkowski (1973)) on
why blacks pay more than whites for structurally identical housing
units. A slight majority of studies (see Yinger (1979) and Follain and
Malpezzi (1979)) support the finding that blacks pay more than whites
for structurally identical housing units. However, there are no
theories detailing why the price and income elasticities of housing
services demand should differ, if at all, between blacks and whites.
There is nothing in the literature to support the following statement
made by de Leeuw (1971): nonwhite households appear to have a slightly
lower income elasticity of demand than all households, perhaps because
of restrictions on choice due to racial discrimination. (p. 8)
A question one could ask of this dissertation is: What is the
motivation and purpose behind wanting to estimate racial housing ser
vices demand elasticities? In response, I can think of two main areas
where racial housing demand elasticities are of particular interest.
The first area concerns the effectiveness of past, current, and
future federal housing policies and whether there are different
responses from blacks and whites to these policies. During the early
1970s the majority of federal housing policies were generally costly and
inefficient supply oriented programs. Examples of these policies were
public housing which gave a subsidy to local housing authorities for the
construction of rental housing, Section 221 which gave an interest
subsidy to private sponsors, and Section 236 which gave an annual
subsidy to project owners. The National Housing Policy Review (NHPR)
Commission, established by President Nixon in 1973, came out in favor of
turning to more demand oriented housing programs. The higher the price
and income elasticities of housing services demand, the greater the
effectiveness of demand oriented programs. The NHPR study led to the
implementation of Section 8, a demand subsidy program that gave an
indirect payment to renters. Also, the Housing Allowance Demand
Experiment (HADE) was conducted which gave housing allowances to renters
and owners in the form of direct income transfers to both tenure groups.
Programs such as the percent of rent subsidy could be evaluated using
racial price and income elasticities of housing services demand to
examine whether it was acting as a housing subsidy or merely an income
transfer to the participants. The success of such housing programs
depends on the magnitudes of the income and price elasticities of
housing demand whichever elasticity is appropriate to the program in
questions. If the two elasticities are higher for blacks than whites,
then demand oriented housing policies have more of a beneficial effect
on blacks due to their greater responsiveness than whites.
A second application for racial housing services demand
elasticities is in the arena of traditional monocentric model theory and
helps explain why blacks are more concentrated in central cities, while
whites prevail in the suburbs. As stated in Mills (1980):
Suppose that the disutility of a mile of commuting is proportionate
to the wage rate, and that the factor of proportionality is no
greater for high than for lowincome workers. Then, if the income
elasticity of demand for housing exceeds 1.0, highincome workers
live further from the urban center than do lowincome workers. If
the income elasticity is less than 1.0, highincome workers
nevertheless live farther out, provided the demand for housing is
not too inelastic with respect to its price. (p. 73).
The income elasticities of housing services demand of blacks and
whites, together with the income levels of the two racial groups, can
help explain the process of white suburbanization over the years.
CHAPTER III
IMPROVEMENTS IN THE MEASUREMENT AND SPECIFICATION OF
HOUSING VARIABLES
The previous literature on housing demand has ignored or
misdefined one or more of the relevant economic variables from the
theory of consumer demand relating to housing as a durable, as well as
an investment, good. This is the first study to correct for all the
previous shortcomings in the same analysis that builds on the work of
prior authors in the housing area.
i. As discussed in the introduction, this study improves on the
work of previous authors by endogenously constructing racial housing
price indices for black and white owners and renters. Virtually all the
prior literature on housing demand has used crosssectional housing
price indices from the family budget survey published annually by the
Bureau of Labor Statistics, which can definitely be improved upon. The
standard unit in the BLS survey for renter families is defined in the
U.S. Department of Labor (1984) as: "...an unfurnished fiveroom unit
in sound condition with a complete private bath, a fully equipped
kitchen, hot and cold running water, electricity, central or other
installed heating, access to public transportation, schools, grocery
stores, play space for children, and location in residential
neighborhoods free from hazards and nuisances" (p.23). The standard
unit in the BLS survey for a homeowner family is defined in the U.S.
Department of Labor (1984) as: "...the same as that for the renter
families insofar as neighborhood and dwelling unit characteristics are
concerned, except that the unit itself was a five or sixroom dwelling
and one or one and onehalf baths..." (p. 23).
The hedonic price indices used in this study control for housing
quality in a superior fashion to the BLS price indices. There can be
much variation in the owner and rental housing units described above
that only have the very basic necessities included. The definition of a
"sound" housing unit is also very subjective.
The hedonic price indices in my study have far more detail on the
structural, neighborhood, and locational features of the housing unit in
question (see Table 1). The structural characteristics in this study
take into account the age of the structure, totally ignored in the BLS
indices. Also, the number of floors and the presence of air
conditioning, a fully working electrical system, a telephone, and
rodents in the housing unit. The neighborhood characteristics in the
BLS are equally as vague as those in the AHS. However, the locational
variables are superior in the AHS as the location of the unit within or
outside the central city is available, as well as the distance and time
the household head is from his place of work. Another superior feature
of the indices computed from the hedonic analysis is that separate price
indices are constructed for homeowners and renters, the BLS only has a
composite shelter cost.
Finally, the BLS does not differentiate between blacks and whites
in either tenure category. My housing price indices are constructed for
both racial groups and for both tenure categories in each of the fifteen
SMSAs in my sample. There are more subgroups available from my AHS
endogenously constructed housing price indices than from the BLS family
budget survey data.
ii. Much of the previous literature uses current (measured) income
instead of permanent (normal) income (see Friedman (1957)). The
problems involved in estimation with current income are shown below:
YC = Yp + YT (identity)
where
YC = Current (Measured) Income
Yp = Permanent (Normal) Income
YT = Transitory Income
The "true" housing demand function can be specified as follows:
Q = Bp Yp + BTYT + rw + U
where
Q = Quantity of Housing Services Demanded
W = a vector of other explanatory variables, including the
constant and a housing price variable
However, many previous studies have a misspecified housing demand
function where current income is used instead of permanent income in the
following form:
Q = CYC + rw + V
Given the above misspecification and that Yp, YT, and W are
uncorrelated, the ordinary least squares (OLS) estimators of BC and r
are
C + C (W'W) V
r r0 (')1W IV
16
EY V
where plim BC = BC + plim L
After some manipulation and using the following expressions:
plim  = o plim T = o2
V = (Bp BC)YP + (T )YT + u
0=
P C
the following is derived:
plim BC = B + (18) B
As permanent income is expected to have a greater impact on housing
demand than transitory income (i.e., p > BT and 0 < 0 < 1), the
following is found:
Bp > plim BC > BT
The final conclusion is that if current income is used instead of
permanent income, the result will be an underestimate of the permanent
income elasticity of housing services demand and an overestimate of the
transitory income elasticity of housing services demand. My paper will
use a measure of permanent income derived from an instrumental variable
technique using Milton Friedman's Permanent Income Hypothesis (see
Chapter IV).
iii. Many housing demand studies do not add net imputed rental income of
a house (NI = gross rental value housing expenses) to the permanent
income of homeowners. De Leeuw (1971) defines this net imputed rental
income as: "the nonmonetary income owneroccupants derive from the
rental value of their homes" (p. 3).
Not taking net imputed rental income into account biases the income
elasticity of demand for housing services of homeowners away from one.
iv. Many housing studies use incorrect price deflators, or even no
price deflators at all. The price index of all goods and services
(excluding shelter), px, is used to deflate nominal price and income
variables. The price index of all goods and services should exclude
shelter; unfortunately many housing studies do not take this into
account. The bias introduced by not excluding shelter depends on the
share of the overall index going to housing. The bias is larger, the
greater the share of the good being estimated is in the person's budget.
As individuals usually spend a large share of their income on shelter,
as opposed to say fish, the bias introduced by not excluding shelter
from the price index can be large. The price index of all goods and
services (excluding shelter) used in this study is derived in Chapter
IV.
v. A further point concerns the definition of e (expenditures on
housing services by homeowners) used in the majority of the literature.
As de Leeuw correctly states: "The variable to which the theory of
consumer demand and most empirical demand studies refer is expense per
unit of time (usually per year), not market value (or sales price)"
(1979, p. 2).
My interpretation of e will follow that of de Leeuw by measuring
the annual expenditures on all housing services. One should also
include in e the net imputed rental income (NI) of the home to the
homeowner, which is the opportunity cost of the homeowner's equity.
Rosen's (1979a) rationale for using an incorrect measure (i.e., market
value) is seen where he states:
Since the theory of consumer demand suggests that housing
services is the appropriate variable, it is implicitly assumed
that the flow of housing services is proportional to the value
of the house. This has been the explicit or implicit
assumption in most studies of the demand for owneroccupied
housing and is retained (here) for lack of a better
alternative. (p. 9)
However, de Leeuw has shown that average housing service expense as
a percent of average market value decrease as market value rise (see de
Leeuw (1971), Table 1, p. 2). Rosen and other writers are empirically
incorrect when using house value (or sales price) as a proxy for expen
ditures on housing services by homeowners.
vi. Many authors fail to adjust P the price index of housing services
for homeowners, for the implicit subsidy given to homeowners under
current federal income tax regulations in the United States.
Under current law, homeowners can deduct property taxes (T) and
mortgage interest payments (MI) from their taxable income. The
adjustment to the price index for homeowners (P ) used in this thesis
incorporates a procedure similar to that reported in Hamilton and Mills
(1984), where
= (1t) + (1t) + D + M (gr+e) ] P
where poj = homeowner price index for individual j
P = homeowner price index for a race/tenure group in a
certain SMSA
MI = mortgage interest payments
V = value of home
t = marginal tax rate
T = property taxes
D = rate of depreciation
M = rate of maintenance
g = real rate of capital gains
e = expected inflation rate
N
g = nominal rate of capital gains
r + e
= g
The above approach links together the rental price and the value
price in housing markets, where p is a rental equivalence index of an
owner's house price index (P ). The above equation takes into account
that both mortgage interest payments and real estate taxes are currently
deductible from taxable income. Also, depreciation and maintenance are
costs to an owner, hence their positive signs, whereas capital gains,
N
g are a negative cost to an owner, hence its negative sign. This
expression also takes into account that the nominal capital gains rate
is made up of two components, a real capital gains rate (gr) and an
expected inflation rate (ne).
CHAPTER IV
THE MODEL
Estimation Technique Theory
The model used in this paper is the one developed by Lee and Trost
(1978) which allows for simultaneity between the decision whether to own
or rent (the tenure choice equation) and the decision on how much to
spend on housing consumption (the housing demand equation). The
theoretical model can be set up as follows:
e = h(X ) + e e = e if I > 0
e= h(X ) + e (41) e = e otherwise
r r r r
I = g (Z) + t
where
e = expenditures on housing services if household head owns
er = expenditures on housing services if household head rents
Xo, X Z = explanatory variables in each equation
I = unobservable index determines tenure choice
It is a switching regression model where the index function
determines whether e or e is observed. The LeeTrost model
o r
incorporates the correlations between o and c, and between Er and E
into the estimation process. Unless E and E are both independent of E
o r
(i.e., no simultaneity), traditional simultaneous equation estimation
yields biased and inconsistent estimates of the parameters in system
(41). Lee and Trost suggest two methods of estimating the above
system of equations which avoid inconsistency, a maximum likelihood
procedure and a twostage procedure. I will use the twostage procedure
(as have Rosen, 1979a and Gillingham and Hagemann, 1983) because it is
computationally easier to implement.
The first stage is to estimate the tenure choice equation. I
specify this as a Probit model (see McFadden, 1976) and use the esti
mated parameters to construct the following variables, which are used as
explanatory variables in the demand equation in the second stage:
A f(I) A f(I )
0 F(I ) r (1F(I))
where Ao, A = expected value of errors in Probit equation,
conditional upon owning and renting, respectively
f(") = standard normal density function
F(') = standard normal cumulative density function
I = g(Z)
F(I ) = estimated owneroccupant probability
(1F(I )) = estimated renter probability
The coefficient on A in the final homeowner demand equation equals
(p*o), where p is the correlation between E and E, and a is the
standard error of E Similarly, the coefficient on A in the final
o r
renter demand equation equals (p*o), where p is the correlation between
E and c, and o is the standard error of E ,
Given the Probit estimates and the linearity of the conditional
expectations of e and e given e, the expected errors in the Probit
o r
equation are proportional to the expected errors in the owner and renter
demand equations taken separately.
The second stage is to estimate the demand equations by ordinary
least squares (OLS), including the constructed variables A and A to
take into account the possible correlation between the errors in the
demand and tenure choice equations. If the A's are statistically
significant, the demand and tenure choice decisions are simultaneous.
Specification of the Model and Construction of Housing Variables
Having discussed the econometric theory behind the model's
estimation in the first section of Chapter IV, I will now explain the
stratification of the data by Standard Metropolitan Statistical Area
(SMSA), race, and tenure. Also I describe in this section the
explanatory variables and show how some of them were constructed and
incorporated in the tenure choice and housing services demand equations.
The first step in my statistical analysis is to stratify the 1981
Annual Housing Survey SMSA data into four subgroups by tenure choice
and by race of household head. I use Lee and Trost's model in (41) on
blacks and whites separately as follows (where the subscripts o, r, w,
and b refer to owner, renter, white, and black):
WHITE BLACK
e = h(X ) + e e h(X ) +
o,w o,w o,w o,b o,b o,b
e = h(X ) + E e h(X ) + E
r,w r,w r,w r,b r,b r,b
I = g(z) + E I = g(z) + Eb
where e = ew if I>0 where e = eo,b if I>0
o,w o,b
e = e otherwise e = e otherwise
r,w r,b
The model specification and explanatory variables I use are the
following:
WHITE BLACK
e = h(Pow/Pxo,w/ x,d) + EO eo,b = h(Po,b/ /Yp,b ,d) + eo,b
r,w h(Pr,w x ,r,w/xd) + cr,w er,b = h(Pr,b/PxYr,b/Pd) + Er,b
I = g(y w/pxP ,w/Pr,wd) + w I = g(yb/Px Po,b/Pr,bd) + Eb
where
e = expenditures on housing services
p = price index of housing services
px = price index of all goods, excluding shelter
y = permanent income of household head
d = a vector of demographic variables
As can be seen, the above analysis requires price indices of
housing services for black and white homeowners and renters, namely
Po,w' o,b' r,w, and pr,b As was noted in the introduction, there
are major problems encountered when using either timeseries or
crosssectional Bureau of Labor Statistics price indices. These indices
also do not attempt to capture any price differentials between blacks
and whites. Fortunately, with the rich data set used in this study, it
is possible to construct racial/tenure housing price indices in the
fifteen cities in my sample and permit estimation of racial housing
demand price elasticities.
By stratifying the data set by tenure choice and by race for each
of the fifteen SMSAs in the survey, it is possible to construct a
housing service price index number for each tenure/racial classification
in each SMSA, i.e., sixty price indices in all. This is accomplished
using hedonic pricing techniques, first developed by Rosen (1974) and
applied to housing demand studies by numerous authors including Linneman
(1980) and Goodman and Kawai (1984), as follows:
V 1
Ri = j(Si, N., Li)
where
V = property value of owneroccupied house
R = annual contract rent
S = a vector of structural characteristics of the housing unit
N = a vector of neighborhood characteristics of the housing unit
L = a vector of locational characteristics of the housing unit
In the separate regressions of (i) V on S, N, and L in the
homeowner market, and (ii) R on S, N, and L in the rental market, each
regression coefficient denotes the implicit dollar value (or marginal
trait price) associated with each structural, neighborhood, or
locational characteristic embodied in the housing unit.
Before discussing the theory behind and actual construction of the
hedonic housing price indices, let us discuss the functional form of the
hedonic regression equation.
Some of the previous literature utilizing hedonic price theory has
rationalized using a particular functional form for the equation,
usually either the linear or semilogarithmic forms. This study,
however, will select the functional form using a BoxCox transformation
(Box and Cox, 1964) of the dependent variable as follows:
V(l = 0+ 1X + 2 2 + ... + et (42)
X
where
V )1 V if X=l (linear)
AX inV if X=0 (semilogarithmic)
The above assumes that there exists a value of A such that in
(42) et is i.i.d. and N(0,o2). The log of the likelihood function of
(42) can be written in vector form as follows:
N M(V XB)'(V XB) N
L = constant ln2 (+ (Xl) E InV (43)
2 o2 i=1
where N = sample size.
The concentrated likelihood function of (42), excluding the
constant, is as follows:
N 2 N
L(A) = ln 2A) + (AI) Z lnV (44)
i=1
The computational burden is simplified by substituting in values
for A of 0 and 1 into (42), separately, then using ordinary least
squares to find 02 (estimated value of the sample variance) for both
values of A. The final step is to select the value of A for which the
concentrated likelihood function (44) is maximized. The above
procedure is employed to avoid, a priori, assuming either the linear or
the semilogarithmic functional form, but instead to empirically
determine the best functional form for each of the sixty hedonic
equations.
The next step in the analysis is to use the hedonic coefficients to
construct a crosssectional Laspeyrestype (fixed weight, as opposed to
a fixed price Paasche index) housing price index for each of the four
race/tenure subgroups in each of the fifteen SMSAs. The housing price
index (Pjk) for the race group j in city k when the functional form of
jk
the hedonic equation is linear is as follows:
P = jk x 100
jk k
WjkP
where city k = 1,...,15
characteristic i = 1,...,15
race j = 1,2
15
Pjk = bi,j,k X
i=1
15 15 2
P = E E b.,, X.
k=l i=1 j=l l k
X. = means of housing variables (characteristics) across entire
1
sample.
Wjk = weight of the racial/tenure group j in city k relative to
the entire owner or renter samples (N).
b. k = hedonic equation regression coefficient for
characteristics i for race group j in city k.
[w == EW =11
[jk N jk 1]
The idea behind the index is to price the characteristics of a
particular racial group in a certain city relative to the price
paid for the same bundle of housing characteristics (note that X. is in
the numerator and denominator of the price index) in the entire owner or
renter samples. An analogous procedure is followed on the above index
TABLE 1: LIST OF DEPENDENT AND INDEPENDENT VARIABLES USED IN THE
HEDONIC EQUATION REGRESSION ANALYSIS
DEPENDENT VARIABLES
V PROPERTY VALUE OF OWNEROCCUPIED HOUSE ($'000)
R ANNUAL CONTRACT RENT ($)
INDEPENDENT VARIABLES
AGEST AGE OF STRUCTURE
BEDR NUMBER OF BEDROOMS IN HOUSING UNIT
S
T FLOORS NUMBER OF FLOORS IN BUILDING
R
U AIRCN 1 IF AIR CONDITIONING IN HOUSING UNIT
C
T WORKELEC 1 IF WORKING ELECTRICAL WALL OUTLETS IN EVERY ROOM
U
R RATS 1 IF SIGN OF RATS OR MICE IN LAST THREE MONTHS
A
L TELEP 1 IF HAVE USE OF A TELEPHONE
BATH* NUMBER OF BATHROOMS IN HOUSING UNIT
N
E
I PBTRANS 1 IF ADEQUATE PUBLIC TRANSPORTATION IN NEIGHBORHOOD
G
H SCHOOL 1 IF ADEQUATE PUBLIC SCHOOLS IN NEIGHBORHOOD
B
0 POLICE 1 IF ADEQUATE POLICE PROTECTION IN NEIGHBORHOOD
R
H RECR 1 IF ADEQUATE OUTDOOR RECREATIONAL FACILITIES IN
0 NEIGHBORHOOD
0
D
L
0 INOUTCC 1 IF HOUSING UNIT LOCATED INSIDE CENTRAL OR SECOND
C CENTRAL CITY IN SMSA
A DIST* MILES FROM HOUSEHOLDER'S HOUSING UNIT TO WORK
T
I TIMWORK* MINUTES FOR HOUSEHOLDER TO TRAVEL FROM HOUSING UNIT
0 TO WORK
N
*indicates quantitative variable
when the functional form of the hedonic equation is semilogarithmic.
This part of the analysis will prodt*f two sets of indices, one for
renters and one for homeowners. Each index has 30 values, corresponding
to the fifteen SMSAs and the two racial groups.
The fifteen variables that are used in this study are listed in the
following table. As can be seen, eight are structural, four neighbor
hood, and three locational characteristics. Though the Annual Housing
Survey provides many more housing characteristics, these fifteen out
perform the others in explanatory power. Unfortunately, the neighbor
hood characteristics are all qualitative in nature. Also, square
footage of the housing unit was an unavailable structural characteristic
together with the locational variable distance of the housing unit to
the central business district.
The final step in the construction of the housing services price
indices for individual homeowners, namely po,w (white owners) and po,b
(black owners), is to adjust the owner SMSA/race indices just calculated
to take into account the implicit subsidy given to homeowners under the
current income tax laws (see Chapter III), such that
p oj [ V(lt) + (l1t) + D + M (grne)] p
V 0
where
poj = individual housing price index for jth homeowner,
P = homeowner housing services price index for the relevant
owner SMSA/race group computed from the hedonic regression
analysis.
Prior to this final step, every white homeowner in Anaheim, for
example, had exactly the same housing price index value. This final
adjustment for homeowners introduces price differentials within each
group. That is, the price varies within Anaheim to reflect tax rate and
equity differences across households. The nominal capital gains rate,
gN(=gr+je), used in this expression uses data from the U.S. Department
of Housing and Urban Development (see Table 41) on the average property
values in the selected SMSAs between 1980 and 1981. That rationale
behind calculating a historical capital gains rate is that it is the
best guess available for an estimate of the future capital gains rate.
The final step in the construction of the housing services price
indices for individual renters, namely pr,w (white renters) and r,
(black renters), examines whether the renter price indices calculated
should take into account discounts given to renters for length of
tenure. In a survey article of the rent discount literature, Marshall
and Guasch (1983) concluded that landlords offer sitting tenants
discounts which average approximately 1% for each year of renter
occupancy, after the first year, as follows:
Prj = Pr (.01)*(n1)*(Pr)
where
prj = individual housing price index for jth renter,
n1 = years of renter residency at present unit 1,
P = renter housing services price index for relevant
SMSA/race group computed from the hedonic regression
analysis.
The final demand equations are estimated with and without the adjustment
to the renter price indices that takes into account any discounts given
to renters for length of tenure.
The price index for all goods and services, excluding shelter (px)
for each SMSA used in this study is constructed based on the relation
ship between the nonhousing and housing budgets for a 4person family
in the United States obtained from the U.S. Department of Labor (1982).
The purpose of this annual budget survey is to determine for each of the
24 metropolitan areas in the survey the cost of purchasing a specific
market basket of goods that reflects the usual purchasing patterns of a
typical 4person family. Each item priced in the budget is placed in
one of the following five categories:
1) food,
2) housing,
3) medical care,
4) transportation,
5) all other categories.
The price index of all goods and services (excluding shelter) used
in this thesis relies on the relationship between the nonhousing and
housing budgets in the 24 metropolitan areas in the 1981 family budget
survey holding true for the 15 SMSAs in my 1981 Annual Housing Survey
dataset (see Appendix, Table 35). The regression of the nonhousing
indices on the housing indices from the BLS budget survey quantifies how
much variation in the nonhousing price index is explained by the
housing component
(Nonhousing index) = a + b (Housing index)
An ordinary least squares regression of the above equation yielded the
following results:
Nonhousing Index = 43.9781 + 0.5602 (Housing Index) (45)
standard errors (9.0256) (0.0897)
tstatistics (4.8776) (6.2418)
R2 = 0.6391
N = 24
Variation in the housing price index explains twothirds of the
variation in the nonhousing price index in the 24 metropolitan areas
included in the family budget survey. Both the constant term and single
regressor are highly significant. My study uses the above relationship
to construct the overall price indices of all goods and services,
excluding shelter (px) in each of the fifteen SMSAs in my sample.
The next stage in the construction of the price index of all
nonhousing goods and services in, say, Anaheim is to weight each of the
four housing price indices in Anaheim calculated from the hedonic
equations by population, as follows:
n1 white n2 black n3 white n4 black
nl whit) + (Po+ (p, )+(p )+ (Pr )
PH N o' owner N o' owner N r' renter N r renter
where
PH = housing price index for Anaheim
n, = number of white owners in Anaheim
n2 = number of black owners in Anaheim
n3 = number of white renters in Anaheim
n4 = number of black renters in Anaheim
N = n1 + n2 + n3 + n4
The next step is to substitute in the pH index for Anaheim on the
righthand side of equation (45) in order to calculate the price index
of all goods and services (excluding shelter) in Anaheim. I repeat the
procedure for the remaining fourteen SMSAs in my sample.
The next variable which has to be constructed is permanent income,
y Numerous methods have been proposed for estimating this unobser
vable variable, including (1) grouping data, (2) income averaging over
an arbitrary number of years, and (3) instrumental variable methods.
There is no widely accepted technique in the literature of calculating
unobservable permanent income. As my data set is crosssectional, it
was not possible to average income over an arbitrary number of years.
However, Mayo (1977) has shown that permanent income elasticities
obtained by income averaging and by instrumental variable techniques are
on the same order of magnitude. In Chapter III the problems encountered
in accurate coefficient estimation were discussed when current income is
used as a proxy for permanent income. This study will utilize Milton
Friedman's (1957) Permanent Income Hypothesis in the construction of a
measure of permanent income:
YC = Yp + YT (identity)
where
YC = Current Income
Yp = Permanent Income
Y = Transitory Income
The Permanent Income Hypothesis assumes that permanent income
depends on human and nonhuman wealth, H and NH, so that:
Y = f(H,NH) (46)
On substituting (46) into the identity we get
YC = f(H,NH) + YT
(47)
On the assumption that permanent income is encompassed by the human
and nonhuman wealth components, the systematic part in the regression
of current income on the human and nonhuman wealth variables represents
an estimate of permanent income. The nonsystematic part, the residual,
represents an estimate of transitory income. The following table lists
the variables chosen in the regression to estimate permanent income.
TABLE 2: LIST OF INDEPENDENT VARIABLES USED IN THE
PERMANENT INCOME REGRESSION EQUATION ANALYSIS
EDUC Years of education of household head
AGE Age of household head
SEXHH 1 if household head is female
MARHH 1 if household head is presently married
CHIL Number of children (under 18 years of age)
RACE 1 if household head is black
SMSA SPECIFIC FEATURES
P Price index of all goods and services (excluding
x shelter) in SMSA where housing unit located
COOL Average number of cooling degree days per annum in
SMSA where housing unit located
See appendix for a complete definition of this variable.
DEP VAR = LOG YC (TOTAL FAMILY INCOME)
HUMAN AND NONHUMAN WEALTH VARIABLES
In the above specification, the AGE variable is a proxy for
experience and the EDUC variable picks up human capital and skills,
while the (AGE)2 and (EDUC)2 terms are experimented with to determine if
there are diminishing or increasing marginal returns associated with
increased age and education. The (AGE)2 variable picks up any falling
investment in human capital as age increases (see Mincer (1974)). The
AGE, MARHH, and CHIL variables all determine the position of the
household head in his life cycle and how this affects his income. The
MARHH variable picks up differences in human capital formation by
married as opposed to single heads of household. It is expected that a
married head of household will have accumulated more human capital than
a single head in order to support his spouse and children, hence a
positive sign on this variable. Unfortunately, the data set has no
detail available on the labor force participation rate within the
household, which is correlated with total family income.The RACE
variable picks up any differences in human capital formation between
blacks and whites with regard to earnings. Similarly, the SEXHH
variable picks up differences in human capital accumulation between
males and females with regard to earnings. Women generally have less
human capital accumulated than men because they work fewer years due to
child rearing responsibilities.
As can be noted in the previous table there are also SMSA specific
features in the permanent income regression. As this is one regression
on the entire sample, one can add such variables for each SMSA to cap
ture any intercity differentials in earnings. These variables capture
cost of living and amenity wage differentials between the SMSAs in the
study. The SMSA specific variables are estimated in this equation in
both linear and logarithmic form.
Heckman and Polachek (1974) conclude that there is overwhelming
evidence that the best functional form relating current income and the
wealth variables is semilogarithmic, with the dependent variable in
logarithmic form. However, there is no, a priori, evidence on the
functional form of the SMSA specific variables. Therefore, these
variables are tried in linear and logarithmic form using ordinary least
squares on the equation.
Having constructed the housing price indices and the permanent
income estimates as described above, I next use the price and income
variables, along with other variables, in the tenure choice and then
finally the housing demand equations.
The variables selected for the tenure choice decision equation
specification are shown in Table 3. The chosen variables give insight
into why a household head would own, rather than rent, a housing unit,
and vice versa. Two of these variables, namely AGEHH and MARHH,
indicate where the household head is and how he is faring on his life
cycle. The AGEHH variable picks up the household head's accumulated net
assets and savings, while the MARHH variable picks up income stability.
There is likely to be less risk of default on a mortgage when the
household head is married as there are two potential wage earners in the
household. The probability of owning is expected to be positively
correlated with both variables.
___j
TABLE 3: LIST OF INDEPENDENT VARIABLES USED IN THE TENURE CHOICE
REGRESSION EQUATION ANALYSIS
DEP VAR = I(INDEX FUNCTION)
LOG(AGEHH) Age of household head
MARHH 1 if household head is married or widowed
MOVER 1 if household head moved to present residence within
the past 12 months
LOG(poi /rj ) Relative price of owning versus renting
The MOVER variable examines how the recent mobility of the head of
household affects the probability of owning. It is anticipated that the
expected probability of owning is negatively correlated with this
variable. Persons constantly on the move are less likely to want to
incur the high fixed costs (e.g., appraisals, origination fees, and
points) associated with buying and selling a house if they are not going
to be living at that location for very long.
The tenure choice equation also has a relative price term
(p oi/p .). It is expected that as the relative cost of owning, as
opposed to renting, rises in an SMSA, the expected probability of a
household head renting increases, and vice versa. Therefore, the
expected sign on this variable is negative. To construct this relative
price term for a household unit there has to be an owner price (poi) as
well as rental price (p .). If the housing unit is a white owner in
Anaheim, the owner price is the calculated price (p .oi) for a white
homeowner in Anaheim, and the rental price is assumed to be the price
for a white renter in Anaheim, namely prj, and vice versa.
The tenure choice equation is estimated on the entire sample,
excluding housing price indices constructed from sample sizes less than
100, using the Probit procedure. The continuous variables in the
equation are experimented with in linear and logarithmic form. Housing
price indices constructed from samples less than 100 are excluded from
the tenure choice regression (and all the subsequent housing demand
regressions) in order to avoid any false inferences drawn from using
housing price indices constructed using small sample sizes. Consequent
ly, a number of black owner and renter groups in certain SMSAs are
excluded from the remainder of this analysis.
The final step in my study is to bring in all the constructed
variables from the previous steps in the analysis and estimate the
housing services demand equations using the following variables:
TABLE 4: LIST OF INDEPENDENT VARIABLES USED IN THE
HOUSING SERVICES DEMAND REGRESSION EQUATION ANALYSIS
DEP VAR = e/P (DEFLATED EXPENDITURES ON HOUSING SERVICES)
x
Y /P Permanent income, deflated by the price index of all
S goods and services
Po/ /Px Price index of housing services, deflated by the
price index of all goods and services
A Expected value of errors in the tenure choice
equation
SEXHH 1 if household head is female
MARHH 1 if household head is presently married
AGE Age of household head
These are standard explanatory variables that should appear on the
right hand side of any housing demand equation; a price, income, and a
set of demographic variables. The one exception is the A variable,
which if statistically significant, shows that there is simultaneity
between the tenure choice decision (own or rent) and the housing demand
decision, i.e., how much housing services to consume. To tie things
together, A is obtained from the tenure choice equation, permanent
income (y ) from the permanent income hypothesis instrumental variable
equation, and the owner price indices (p ) and the renter price indices
(pr) from the hedonic price equations.
The housing services demand equations have housing expenditures as
the dependent variables, and use the same manipulations described in
Chapter I to derive the relevant housing demand elasticities. Using the
white owner housing services demand equation as an example
log(qw) = 0 + 8 log(p O) + 62 log( w ) + 3 log(px) + Aow +
7
E B.D. + E (48)
j=5 3 j,o,w o,w
Here, B1 and 82 are the price and permanent income elasticities of
housing services demand, respectively, for white homeowners in the
entire sample. Using the same equation transformations found in Chapter
I, one can derive the following estimable logarithmic housing demand
equation:
log(eow/P ) = + (1+Bl)log(pow/P ) + 82 log(yo w/Px) + 4Aow +
7
Z 8. D. + (49)
j=5 j',o,w o,w
The estimation of equation (49) using ordinary least squares
yields the price and income elasticities of housing services demand for
white owners in the entire sample. By stratifying the entire sample
into three further groups, namely black owners, white renters, and black
renters, and following the same procedure described above, the price and
income elasticities of housing services demand for these three race/tenure
groups can also be estimated. The main purpose of this dissertation is
to estimate these eight racial price and income housing services demand
elasticities. The demand equations are run with and without the vari
ables measuring the expected value of the errors in the Probit equation
(A or A ) to examine how sensitive the price and income elasticities of
o r
housing services demand are to the exclusion of these variables.
A further piece of empirical work is to stratify each of the four
race/tenure groups into three educational attainment levels:
i) elementary education: no school, kindergarten, or did not
graduate from high school.
ii) high school education: graduated from high school.
iii) college education: attended college for any amount of time.
The purpose of this piece of analysis is to examine whether the price
elasticity of housing services demand varies by educational attainment of
the household head. An Ftest is conducted on each of the four
race/tenure groups to see whether there are statistically significant
differences in the price elasticity of housing services demand across the
three levels of educational attainment. By holding the level of education
constant, there should be less variation in permanent income, which makes
it very hard to estimate an income elasticity. The idea behind this final
section is to compare, say, white homeowners in Dallas to white homeowners
in Boston with college educations, and compare their price elasticity of
demand to that of white homeowners in the same two SMSAs with high school
levels of education.
The final piece of empirical work is to compare the price and income
elasticities of housing services demand obtained using the endogenously
constructed hedonic price indices from the Annual Housing Survey to those
obtained from the Bureau of Labor Statistics family budget survey.
Although other authors, namely Gillingham (1975) and Follain, Ozanne and
Alburger (1979), have looked at differences between hedonic housing price
indices and housing price indices from the family budget survey, nobody
has looked at the consequences of using the two types of indices in a
housing demand study and their consequences, if any, on estimates of price
and income housing demand elasticities.
The SMSAs covered in the 1981 Annual Housing Survey and the Bureau of
Labor Statistics family budget survey in any year are not identical.
However, using the 1978 family budget survey when the BLS last conducted
its survey in 39 cities (since 1978 it surveys 24 cities) resulted in
eight common SMSAs between the Annual Housing and the BLS family budget
surveys. These cities were Boston, Dallas, Detroit, Minneapolis, Orlando,
Pittsburgh, Washington D.C., and Wichita. Housing and nonhousing price
indices were computed for these eight SMSAs from the BLS budget data (see
Table 42) and used in the final housing demand equations to compute
housing demand elasticities. These elasticities were compared to those
generated using endogenously constructed hedonic housing and nonhousing
price indices from the 1981 Annual Housing Survey.
41
The Mills ratio variable (Ao/r) was dropped from this set of
regressions because in its construction back in the Probit analysis, one
of the variables used in the Probit regression is a relative price of
owning versus renting variable (poi /Prj). As the BLS housing index does
not differentiate between owning and renting costs, it is an overall
shelter cost, it was decided that adding the Mills ratio variable would
cause serious methodological problems in the BLS set of regressions.
Hence, for consistency, it was dropped from both the BLS and AHS set of
demand equation regressions.
CHAPTER V
EMPIRICAL RESULTS AND DISCUSSION
This chapter analyzes the results from the intermediate steps on
the way to obtaining the price and income elasticities of housing
demand. The order of discussion of the regression results will be as
follows:
1. hedonic equations used in the construction of the price
indices,
2. instrumental variable equation used to construct an estimate
of permanent income,
3. tenure choice decision equation,
4. the housing demand equations from which the housing demand
elasticities are computed.
Tables 5 through 19 tabulate the results from the hedonic
regression analysis used to compute the Laspayretype housing services
price indices. It is not practical to individually discuss every
regression coefficient in these tables as for each of the four
race/tenure groups examined in each of the fifteen SMSAs there are
fifteen regression coefficients (excluding the constant term) to
explain, a total of 9001 regression coefficients. Therefore, the Pearson
P test (see Rao (1952)) is employed to determine whether the individual
explanatory variables are generally significant. This test assumes that
each hedonic regression is independent from every other one within a
tenure category. Table 20 presents the results from this test, together
with the mean effects of each explanatory variable in the sample. Using
this test, all the explanatory variables used in the hedonic equations
were significant overall, except POLICE for renters and TIMWORK for
homeowners.
The independent variables used in the hedonic regressions also
performed well in explaining the variation in the dependent variables,
as can be seen from the magnitudes of the coefficients of determination
(R2). The mean R2 was 0.48 in the twentynine owner regressions and
0.37 in the thirty renter regressions. The owner and renter equations
are not comparable by looking at R2's, as the dependent variables
differ, logarithmic house value for homeowners and linear annual
contract rent for renters. It should be noted that crosssectional data
are used in this study, and that the R 's are not comparable to the
generally higher R2's obtained when using timeseries data.
Another result from the hedonic equation regression analysis is the
best functional form chosen for the owner and renter equations from the
BoxCox transformations. All the owner regressions resulted in an
optimal value of A of zero, implying a semilogarithmic form for all the
2
owner regressions. All but one of the renter regressions resulted in
an optimal value of A of one, implying a linear form for these
equations.
The above results are consistent with the notion that a renter pays
for specific housing accessories through explicit extra rental payments
to a landlord. The coefficients in a linear model measure the extra
dollar cost in the dependent variable (in this case annual contract
rent) associated with a one unit change in an explanatory variable. An
example is where a renter pays $x in rent when he moves to an apartment
complex with a swimming pool, when he was paying $y when he used to live
in an apartment complex without a pool, the two apartment complexes
being virtually identical in all other attributes. The $(xy) is the
amount of money the renter is willing to pay in order to have pool
facilities. Theoretically, introducing a dummy variable for pool
facilities into a linear hedonic equation for renters would produce a
coefficient on the pool variable of (xy).
The semilogarithmic form for the owner hedonic regressions
measures the percentage change in the dependent variable (in this case
value of the owner's house) associated with a one unit change in an
explanatory variable. Therefore, the semilogarithmic form allows the
value added by an extra unit of an explanatory variable to vary with the
value of the owner's house. An additional bathroom adds z% to the value
of a house, avoiding the linear form inference that an additional
bathroom adds the same extra $k to a $10,000 house as a $300,000 house.
A plausible explanation for this is that there is more heterogeneity in
terms of quality and quantity in owneroccupied housing than in rental
housing. The mean effects of individual housing characteristics in
owner and rental housing markets are contained in Table 20.
One thing that becomes evident from this analysis is that certain
housing characteristics play differing roles across the SMSAs in the
sample. Numerous characteristics are significant in one SMSA with, say,
a positive sign, and are significant in another SMSA with the opposite
sign. It is clear from this study that some housing characteristics
have indeterminate signs and that the role of the housing characteristic
is determined partly by the SMSA in which it is located.
The analysis now turns to focus in more detail on the magnitudes of
the variables in the hedonic equations and the expected effects of the
variables in terms of economic theory.
One expects the sign of AGEST to be negative, as housing stock
depreciates with age. As Table 20 shows, this was the case overall for
renters and homeowners. However, one can think of instances in certain
downtown neighborhoods (e.g., Baltimore and Jacksonville) where
tremendous incentives have been given by city councils to individuals
who renovate old houses in downtown neighborhoods. The success of this
type of program on a wide scale would lead to the AGEST variable having
a positive sign. Another scenario for the AGEST having a positive sign
is if there are some unaccounted for locational features positively
correlated with the age of the unit. Such features include, for
example, proximity to a lake or a nature trail. In this study, the
AGEST variable was significant and positive for white owners in
Washington D.C., as well as black renters in Minneapolis, Newark, and
Phoenix. For each year a housing unit ages, the value falls by i% for
an owneroccupied home and by $11 in annual contract rent for an
apartment.
Both BEDR and AIRCN had positive signs, reflecting that the more
bedrooms and the presence of air conditioning units both add value or
rent to a housing unit. Each bedroom adds nearly 9% in value to a
homeowner's house and $238 in annual contract rent to a rental unit.
AIRCN was significant, not surprisingly, across all four race/tenure
groups in the following SMSAs with high mean annual temperatures, namely
Dallas, Fort Worth, Orlando, and Phoenix. The structural characteristic
that performed best in terms of overall significance was BATH. This
characteristic had a positive sign for renters and owners, reflecting
that additional bathrooms add value or rent to a housing unit. The
presence of rats or mice in a housing unit did not add dollars in value
or rent to a housing unit as in no case was this variable significant
and positive! The presence of these rodents reduces home values by
approximately 6% while reducing annual rent for a renter by $155.
The presence of a telephone (TELEP) and working electrical wall
outlets in every room (WORKELEC) of a housing unit both entered the
hedonic regression equations, as expected, with positive signs.
The last structural characteristic, FLOORS (the number of floors in
the housing unit) entered the owner equation with a positive sign,
reflecting that the more floors in the house, the larger it probably is
and hence has a higher value. The sign of this variable in the renter
equations was also positive. However, it was not clear before the
regressions were run whether skyscraper rental apartments should command
higher rents than, say, twostory rental housing complexes. The overall
result from the regression analysis supports the former hypothesis.
On examining the four neighborhood variables employed in the
analysis, all four are specified as dummy variables with a value of one
for an adequate neighborhood characteristic and zero otherwise. The
RECR variable asks whether there are adequate outdoor recreational
facilities in the neighborhood. This variable had a positive effect on
housing values and rent, since land near recreational facilities is more
valued than other land. The presence of adequate outdoor recreational
facilities close to a housing unit adds just over 2% to the value of a
home and $145 in annual contract rent for a rental unit.
The POLICE variable asks the household head whether he considers
there is adequate police protection in the neighborhood. At first glance,
one might expect this variable to have a positive sign, reflecting high
values and rent in locations with high standards of police protection.
However, a convincing argument could be made for this variable having a
negative sign if crime and burglaries occur more frequently in areas of
high income households, i.e., criminals are more likely to be operating in
areas where the rich are their targets, not the poor. The POLICE vari
able came in negative overall for homeowners, bearing out the latter
hypothesis, while for renters it was one of only two variables not
generally significant at the 10% level.
The PBTRANS variable asks household heads whether their
neighborhoods have adequate public transportation, namely bus routes.
At first glance this variable might be expected to have a positive sign
for owners and renters. However, in owner regressions it was generally
significant but negative. A rationale for the negative sign in owner
hedonic regressions is that bus routes do not usually go through high
income neighborhoods, but instead provide poorer districts of an SMSA
with the means of transportation to the downtown and shopping malls.
The final neighborhood variable included in the hedonic analysis is
SCHOOL, which asks the household head whether there are adequate public
schools in the neighborhood. One associates good neighborhoods with
high quality schools in the suburbs of an SMSA. For owners, this
variable was generally significant and positive, supporting the previous
notion. However, it was negative and generally significant for renters.
A rationale for the negative signs is that the question asked of the
household head related to adequate public schools, with no mention of
private schools. This could be the premiere schooling choice of the
siblings of the household heads in the highincome neighborhoods.
The final set of variables included in the hedonic equations are
three locational variables, namely INOUTCC, DIST, and TIMWORK. The
variable that I really wanted is the distance of the housing unit from
the central business district. These three locational variables act as
proxies for this unavailable variable. INOUTCC has a value of one if
the housing unit is within the central or second central city of the
SMSA, zero if outside the central city. For owners and renters, it was
generally significant and negative. The location of the housing unit
within the boundary of the central city reduced, on average, the value
of the owner's home by nearly 12% while reducing annual rent payments by
$375 for renters. From the traditional monocentric model theory of
Mills and Muth, one expects the sign of this variable to be negative.
The assumptions underlying such traditional models include: (1) the
SMSA is located on a flat, featureless plain, and (2) all the production
and economic activity in the SMSA takes place in a single area in the
center, the central business district (CBD). The rationale for this
sign is that as income rises, individuals will trade off access to the
central business district (CBD) for more housing and land (space), which
is more available in the suburbs outside the central city. The
traditional theory incorporates the notion that the income elasticity of
demand for space (land) exceeds the income elasticity of the marginal
cost of commuting. A supporting argument relies on highincome families
having shallower sloped bidrent curves than lowincome families. As a
result, high income families buy large lots on relatively cheap land on
the outskirts of the SMSA. Also, central cities are generally more run
down and decaying gradually due to flight to the suburbs, this would be
particularly true for some northern cities. A negative sign can also be
expected if there is an inappropriate housing stock in the central city
of an SMSA, an example is the older cities that were built for downtown
rail transit. The INOUTCC variable will also have a positive sign if
the structural and neighborhood characteristics in the hedonic equation
capture all the quality and quantity aspects of the housing unit. If
this is the case, the remaining locational variables should measure the
price of land on which the housing unit sits. As the price per parcel
of land decreases as you move away from the CBD, the INOUTCC variable
should have a positive sign by this line of thought. However, the
structural and neighborhood variables in the hedonic analysis might not
capture all the quantity and quality aspects of the housing unit. As a
result of unmeasured housing quantity and quality measures, the sign of
INOUTCC can be expected to be positive. INOUTCC was negative and
significant for all four race/tenure groups in Detroit, MinneapolisSt.
Paul, and Newark, appearing to support the view concerning decaying
central cities within certain northern cities. However, this variable
was significant and positive in three cases for both owners and renters,
in particular in Dallas. In Dallas, this positive and significant sign
was the case for black and white owners, along with white renters. An
argument for the positive sign is relying on the traditional monocentric
model theory no longer holding for newer cities, such as Dallas.
The expected signs on the coefficients of the two remaining
locational variables, DIST (miles to work) and TIMWORK (time to work),
follow an analogous line of reasoning to INOUTCC. If the structural
50
and neighborhhod characteristics capture all the quantity and quality
aspects of the housing unit then the signs of these two variables will
be negative. However, if there are housing attributes not captured in
the hedonic equation, the signs on these variables will be positive. As
it turns out, these variables produce a mixed bag of overall positive
and negative significant coefficients in the hedonic regression
analysis.
TABLE 5: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
ANAHEIMSANTA ANAGARDEN GROVE SMSA
HOMEOWNERS: RENTERS:
V 1 RX1
DEP VAR DEP VAR 
WHITE BLACK WHITEBLACK
WHITE BLACK WHITE BLACK
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
x
R
N
10.83***
(0.16)
0.0004
(0.0007)
0.0576***
(0.0107)
0.0507***
(0.0170)
0.0503***
(0.0160)
0.1019
(0.1275)
0.0425
(0.0290)
0.0133
(0.0850)
0.3266***
(0.0162)
0.0338**
(0.0165)
0.0193
0.0187
0.0014
(0.0242)
0.0017
(0.0269)
0.1845***
(0.0197)
0.0039***
(0.0016)
0.0023**
(0.0011)
10.98***
(0.42)
0.0013
(0.0074)
0.0169
(0.0707)
0.0353
(0.1362)
0.2773**
(0.1097)
NA
NA
NA
0.3862***
(0.1107)
0.0173
(0.1068)
0.1770
(0.1306)
0.3651
(0.2260)
0.3354*
(0.1678)
0.3956**
(0.1484)
0.0094
(0.0096)
0.0004
(0.0055)
1706.46***
(657.32)
0.402
(3.069)
531.691***
(63.604)
12.177
(41.372)
182.600**
(89.105)
113.588
(595.233)
154.966
(173.513)
142.709
(176.764)
1138.435***
(100.909)
286.925***
(92.656)
64.529
(92.193)
52.999
(112.809)
500.971***
(123.520)
492.222***
(94.235)
2.285
(9.329)
5.919
(6.206)
4788.456*
(2523.281)
4.527
(11.862)
954.725**
(410.578)
95.464
(721.022)
294.498
(488.084)
589.986
(1294.244)
1397.370
(1159.442)
1081.681
(1193.806)
325.152
(694.979)
569.903
(545.716)
332.197
(676.789)
566.881
(759.258)
1155.930
(767.277)
747.876
(558.046)
10.995
(57.468)
59.948
(42.566)
0 0 1 1
0.39 0.92 0.33 0.75
2,103 22 1,360 28
(where standard errors are in parentheses)
*** indicates significant at
** indicates significant at
* indicates significant at
1% level
5% level
10% level
TABLE 6: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
BOSTON SMSA
HOMEOWNERS: RENTERS:
V l R11
DEP VAR DEP VAR 
SA
WHITE BLACK WHITE BLACK
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
x2
R
N
10.22***
(0.14)
0.0028***
(0.0008)
0.0560***
(0.0114)
0.0607***
(0.0119)
0.0453**
(0.0201)
0.1461
(0.1025)
0.1255***
(0.0401)
0.0405
(0.0824)
0.3472***
(0.0177)
0.0617***
(0.0206)
0.0085
(0.0239)
0.0285
(0.0289)
0.0633***
(0.0248)
0.2556***
(0.0298)
0.0021
(0.0020)
0.0008
(0.0012)
10.92"**
(0.72)
0.0253***
(0.0079)
0.0572
(0.0756)
0.3827***
(0.1515)
0.0541
(0.1430)
0.0307
(0.4674)
0.1568
(0.1840)
0.1458
(0.1756)
0.0899
(0.1222)
0.0242
(0.1576)
0.0523
(0.1558)
0.0479
(0.1747)
0.1251
(0.1465)
0.2528
(0.2232)
0.0078
(0.0125)
0.0026
(0.0055)
48.331
(457.785)
3.054
(3.245)
203.424***
(49.341)
101.818***
(15.912)
264.158***
(85.041)
253.935
(350.829)
57.836
(119.452)
181.820
(140.406)
1901.052***
(183.066)
44.678
(92.537)
440.972***
(84.610)
264.271***
(92.378)
365.731***
(88.753)
180.999**
(86.918)
26.486***
(8.456)
8.291*
(4.450)
689.409
(916.322)
9.456
(6.878)
52.598
(100.724)
109.791***
(36.873)
468.268***
(201.494)
1176.538**
(576.177)
151.423
(178.159)
143.494
(200.268)
1409.611***
(437.811)
7.913
(198.890)
294.673
(184.239)
57.251
(188.842)
354.574*
(183.480)
104.649
(343.974)
59.322***
(22.313)
7.088
(5.183)
0 0 1 1
0.40 0.58 0.18 0.19
1,510 43 1,727 268
(where standard errors are in parentheses)
*** indicates significant at
** indicates significant at
* indicates significant at
1% level
5% level
10% level
TABLE 7: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
DALLAS SMSA
HOMEOWNERS: RENTERS:
VX1 R_1
DEP VAR = DEP VAR =
WHITE BLACK WHITE BLACK
WHITE BLACK WHITE BLACK
9.54***
(0.17)
0.0004
(0.0009)
0.0844***
(0.0175)
0.0767***
(0.0182)
0.2397***
(0.0656)
0.0184
(0.1178)
0.0482
(0.0351)
0.0470
(0.0906)
0.5650***
(0.0192)
0.0452**
(0.0222)
0.0655**
(0.0274)
0.0111
(0.0320)
0.0526*
(0.0297)
0.0844***
(0.0239)
0.0003
(0.0023)
0.0023
(0.0016)
9.94***
(0.61)
0.0038
(0.0032)
0.1181*
(0.0631)
0.0819
(0.1545)
0.2616**
(0.1166)
0.7319
(0.5291)
0.1602*
(0.0838)
0.2252
(0.2108)
0.5457***
(0.0895)
0.1137
(0.1023)
0.2404*
(0.1270)
0.2757***
(0.0987)
0.0183
(0.0955)
0.3487***
(0.1103)
0.0020
(0.0078)
0.0024
(0.0051)
4.57
(533.40)
10.42***
(3.33)
147.11*
(66.62)
262.67***
(39.34)
1021.468***
(168.61)
292.04
(465.50)
75.56
(134.83)
148.49
(150.02)
1626.21***
(107.19)
196.44**
(91.56)
124.61
(94.81)
244.72**
(122.22)
516.09**
(105.66)
177.10*
(93.40)
12.96
(8.44)
0.90
(5.17)
1328.95**
(555.94)
30.92***
(5.39)
64.40
(94.92)
454.00***
(135.94)
857.09***
(179.30)
253.56
(403.81)
368.95***
(133.81)
31.41
(153.90)
1266.65**
(172.92)
315.44*
(173.05)
360.68**
(158.67)
24.09
(144.77)
227.53*
(131.22)
394.49**
(193.68)
10.75
(10.74)
6.82
(6.89)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
K2
R
N
*** indicates significant at
** indicates significant at
* indicates significant at
1% level
5% level
10% level
0 0 1 1
0.52 0.45 0.40 0.59
1,826 217 977 271
(where standard errors are in parentheses)
TABLE 8: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
DETROIT SMSA
HOMEOWNERS: RENTERS:
V 1 R 1
DEP VAR= DEP VAR 
ITEBLACKWHITE BLACK
WHITE BLACK WHITE BLACK
9.77***
(0.15)
0.0083***
(0.0008)
0.0571***
(0.0128)
0.0545***
(0.0155)
0.0319*
(0.0164)
0.0763
(0.0929)
0.1556***
(0.0339)
0.3589***
(0.1106)
0.3632***
(0.0156)
0.0610***
(0.0169)
0.0518***
(0.0194)
0.0837***
(0.0245)
0.0394*
(0.0214)
0.5768***
(0.0245)
0.0023
(0.0020)
0.00005
(0.00140)
10.06***
(0.21)
0.0116***
(0.0021)
0.0009
(0.0287)
0.0391
(0.0457)
0.1891***
(0.0401)
0.2093*
(0.1223)
0.1097**
(0.0517)
0.0809
(0.1014)
0.2984***
(0.0429)
0.0146
(0.0438)
0.0058
(0.0444)
0.0131
(0.0429)
0.0870**
(0.0419)
0.2161***
(0.0661)
0.0045
(0.0039)
0.0008
(0.0026)
1366.86***
(481.47)
11.22***
(3.60)
154.33**
(65.39)
16.39
(21.39)
467.49***
(106.83)
438.30
(330.31)
96.70
(156.89)
64.47
(164.13)
676.37***
(177.34)
135.99
(94.96)
93.94
(95.06)
217.10*
(125.06)
240.51**
(111.22)
551.19***
(119.48)
12.34
(12.34)
6.91
(7.15)
2319.13"**
(328.58)
7.06**
(3.29)
63.77
(41.32)
47.53***
(11.76)
433.12***
(83.31)
53.45
(156.12)
16.12
(76.96)
64.03
(91.83)
383.86***
(188.15)
94.17
(84.15)
18.54
(73.68)
15.78
(75.09)
169.25**
(74.77)
662.49***
(140.23)
3.42
(7.79)
2.97
(3.37)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
A
R
N
*** indicates significant at
** indicates significant at
* indicates significant at
1% level
5% level
10% level
0 0 1 1
0.60 0.25 0.25 0.24
2,207 570 665 447
(where standard errors are in parentheses)
TABLE 9: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
FORT WORTH SMSA
HOMEOWNERS: RENTERS:
V_1 RR1
DEP VAR = DEP VAR 
WHITE BLACK WHITE BLACK
9.27***
(0.17)
0.0020**
(0.0008)
0.0705***
(0.0150)
0.0765**
(0.0322)
0.3630***
(0.0477)
0.0736
(0.1195)
0.0566**
(0.0259)
0.1482*
(0.0920)
0.5499***
(0.0181)
0.0375*
(0.0199)
0.0292
(0.0231)
0.0128
(0.0250)
0.0725***
(0.0215)
0.0118
(0.0209)
0.0004
(0.0017)
0.0003
(0.0013)
8.36***
(0.45)
0.0163***
(0.0031)
0.0669
(0.0552)
0.4068*
(0.2465)
0.2201**
(0.1050)
0.4569
(0.2882)
0.0785
(0.0738)
0.3401**
(0.1507)
0.4363***
(0.0850)
0.0105
(0.0983)
0.2330**
(0.1170)
0.0761
(0.0817)
0.1390*
(0.0744)
0.0799
(0.1162)
0.0084
(0.0072)
0.0007
(0.0047)
239.39
(561.66)
15.19***
(3.65)
178.61**
(68.80)
176.94***
(48.02)
739.48***
(157.91)
157.60
(514.25)
277.36**
(130.37)
17.32
(140.39)
1337.97"**
(118.46)
388.29***
(100.00)
53.62
(104.23)
7.49
(123.70)
314.91***
(111.66)
100.62
(101.51)
2.91
(8.97)
1.33
(6.71)
1101.91
(868.37)
17.06***
(5.41)
12.44
(122.32)
209.36
(184.32)
420.96**
(194.15)
1985.67***
(762.06)
111.54
(164.82)
220.87
(181.55)
1350.81***
(248.56)
12.46
(212.77)
67.44
(222.04)
271.63
(190.66)
189.09
(183.25)
920.81***
(283.31)
5.58
(15.55)
1.00
(9.32)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
R
N
0 0 1 1
0.50 0.49 0.34 0.42
2,262 202 881 173
(where standard errors are in parentheses)
*** indicates significant at 1% level
** indicates significant at 5% level
* indicates significant at 10% level
TABLE 10: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
MADISON SMSA
HOMEOWNERS: RENTERS:
V 1 R1
DEP VAR =  DEP VAR 
WHITE BLACK WHITE BLACK
WHITE BLACK WHITE BLACK
9.98***
(0.12)
0.0041***
(0.0005)
0.0738***
(0.0098)
0.0381***
(0.0130)
0.0447***
(0.0134)
0.2411***
(0.0621)
0.0145
(0.0215)
0.2202**
(0.0961)
0.2784***
(0.0115)
0.0231
(0.0147)
0.0260
(0.0194)
0.0133
(0.0240)
0.0005
(0.0247)
NA
0.0012
(0.0016)
0.0003
(0.0011)
308.41
(387.04)
1.57
(2.12)
448.00***
(37.13)
140.33***
(22.32)
346.18***
(68.89)
1141.11***
(293.95)
36.40
(101.95)
173.14
(169.41)
552.55***
(112.47)
325.64***
(69.74)
89.96
(61.77)
140.28*
(85.96)
16.74
(91.43)
NA
4.00
(6.55)
3.37
(3.75)
196.48
(1427.52)
6.04
(10.24)
266.86
(246.48)
86.93
(156.44)
1062.12**
(406.08)
NA
962.15
(757.43)
283.83
(558.47)
647.81
(690.92)
333.88
(549.70)
353.05
(440.83)
30.37
(515.05)
83.94
(501.45)
NA
17.47
(76.64)
45.69
(35.79)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
1
R
N
*** indicates significant at 1% level
** indicates significant at 5% level
* indicates significant at 10% level
0 NA 1 1
0.42 NA 0.20 0.52
1,936 8 1,311 43
(where standard errors are in parentheses)
TABLE 11: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
MINNEAPOLISST. PAUL SMSA
HOMEOWNERS: RENTERS:
V X1I RX1
DEP VAR =  DEP VAR =
WHITE BLACK WHITE BLACK
10.75 11.13*** 951.54** 323.71
(0.14) (0.91) (488.71) (1345.46)
0.0020*** 0.0108 2.12 30.26*
(0.0006) (0.0074) (3.06) (15.65)
0.0832*** 0.0386 474.67*** 561.04**
(0.0084) (0.0744) (58.55) (273.31)
0.0422*** 0.1436 94.92*** 238.95***
(0.0076) (0.1232) (14.77) (79.77)
0.0536*** 0.2703* 565.94*** 15.05
(0.0145) (0.1553) (94.36) (406.04)
0.0310 296.61
(0.0580) NA (362.66) NA
0.0131 0.0970 159.82 283.31
(0.0223) (0.1402) (131.11) (460.68)
0.1994* 0.1994 276.91 245.92
(0.1173) (0.3096) (222.90) (637.79)
0.2868*** 0.4371** 944.33***
(0.0113) (0.1599) (140.73) NA
0.0328** 0.2970* 86.52 766.38
(0.0153) (0.1676) (109.22) (552.95)
0.0190 0.1418 223.62*** 404.64
(0.0184) (0.2138) (84.38) (457.17)
0.0185 0.1016 57.92 1719.43***
(0.0238) (0.1650) (116.10) (584.77)
0.0052 0.0178 78.93 882.19*
(0.0225) (0.3834) (121.38) (495.05)
0.0870*** 0.6879** 264.38*** 2374.58***
(0.0182) (0.2403) (94.95) (696.16)
0.0054*** 0.0219** 7.95 51.77
(0.0017) (0.0104) (10.24) (58.49)
0.0039*** 0.0098 1.50 50.82*
(0.0011) (0.0071) (6.46) (30.45)
0 0 1 1
0.43 0.79 0.29 0.52
2,275 28 1,005 50
(where standard errors are in parentheses)
*** indicates significant
** indicates significant
* indicates significant
at 1% level
at 5% level
at 10% level
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
X
S
R
N
TABLE 12: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
NEWARK SMSA
HOMEOWNERS: RENTERS:
V _ R_1
DEP VAR DEP VAR 
WHITE BLACK WHITE BLACK
10.71***
(0.16)
0.0059***
(0.0008)
0.1081***
(0.0120)
0.0431**
(0.0180)
0.0112
(0.0207)
0.0085
(0.1216)
0.0378
(0.0445)
0.0902
(0.0956)
0.2922***
(0.0139)
0.0111
(0.0188)
0.0366
(0.0234)
0.0692*
(0.0363)
0.0603**
(0.0256)
0.5598***
(0.0772)
0.0032*
(0.0017)
0.0009
(0.0009)
10.67"**
(0.42)
0.0163***
(0.0044)
0.0613
(0.0497)
0.1932**
(0.0945)
0.0327
(0.0843)
0.0639
(0.2626)
0.0092
(0.1242)
0.1446
(0.2009)
0.2809***
(0.0710)
0.0182
(0.0942)
0.0007
(0.1044)
0.0099
(0.1257)
0.0773
(0.1048)
0.3172**
(0.1503)
0.0090
(0.0070)
0.0015
(0.0051)
2366.79***
(521.77)
25.02***
(3.99)
296.64***
(67.36)
8.00
(19.19)
263.53**
(107.03)
413.08
(395.69)
173.71
(170.50)
367.92*
(196.20)
974.61"**
(173.94)
18.25
(103.27)
116.32
(100.99)
24.25
(136.66)
221.64**
(108.33)
817.72***
(151.52)
16.88*
(10.35)
0.36
(5.24)
1482.36***
(446.61)
9.60**
(4.32)
246.00***
(59.28)
22.71
(15.29)
716.29***
(111.49)
145.88
(220.27)
131.32
(110.18)
130.47
(138.42)
482.57*
(273.48)
180.86
(133.20)
97.97
(109.48)
12.28
(123.10)
51.29
(116.36)
549.44***
(116.90)
6.19
(9.79)
4.44
(5.24)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
2
R
N
*** indicates significant at
** indicates significant at
* indicates significant at
1% level
5% level
10% level
0 0 1 1
0.49 0.40 0.22 0.24
1,446 118 835 429
(where standard errors are in parentheses)
TABLE 13: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
ORLANDO SMSA
HOMEOWNERS: RENTERS:
V_1 R 1
X A
ITDEP VAR = ITDEP VAR BLACK
WHITE BLACK WHITE BLACK
9.42***
(0.21)
0.0002
(0.0007)
0.1191***
(0.0135)
0.0501***
(0.0153)
0.2402***
(0.0391)
0.0940
(0.1954)
0.0904*
(0.0468)
0.1807***
(0.0634)
0.4601***
(0.0176)
0.0214
(0.0190)
0.0280
(0.0195)
0.0008
(0.0233)
0.0881**
(0.0190)
NA
0.0013
(0.0022)
0.0008
(0.0017)
9.40***
(0.31)
0.0048*
(0.0025)
0.2234***
(0.0511)
0.0812
(0.1604)
0.2143***
(0.0696)
0.3094*
(0.1933)
0.0354
(0.0743)
0.0103
(0.1089)
0.3380***
(0.0748)
0.0426
(0.0680)
0.1950**
(0.0820)
0.1594**
(0.0710)
0.0247
(0.0641)
NA
0.0041
(0.0065)
0.0008
(0.0032)
869.95*
(464.39)
10.63***
(2.90)
342.04***
(57.05)
43.42**
(19.30)
655.07***
(139.70)
25.29
(407.99)
373.59**
(175.76)
19.44
(106.78)
800.11**
(96.14)
78.01
(82.77)
32.41
(80.36)
122.30
(92.85)
201.35**
(88.32)
NA
5.22
(9.16)
3.15
(6.35)
96.60
(516.34)
8.78*
(5.17)
103.66
(80.19)
149.02
(142.56)
612.75**
(156.50)
292.29
(286.44)
520.18***
(157.92)
255.50*
(134.10)
1404.07**
(207.61)
280.44*
(147.51)
88.24
(141.35)
96.22
(154.60)
155.90
(132.83)
NA
15.04
(15.82)
0.55
(9.87)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
x
R2
N
*** indicates significant
** indicates significant
* indicates significant
at 1% level
at 5% level
at 10% level
0 0 1 1
0.46 0.38 0.31 0.52
2,037 230 879 193
(where standard errors are in parentheses)
TABLE 14: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
PHOENIX SMSA
HOMEOWNERS: RENTERS:
V 1 R 1
DEP VAR DEP VAR 
HITE BLACK WHITE BLACK
WHITE BLACK WHITE BLACK
9.71"**
(0.14)
0.0016**
(0.0006)
0.1233***
(0.0112)
0.0134
(0.0160)
0.3060***
(0.0222)
0.2405*
(0.1273)
0.0035
(0.0364)
0.0130
(0.0501)
0.3545***
(0.0176)
0.0449***
(0.0169)
0.0087
(0.0179)
0.0191
(0.0215)
0.0063
(0.0183)
0.0274*
(0.0162)
0.0013
(0.0020)
0.0018
(0.0015)
9.47***
(0.88)
0.0022
(0.0039)
0.1491*
(0.0826)
0.3069
(0.3526)
0.3849***
(0.1369)
0.2903
(0.3702)
0.2144
(0.1576)
1.0349*
(0.5712)
0.0614
(0.1028)
0.1264
(0.1011)
0.0003
(0.1312)
0.0608
(0.1199)
0.0571
(0.1062)
0.0546
(0.1547)
0.0150
(0.0131)
0.0044
(0.0058)
311.79
(435.02)
8.89***
(3.47)
236.09***
(57.45)
228.34***
(55.44)
831.73***
(110.17)
393.59
(387.01)
305.87*
(166.43)
66.67
(116.33)
997.20***
(107.87)
86.09
(83.72)
202.45**
(84.54)
9.21
(91.92)
208.16**
(96.41)
146.29*
(84.69)
15.33*
(8.68)
9.36
(6.20)
123.98
(1256.60)
25.96*
(15.02)
98.16
(195.99)
447.45
(407.08)
2476.42***
(444.82)
37.39
(839.21)
412.11
(545.20)
164.72
(412.61)
1056.82**
(477.16)
198.23
(381.12)
300.86
(342.39)
429.97
(379.48)
649.55*
(359.62)
145.06
(403.80)
3.44
(24.82)
24.94*
(15.39)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
12
R
N
0 0 1 1
0.41 0.54 0.34 0.69
2,491 58 997 51
(where standard errors are in parentheses)
** indicates significant at 1% level
* indicates significant at 5% level
indicates significant at 10% level
TABLE 15: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
PITTSBURGH SMSA
HOMEOWNERS: RENTERS:
V 1 RA1
DEP VAR DEP VAR 
WHITE BLACK WHITE BLACK
WHITE BLACK WHITE BLACK
9.95***
(0.16)
0.0101***
(0.0009)
0.1239***
(0.0134)
0.0349**
(0.0151)
0.0823***
(0.0192)
0.2604***
(0.0839)
0.0089
(0.0388)
0.0526
(0.1273)
0.2715***
(0.0175)
0.0290
(0.0201)
0.0051
(0.0245)
0.0138
(0.0259)
0.0545***
(0.0204)
0.1500***
(0.0299)
0.0004
(0.0022)
0.0012
(0.0012)
10.56***
(0.51)
0.0090*
(0.0048)
0.0310
(0.0702)
0.0616
(0.1145)
0.3729***
(0.1355)
0.5174
(0.3291)
0.1734
(0.1553)
0.6067**
(0.2872)
0.1004
(0.1000)
0.0017
(0.1271)
0.2476*
(0.1380)
0.3104**
(0.1386)
0.0457
(0.1187)
0.3288**
(0.1344)
0.0133
(0.0181)
0.0064
(0.0071)
443.56
(471.64)
25.71***
(3.58)
114.98**
(56.44)
99.82***
(21.19)
333.97***
(94.51)
82.38
(345.45)
121.51
(191.11)
543.79***
(202.01)
903.00***
(142.35)
355.51***
(102.08)
88.78
(97.71)
60.80
(111.25)
268.26***
(93.05)
402.30***
(111.85)
7.10
(10.35)
13.38**
(5.47)
1548.00
(976.95)
12.03*
(7.40)
71.86
(121.26)
20.21
(38.98)
374.98
(241.43)
41.35
(637.91)
492.43
(353.64)
424.97*
(252.20)
1003.63**
(479.20)
15.48
(211.95)
51.24
(223.31)
90.39
(237.01)
87.12
(198.07)
94.25
(195.55)
119.54***
(33.18)
6.04
(5.80)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
A2
R
N
*** indicates significant at 1% level
** indicates significant at 5% level
* indicates significant at 10% level
0 0 1 1
0.38 0.31 0.32 0.27
2,084 103 770 136
(where standard errors are in parentheses)
TABLE 16: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
SPOKANE SMSA
*** indicates significant at 1% level
** indicates significant at 5% level
* indicates significant at 10% level
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
x2
R
N
TABLE 17: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
TACOMA SMSA
HOMEOWNERS: RENTERS:
VX1 R 1
DEP VAR DEP VAR 
x x
WHITE BLACK WHITE BLACK
10.15*** 10.53*** 1146.93*** 885.26
(0.10) (0.35) (297.89) (1019.26)
0.0044*** 0.0044** 14.44*** 25.52***
(0.0007) (0.0022) (2.23) (4.90)
0.0761*** 0.1028* 373.57*** 351.98***
(0.0115) (0.0537) (39.28) (112.83)
0.0342*** 0.0759 5.99 56.30
(0.0132) (0.0647) (24.00) (136.69)
0.2135*** 0.1518 61.64
(0.0376) (0.1377) (229.48) NA
0.1688** 0.0128 515.85** 813.64
(0.0693) (0.1962) (243.34) (842.75)
0.0109 0.0608 281.82** 450.49
(0.0326) (0.1531) (121.82) (612.61)
0.1343** 0.0267 132.51 111.91
(0.0592) (0.1673) (86.39) (174.37)
0.3171*** 0.2588*** 648.99*** 789.71**
(0.0154) (0.0550) (101.43) (355.61)
0.0682*** 0.1036 64.51 350.17
(0.0188) (0.0720) (69.72) (232.54)
0.0185 0.0850 20.38 271.86
(0.0220) (0.0828) (66.45) (182.82)
0.0287 0.0399 16.22 55.94
(0.0197) (0.0718) (73.46) (186.82)
0.0222 0.0257 121.87* 47.88
(0.0214) (0.0812) (74.40) (201.75)
NA NA NA NA
0.0035** 0.0073 8.56 32.50*
(0.0017) (0.0069) (7.15) (17.58)
0.0013 0.0026 1.47 10.72
(0.0013) (0.0058) (5.31) (8.43)
0 0 1 1
0.37 0.52 0.25 0.43
2,158 79 1,043 119
(where standard errors are in parentheses)
*** indicates significant at 1% level
** indicates significant at 5% level
* indicates significant at 10% level
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
A
R
N
TABLE 18: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
WASHINGTON, D.C. SMSA
HOMEOWNERS: RENTERS:
V _ R 1
DEP VAR DEP VAR 
WHITE BLACK WHITE BLACK
WHITE BLACK WHITE BLACK
10.66***
(0.18)
0.0021**
(0.0008)
0.1475***
(0.0117)
0.0158***
(0.0048)
0.0581
(0.0409)
0.2068
(0.1433)
0.0271
(0.0372)
0.0054
(0.0829)
0.2510***
(0.0144)
0.0202
(0.0202)
0.0121
(0.0215)
0.0024
(0.0293)
0.0008
(0.0269)
0.3156***
(0.0305)
0.0065***
(0.0018)
0.0011
(0.0010)
10.60***
(0.27)
0.0005
(0.0015)
0.0822***
(0.0207)
0.0212
(0.0167)
0.1096***
(0.0403)
0.2768
(0.2115)
0.0611*
(0.0380)
0.1437
(0.1379)
0.2216"**
(0.0243)
0.0522
(0.0390)
0.0184
(0.0362)
0.0031
(0.0387)
0.0471
(0.0364)
0.0098
(0.0426)
0.0070**
(0.0032)
0.0003
(0.0015)
1046.95
(1034.45)
2.34
(4.66)
509.74***
(72.50)
48.59***
(14.59)
795.81***
(162.78)
1504.52*
(935.09)
233.46
(181.67)
546.21**
(240.71)
894.56***
(130.81)
345.10***
(133.84)
441.70***
(110.04)
233.78*
(135.40)
422.74***
(128.45)
486.08***
(138.23)
10.85
(10.42)
4.73
(5.09)
2044.08***
(345.37)
2.74
(3.01)
224.60***
(43.45)
51.28"**
(13.78)
411.97***
(78.27)
298.88
(242.42)
340.70***
(76.43)
209.21
(136.35)
700.18"**
(122.61)
11.55
(102.50)
92.19
(78.02)
6.98
(83.18)
61.23
(76.55)
889.35***
(96.95)
9.60
(6.56)
1.05
(2.45)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
S2
R
N
*** indicates significant at
** indicates significant at
* indicates significant at
1% level
5% level
10% level
0 0 1 1
0.46 0.27 0.28 0.29
1,466 569 960 1,004
(where standard errors are in parentheses)
TABLE 19: 1981 HEDONIC EQUATION REGRESSION COEFFICIENTS FOR
WICHITA SMSA
HOMEOWNERS: RENTERS:
V _ R_1
DEP VAR = DEP VAR = 
WHITE BLACK WHITE BLACK
9.31***
(0.13)
0.0065***
(0.0007)
0.0943***
(0.0116)
0.0694***
(0.0162)
0.1516***
(0.0446)
0.2521***
(0.0904)
0.0366
(0.0278)
0.4506***
(0.0916)
0.3683***
(0.0140)
0.0218
(0.0162)
0.0104
(0.0208)
0.0168
(0.0244)
0.0085
(0.0199)
NA
0.0020
(0.0022)
0.0022
(0.0016)
9.18***
(0.73)
0.0081
(0.0054)
0.1588**
(0.0678)
0.0474
(0.1445)
0.5512***
(0.2092)
0.5238
(0.3807)
0.0940
(0.1327)
0.3379
(0.3685)
0.4103***
(0.0970)
0.1291
(0.1464)
0.1157
(0.1337)
0.0985
(0.1198)
0.1060
(0.1291)
NA
0.0373*
(0.0221)
0.0103
(0.0100)
1949.48***
(488.47)
25.42***
(2.76)
300.13***
(47.61)
19.14
(38.99)
263.62**
(126.93)
137.18
(394.69)
301.28***
(112.85)
52.52
(141.57)
695.26***
(121.76)
21.92
(77.34)
80.00
(77.55)
5.39
(98.10)
42.87
(91.99)
NA
17.08*
(10.35)
14.40**
(6.73)
1617.81
(1123.88)
28.18***
(9.09)
17.10
(151.16)
179.64**
(91.97)
220.41
(293.50)
733.79
(854.50)
337.02
(270.53)
12.72
(362.31)
591.14
(423.04)
239.79
(302.30)
44.80
(250.10)
88.29
(285.80)
126.70
(246.53)
NA
25.07
(30.98)
9.73
(15.77)
CONSTANT
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
A
R
N
*** indicates significant at 1% level
** indicates significant at 5% level
* indicates significant at 10% level
0 0 1 1
0.47 0.46 0.24 0.21
2,124 98 938 116
(where standard errors are in parentheses)
TABLE 20: SIGNIFICANCE AND MEAN EFFECTS OF HEDONIC EQUATION REGRESSION
COEFFICIENTS USING THE PEARSON P TEST
A
AGEST
BEDR
FLOORS
AIRCN
WORKELEC
RATS
TELEP
BATH
PBTRANS
SCHOOL
POLICE
RECR
INOUTCC
DIST
TIMWORK
*** indicates
** indicates
* indicates
significant at
significant at
significant at
1% level
5% level
10% level
k
P = 2* loge i
i=1
P 2
A X2k
where k = number of tests
p = statistical significance of test
HOMEOWNERS RENTERS
0.0048*** 11.1753***
0.0863*** 238.1041***
0.0372*** 48.3248***
0.1584*** 534.0739***
0.0400*** 333.5762**
0.0573*** 155.1904***
0.1254*** 81.6752**
0.3316*** 969.1369***
0.0338*** 1.7156***
0.0129** 109.1637***
0.0075** 66.0267
0.0236*** 144.7370***
0.1166*** 375.3105***
0.0013*** 8.0522***
0.0004 3.1007*
TABLE 21: MEANS OF HEDONIC HOUSING VARIABLES (X.'s)
1
USED IN THE CONSTRUCTION OF THE HEDONIC
HOUSING SERVICES PRICE INDICES
1
AGEST 21.7500
BEDR 3.1047
FLOORS 1.4720
AIRCN 0.6733
WORKELEC 0.9927
RATS 0.0865
TELEP 0.9877
BATH 1.7816
PBTRANS 0.5334
SCHOOL 0.8005
POLICE 0.8427
RECR 0.8007
INOUTCC 0.5105
DIST 10.2642
TIMWORK 21.0202
The next step is to construct Laspeyres housing services price
indices for black and white homeowners and renters using the hedonic
equation regression coefficients and the methodology detailed in Chapter
IV. These hedonic indices are the righthand side price variables used
in the tenure choice and final housing demand equations. Price indices
constructed from sample sizes less than 100 are ignored in this analysis
to avoid any false inferences drawn from small samples.
The Laspeyres housing services price indices for homeowners in the
sample are found in Table 22. For white homeowners, the highest price
index of 175.0 was found in Newark (with Anaheim a close second) and the
lowest price index of 40.3 was found in Fort Worth. For black
homeowners, the highest price index of 152.2 was found in Newark, while
the lowest price index of 40.2 was found in Fort Worth. The seven SMSAs
where the price index for whites is greater than 100 are Anaheim,
Boston, Detroit, Minneapolis, Newark, Pittsburgh, and Washington, D.C.,
while the two SMSAs where the price index for blacks is greater than 100
are Newark and Washington, D.C. The relatively more expensive SMSAs for
homeowners are located in the northern part of the United States.
Black owners pay more than white owners for the same bundle of
housing services in two out of seven SMSAs in the sample, namely Dallas
and Washington, D.C. In Dallas, black owners pay on average 77% higher
than their white counterparts for the same bundle of owner housing
services. However, white owners pay more than black owners for the same
bundle of housing services in five out of seven SMSAs in the sample,
namely Detroit, Fort Worth, Newark, Orlando, and Pittsburgh. The
largest markup, in percentage terms, is for white owners in Pittsburgh
who, on average, pay 123% more for the same bundle of owner housing
services than their black counterparts.
The Laspeyres housing services price indices for renters in the
sample are found in Table 23. For white renters, the highest price
index of 151.6 was found in Washington, D.C., 92% higher than the lowest
price index of 79.1 found in Spokane. For black renters, the highest
price index of 103.5 was found in Fort Worth, while the lowest price
index of 61.4 was found in Pittsburgh. The five SMSAs where the price
index for white renters is greater than 100 are Anaheim, Boston,
Minneapolis, Newark, and Washington, D.C., all in the northern section
of the country. The three SMSAs where the price index for black renters
is greater than 100 are Boston, Fort Worth, and Tacoma.
Black renters pay more than their white counterparts for the same
bundle of rental housing services in two out of the ten SMSAs in the
sample, namely Fort Worth and Tacoma. In Tacoma, black renters pay on
average 22% more than white renters for an equivalent bundle of housing
services. However, white renters pay more than black renters for the
same bundle of housing services in eight out of ten SMSAs in the sample,
namely Boston, Dallas, Detroit, Newark, Orlando, Pittsburgh, Washington,
D.C., and Wichita. The largest markup, in percentage terms, is for
white renters in Washington, D.C. who, on average, pay 63% more for the
same bundle of rental housing services than their black counterparts.
The next stage in the analysis is to compute the price index of all
goods and services (excluding shelter), px, for each of the fifteen
SMSAs in the sample using the metholodogy discussed in Chapter IV. This
variable enters the permanent income regression as a variable capturing
wage differentials between SMSAs. It also enters the final housing
demand equations as a deflator for the nominal housing expenditures,
price, and permanent income variables.
On examining the price indices of all goods and services, excluding
shelter (px) for each SMSA (see Table 24), one finds the highest index
in Anaheim of 133.6 and the lowest index of 74.9 in Wichita. These two
indices reflect a 78% higher cost of living in Anaheim relative to
Wichita. All six SMSAs with a price index greater than 100 (excluding
Anaheim) are to be found in the northern section of the United States;
these SMSAs are Boston, Detroit, Minneapolis, Newark, Pittsburgh, and
Washington D.C. The three fast growing "sunbelt" SMSAs in the sample,
namely Dallas, Fort Worth, and Orlando, all had price indices less than
100. This is more than likely due to the fact that labor used in
housing construction is generally less expensive in the South.
The next step is to use an instrumental variable technique to
produce an estimate of permanent income which is used as an explanatory
variable in the final housing demand equations. The results from the
permanent income regression of current income on the human and nonhuman
wealth variables, as well as px, the SMSA specific price index of all
goods and services (excluding shelter), and an SMSA specific climatic
variable, are shown in Table 25. Whereas diminishing marginal returns
are associated with age, denoted by the negative and statistically
2
significant coefficient on (AGE) increasing marginal returns are
associated with education, denoted by the positive and statistically
2
significant coefficient on (EDUC)2. The experience (AGE) variable in
the linear form is highly significant and positive in determining the
permanent income of a family. Marriage and the number of children also
have strong positive effects. The high coefficient of 0.41 on the MARHH
variable suggests the possibility of twowage earners in a number of the
households surveyed. Unfortunately, the data set has no information on
the number of paid workers in a family. It is quite probable that the
MARHH variable acts as a proxy for labor force participation.
TABLE 22: 1981 HEDONIC HOUSING SERVICES PRICE INDICES FOR
BLACK AND WHITE HOMEOWNERS IN EACH OF THE 15 SMSAS
P
o
WHITE BLACK
ANAHEIM 173.2 180.1
BOSTON 143.0 177.0
DALLAS 53.4 94.3
DETROIT 120.3 91.9
FORT WORTH 40.3 40.2
MADISON 70.2
MINNEAPOLIS 154.5 178.5
NEWARK 175.0 152.2
ORLANDO 58.2 52.9
PHOENIX 52.0 52.3
PITTSBURGH 159.5 71.3
SPOKANE 70.2 40.1
TACOMA 90.4 173.5
WASHINGTON D.C. 104.4 132.6
WICHITA 42.5 41.7
The homeowner price indices in the above table
do not take into account the implicit subsidy
given to homeowners under the present tax system
(see p. 26 for the individual homeowner adjustment).
TABLE 23: 1981 HEDONIC HOUSING SERVICES PRICE INDICES FOR
BLACK AND WHITE RENTERS IN EACH OF THE 15 SMSAS
P
r
WHITE BLACK
ANAHEIM 139.8 153.5
BOSTON 114.8 100.1
DALLAS 98.3 87.3
DETROIT 87.9 73.4
FORT WORTH 91.9 103.5
MADISON 87.8 103.3
MINNEAPOLIS 116.6 119.6
NEWARK 109.0 82.6
ORLANDO 83.6 73.3
PHOENIX 97.1 81.3
PITTSBURGH 88.6 61.4
SPOKANE 79.1 60.5
TACOMA 83.9 102.1
WASHINGTON D.C. 151.6 92.8
WICHITA 84.2 65.8
The renter price indices in the above table
do not take into account any rent discounts
given to renters by landlords (see p. 26 for the
individual renter adjustment).
TABLE 24: 1981
ANAHEIM
BOSTON
DALLAS
DETROIT
FORT WORTH
MADISON
MINNEAPOLIS
NEWARK
ORLANDO
PHOENIX
PITTSBURGH
SPOKANE
TACOMA
WASHINGTON D.C
WICHITA
PRICE INDEX FOR ALL GOODS AND SERVICES
IN EACH OF THE 15 SMSAS
P
x
133.6
114.8
84.4
102.9
75.5
87.4
124.0
122.7
80.6
80.3
119.4
84.5
94.8
109.5
74.9
The statistically significant and negative coefficients on the
SEXHH and RACE variables could be interpreted as showing that females
and blacks may suffer from discrimination in the labor market. However,
it is more likely that the SEXHH and RACE variables are merely acting as
proxies for other excluded variables. The results from using the two
SMSA specific features were very encouraging. These two variables were
included to capture any premiums paid to individuals in terms of
increased wages for living and working in "high cost" cities and
different geographical location. The px variables, constructed in
Chapter III, came in positive and statistically significant showing that
in "high cost" cities workers are paid more than workers in "low cost"
cities. In preliminary work, three climate variables were experimented
with, namely COOL (number of cooling degree days per annum), HEAT
(number of heating degree days per annum), and TEMP (mean annual
temperature). The final permanent income equation includes COOL, the
positive and statistically significant coefficient on this variable
shows that premiums are paid to workers for living and working in colder
regions of the United States, namely the North Central and Northeast.
The results from the tenure choice regression, which are used in
the construction of the A and A variables, are presented in Table 26.
o r
This is the final step prior to estiamtion of the housing demand
equations. All the included variables had the hypothesized signs and
were significant at 1% level. The expected probability of a household
head owning, rather than renting, increases if he is or has been
married, and decreases if he has moved within the past twelve months to
his current residence. The relative price term, LOG(poi /prj), appears
to be the dominant explanatory variable in the tenure choice decision.
TABLE 25: 1981 PERMANENT INCOME EQUATION REGRESSION
COEFFICIENTS FOR GROUPED SAMPLE
DEP VAR = LOGYC
CONSTANT 7.2035***
(0.2971)
EDUC 0.0298
(0.0280)
(EDUC) 0.0013*
(0.0008)
AGE 0.0583***
(0.0058)
(AGE)2 0.0006***
(0.0001)
(EDUC* AGE) 0.0001
(0.0001)
SEXHH 0.3050***
(0.0352)
MARHH 0.4116***
(0.0360)
CHIL 0.0410***
(0.0097)
RACE 0.3267***
(0.0394)
COOL 0.00003**
(0.00001)
p 0.0029***
x (0.0007)
R2 0.25
N1 6,134
(where standard errors are in parentheses)
*** indicates significant at 1% level
** indicates significant at 5% level
indicates significant at 10% level
approximately a 10% sample of the entire
grouped population of 73,173
TABLE 26: 1981 PROFIT EQUATION REGRESSION COEFFICIENTS1
CONSTANT
MARHH
LOG(AGEHH)
MOVER
LOG(p i/prj)
Sample size
Convergence
Criterion
Significance
Probability
Maximum Likelihood
Converged at
Iteration
(whe
2.6614***
(0.4210)
0.9763***
(0.0873)
0.2582***
(0.1146)
1.1447***
(0.1089)
0.2892***
(0.0430)
1,369
0.00011
0.404
7
ire standard errors are in parentheses)
*** indicates
** indicates
* indicates
1
significant at 1% level
significant at 5% level
significant at 10% level
with housing price indices from SMSA
race/tenure groups greater than 100
tenure choice decision. As anticipated, as the relative price of owning
relative to renting increases, the expected probability of an individual
owning falls.
The conclusion of the empirical work is to bring together the
variables constructed in the prior steps of this analysis into the
housing services demand regression equations. Tables 27 and 28 show the
results from the housing services demand regressions using the four
race/tenure groups, with and without the A term. Tables 29 through 32
show the results from a further breakdown into the three educational
attainment levels within those groups. Table 33 summarizes the final
price and income elasticities of housing services demand from Tables 27
through 32. It should be noted that in the rental housing services
demand equations the unadjusted price index of renters was used in all
the regressions. In preliminary work, the regression including the
price index adjusted for rent discounts produced numerous instances of
statistically insignificant price elasticities.
Tables 22 and 23, the most important tables in the entire study,
show the results from the regressions of housing services expenditures
on permanent income, price, and a set of demographic variables for both
black and white homeowners and renters. Looking first at owners, for
black and white owners the income elasticities of housing services
demand are an elastic 1.42 and 1.30, respectively, signifying that a 10%
increase in income would lead to approximately a 13%14% increase in
housing services consumption by both black and white owners. Turning to
the price elasticity, black owners are slightly more responsive to price
changes than their white counterparts. The price elasticities of
housing services demand are 1.04 and 1.01 for white and black owners,
respectively, both elastic.
On the rental side, black renters are more responsive than white
renters to income changes with regard to their future housing
consumption. The income elasticities for the black and white rental
groups as a whole are 0.53 and 0.36, respectively, both inelastic. As
in the owner market, black renters are more responsive to changes in the
price of housing services than white renters. The price elasticity of
housing services demand are 0.62 and 0.12 for black and white renters,
respectively, both inelastic. On further examination of Tables 27 and
28, one sees that the demographic variables are virtually all
significant at the 1% level. Also from Tables 27 and 28 there is strong
evidence of simultaneity between the rent and housing consumption
decisions, but inclusive evidence of any simultaneity between the own
and housing consumption decisions as witnessed by the significance of
the A variable. A major focus of this study emphasized the estimation
of the relevant housing services demand elasticities taking into account
any simultaneity between the tenure choice and housing services demand
decisions. Although the A variable looks at the simultaneity between
the tenure choice and housing consumption decisions, it could well be
just capturing unobservable variables in the two decision processes.
The generally positive signs on the A and A variables indicate that
o r
the expected errors in the Probit equation are positively correlated
with the epxected errors in the owner and renter demand equations taken
separately.
The exclusion of the A variable in the homeowner market had a
minimal effect on the income elasticities of housing services demand for
blacks and whites. Omitting this variable changed the price elastici
ties of housing services demand by less than two percent for black and
white homeowners. However, the exclusion of the A variable in the
rental market had more of an effect on the relevant housing services
demand elasticities. By excluding the A variable, the income elasticity
of housing demand rose by nearly three percent for white renters and by
nearly five percent for black renters. Omitting this variable increased
the price elasticity of housing demand by 36% for white renters and by
nearly five percent for black renters.
The three demographic variables, AGEHH, SEXHH, and MARHH, were in
the most part significant with the hypothesized signs. The age of the
household head was positively correlated with housing expenditures in
the owner market, but negatively correlated with housing expenditures in
the rental market. In the homeowner market, as people age they
generally have larger asset accumulation, move into larger homes and
thus incur larger housing expenses than younger families in smaller
homes. In the rental market, as people age their rental expenditures
decrease. The coefficient on SEXHH shows that the owner and rental
housing service expenditures of female headed households is higher than
that of male headed households. The MARHH variable was generally
statistically insignificant in the rental market, but statistically
significant and negative in the homeowner market.
Turning now to Tables 29 through 32, the four race/tenure groups
are each broken down into three levels of educational attainment, namely
(1) no schooling through eleventh grade (did not graduate from
high school),
(2) graduated high school, and
(3) attended college.
Table 28 again summarizes the price elasticity estimates of housing
services demand from these tables.
The motivation behind this section is to see how the price
elasticity of housing services demand varies, if at all, with
educational attainment. The income elasticity of housing demand is not
reported here because educational attainment, which is highly correlated
with income, is held constant in this set of regressions, and hence the
income elasticity derived is not meaningful.
The price elasticities of housing services demand for white owners
who did not graduate from high school, graduated from high school, and
attended college are 0.981, 0.986, and 0.994, respectively. Although
the price elasticity increases with the level of educational attainment,
no significant difference was found to exist between these three
elasticities. The price elasticities of housing services demand for
black owners who did not graduate from high school, graduated from high
school, and attended college are 1.020, 1.012, and 1.004. No
significant difference was found to exist between these three price
elasticities of housing services demand which diminished with the
increased education of the household head.
For white renters who did not graduate from high school and
attended college there were obtained statistically significant price
elasticities of 0.390 and 0.056. The remaining price elasticity for
white renters that graduated from high school was statistically
insignificant. However, the results obtained for black renters show
that the housing price responsiveness decreased with the household
head's level of schooling. However, there was no statistically
significant differences found between these three elasticities. The
price elasticities for black renters who did not graduate from high
school, graduated from high school, and attended college are 0.737,
81
0.650, and 0.489, respectively. The set of demographic variables used
in the black and white owner and renter demand equations were generally
statistically significant with the hypothesized signs. The A variable
was statistically significant in four out of the six owner demand
equations and also in four out of the six renter demand equations
broken down by educational attainment. It appears that there is
fairly strong evidence of simultaneity between the decisions to rent and
of how much housing services to consume, and the decisions to own and of
how much housing services to consume as was the case from the results
on the four race/tenure groups not broken down by level of educational
attainment.
TABLE 27: 1981 HOUSING SERVICES DEMAND EQUATION REGRESSION
COEFFICIENTS FOR HOMEOWNERS
DEPENDENT VARIABLE = LOG(HOUSING SERVICE EXPENDITURES)
HOMEOWNERS
WHITE BLACK
2.2936*** 2.3335*** 3.1491*** 2.8080***
(0.1236) (0.1016) (0.2039) (0.1587)
0.0048*** 0.0050*** 0.0077*** 0.0066***
(0.0005) (0.0004) (0.0009) (0.0008)
0.2186*** 0.2207*** 0.1940*** 0.1850***
(0.0218) (0.0215) (0.0306) (0.0305)
0.3534*** 0.3468*** 0.3509*** 0.3958***
(0.0239) (0.0208) (0.0356) (0.0314)
1.2995*** 1.3001*** 1.4163*** 1.4051***
(0.0182) (0.0182) (0.0302) (0.0300)
0.0073 0.0098** 0.0430*** 0.0240***
(0.0068) (0.0051) (0.0105) (0.0077)
0.0108 0.0811***
(0.0191) (0.0306)
0.70 0.70 0.70 0.69
2,717 2,717 1,128 1,128
(where
**
**
*
standard errors are in parentheses)
indicates significant at 1% level
indicates significant at 5% level
indicates significant at 10% level
CONSTANT
AGEHH
SEXHH
MARHH
LOG(Y /p )
LOG(p/p )
A
R2
N
TABLE 28: 1981 HOUSING SERVICES DEMAND EQUATION REGRESSION
COEFFICIENTS FOR RENTERS
DEPENDENT VARIABLE = LOG(HOUSING SERVICE EXPENDITURES)
RENTERS
WHITE
1.9114***
(0.1658)
0.0067***
(0.0007)
0.1538***
(0.0269)
0.0093
(0.0315)
0.3631***
(0.0328)
0.8848***
(0.0733)
0.3643***
(0.0751)
1.9116***
(0.1660)
0.0088***
(0.0006)
0.1477***
(0.0269)
0.0634**
(0.0277)
0.3725***
(0.0328)
0.8431***
(0.0729)
BLACK
1.1157"**
(0.2615)
0.0047***
(0.0011)
0.1380***
(0.0354)
0.0848*
(0.0507)
0.5288***
(0.0543)
0.3771***
(0.0689)
0.5564***
(0.1175)
1.0674***
(0.2622)
0.0076***
(0.0009)
0.1301***
(0.0355)
0.0396
(0.0435)
0.5522***
(0.0542)
0.3417***
(0.0687)
0.08 0.08 0.13 0.12
9,184 9,184 3,007 3,007
(where standard errors are in parentheses)
*** indicates significant at 1% level
** indicates significant at 5% level
* indicates significant at 10% level
CONSTANT
AGEHH
SEXHH
MARHH
LOG(Y /p )
LOG(p/p )
A
I
i
TABLE 29: 1981 HOUSING SERVICES DEMAND EQUATION REGRESSION
COEFFICIENTS FOR WHITE HOMEOWNERS BY EDUCATION CLASSIFICATION
DEPENDENT VARIABLE = LOG(HOUSING SERVICE EXPENDITURES)
11th GRADE OR GRADUATED HIGH COLLEGE
LESS SCHOOL EDUCATION
3.6814*** 3.7650*** 3.2283***
(0.1768) (0.1219) (0.0914)
1.5086*** 1.5731*** 1.4721***
(0.0270) (0.0205) (0.0146)
0.0190** 0.0136** 0.0059*
(0.0080) (0.0056) (0.0035)
0.0128*** 0.0043*** 0.0030***
(0.0006) (0.0004) (0.0003)
0.2685*** 0.3050*** 0.2755***
(0.0240) (0.0171) (0.0154)
0.3546*** 0.3871*** 0.3806***
(0.0261) (0.0190) (0.0165)
0.0005 0.0609*** 0.0119
(0.0285) (0.0163) (0.0123)
0.66 0.67 0.71
1,975 3,632 5,494
(where standard errors are in parentheses)
*** indicates
** indicates
* indicates
significant at 1% level
significant at 5% level
significant at 10% level
CONSTANT
LOG(Y /p )
p x
LOG(p/p )
AGEHH
SEXHH
MARHH
A
TABLE 30: 1981 HOUSING SERVICES DEMAND EQUATION REGRESSION
COEFFICIENTS FOR BLACK HOMEOWNERS BY EDUCATION CLASSIFICATION
DEPENDENT VARIABLE = LOG(HOUSING SERVICE EXPENDITURES)
llth GRADE OR GRADUATED HIGH COLLEGE
LESS SCHOOL EDUCATION
4.1092*** 3.8727*** 3.7203***
(0.2889) (0.2547) (0.2499)
1.5803*** 1.6282*** 1.5837***
(0.0415) (0.0434) (0.0424)
0.0197* 0.0118* 0.0039
(0.0101) (0.0070) (0.0124)
0.0142*** 0.0020 0.0016*
(0.0012) (0.0009) (0.0010)
0.1454*** 0.2714*** 0.2621***
(0.0384) (0.0319) (0.0349)
0.4550*** 0.3913*** 0.3592***
(0.0434) (0.0390) (0.0408)
0.0915** 0.0817** 0.0696**
(0.0465) (0.0335) (0.0314)
0.70 0.73 0.72
728 769 709
(where standard errors are in parentheses)
*** indicates significant at 1% level
** indicates significant at 5% level
indicates significant at 10% level
CONSTANT
LOG(Y /p )
LOG(p/p )
AGEHH
SEXHH
MARIRH
TABLE 31: 1981 HOUSING SERVICES DEMAND EQUATION REGRESSION
COEFFICIENTS FOR WHITE RENTERS BY EDUCATION CLASSIFICATION
DEPENDENT VARIABLE = LOG(HOUSING SERVICE EXPENDITURES)
11th GRADE OR GRADUATED HIGH COLLEGE
LESS SCHOOL EDUCATION
2.2984*** 2.0839*** 2.8283***
(0.6014) (0.4910) (0.3680)
0.2645** 0.3243*** 0.1726**
(0.1205) (0.1035) (0.0743)
0.6104** 1.2081 0.9445***
(0.2590) (0.9850) (0.1366)
0.0089*** 0.0063*** 0.0060***
(0.0024) (0.0018) (0.0015)
0.1517 0.0754 0.1098**
(0.1021) (0.0670) (0.0497)
0.1291 0.0396 0.0477
(0.1181) (0.0855) (0.0635)
0.4002* 0.2432* 0.0772
(0.2372) (0.1505) (0.1510)
0.08 0.06 0.03
1,023 1,936 2,517
(where standard errors are in parentheses)
*** indicates
** indicates
* indicates
significant at 1% level
significant at 5% level
significant at 10% level
CONSTANT
LOG(Yp/Px)
LOG(p/p )
AGEHH
SEXHH
MARHH
A
TABLE 32: 1981 HOUSING SERVICES DEMAND EQUATION REGRESSION
COEFFICIENTS FOR BLACK RENTERS BY EDUCATION CLASSIFICATION
DEPENDENT VARIABLE = LOG(HOUSING SERVICE EXPENDITURES)
11th GRADE OR GRADUATED HIGH COLLEGE
LESS SCHOOL EDUCATION
0.8612** 1.1821** 0.9221*
(0.4457) (0.4669) (0.5032)
0.5545*** 0.5354*** 0.5801***
(0.0922) (0.1062) (0.1110)
0.2635** 0.3504*** 0.5111***
(0.1172) (0.0985) (0.1159)
0.0043** 0.0061*** 0.0039*
(0.0018) (0.0018) (0.0023)
0.1274** 0.1086** 0.2022***
(0.0592) (0.0535) (0.0605)
0.1087 0.0718 0.0642
(0.0820) (0.0798) (0.0852)
0.2294 0.6622*** 0.8093***
(0.1664) (0.1779) (0.2216)
0.13 0.08 0.10
1,114 1,495 1,025
(where standard errors are in parentheses)
*** indicates significant at 1% level
** indicates significant at 5% level
indicates significant at 10% level
CONSTANT
LOG(Y /p )
p x
LOG(p/px)
AGEHH
SEXHH
MARHH
A
R2
N
88
TABLE 33: FINAL PRICE AND INCOME ELASTICITIES OF HOUSING SERVICES
DEMAND FOR BLACK AND WHITE HOMEOWNERS AND RENTERS
HOMEOWNERS
WHITE BLACK
With Without Withy Without With Without Withy Without
A A A A A A A A
ALL 1.007 1.010* 1.300* 1.300* 1.043* 1.024* 1.416* 1.405*
LITTLE H.S. 0.981* 1.020* 
GRAD H.S. 0.986* 1.012* 
COLLEGE 0.994* 1.004 
F(2,2749) = 0.51 F(2,1170) = 0.55
(not significant at 10% level) (not significant at 10% level)
RENTERS
WHITE BLACK
np ny p
With Without With Without With P Without With y Without
A A A A A A A A
ALL 0.115* 0.157* 0.363* 0.373* 0.623* 0.658* 0.529* 0.552*
LITTLE H.S. 0.390* 0.737* 
GRAD H.S. 0.208 0.650* 
COLLEGE 0.056* 0.489* 
F(2,1085) = 0.94 F(2,2986) = 0.49
(not significant at 10% level) (not significant at 10% level)
indicates elasticity coefficient significant in
housing expenditures demand equations
The final piece of empirical work in this dissertation examines how
sensitive, if at all, the price and income elasticities of housing
services demand are to using (1) endogenously constructed and then (2)
Bureau of Labor Statistics family budget data price indices. This
dissertation constructed the three following set of price indices, p
(housing price index for owners), pr (housing price index for renters),
and px (price index for all goods, excluding shelter) from the Annual
Housing Survey. The equivalent set of indices are computed from the BLS
family budget data. It should be noted that the BLS price indexes have
shelter costs as a component which does not break down into owner and
renter costs within a city. The results of this exercise are presented
in Tables 34 through 36.
In the owner regressions, using the BLS price indices resulted in a
decrease in the price elasticity of housing services demand for white
owners by 2%, while increasing the same elasticity for black owners by
2%. The income elasticity of housing services demand using BLS price
indices increased by nearly 4% for white owners and increased by nearly
5% for black owners. In the homeowner regressions, all the demographic
variables were statistically significant and had the hypothesized signs.
Although using the two sets of price indices did not produce
startlingly different elasticity estimates in the homeowner market, the
results were more divergent in the rental market. The black price
elasticity of housing services demand using the BLS price index was
statistically insignificant at the 10% level. The same elasticity using
the price index endogenously constructed from the Annual Housing Survey
was 0.45. The price elasticity of housing services demand for white
renters when using the BLS price indices relative to the AHS price
indices was decreased by nearly 30%. The income elasticity of housing
services demand when using the BLS price indices relative to the AHS
price indices was reduced by 54% and by 5% for white and black renters,
respectively. In the renter demand equations the R 2's were higher in
the AHS than in the BLS regressions. The demographic variables were
generally statistically significant with the hypothesized signs.
TABLE 34: COMPARISON OF HOMEOWNER HOUSING SERVICES DEMAND EQUATIONS
USING (1) AHS ENDOGENOUSLY CONSTRUCTED AND (2) BLS PRICE INDICES
WHITE BLACK
AHS BLS AHS BLS
2.3121*** 2.6175*** 2.6082*** 2.9386***
(0.1340) (0.1445) (0.1429) (0.1628)
1.2887*** 1.3362*** 1.3574*** 1.4191***
(0.0242) (0.0259) (0.0274) (0.0313)
0.0020 0.0169** 0.0296*** 0.0509***
(0.0072) (0.0075) (0.0071) (0.0078)
0.0060*** 0.0059*** 0.0068*** 0.0066***
(0.0006) (0.0006) (0.0007) (0.0008)
0.2523*** 0.2539*** 0.2009*** 0.1355***
(0.0297) (0.0298) (0.0270) (0.0289)
0.3135*** 0.3635*** 0.3935*** 0.4746***
(0.0293) (0.0285) (0.0278) (0.0298)
0.70 0.69 0.74 0.72
1,467 1,437 1,066 1,076
(where standard errors are in parentheses)
*** indicates significant at 1% level
** indicates significant at 5% level
indicates significant at 10% level
CONSTANT
LOG(Yp/px)
LOG(p/p )
AGEHH
SEXHH
MARHH
R2
N
