Demand for Housing Estimation

Regional Science and Urban Economics 15 (1985) 77-107. North-Holland

ESTIMATING THE DEMAND FOR HOUSING CHARACTERISTICS:

A Survey and Critique*

James R. FOLLAIN University of Illinois, Champaign, IL 61820, USA

Emmanuel JIMENEZ University of Western Ontario, London, Ontario N6A 5C2, Canada

Received December 1983, final version received April 1984

Many economists criticize the concept of the composite commodity ‘of housing that forms the basis of modern urban economics. As a result, much empirical work has been produced that attempts to estimate the household demand for housing and locational characteristics. The purpose of this paper is to take stock of the literature. The theoretical foundations of the literature and the econometric procedures employed are analyzed and critiqued. In addition, the empirical results are examined in order to identify any patterns that exist. The principal conclusion of this survey is that the theoretical basis is sound, but the econometric applications leave much to be desired. One consequence is that the literature has produced few empirical regularities. Another is that more studies using better estimation procedures and better data are needed before it can be safely argued that the composite commodity concept is replaced by the characteristics approach.

1. Introduction

The textbook model of the demand for housing services assumes that there is an infinite. variety of housing types, so that standard economic analysis can be applied to a composite commodity whose units are homogeneous [see Muth (1969) and Mills (1980)]. A more general approach focuses the analysis on the physical and locational characteristics which determine the level of services offered by a housing unit. Because it avoids assumptions that are not

*This paper is one of several papers of a research project sponsored by the World Bank and directed by Stephen Mayo (RPO 672-49). We have benefited a great deal from conversations and comments from Steve Mayo and other members of the project, Steve Malpezzi, Dave Gross and Sungyong Kang. In fact, all members of the project helped assemble an annotated bibliography that contains citations and brief abstracts on over 100 papers on this general topic. The bibliography will soon be published by the World Bank. Helpful comments have also been made by others outside the project. These include Jan Brueckner, Jan Ondrich, Doug Diamond and Serena Ng. Of course, all errors and opinions are our own. Esther Gray, Stephanie Waterman, and Cynthia Lowe also deserve our thanks for the wonderful job they did to prepare this manuscript.

01660462/85/$3.30 0 1985, Elsevier Science Publishers B.V. (North-Holland)

78 J.R. Follain and E. Jimenez, Estimating demand for housing characteristics

intuitively appealing, such as complete divisibility, there has been considerable research utilizing the latter approach. Moreover, the analysis of characteristics yields important insights regarding the tradeoffs consumers are willing to make between dwelling unit and location characteristics. Such information is important in understanding the dynamics of the housing market and its impact on the urban structure.

The theoretical and empirical developments in the use of the hedonic technique in the analysis of the demand for housing characteristics have been extensive. A recent survey by Freeman (1979) provides an excellent summary of the issues in investigating the demand for one characteristic - environmental benefits. This paper extends that review to more general studies. More importantly, it focuses on the issues in econometric applications. Although the theoretical basis for sound analysis has been established, empirical applications of the theory are of widely varying quality. Significant problems remain: the data requirements are stringent and the econometric procedures to implement the theory are quite complex. This paper attempts to clarify some of these outstanding issues and to give a broad picture of how recent developments relate to earlier work.

The survey is divided into three sections. First, the theoretical foundations for an econometric analysis of the demand for housing characteristics are discussed. Second, the empirical approaches that have been used are sum- marized and categorized. The final section highlights the major conclusions of the survey and indicates how future work might proceed. In addition, some thoughts are offered as to the implications of the hedonic literature concerning the traditional composite commodity model.

2. Theoretical basis

The theoretical basis for the recent literature is Rosen’s (1974) pioneering study of a market for a single commodity with many characteristics. This section outlines Rosen’s model and applies it to housing.

Let z=(zl,..., z,) be a vector of housing characteristics and p(z) be a hedonic price function defined by some market clearing conditions. House- holds and firms take this price function as given in a competitive world. In general, p(z) is non-linear.

The household decision is characterized by the utility function u = u(x,z), where x is a composite commodity whose price is unity. Households then maximize utility subject to a non-linear budget constraint y =p(z) +x. First- order conditions require that ap/dzi E pi = u&,, i = 1,. . . , n, under usual properties of U. An essential ingredient to the Rosen model is the bid-rent function. Define a bid-rent function 8(zi, U, y, a) as the amount of money a consumer is willing to pay for alternative values of z at a given utility index and income:

J.R. Follain and E. Jimenez, Estimating demand for housing characteristics 79

where CI is a parameter that differs from household to household (tastes). Solving the above for 8 will obtain a schedule like fF pictured in the upper panel of fig. 1. The household represented by O1 is everywhere indifferent along @. 8 schedules which are lower correspond to higher utility levels. It can be easily shown that

8i =u,/uX = the additional expenditure a consumer is willing to make on another unit of zi and be equally well off,

= compensated demand curve.

P(Z)

s2

P(Z).

B 82

m’ K

81 A

=i

'i

1 z. 1 G

Fig. 1


If p(z) is given, it denotes the minimum price the household must pay. Thus, utility is maximized when

and

0”; u*, Y, 4 = P(z*), (1)

where * denotes optimum quantities. The upper panel of fig. 1 denotes two such equilibria: A for household O1 and B for household d2.

Since p(z) is determined by the market, the supply side must also be considered. Like buyers, suppliers accept p(z) as given. Constant returns to scale are assumed. Each firm’s costs per unit are assumed to be convex and can be denoted as c(z;/?) where p denotes factor prices and production function parameters. The firm then maximizes profits per unit rc =p(z) - c(z; p) which would yield the condition that the additional cost of providing that ith characteristic, Ci, is equal to the revenue that can be gained so that pi = ci. To establish a relationship comparable to consumers’ bid-rents, let 4(z; rc,/?) be an offer function of unit prices at which a firm is willing to sell a given design at constant profit per unit:

7-c=@-c(z;j3).

4’ corresponds to one such schedule in fig. 1. It can be easily shown that

ci = the additional price a firm will want to obtain for providing another unit of a characteristic,

= MC of providing that characteristic,

which in standard microeconomic terms defines the (short-run) supply curve. If profits are maximized, then 0

do*; x*, P) = P(z*), (2)

and h(z”; n*, P) = Pi(Z”).

Fig. 1 also denotes a firm equilibrium. Equilibrium points are those points where supply equals demand and p(z)

then represents a function consisting of the various tangencies. The basic empirical problem is to infer preference structures from p(z) and data on household and (possibly) firm characteristics.


3. Estimation techniques

The literature has been primarily concerned with estimates of the determinants of the demand for housing characteristics. The simple hedonic approach, in which demand parameters are inferred directly from the coefficients of the estimated hedonic function, works only under certain very restrictive assumptions. The other approaches are significantly more com- plicated. The Rosen two-step and the Lancasterian index approaches entail the estimation of compensated demand curves for characteristics. Another approach is to estimate the structure of preferences directly through the use of bid-rents. A fourth approach treats characteristics packages as discrete consumption bundles. Each of these is discussed below.

3.1. Simple hedonic approach

This straightforward approach assumes that the coefficients of the estimated hedonic regression are sufficient to reveal the preference structure. In particular, the marginal willingness to pay for a particular characteristic is interpreted as the derivative of the hedonic regression with respect to the characteristic. However, the marginal price derived from the hedonic function does not measure what a particular household is willing to pay for additional units of a housing characteristic. Rather, it is the valuation that is the result of demand and supply interactions of the entire market.

In the example depicted in fig. 1, the partial derivative of the hedonic, p(z), is depicted by pi in the lower panel. In general, the hedonic equation will overstate the valuation of an additional unit of the characteristic since, to the right of points a and b, pi > 19: and 0;. This is the basis of the criticism by Harrison and Rubinfeld (1978), Freeman (1979) and Blomquist and Worley (1981) of early studies like those of Ridker and Henning (1967). This difference can sometimes be important if one is doing a benefit-cost analysis. For example, Harrison and Rubinfeld show that use of the hedonic regression results versus the use of estimates of household marginal rates of substitution (obtained via other methods discussed below) can overstate the benefits of air pollution abatement by as much as 30 percent.

Under restrictive conditions, the hedonic equation can reveal the under- lying demand parameters. For example, if all households in the sample are alike in terms of income and socio-economic characteristics, but supplies are not, p(z) would correspond exactly to 8 in fig. 1. In this case, the hedonic coefficients will be the marginal willingness to pay.

Many papers, which are too numerous to summarize here, have used the simple hedonic approach to obtain measures of the market valuation of particular characteristics. Some of the papers in this group include: Ridker and Genning (1967), Follain and Malpezzi (1981), Goodwin (1977), Halvor- sen and Pollakowski (1981), Jud (1980), Krumm (1980), Lang and Jones


(1979) Li and Brown (1980), Nelson (1981), Schnare and Struyk (1976), Wilkinson and Archer (1976), Borukhov, Ginsberg, and Werczberger (1978), Abelson (1979), Brown and Pollakowski (1977), Dubin and Goodman (1982), and Diamond (1980a). The applications include the study of household valuation of shoreline, access measures, neighborhood characteristics like crime rates and education quality, fuel types, zoning restrictions, and aircraft noise.

3.2. The two-step approach

Rosen suggests a two-step approach to estimate the compensated demand curve. First, a hedonic equation, e(z), is estimated. Second, the derivative of the hedonic with respect to each characteristic, j+(z), is evaluated at a particular bundle of z and used as the price vector in a system of demand and supply equations:

$i!z) = OiCz; Y, a),

(3’4

The claim is that the simultaneous estimation of the above equation will yield the desired parameters of the structural system. This would be equivalent to tracing the demand and supply curves of fig. 1. Observed values of zi are combined with the estimated pi’s in the lower panel to yield points a and b for their households. A simple regression that draws a line through these points would yield the hedonic equation. A regression that held constant for demand and supply shifts would theoretically yield the structure.

There have been many applications of this approach. They can be roughly divided among those which: (i) investigate one or many housing characteristics; (ii) use micro-level or aggregate data; (iii) use data from one metropolitan market or many markets; (iv) estimate compensated demand (and supply) equations such as (3) or estimate the parameters of the utility function to obtain willingness to pay measures; and (v) use various assumptions about the supply side. These distinctions are useful since they will determine which estimation technique is appropriate for a particular problem and data set.

Table 1 categorizes the studies which have utilized the two-step procedure, i.e., those that use hedonic functions to generate prices to be used in the identification of preference structures. The categories have important implications for estimation that have yet to be fully resolved. Two of the most important are possible simultaneity biases inherent in the approach and the identification of the structural parameters. The rest of this subsection

Table

1

Categ

oriza

tion

of tw

o-ste

p ap

plica

tions

.

Numb

er

of Nu

mber

of

Leve

l of

Supp

ly sid

e Au

thor

and

year

chara

cteris

tics”

Type

of

data

b ma

rketsc

an

aly&

assu

mptio

n

(1)

Bajic

(1

983)

Mu

ltiple

Micro

Mu

ltiple

CD

Fixed

su

pply

(2)

Bartik

(1

983)

Si

ngle

Micro

Mu

ltiple

CD

Price

-struc

ture

taken

(3)

Bl

omqu

ist

and

Worl

ey

(198

1)

Multip

le Ce

nsus

tra

ct Si

ngle

CD

Vario

us

(4)

Folla

in an

d Jim

enez

(1

983)

Mu

ltiple

Micro

Si

ngle

UFP

Price

-struc

ture

taken

(5)

Ha

rriso

n an

d Ru

binfe

ld (1

978)

Si

ngle

Cens

us

tract

Sing

le CD

Fix

ed

supp

ly (6)

Ju

d (1

982)

Si

ngle

Micro

Si

ngle

CD

Simu

ltane

ous

(7)

Kauf

man

and

Quigl

ey

(198

2),

Quigl

ey

(198

2)

Multip

le Mi

cro

Sing

le UF

P Fix

ed

supp

ly (8)

Lin

nema

n (1

981)

Mu

ltiple

Micro

Si

ngle

CD

(9)

McMi

llan

et ~2

. (19

80)

Sing

le Mi

cro

Sing

le UF

P Pr

ice-ta

ken/o

nly

one

type

of su

pplie

r (10

) Ne

lson

(197

8)

Sing

le Ce

nsus

tra

ct Si

ngle

CD

Simu

ltane

ous

(11)

Witte

et

al. (

1979

) Mu

ltiple

Micro

Mu

ltiple

CD

Simu

ltane

ous

“The

typ

es

of ch

aracte

ristic

s inc

luded

in

each

stu

dy

vary

grea

tly.

See

table

2

for

a pa

rtial

list.

“Micr

o sta

nds

for

dwell

ing-u

nit

level

obse

rvatio

ns.

‘Mult

iple

marke

ts ind

icate

tha

t va

rious

he

donic

pr

ice

struc

tures

es

timate

d in

the

first

step

were

us

ed

to ge

nera

te the

ma

rgina

l pr

ice

terms

us

ed

in the

se

cond

ste

p. %

D cc

ompe

nsate

d de

mand

es

timate

; UF

P=

utilit

y fun

ction

pa

rame

ters.


discusses these and other issues. The categories depicted in table 1 determine whether or not an issue is relevant for the study.

3.2.1. Simultaneity There has been a considerable amount of intellectual energy expended on

this subject. Aside from brief discussions in most of the empirical work, papers by Diamond and Smith (1983) Murray (1983), Ohsfeldt (1983) and Blomquist and Worley (1982) specifically address the issue. However, much confusion still prevails.

There are two sources of possible simultaneity problems. The first is the traditional simultaneity problem in which error terms are correlated with right-hand side variables in either the supply or demand equations because of the fact that price and quantity are simultaneously determined. The second simultaneity problem is quite different from the traditional one and stems from the non-linearity of the price function. The nature of the data base and the hedonic price function (see table 1) determines whether one or both of these problems is confronted by the researcher. The resolution of the problem depends upon assumptions regarding the supply curves in the first case and estimation techniques in the second case.

The traditional simultaneity problem may arise if one is using aggregate data. In this case, it is possible that the unit of observation is large enough to influence the hedonic price function that clears the market. The parameters of the price function used to calculate the marginal prices may be dependent upon the error terms in either the supply or demand equations being estimated. Therefore, using OLS to estimate the supply and demand equations leads to biased and inconsistent parameter estimates.

The problem is well illustrated in fig. 1, where it is assumed that all observations come from a single market [Nelson (1978), Jud (1980)]. The goal of the estimation is the structure of tJi and $i in the lower panel. Some studies [Witte et al. (1979)] attempt to estimate simultaneous systems for many markets, as in fig: 2.

Another simultaneity problem (of the second kind) may exist even if micro-level data are being used. Because the price function depends upon the vector of characteristics consumed by the household, the marginal price depends upon the choices of the households. In other words, the consumer faces a given price function, but is free to choose points along the function. Since the derivative of the function varies as one moves along the function, so too does the marginal price. In this sense, then, the marginal price paid by a consumer is simultaneously determined along with the choice of the quantity of the characteristic consumed. This problem exists if p(z) is non- linear in z.

Theoretically, the simultaneity problem in the micro-data case of a single market can be easily seen in fig. 3. In the lower panel, there are two


k pi

1 pi

Fig. 2

observation points, a, ($f,z!), and b, (@f,z”), which both lie on the same price structure pi. These points represent the equilibrium consumption points and marginal prices faced by two individuals, with preference structures - 0: and l$, who are the same in all respects except for one socio-economic characteristic (say, incomes). If each individual accepted the & that it faced as given - i.e., the price that rules, no matter how much zi he or she consumed - a regression of zi on pi, holding constant for income, would yield the slope of segment ‘ad’. Preference structure 0: would then be estimated if enough data are available. However, the assumption of pi as fixed is unjustified. The household accepts the entire price structure pi as


P(Z)

'i

‘ i

given, but can choose where to be on that curve at the same time as choosing how much zi to consume. Thus, pi and Zi are simultaneously determined and OLS estimation generates biased results. The regression of Zi and fii would be biased, not because of any effect of the supply curve, but because of the non-linear price structure.

There is one important difference to note between the first and second problems in terms of estimation. The single-market micro studies focus upon the behavior of individuals; thus, it is safely assumed that the market hedonic

J.R. Follain and E. Jimenez, Estimating demandfor housing charhcteristics 87

price function and its parameters are independent of the error terms associated with individual demand equations. Therefore, it is not necessary to incorporate supply-side variables into the estimation procedure.

Given this view of the simultaneity problem, the empirical literature can be criticized on several points. First of all, studies by Witte et al. (1979) of several housing characteristics and by Jud (1982) of access to schools correct for a problem they do not have. The papers use micro data but employ estimation techniques appropriate for a conventional simultaneous system. The studies thus imply that the error terms in an individual demand equation are correlated with right-hand side variables because of the supply equation. This is misleading since an error term in an individual consumer’s demand equation should not influence the price function that clears the market. Surely the sum of all demands would affect it, but not the demand of an individual consumer. This does not mean that a simultaneity problem of the second kind does not exist. Consequently, the use of an instrumental variables estimator like two-stage least squares may be quite valid, although even this is not at all obvious since the model that makes two-stage least squares a valid instrumental variables estimator is not the one analyzed by Witte et al. (1979). Thus, the estimation of simultaneous demand and supply systems is inappropriate in micro data sets.

A second criticism pertains to the assumption regarding the nature of the supply function. As evident in table 1, both micro [Bajic (1983)] and aggregate [Harrison and Rubinfeld (1978)] studies have utilized the assumption of fixed supply to circumvent the simultaneity issue. This assumption is inappropriate for micro data since individual households cannot affect the price structure. For aggregate data, the situation is depicted in fig. 4. Fixed supply at each location enables the researcher to use demand shifters to estimate the preference structure 8i in an unbiased way.

Harrison and Rubinfeld (1978) are technically correct when they argue that a simultaneous equations estimator like two-stage least squares is not necessary if it is assumed that supply is fixed at each location. In terms of the system of equations in (2), since zi is fixed, it remains on the right-hand side of the estimating equation. (In the lower panel of fig. 4, a regression of I on zi with zi fixed would yield segment “ac” of Qf.) While the assumption may be valid for the particular attribute, air quality, that they analyze, its general applicability is largely an empirical issue that should be examined whenever possible, as appropriately suggested by Blomquist and Worley (1982). They analyze the severity and existence of the simultaneity bias via empirical methods developed by Hausman (1978).

Of course, suggesting that two-stage least squares should be used when aggregate data are used begs the difficult question of where to find good variables that affect the supply side of the market. Typical supply-side variables like input prices do not vary within a metropolitan area, except for

88 J.R. Follbin and E. Jimenez, Estimating demand for housing characteristics d2 r P(Z)

B 82

ml c 01

A

pi

61

pi A2

'i pi

Fig. 4 a

land prices, and land-price data are quite difficult to obtain. What variables should then be included as instruments? More research needs to be done to explore the question and future data collection be done to include more supply-side variables, such as landlord specific information.

A third criticism deals with the correct econometric treatment of the simultaneity problem that arises as a result of the non-linearity in the price term. The standard procedure is to replace the marginal price by an instrumental variable. This has been used by Quigley (1982), Linneman (1981), and Follain and Jimenez (1983). The instrumental variable is obtained

J.R. Follain and E. Jimenez, Estimating demandfor housing characteristics 89

via regression of the marginal price against a set of variables thought to be correlated with the marginal price but not correlated with the error term in the individual consumer’s demand equation. For example, Follain and Jimenez (1983) use household current income, permanent income and. household size.

An alternative is to replace the marginal price by its definition in terms of the hedonic price function parameters and the characteristics. Then, the system (3) reduces to one of m endogenous variables, the m ,q’s. The estimation of this simultaneous system is difficult because it is likely to be nonlinear and consist of a set of implicit functions. Estimation of a non- linear set of simultaneous and implicit ‘equations is discussed by Gallant (1977). Another approach is to use non-linear three-stage least squares with a linearized version of the demand system. One obvious problem with this approach is the lack of good instruments. Ohsfeldt (1983) conducts some interesting Monte Carlo experiments aimed at improving our understanding of the small sample properties of various estimators that have been used to estimate systems of demand for housing characteristics. Although his work is not definitive, making use of Monte Carlo methods to study the properties of the various estimators seems to be a good idea because of the complexity of the equation system.

A final word is in order regarding this view of the simultaneity problem. That is, it excludes the possibility of a third type1 of simultaneity. This third type has to do with the relationship between the total number of dwelling units and the aggregate quantities of the characteristics. For example, the price structure associated with a market with two dwellings each with 50 rooms would likely be different than the structure in a market with 100 units each with one room. An examination of this simultaneity problem is likely to be quite complex. Because of this complexity and the fact that studies that examine the aggregate quantity of dwellings and its characteristics are rare, further discussion of it brings us beyond the scope of this paper. It should be added, though, that if such aggregate studies are attempted in the future, this third simultaneity problem should be addressed.

3.2.2. Identification The problem is raised by Brown and Rosen (1981). If j&(z), which is the

dependent variable in the system (3), is a function of all the variables z on the right-hand side and comes from the same data base, then the variation that enables the system’s estimation is caused by the functional forms of the behavioral relationships. For some functional forms (a quadratic hedonic and a linear demand equation, for example), the coefficients of the behavioral demand relationships between jii and zi can be derived exactly from the

‘This point was brought to out attention by Douglas Diamond.

90 J.R. Follain arid E. Jimenez, Estimating demand for housing characteristics

hedonic coefficients. Thus, estimation of (3a) and (3b) is unnecessary. One way to surmount this problem is to ensure that the observations in (3) come from different markets (see fig. 2). The estimation of the behavioral relationships in (3) would thus use new information provided by the inter-market price variation.

A simple example demonstrates the point. Consider a hedonic model with one characteristic,

and a demand equation for zr,

Then OLS estimates of a, and a0 are exactly equal to the hedonic coefficients estimated in step one. The OLS estimator of cur when the data are in deviation form is

2&z;z, &(OLS) =-------

4% - 28,.

The OLS estimator of a, is

B,(OLS) = 8, + 2&) - 2&& = 8,.

Obviously, then, the two-step procedure yields nonsensical results in the case in which all data are from the same market. If, however, the data are from several markets, then the result obtained above does not occur because the dependent variable in step two is no longer a linear transformation of the right-hand side variable. Keep in mind this is a simple and unrealistic example, it does seem to capture the essence of the problem identified by Brown and Rosen (1982). * J

There is one other way of estimating the parameters of a demand or supply system using data from only one market. That is, the researcher can specify a functional form -for the hedonic equation that is different and, generally more complex, than the functional forms of the demand and supply equations, For example, Quigley (1982) and Follain and Jimenez (1983) have used a Box-Cox framework to derive a form for the hedonic equation. This, combined with knowledge of the functional form of the compensated demand system, enables the identification of the demand structure.

3.2.3. Other issues The literature has left virtually unexplored an important issue. That is,


what should be the appropriate specification of the error terms in the hedonic and the behavioral equations. Epple (1982) provides the only paper that even raises the issue. He explores the implications of placing error terms in the hedonic equation versus the behavioral equations. The main lessons of the paper are that the error specification can make quite a difference in the selection of an estimation procedure and that some of the error specifications (the most general ones) lead to the need of- employing estimators that are quite complex. However, he presents no empirical results and offers little guidance as to how the error specification should be made.

Finally, it should be noted that the two-step studies done to -date do little to analyze the demand for discrete characteristics. Quigley (1982) and Follain and Jimenez (1983) try to derive estimates consistent with the bid-rent approach, but the methods are largely ad hoc and not altogether successful. There is a wholly different approach that has been used to estimate the demand for housing characteristics in which the entire choice process is treated as a problem of choosing from among discrete alternatives. This approach is discussed below.

3.3. Bid-rent approach

The bid-rent approach involves direct estimation of the bid-rent function rather than first-order conditions or compensated demand equations associated with a particular bid-rent function. The procedure is as follows. First, the bid-rent function is calculated for a particular utility function that shows p(z) as a function of household income, the characteristics, the utility function parameters, and the exogenous level of utility. Second, the households are divided into groups in which each member of the group is assumed to receive the same level of utility from the bundle being consumed. Third, the bid-rent function is estimated via non-linear least squares for each group. The dependent variable is the rent or value of the household’s housing unit and the independent variables are income and the various housing and location characteristics. The output of the estimation is a set of estimates of the utility function parameters.

The relationship between this and the two-step approach is easily shown. In the upper panel of fig. 1, suppose that O1 and 8’ represent the preference structure of two types of individuals in the sample. If the analyst can distinguish between these types then the estimation is straightforward. If they are the only types, O1 will correspond exactly to p(z) over the range where type 1 individuals consume Zi. All households of type 1 are alike and are of equal utility. The observed price differentials compensate individuals for variations in the consumption of zi. A regression of observed p(z) on zi for all type 1 households in the sample identifies the structure of tI1 if its functional form is presumed. There is no need to involve first-order conditions.


This approach has been used by Wheaton (1977) to estimate household willingness to pay for various characteristics for a sample of households from the San Francisco Bay Area. He used a variety of utility functions (e.g., Cobb-Douglas and CES) and a variety of variables to define groups of equal utility (e.g., income class, race, household size and age). In a very interesting application of the same methodology, Galster (1977) studied the willingness to pay for housing characteristics of black versus white households in the St. Louis area. Follain et al. (1982) analyze the willingness to pay of Korean households for various measures of living space. Diamond (1980a) uses a variant of this approach in his analysis of Chicago households. He ranks households by income and makes use of the assumption that households of similar income (ranked next to one another) must enjoy the same level of utility to estimate a function similar to the bid-rent function.

In theory, the bid-rent approach is a very convenient and straightforward way to estimate the household parameters for housing and locational characteristics. It does, however, suffer from a serious, if not critical, flaw. How does one identify groups of households who receive the same level of utility? If one has access to a very large data set - Wheaton’s data set includes over 50,000 households - then perhaps the method has some merit. However, as the data set decreases in size, so does the possibility of identifying groups that are at least comparable in utility and large enough to permit estimation. In an attempt to deal with this problem, Wheaton (1977), Galster (1977), and Follain et al. (1982), allow the intercept in the regression (i.e., the exogenous level of utility) to depend upon household income, or some function of it. This may improve the quality of the results produced by the method, but it is difficult to say by how much without further analysis.

3.4. Index approach

A fourth approach in studying the demand for housing characteristics is based on the Lancaster household production model of consumer behavior [e.g., King (1976)]. However, to the extent it is based upon the use of hedonic regressions, this approach is closely akin to the Rosen model. The name is used to signify that hedonic regressions are used to create indexes of various housing and locational characteristics; these indexes are then used to conduct traditional demand analysis.

The method generally consists of three steps. First, a hedonic regression is estimated. Second, the coefficients of the hedonic are used to construct weighted sums of various subsets of characteristics. For example, a living space index might be constructed by using the coefficients of indoor and outdoor living space. The inside space coefficient is multiplied by the amount of inside space occupied by a household. The same is done for the outside living space. The sum of the two products is computed to constitute an index


of the variable, SPACE. Several indexes of this type are constructed. Third, the various indexes are used as measures of the dependent variable on each category of characteristics to conduct standard demand analysis. A price variable is usually not used. If one is, it is constructed as a weighted average of the hedonic price coefficients (fixed weights). The number of price indexes constructed equals the number of categories of characteristics.

Several authors employ this approach. Barnett and Noland (1981) use the approach to study the demand for living space versus housing quality using experimental housing allowance data. Only two equations, a hedonic and a demand equation for space, are estimated. More elaborate applications include King (1976), who estimates a full-system of demand equations and then uses the estimates to test assumptions regarding household preferences, e.g., homogeneity of demand, additivity, homotheticity, etc. One of the techniques used in the paper by Follain et al. (1982), employs an approach that is categorized for the purposes of this paper as an index approach, but it is not an obvious example of the approach. They have available to them two indexes - a land price index and a construction cost index - and they use these as price variables to estimate the demand for living space and lot size for Korean households.

The primary criticism of this approach is that the indexes are necessarily arbitrary and dependent upon the data available and the ideas of the researchers as to how characteristics should be grouped. Consequently, application of the approach yields estimates that are difficult to compare among studies and difficult to use for policy analysis.

A second criticism applies to its ability to estimate price elasticities. If the data are from one metropolitan area, then price indexes cannot be defined since weighted averages of the hedonic coefficients are the same for all households. Therefore, multiple market data are essential to this approach if price elasticities are to be obtained [or the local market must be segmented, as in King (1976)]. Even if multiple market data are available, using a weighted average of the hedonic coefficients as a price index introduces measurement error since the true marginal price is not a simple weighted average of the coefficients, but is rather the derivative of the hedonic price function evaluated at the bundle consumed by the household. The serious- ness of the measurement error is unknown.

3.5. Discrete choice approaches

Implicit in the analyses presented so far is the assumption that the characteristics in question are continuous and the consumer is able to purchase as many as he or she wants given the hedonic price function. Of course, there are some types of characteristics that are not continuous and are inherently discrete, such as the availability of types of water supply.

R.S.U.E.- D


Moreover, some believe the housing market is inherently a discrete choice problem. That is, a given number of households are bidding against one another for a given stock of housing that is not changeable, or at least not very easily changed. In this sense, then, the problem is one of matching a finite number of households with a finite number of housing units. The problem facing the consumer is one of choosing the single best unit for itself given the existing housing stock.

The approach has its roots in the econometric literature devoted to the development of logit, probit and other discrete choice models of consumer choice. The consumer chooses from among a set of discrete characteristic bundles to maximize utility. Since the comparisons are not continuous, the estimation procedure attempts to identify the parameters that determine the probability that a consumer will choose one bundle versus another.

McFadden has presented numerous papers that discuss the general problem of consumer choice in a discrete framework. For an example of his work, see Domencich and McFadden (1975). A very good discussion of the discrete choice approach as it applies to housing is presented by Ellickson (1981), who shows that the problem can be addressed in one of two ways. The problem can be viewed as a large number of distinct consumers (distinct, say, due to income differences) choosing a finite number of housing unit types, or as a small number of household types choosing from a large number of housing units. The first approach leads to the estimation of the probability that a consumer will choose to live in a house of a particular type, e.g., more than two bedrooms. The second approach leads to the estimation of the probability that a house will be occupied by a household of a particular type. Another excellent aspect of the Ellickson paper is that he presents the approach in the context of the Rosen bid-rent framework.

In addition to Ellickson, Quigley (1981) has applied a methodology developed by McFadden (1978) to study consumer choice in a discrete choice framework. He is interested in two questions. First, how does one solve the domputational problem of analyzing consumer choice when the number of alternatives is quite large? Second, how does one test one of the quite restrictive assumptions associated with the most popular discrete choice model - the logit estimator - that is, independence of irrelevant alternatives? Two others who have done work of this type include Anas (1983) and Zorn (1985). Anas analyzes consumer bid-rents in Chicago to see how they are influenced by transportation alternatives. Zorn analyzes how consumers choose between the central city and the suburban areas.

One criticism of the earlier literature using the discrete approach is that it does not produce estimates of willingness to pay for various attributes; rather, it produces estimates of probabilities. This makes the results a little more difficult to use from a policy point of view since an important question to many policymakers concerns cost recovery; that is, how much can be

Table 2

Income and price elasticities reported in the literature.

Characteristic Income elasticity

Price elasticity Author Approach

Size

Space

Rooms

Site

Lotsize

Quality

Dwelling quality

Age and dwelling unit type

Structure

Existence of amenities

Good social neighborhood

Low stability of neighborhood

Public safety

Homogeneity (probability)

Quiet

Distance to nearby highway

Access to rail

Access to CBD

Access

Low accessibility

. Living space measures

0.45 -0.94 -0.05 -1.61

0.35 (owners) 0.26 (renters) 1.20 - 3.41 0.64 -0.14

0.03 -0.77 0.31 -0.87 0.30

-0.26

Follain et al. Witte et al.

Barnett and Noland

2.62 -6.56 0.54 -0.82

0.32 -0.40

Structural 1.65 (owners) 2.32 (renters) 1.09 - 1.61 1.72 - 0.20

2.50 3.80 -

2.04 -0.15 -0.31 3.89

Neighborhood quality 15.7

0.2

McMillan King

Linneman Follain et al. Awan et al. Blomquist and

Worley

McMillan King

Witte et al.

Barnett and Noland

Witte et al. King

Awan et al.

Awan et al.

King McMillan

Awan et al.

Awan et al.

7.80 Awan et al.

2.36 Diamond (198Oa)

-0.01 Linneman

0.29 - 1.42

Access -0.29

McMillan

2.88 \

2.11

0.01 -0.79

- 3.40

Blomquist and Worley

Diamond (198Oa)

Diamond (1980a)

Linneman

Awan et al.

Index Two-step

Index

Index Index

Two-step Index Index Two-step

Index Index

Two-step

Index

Index

Index

Index

Index Index

Index

Index

Index

Index

Two-step

Index

Two-step

Index

Index

Two-step

Index

table continued on next page

table 2 continued

All attributes

Reduction in: Air pollution

Air quality

0.4

4.3

1.0

Others -

-0.87

- 1.22

Awan et al.

Harrison and Rubinfield

Nelson (1978)

Index

Two-step

Two-step

Table 3

Description of variables in elasticity measures.

Awan et al.

Barnett and Noland Space -interior living area Quality -aggregate dwelling quality

Blomquist and Worley Rooms -number of rooms Distance to Highway 66 -accessibility measures Distance to Highway 55 -accessibility measures

Diamond (1980a) Public safety -incidents of crimes against persons, by municipality (cases per thousand) Access to rail -miles to nearest commuter rail station Access to CBD -miles to CBD along major roadways

Follain et al. Size -inside living area, measured in pyongs Rooms -number of rooms

Harrison and Rubinfield Reduction in air pollution -measured as a reduction in the level of nitrogen oxide

King Space -interior square feet, presence of small special purpose rooms, basement

Site characteristics, number-of stories in home

-lot size, distance to CBD, perceived neighborhood quality, provision of public garbage removal and sewers

Quality -interior and exterior quality measure Structural -presence of full insulation, number of garages, number of baths, basement

laundry facilities I Linneman

Rooms -number of rooms in dwelling unit, excluding bathrooms Homogeneity -dummy variable equal to one if the highest density structure category equals

the lowest density structure category Accessibility -variable equal to one if the dwelling unit is less than 5 miles to the nearest

city center; to 0.5 if 5 to 14.9 miles; to 0.33 if 15 to 29.9 miles; to 0.25 if 30 to 49.9 miles; to 0.20 if 50 miles or greater

McMillan Space -floor area, number of four piece bathrooms, number of bedrooms, developed

basement Site -lot size, distance to CBD, local zoning laws Structure -age of house, presence of fireplace, garage with property, brick exterior, style of

house Quiet -measure of freedom from local airport noise

Nelson Air quality -Inverse of air pollution level, as measured by the average monthly particulate

concentration


extracted from the tenants in rent for a particular dwelling type. A recent paper by Lerner and Kern (1983) shows how willingness to pay estimates can be extracted from a discrete choice model, although we know of no applications of their approach.

The most significant criticism of the discrete choice approach is that computational considerations force the model to be quite restrictive in terms of the number of choices available to the consumer. For example, Ellickson (1981) assumes that there are about twenty different types of households in the housing market. The twenty different types of households emerge from assuming that households are either high or low income, black or white, large or small family, married or not. This approach masks one of the most important variables in economics, income. The approach taken by Quigley (1981) is designed to combat this problem in that it allows, at least in theory, for the consumer to face a large number of choices, or alternatively, allows the number of consumer types to be quite large. In order to apply the Quigley approach, though, some additional assumptions are required regarding the possible choices a household considers. The restrictiveness of these assumptions requires more analysis.

4. Empirical applications: Results

The focus thus far has been on the analysis of the techniques used in the various empirical studies of the demand for housing characteristics. What have they taught us about consumer demand? To summarize the results of the research, attention is focused on income and price elasticity estimates, and willingness to pay estimates.

The results are presented in two tables. Table 2 contains a listing of all the income and price elasticity estimates that could be gleaned from the empirical studies. Table 4 contains estimates of the various willingness to pay measures as well as willingness to pay for a particular characteristic as a percent of rent and income. Both tables present the results in terms of groups of housing and locational characteristics. The groups are: living space, structural quality, neighborhood quality, access, and other. Tables 3 and 5 provide detailed descriptions of the various variables referred to in tables 2 and 4.

Consider first the estimates of the income and price elasticities of the demand for living space. The exact measure of living space varies from study to study, but a consistent pattern does emerge. That is, the income elasticity of the demand for living space seems quite inelastic. Only the estimates by McMillan exceed unity, but none of the others exceed 0.64. Although it is difficult to compare these to estimates of the income elasticity of the demand for the composite housing good, housing services, the numbers suggest that the income elasticity of the demand for living space is less than that for the

Table

4

Willi

ngne

ss

to pa

y me

asur

es

as r

epor

ted

by

prev

ious

litera

ture.

Char

acter

istic

1983

U.

S.

dolla

rs (m

onthl

y)

As

a pe

rcent

of re

nt/va

lue

As

a pe

rcent

i- of

incom

e Au

thor

Appr

oach

P 3

Living

sp

ace

meas

ures

Ro

oms

Living

ar

ea

( 10

m’)

Living

ar

ea

(10

m’)

i

94.6

3 5.4

1 0.2

1 (B

ogota

ren

ters)

5.30

(Cali

ren

ters)

38.7

3 (S

eoul

renter

s) 34

.89

(Bus

an

renter

s) 3.5

4 (D

avao

ren

ters)

4.00

(Bog

ota

owne

rs)

12.2

7 (C

ali

owne

rs)

15.2

4 (S

eoul

owne

rs)

21.2

4 (B

usan

ow

ners)

2.1

2 (D

avao

ow

ners)

2.01

3.24

(Bog

ota

renter

s)

Lot

size

(10

m’)

8.53

(Cali

ren

ters)

52.0

6 (S

eoul

renter

s) 53

.35

(Bus

an

renter

s)

5.73

(Bog

ota

owne

rs)

15.2

7 (C

ali

owne

rs)

39.2

8 (S

eoul

owne

rs)

41.6

9 (B

usan

ow

ners)

2.45

0.066

”

0.003

”

0.02

9 - 5.1

x 1

o-4

0.077

” 0.

013

Q.26

8”

0.06

4 0.3

52”

0.06

6 0.1

50”

0.01

7

0.017

” 0.

006

0.089

” 0.

023

0.045

” 0.

019

0.084

” 0.

031

0.097

” 0.

009

0.13

- 0.02

2

0.040

”

0.123

” 0.3

61”

0.539

”

0.024

” 0.1

10”

0.117

” 0.1

65”

0.05

3

0.00

8

0.02

1 0.

086

0.10

1

0.00

8 0.

029

0.01

9 0.

062

0.00

9

Whe

aton

Quigl

ey

Folla

in an

d Tw

o-step

Jim

enez

Quigl

ey

Folla

in et al.

Fo

llain

and

Two-s

tep

Bid-

rent

Two-s

tep

Folla

in an

d Jim

enez

Bi

d-re

nt

Age

of dw

elling

St

ructu

ral

quali

ty

Dista

nce

to CB

D

Acce

ss

Quiet

0.55

(Dav

ao

renter

s) 0.0

23”

0.18

(Dav

ao

owne

rs)

0.025

”

51.0

5 0.0

58”

2.58

(Bog

ota

renter

s) 0.0

32”

6.38

(Cali

ren

ters)

0.092

” 1

x 1O

r5 (C

ah

owne

rs)

7.22

x 10

rZa

Neigh

bour

hood

17

9.63

1.9

8”

Air

quali

ty 55

31.2

1 0.1

9

Sanit

ary

quali

ty 1.

023

Aggr

egate

qu

ality

1.22

0

Stru

ctura

l qu

ality

16.5

8 0.0

07”

4.77

(Dav

ao

renter

s) 0.2

02”

7.15

(Dav

ao

owne

rs)

0.328

”

Acce

ss

764.

05

Othe

r 0.0

67”

0.079

”

0.00

2 0.

023

0.03

1

0.01

1

0.00

3

0.00

1

0.01

6 0.

006

0.01

6 1.8

9 x

10”

0.01

6 Qu

igley

0.02

0 Qu

igley

Whe

aton

Folla

in an

d Jim

enez

Bid-

rent

Two-s

tep

Diam

ond

Bid-

rent

(198

0b)

Folla

in an

d Tw

o-step

Jim

enez

Whe

aton

Folla

in an

d Jim

enez

Bid-

rent

Two-s

tep

McMi

llan

et al.

Harri

son

and

Rubin

feld

“Sign

ifies

WTP

as

a p

erce

ntage

of

rent.

%

ignitie

s W

TP

as a

per

centa

ge

of va

lue.


Table 5

Description of variables in willingness to pay measure.

Diamond 1980(b) Distance to CBD -distance to CBD along major roadways, in miles; expressed as WTP per

mile, for household income =$27,100 (1970 $)

Follain et al. Living area -an additional pyong (3.3 square meters) of inside living space. The figures

presented in table B-3 have been calculated for 10 square meters, evaluated for family size of 4 and monthly consumption of 50,000 won

Follain and Jimenez Living area -willingness to pay for one additional square meter of living area Rooms -willingness to pay for an additional room Structure quality -measured by index Access -measure of accessibility to concentrations of workplace

Harrison and Rubinfeld Air quality -marginal willingness to pay for an improvement in air quality at a ‘high’ level

of concentration of nitrogen oxides, at an income level of $11,500

McMillan et al. Quiet -noise exposure forecast contour corresponding to location of property, as calculated

by the Canadian Air Transport Administration; evaluated for the average price house with average quiet and non-quiet services

Quigley Rooms -average willingness to pay for an additional room Living area -willingness to pay for an additional 10 square meters of inside living

area Sanitary - 14 index of sanitary quality in dwelling unit Aggregate quality -1-9 index of aggregate dwelling quality

Wheaton [all values evaluated for family size 34, income 10,00~15,000 (1965 US $), household head

age 31-551 Rooms -value of one more room (evaluated at 7 rooms) Age of dwelling -willingness to pay for unit one year newer, evaluated at 10 years old Access -compensation for one unit change in access index

I

composite good if one takes the consensus estimate of housing income elasticity as being between 0.5 and 1.0 [see Mayo (1981), Mayo et al. (n.d.) Polinsky (1977) and Goodman and Kawai (1982)]. “

The pattern for price elasticity also exists, although it is not as pronounced. Demand seems slightly inelastic although the range is large and the estimates seem sensitive to the type of living space, i.e., lot size is more elastic than inside living space.

The second panel of table 2 also reveals a pattern. The income elasticity of the demand for quality seems quite elastic. Every study suggests the income elasticity is in excess of one, and most suggest it is quite above unity. Unfortunately, the price elasticity estimates are few.

Neither does analysis of the other variable types reveal any interesting patterns. The only one might be a negative one. That is, the range of


estimates is so wide one is tempted to conclude that the econometric analyses have taught us very little about the demand for characteristics like access and neighborhood quality.

Table 4 is more diflicult to interpret. Since willingness to pay obviously varies depending upon the income and price level of the household, there is substantial variation in the estimates obtained from the literature. In an effort to lessen these differences, the estimates have all been put in 1983 U.S. dollars. In addition, the estimates have been expressed as a percent of household income and the rent paid for the unit (all in monthly terms). Despite all of these attempts to standardize the results, they remain rather scattered. For example, willingness to pay for a room of about 10 square meters as a percent of income ranges from about 3 percent of income to almost 9 percent of income.

5. Conclusions

5.1. Summary of the issues

This paper has reviewed the different methods which have been used to determine empirically the parameters of the demand for housing characteristics. They include the following approaches: simple hedonic, two-step, bid-rent, index, and discrete. Which approach is the most appropriate depends very much on the economic issues that are being addressed in a particular study as well as the nature of the available data base. For example, being able to confidently segment a micro-sample into subsamples of households of homogeneous characteristics allows one to estimate bid-rent functions directly.

The most popular method in the recent literature, and the one which is closest to Rosen’s elegant theoretical model of the implicit market for characteristics, is the two-step approach. This study concludes that, while significant advances have been made, the empirical applications have yet to match the rigor of the analytical framework. The issues which seem to have caused the most problems are related: simultaneity and identification.

The confusion regarding simultaneity in the estimation of demand parameters stems from the fact that there are several types of simultaneity bias. This paper categorizes these into three: the ‘garden-variety’ demand-supply simultaneity bias to which Rosen refers in his original work; the bias caused in estimating compensated demand equations when prices are determined endogenously in the system; and the relationship between the total number of dwelling units in a market and the aggregate quantities of the characteristics. The presence of any one or all the types of bias depends on the data base (for example, whether it is a micro or an aggregate data set) and the structure of the system being estimated.

R.S.U.E.-E


The other issue is identification and it arises because the dependent variable used in the hedonic regression, the first step, is an explicit function of #. It is thus generally difficult to distinguish between the estimated parameters of an ad hoc demand system and those of a hedonic regression, particularly if all of the data come from a unified market in which all observations face the same hedonic price structure. Indeed, as Brown and Rosen (1982) have shown, under certain functional forms (quadratic for the hedonic and linear for demand), the coefficients of the characteristics in the second-step (demand equation) regression are exact functions of the coefficients of the hedonic equation. In general, either a rich multi-market data base or the imposition of a prior structure on the estimated system is needed to surmount this problem.

5.2. Recommended procedures

Given the difficulties mentioned above, what procedure can be recommended for future work? The ideal estimation procedure depends partly upon the data as well as the objective of the researcher. Three different types of models can be specified. The first consists of a system of m demand equations, the second consists of a system of m compensated. offer functions, and the third consists of 2m equations, m supply and m demand equations. Each system is likely to be non-linear, simultaneous and implicit given reasonably general utility and production functions. The parameters of the system are the parameters of utility and production. The endogenous variables are the m quantities of the characteristics and the exogenous variables are the shift variables for either supply or demand, i.e., income, household size, input prices. The parameters of the hedonic price function unique to each market also enter the system, but they are assumed known.

How does one estimate any of these rather complex systems? Estimation is undoubtedly going to be difficult; however, some recent work by Gallant suggests that it is at least possible. In a series of papers in which he has collaborated it has been shown how a system of this type can be estimated via maximum likelihood, non-linear three-stage least squares and instrumental variables. Gallant (1977), Gallant and Holly (1980), and Gallant and Jorgenson (1981), although application of any of these procedures is undoubtedly a difficult and time-consuming task, a very useful area for further research would be to apply one or all of these techniques.

Given the complexity of the ideal model specification and estimation procedure, simpler and more ad hoc procedures are likely to remain popular. Among the methods surveyed in this paper, the Rosen two-step seems the best. It is well-rooted in theory, and relatively simple to apply. There are, however, several aspects of this approach that should receive more attention.

First, attention should be given to the problem of selecting good instru-


ments for the two-stage least squares or instrumental variables approach. No one would deny that the procedure is a reasonable one in theory, but one must question how good can the approach be in practice given the paucity of good instruments. One way this might be investigated is via Monte Carlo studies. The work begun by Ohsfeldt (1983) seems well worth pursuing.

Second, more attention needs to be given to the specification of the error terms in the model. Epple (1982) has done an excellent job of initiating this research. Further work would involve actual estimation of systems under the various error specifications suggested by Epple to determine the sensitivity of estimates to the error specification.

Third, work should be done to determine how best to estimate simultaneously characteristics that are both discrete and continuous. Currently, as mentioned above, the practice is to do either one or the other. However, the reality of the world is such that some characteristics are continuous and some are discrete. Our models should reflect this fact. The recent econometric work that explores how systems of discrete and continuous variables should be estimated is likely to be quite helpful [e.g., see Heckman (1978)].

Comments are also in order regarding the quality of data available for this type of analysis. The ideal data set is a multiple market data set that includes variables on individual housing units, the neighborhood in which the unit is located, the landlord, and the household and infrastructure associated with the neighborhood. Also, information regarding input prices for each market is needed. Unfortunately, data sets of this type do not exist. The best data set in the U.S. for this type of analysis is the Annual Housing Survey. However, it contains little information regarding the neighborhoods of the housing units or the landlords. This needs to be improved. In other countries, the situation seems to be worse. Canada has no national housing survey, and the United Kingdom has a one time survey that is not nearly adequate. Other data sets have been discovered in several developing countries, but these are not standardized or always adequate. Recently, however, the World Bank has initiated efforts to develop adequate data bases for this type of analysis in Korea, ‘Philippines, Egypt, Kenya, and Columbia. Future analysis of these data bases can contribute substantially to lessening the purely data-related problems of many earlier analyses. Then, perhaps, this literature can begin to produce results that are of substantial help to policymakers because no matter how fancy the model or estimation technique, the old adage remains true - garbage in, garbage out.

5.3. Broader implications

The standard urban economic (SUE) model can be viewed as a special case of the Rosen characteristics model. The SUE model focuses on two


characteristics, access to CBD, k, and everything else about a house and its neighborhood that generates utility, 4. The SUE model has been a mainstay of the field of urban economics for more than a decade. Its strengths lie in its simplicity, elegance and ability to produce numerous testable hypotheses and policy implications about the process of urbanization. The question addressed here is whether the empirical analyses of the more general hedonic model shed any light on the validity of the SUE model and its conventional treatment of housing as a composite good. Owing to the diversity of the econometric results surveyed, it is necessary to be quite humble regarding any answers presented. Nonetheless, several points do seem valid.

First, if stability and consistency of empirical results are acceptable criteria, much can be said in favor of the SUE model. Surveys of income and price elasticity estimates of the demand for the composite good 4 yield a range of estimates that is much smaller than those observed for subcategories of 4. This suggests that the concept of an aggregate commodity 4 is a good one that should not be readily abandoned.

Second, the focus of the SUE model on the characteristic access to CBD (k) seems unwarranted. Such a focus is warranted if the income and price elasticities of the demand for CBD access are found to be consistently different than those for other characteristics. Such is not the case. Little consistent evidence exists to show the income and price elasticities of the demand for CBD access are so quantitatively different as to warrant special attention. This may be due to the decline in the importance of the CBD or it might simply reflect consumer preferences. Whichever explanation is correct, the fact remains that the empirical literature on the demand for characteristics does not indicate CBD access is a particularly significant one. Given that many of the important results in the SUE model are derived under the assumption that the income elasticity of the demand for 4 is greater than the demand for CBD access, it is necessary to question those results.

A third and related point is that the only empirical regularity in the literature on characteristic demand suggests an important alternative to the SUE model - the Blight Flight Model - may be more appropriate. ,The Blight Flight Model is a term coined to explain U.S. suburbanization as a process caused by a deterioration of the quality of life inside many of the large U.S. cities. The SUE model deemphasizes this aspect of the U.S. experience and emphasizes instead the income growth and the decrease in transportation costs enjoyed during the 20th century. The empirical results on characteristic demand indicate the income elasticity of the demand for living space is less than the income elasticity of the demand for amenities. If this is true, then the role played by the amenities of city life is probably more important than the SUE model indicates. This suggests the application of the characteristic demand approach to the study of suburbanization offers opportunities for insights not possible within the SUE. Only Diamond

J.R. Follain and E. Jimenez, Estimating demandfor housing characteristics 105

(1980b), Diamond and Tolley (1982), and Linneman (1982) seem to have pursued this in any great detail. More work along these lines could be quite productive.

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Blomquist, Glenn and Lawrence Worley, 1982, Specifying the demand for housing characteristics: The exogeneity issue, in: Douglas B. Diamond, Jr. and George S. Tolley, eds., The economics of urban amenities (Academic Press, New York) 89-102.

Borukhov, Eli, Yona Ginsberg and Elia Werczberger, 1978, Housing prices and housing preferences in Israel, Urban Studies, 187-200.

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Demand for Housing Estimation