the value of housing attributes

This PDF is a selection from an out-of-print volume from the National Bureauof Economic Research

Volume Title: Housing Markets and Racial Discrimination: A MicroeconomicAnalysis

Volume Author/Editor: John F. Kain and John M. Quigley

Volume Publisher: NBER

Volume ISBN: 0-870-14270-4

Volume URL: http://www.nber.org/books/kain75-1

Publication Date: 1975

Chapter Title: The Value of Housing Attributes

Chapter Author: John F. Kain, John M. Quigley

Chapter URL: http://www.nber.org/chapters/c3718

Chapter pages in book: (p. 190 - 230)

8

The Value of Housing Attributes

A fundamental proposition of the analyses which we have presented inthis work is that the long-run equilibrium model employed implicitly orexplicitly in nearly all economic studies of urban housing marketsdepicts housing outputs, housing production relationships, and thenature of consumer demand in an analytically incorrect and misleadingway. As we have discussed in Chapter 2, the traditional model assumesthat households demand a homogeneous good which is produced com-petitively in a market characterized by long-run equilibrium. The influ-ence of this traditional model of the housing market is not confined to theeconomics discipline. Many policymakers, often unknowingly, acceptthe assumptions, conclusions, or policy prescriptions of such a model.

An essential element of the revised theory that underlies ourempirical analyses is that housing consumers demand not a homogene-ous good "housing," but rather bundles of specific housing attributes. Inthis chapter, we use statistical methods to estimate the market value ofindividual housing attributes. These imputations, made by regressionanalysis, are analytically equivalent to the market comparisons made byindividual demanders. The principal difference is that prospective buy-ers will generally confine their detailed comparisons to a fairly limitedportion of the market, whereas we seek to describe the structure ofattribute prices for the entire housing market. Several earlier studieshave attempted to make similar statistical estimates of the contributionof these specific attributes to the total price (rent or market value) ofresidential services. For example, Ridker and Henning use census-tractdata for St. Louis to estimate the effect of variables such as air pollution,accessibility to the downtown area, school quality, and substandardconditions on the value of single-family homes.' Similar analy-

'G. Ridker and J. A. Henning, "The Determinants of Residential Property Valueswith Special Reference to Air Pollution," Review of Economics and Statistics 44, no. 2(May 1967).

190

-w

The Value of Housing Attributes 191

ses, incorporating other variables, have been done by Muth, Oates andPendleton, and others.2

Most previous attempts to estimate the market value of specificattributes of the bundle of residential services are deficient because theyfail to represent adequately the complexity of bundles of residentialservices, because they lack adequate measures of residential quality, orbecause they rely exclusively on aggregate data. In this chapter, we seekto correct these deficiencies by using information for individual dwellingunits, by describing the bundles of residential services more completelyand, in particular, by making a serious attempt to measure physical andenvironmental quality.

Quantitative estimates of the value of individual attributes of thebundle of residential services are obtained by regressing market price(value for owner-occupied dweffings and monthly rent for renter-occu-pied dwellings) on several housing attributes. The coefficients for indi-vidual variables then measure the market value of additional quantitiesof each attribute. If the housing market could be assumed to be in long-run equilibrium, this would be a fairly unambiguous measure, since itwould also be equal to the supply price of adding an increment of thatattribute to the bundles. However, because stocks are so important inthe housing market, we expect to find substantial departures from long-run equilibrium for at least some attributes. For reasons outlined inChapter 2 and discussed further in this chapter, imputing values toindividual housing attributes is somewhat artificial. Each bundle earns acomposite quasi rent; it is these quasi rents that are imputed to specificattributes.

2Richard F. Muth, Cities and Housing (Chicago: University of Chicago Press, 1969);M. Stengel, "Racial Price Discrimination in the Urban Rental Housing Market" (Ph.D.diss., Harvard University, 1970); R. N. S. Harris, G. S. Tolley, and C. Harrell, "TheResidence Site Choice," Review of Economics and Statistics 50, no. 2 (May 1968): 325—34;W. C. Pendleton, "The Value of Highway Accessibility" (Ph.D. diss., University ofChicago, 1962); Benton F. Massell and Janice M. Stewart, "The Determinants of Residen-tial Property Values" (Institute for Public Policy Analysis, Stanford University, DiscussionPaper No. 6, Oct. 1971); Thomas King and Peter Mieszkowski, "Racial Discrimina-tion, Segregation, and the Price of Housing," Journal of Political Economy 81 (May/June 1973): 590—606. John C. Musgrave, "The Measurement of Price Canges in Con-struction," Journal of the American Statistical Association 64 (1969): 771—86; WallaceE. Oates, "The Effects of Property Taxes and Property Values: An Empirical Study of TaxCapitalization and the Tiebout Hypothesis,"Journal ofPolitical Economy 70, no. 6 (Nov.!Dec. 1969): 957—71; John F. Kain and John M. Quigley, "Measuring the Value of HousingQuality," Journal of the American StatisticalAssociation 70, no. 330 (June 1970): 532—48;Mahion R. Straszheim, An Econometric Analysis of the Urban Housing Market (NewYork: National Bureau of Economic Research, 1975).

192 HOUSING MARKETS AND RACIAL DISCRIMINATION

Even so, the imputed market value of specific housing attributes isof considerable theoretical interest and is valuable for many kinds ofpublic and private decisions. For example, estimates of the market valueof residential quality obtained from earlier regressions for St. Louis wereused to obtain lower-bound estimates of the benefits of urban renewalprograms.3 Similarly, models of this kind would be extremely useful toappraisers in estimating the market value of real estate for tax andcomparative purposes.

The coefficients may also be thought of as weights in a hedonicprice index.4 In the September 1969 issue of the Journal of the AmericanStatistical Association, John C. Musgrave describes Census Bureauresearch aimed at the development of such an index for new single-family homes.5 If measures of quality, such as those which we developfor St. Louis dwelling units, could be obtained for other cities andreproduced over time, it would be possible to develop similar indexes forthe housing stock.

Throughout this analysis we allow for possible distortions in thehousing market caused by racial discrimination and the existence of thecentral-city ghetto. Indeed, one of the major objectives of the analysis isto assess the distortions in housing prices and valuations attributable tohousing-market discrimination. As we shall discuss subsequently, thereis reason to suspect that racial discrimination distorts the housing pricesfaced by black households, thus influencing consumption of residentialservices by blacks. Accordingly, separate statistical models are esti-mated for ghetto and nonghetto properties.

The representativeness of the underlying data is also affected by thefact that the sample of dwelling units includes relatively few observa-tions on suburban housing alternatives. Moreover, some information iscompletely unavailable for the suburban observations in the sample. Asa result, separate estimates of the parameters of the models are made forthe city sample and for an expanded sample including suburban observa-tions. Finally, because the price data for renter and owner-occupieddwelling units are not comparable, separate. estimates are obtained for

3John F. Kain and John M. Quigley, "Evaluating the Quality of the ResidentialEnvironment," Environment and Planning 2 (Jan. 1970): 23—32.

4Musgrave, "The Measurement of Price Changes": Martin J. Bailey, Richard F.Muth, and Hugh 0. Nourse, "A Regression Method for Real Estate Price Index Construc-tion," Journal of the American Statistical Association 58 (1963): 933—42; Zvi (iriliches,"Hedonic Price Indexes Revisited: Some Notes on the State of the Art," AmericanStatistical Association, Proceedings of the Business Economics and Statistics Section,1967.

5Musgrave, "The Measurement of Price Changes."


renter and owner submarkets. These stratifications by owner/renter,ghetto/nonghetto, central city/metropolitan area are chosen to increasethe homogeneity of the samples employed. In this as in any othereconometric study, the accuracy of individual parameters depends bothupon the representativeness of the underlying data and upon the correctspecification of the statistical models.

With regard to the second issue, specification, the availability ofdetailed information about the characteristics of dwelling units reducesthe likelihood of bias resulting from the omission of important explana-tory variables. The use of individual dwelling-unit data should reduce theproblems of collinearity so often encountered in econometric investiga-tion of urban housing markets and permit better estimates of individualparameters. Nevertheless, such problems remain, because fully inde-pendent variation in the underlying attributes of housing consumption isnot observed.

The specification of the appropriate functional form remains diffi-cult. In particular, the joint purchase of housing attributes, the antici-pated departures from long-run equilibrium, and the nonmarket produc-tion of many housing attributes virtually insure a jointness in thedetermination of attribute prices. Theoretical and empirical guidance onwhat functional form to use for the value and rent equations is sparse.We have dealt with this uncertainty by providing alternative estimates ofthe rent and value equations for three common and easily interpretedfunctions, linear (additive), semilog, and multiplicative (logarithmic).

This approach, though widely used in econometric research, is farfrom satisfactory, since there are no clear-cut criteria for deciding whichof the various estimates is "best." Moreover, we have serious reserva-tions about all of the functional forms used in the analysis. This dilemmais not unprecedented in econometric research.

Previous researchers have used a variety of criteria to chooseamong competing functional forms. The first, and most reputable, is toderive the appropriate functional form from an underlying theoreticalmodel. For example, the semilog form may be chosen to insure diminish-ing returns in the pricing of housing attributes. Unfortunately, thetheoretical model we have outlined, particularly as regards its dynamics,remains too incomplete to provide any but the most general guidance. Asecond commonly used method is to choose that functional form whichfits the data best. In some cases, researchers will have precedent on theirside as well, i.e., the fact that a particular functional form worked best inone or more earlier studies. This method, though widely employed, hasserious conceptual and statistical weaknesses. We are saved from thetemptation of using the "goodness of fit" criterion, because in this, as in


many other econometric studies using large numbers of explanatoryvariables, none of the three specifications employed clearly dominatesby this standard.

Some functional forms may be preferred for statistical reasons. Inparticular, several earlier rent and value studies have used the semilogform of the model because of fears about heteroscedasticity if theuntransformed dependent variables were employed. Heteroscedasticity,increasing variance of the dependent variable along some dimension,typically size, may be a minor problem in our samples, but we do notfind it a compelling basis for preferring one equation form over another.A particular functional form may be chosen simply because it is easy tointerpret. The popularity of additive, semilogarithmic, and logarithmicmodels is due in no small part to the convenient interpretation ofindividual coefficients.

All three of these specifications are employed for the rent and valueequations presented in this chapter. Finally, to permit a fuller interactionbetween dwelling-unit size and the remaining attributes of the housingbundles in the determination of prices, we stratify the nonghetto renterand owner properties by number of rooms and estimate separate regres-sions for each size unit.

All coefficients of the additive value equations are divided by onehundred so that they may function as rental equivalents. This is, ofcourse, analogous to the convention used in Chapter 7. As before, thecorrectness of this procedure depends on the appropriateness of thegross rent multiplier used. In fact, the rent and value equations obtainedin this chapter can be used to estimate some rent/value equivalents. Thisis accomplished by solving the additive renter equation using meanvalues of the explanatory variables for owners and by solving the ownerequation using means for renters. When mean attributes of owner-occupied units are used in the additive renter equation, a multiplier of132 is obtained; solving the owner equation with renter means yields amultiplier of 185. In spite of this finding, we continue to use a multiplierof 100 to enable the reader to convert the coefficients to value termsmore easily.

No adjustments are needed for the semilog and log-log models,since the coefficients of both have convenient interpretations that do notdepend upon the level of the explanatory variables. As noted in Chapter7, coefficients of the semilogarithmic equations show the percentagechange in the dependent variable that would result from a one-unitchange in one of the explanatory variables; the coefficients of the log-logmodels, which are constant elasticities, show the percentage change inthe dependent variable resulting from a 1 percent change in an explana-tory variable.


THE MEASURES OF HOUSING ATTRIBUTES

Table 8-1 presents a summary of the information on housing attri—butes, market prices, and tenancy terms used in the housing-valuationmodels. The means and standard deviations of the variables are shownseparately for the complete sample, which includes 26 rental units and136 owner-occupied units in the suburbs (Table 9-i).

The explanatory variables used in the attribute-price models aregrouped into five categories of conceptually similar attributes. The firstcategory, dwelling-unit quality, comprises five variables that measurevarious aspects of quality and amenity of the sample dwelling unit andstructure.6 Interior quality, the first of the five, is the mean of sevenindividual measures of dwelling-unit condition and quality—the condi-tion of floors, windows, walls, levels of housekeeping, and the like—obtained in the Home Interview Survey (see Appendix A, second page).Exterior quality, the second index, is a measure of the condition of theexterior of the structure in which the sample dwelling unit is located. Forsingle detached units, a fairly close correspondence might be expectedbetween these measures of exterior and interior quality. The correspon-dence would be less for multifamily units, even though there is atendency for better-quality apartments to be located in better-qualitystructures. The index of exterior quality that we employ is constructedfrom several individual measures of structure quality and condition in amanner analogous to the construction of the index of interior quality.The underlying variables used to construct the exterior quality indexwere collected by building inspectors as part of the Physical BlightParcel Survey, whereas the variables used in constructing interior qual-ity were obtained in the Home Interview Survey. Thus, exterior qualitynot only measures a different dimension of quality, but it provides anindependent opinion about the quality of the dwelling unit. Since bothmeasures must depend on interviewer judgments, we hope that theseindependent measurements of closely related attributes have served toreduce enumeration error. On the average, sample owner-occupied unitsare higher in both interior and exterior quality, have hot water andcentral heating more often, and are newer than rental units (Table 8-1).

Unit size is measured by four variables: the logarithm of the numberof rooms, the number of baths, first-floor area, and parcel area. First-

61n Appendix F we present alternative models using somewhat different measures ofthe quality of dweHing units, structures, parcels and neighborhoods. The derived measuresin the appendix rely upon aggregation of some 39 independent measures of the quality ofaspects of the housing bundle by the method of principal components (factor analysis).


TABLE 8-1

Means and Standard Deviations of Housing Attributes for Renter andSingle-Family Owner-Occupied Units in the City

Renters Owners

Standard StandardVariables Mean Deviation Mean Deviation

Dwelling qualityInterior 3.80 .68 4.15 .54Exterior 2.42 .64 2.85 .43Hot water .90 S •97

Central heating .67 — .93Age 59.80 21.12 50.78 20.55

SizeRooms (logarithm) 1.28 .33 1.68 .34Baths 1.01 .26 1.20 .68First-floor area (00's sq. ft.) — — 9.47 2.72Parcel area (000's sq. ft.) 1.94 1.56 4.72 3.58

Neighborhood characteristicsAdjacent units 2.81 .80 3.32 .66Block face 2.87 .85 3.39 .75Median schooling 8.93 .88 9.26 .82Proportion white .53 .46 .71 .43Miles from CBD 3.18 1.51 4.56 1.44School quality 7.88 .56 8.19 .62Crime 1.15 .84 .63 .65

Structure typeSingle detached .10Duplex .03Row house .08Apartment .27Flat .43

Rooming house .02Tenancy terms

No heat .73No water .18No furniture .91No major appliances .83

Owner in building .19 — — —

Years of occupancy 5.74 10.29 15.49 12.90Race of occupant .47 — .26 —

Rent (value) $61.34 $25.41 $14,596 $6,722

NOTE: A flat is a rental unit located in one of the old, small multifamily structurescommon in St. Louis, as distinct from an apartment, which is a rental unit located in alarge apartment structure.


floor area,7 a surrogate for total area, is not a meaningful measure of unitsize for multifamily structures. Inasmuch as single-family units do nothave a uniform number of floors, some measurement error exists evenfor these units.

From Table 8-1, it is evident that owner-occupied single detachedunits are not only of better quality than renter units but are also larger.Owner-occupied units have an average of about 5.4 rooms, as contrastedwith 3.6 rooms for rental units; they have an average of 1.2 baths ascompared to an average of 1 bath for rental units; and their parcel areas(lot size in square feet divided by number of dwelling units) averagenearly five-thousand square feet, as contrasted with about two-thousandsquare feet for rental units.

The category "neighborhood characteristics" includes a diversecollection of variables which describe the condition of adjacent andnearby properties, socioeconomic characteristics of the neighborhood,quality of some critical public services, and accessibility to the CBD.The first two neighborhood characteristics, quality of adjacent units andquality of the block face, were obtained from the Physical Blight Parceland Environmental Block Face surveys. In the Physical Blight ParcelSurvey, teams of building inspectors provided detailed evaluation of thecondition of properties on each side of the sample property, as well as ofthe exterior—structure and parcel—of the sample property. The quality-of-adjacent-structures variable is the simple average of the overall evalu-ations of the condition of the properties on each side of the sample unit(items 32 and 27 of the Physical Blight Parcel Survey). In the Environ-mental Block Face Survey, the second member of the two-man buildinginspector teams made detailed observations about the characteristicsand condition of the block face for sampled units and provided an overallor combined block-face rating. This overall rating of the block face has aminimum value of 1 ("Bad—major degree of structural deficiencies inmaintenance, landscaping, accumulation of trash or adverse influ-ences") and a maximum value of 5 ("Excellent—no deficiencies—evidence of considerable spending"). Data describing adjacent units andthe block face were collected to measure the effect of neighboringdwelling units on the value of sample units.

The median-schooling and the proportion-white variables measurethe racial and socioeconomic composition of the neighborhood. Theneighborhood, in both cases, is defined as the census tract in which theunit is located. Median schooling is the median number of years offormal schooling completed by adult residents of the census tract in1960. The proportion white is also defined for census tracts, but it is the

7This measure was obtained from assessors' records for the structure.


estimated proportion white in 1967. Preliminary analyses employed thecensus-tract proportion white in 1960 from the Census of Population tomeasure the racial composition of the neighborhood.8 Subsequent analy-ses suggested that the rapid expansion of the ghetto between 1960 and1967 produced major changes in boundaries of the ghetto between 1960and the time of the survey. Therefore, we determined to use the sampleof St. Louis households to estimate the 1967 proportion white by censustract.

Miles from the CBD, shown in Table 8-1, was but one of severalaccessibility measures evaluated in the analysis. Several other accessi-bility indexes were obtained from the East-West Gateway CoordinatingCouncil; and one of them, the accessibility of each dwelling unit toemployment, was used in rent and value equations similar to thoseshown in Table• 8-2. These were computed from origin and destinationdata obtained in the 1967 St. Louis travel survey. All of these accessibil-ity indexes are highly correlated with one another and with distance fromthe CBD. Rent and value equations were estimated using employmentaccessibility and distance from the CBD with essentially similar results.Because it is so much easier to interpret, distance from the CI3D ratherthan the accessibility indexes is reported in these analyses.

The last two neighborhood characteristics, school quality andcrime, are intended as measures of the quality of neighborhood services.These and other local public goods are featured prominently in publicgoods—residential location models.9 Moreover, opinion surveys andpublic commentary have evidenced widespread concern regardingneighborhood schools and safe streets among urban residents.

The public-goods dimensions of the bundle of residential servicespresent special problems for the analyst. There are few neighborhoodmeasures of these services and little theoretical or empirical guidanceabout how such measures should be constructed. An important concep-tual issue, for example, is whether to measure public service inputs oroutputs, presuming that the latter can be defined. Wherever possible, wecollected and evaluated both input and output data. Howev,er, outputmeasures—achievement scores for neighborhood public elementaryschools and the number of major crimes reported per Pauly block—areused in the rent and valUe equations. As has been discussed in Chapter

8Kain and Quigley, "Value of Housing Quality."9Charles M. Tiebout, "A Pure Theory of Local Expenditures," Journal of Political

Economy 64, no. 3 (Oct. 1956): 416—24; Bryan Ellickson, "Jurisdictional Fragmentationand Residential Choice," The American Economic Review 61, no.. 2 (May 1971): 334—39;Oates, "The Effects of Property Taxes"; Jerome Rothenberg, "Strategic Interaction andResource Allocation in Metropolitan Intergovernmental Relations," American EconomicReview 59, no. 2 (May 1969):


4, we assume that in choosing a residential bundle, households are moreconcerned with public-goods outputs (number of serious crimes in thevicinity, school test scores their children may receive) than with theirproduction process or their inputs (number of policemen or teachers). Ofcourse, as taxpayers, they may be concerned about the cost (taxes) ofliving in each community.'0

Output and input measures were obtained for both private andparochial elementary schools within the city, and these measures werecoded to the dwethng units served by each school in the city. Output wasmeasured by three achievement-test scores for eighth-grade pupils—reading, literary-writing, and math. All three scores are highly cone-lated; the eighth-grade math achievement score is used to measureschool quality in these analyses. The input measures obtained werestudent-teacher ratios, student-classroom ratios, the percentage of stu-dents and teachers that were nonwhite, the age of the school, and ameasure of the condition of the physical plant. Similar data wereobtained for both public and parochial schools. However, public andprivate school achievement scores were highly correlated, and prelimi-nary analyses led us to omit the measures of parochial school qualityfrom the rent and value equations.

• It was not possible to obtain at reasonable cost input measures ofpolice protection for each neighborhood. Thus, only output measures—the number of major crimes and the number of minor crimes per Paulyblock—were used in the analysis. These were coded to each sampledwelling unit.

Unfortunately, comparable neighborhood-services data are notavailable for units located outside the city. Many explanations of central-city decline and of the movement.of middle- and upper-income familiesto the suburbs have emphasized the role of the better schools and thelower level of criminal activity to be found there. Obviously, we wouldhave liked to be able to evaluate the importance of these considerations.

toOates makes an attempt to measure these countervailing influences on the desirabil-ity of specific locations by regressing property values on expenditures per pupil (an inputmeasure of school quality), effective tax rates, and several other determinants of propertyvalue, using census data for fifty-three municipalities in New Jersey. His results indicatethat local property values bear a significant negative relationship to the effective tax rateand a significant positive correlation with expenditure per pupil in the public schools. Heconcludes that "the size of the coefficients suggests that for an increase in property taxesunaccompanied by an increase in the output of local public services the bulk of the rise intaxes will be capitalized in the form of reduced property values. On the other hand, if acommunity increases its tax rates and employs the receipts to improve its school system,the coefficients indicate that the increased benefits from the expenditure side of the budgetwill roughly offset (or perhaps even more than offset) the depressive effect of the higher taxrates on local property values" (Oates, "Effects of Property Taxes," p. 968).

TA

BLE

8-2

Alte

rnat

ive

Spe

cific

atio

ns o

f Ren

t and

Val

ue M

odel

s fo

r th

e C

ity

Lin

ear

Var

iabl

esR

ente

rO

wne

r

Sem

ilog

Ren

ter

Ow

ner

Log

-Log

Ren

ter

Ow

ner

Uni

t qua

lity

Inte

rior

.062

2.0

41.2

12'

Ext

erio

r4.

77'

—4.

63—

.013

—.0

15—

.040

Hot

wat

er—

.248

'—

.262

'—

Cen

tral

heat

ing

4•44

1—

.129

'—

.138

'—

Age

—.2

9'—

1.00

'—

.004

'_.

0081

—.1

72'

—.2

18'

Size R

oom

s22

.63'

14.5

3'.3

74'

.262

'.3

67'

.195

'B

aths

9.07

'7.

69'

.123

'.0

09.1

29'

.045

'Fl

oor

area

—6.

34'

—03

31—

.417

'Pa

rcel

are

a6.

48'

—.0

02.0

11'

—.0

12.0

642

Nei

ghbo

rhoo

dA

djac

ent u

nits

7•77

4.0

422

.065

2.1

082

.175

'B

lock

fac

e3.

71'

4.19

.054

'.0

23.1

31'

.174

2

Med

ian

scho

olin

g2.

95'

14.9

1'.0

78'

P433

1•9

531

Pro

port

ion

whi

te_3

•743

—1.

47—

.038

—.0

01'

—.0

00M

iles

from

CB

D—

.30

_3•5

43.0

09—

•ØØ

Ø4

—.0

00—

.044

Scho

ol q

ualit

y2.

76'

4•9Ø

4.0

48'

.312

'C

rim

e—

.17

3.39

.013

—.0

13—

.014

—.0

15

I') 0 0

N) 0

Stru

ctur

e ty

peSi

ngle

det

ache

d7.

682

.143

1.1

441

Dup

lex

12.3

31.2

271

.216

1

Row

hou

se.1

202

.114

2

Apa

rtm

ent

5752

.145

'.1

25'

Flat

6.28

2.1

49'

.146

'R

oom

ing

hous

e.1

642

.

Ten

ancy

term

sN

o he

at—

9.18

'—

.157

'—

.180

'N

o w

ater

—.0

17—

.006

No

furn

iture

_594

2—

—

No

appl

ianc

es—

12.0

0'—

.134

'_.

0862

Ow

neri

nbui

ldin

g—

.071

'—

.064

'Y

ears

of

occu

panc

y—

.25'

—00

41—

.004

1

Con

stan

t_1

52.3

122.

581

7.56

'2.

226'

3.63

2'.7

14.7

72.7

45.7

24.7

57.7

21

NO

TE

: Tab

le n

otes

indi

cate

sig

nifi

canc

e of

t ra

tios

for

coef

fici

ents

(tw

o-ta

iled

test

).1>

.01.

2> .0

5..1

0.4t

rat

io g

reat

er th

an 1

.0.


The desirability of extending the analyses of the metropolitan housingmarket to this broader and more critical set of questions cannot beoveremphasized.

Structure type constitutes the fourth category. The owner-occupantsample includes only single-family units. Single detached units compriseonly 10 percent of the city renter sample (Table 8-1). Flats and apart-ments are the most common type of rental units occupied by samplehouseholds; 43 and 27 percent, respectively, of all city renters reside inthese types of structures. A flat is a rental unit located in one of the old,small multifamily structures common in St. Louis, as distinct from anapartment, which is a rental unit located in a large apartment structure.

The housing attributes included in the final category pertain only torenters and describe aspects of the contractual agreement between thelandlord and the tenant. The first four attributes indicate whether therental contract includes the provision of various utilities and furnishingsby the landlord. For example, 73 percent of tenants had to pay their ownheating bills, 18 percent had to pay their own water bills, 91 percent ofthe units were unfumished, and 83 percent did not include major appli-ances (refrigerator and/or stove).

CITY EQUATIONS

The variables included in price-determination equations for cityowners and renters shown in Table 8-2 are generall.y similar, but they arenot identical. For both owners and renters, the models include sevenneighborhood characteristics, the number of rooms, the number ofbaths, parcel area, and three of the five unit-quality variables. In addi-tion, the renter equation includes dummy variables for hot water andcentral heating, which are excluded from the owner equation, sincepractically all owner-occupied units include these amenities. Similarly,the owner equation includes first-floor area, which is omitted from therenter equation because it refers to the structure rather than to thedwelling unit.

Finally, the renter equation includes six dummy variables for struc-ture type and six measures of tenancy terms. A seventh structure type isincorporated in the intercept. The first four tenancy-term variablescorrect the dependent variable, contract rent, for the utilities providedby different landlords. The "owner in building" dummy variable isdesigned to test the hypothesis that resident landlords accept lower rentsto exercise greater control over tenant selection.

Duration of occupancy, though shown for owners in Table 8-1, is


not included in the value equations. In the rent equation it provides anestimate of the discounts given to long-term tenants. Landlords aresensitive to turnover because both vacancies and redecorating areexpensive. Therefore, it is rational for landlords to share some of thesavings from lower expenses with long-term tenants in the form ofdiscounts. The years-of-occupancy variable, which assumes that dis-counts are proportional to duration of tenure, is, of course, only one ofseveral ways in which this hypothesis might be represented.

Race of occupant is shown in Table 8-1 but is not included in eitherthe renter or owner equations. We hypothesize that housing-marketdiscrimination operates by limiting black housing search and residenceto certain well-prescribed neighborhoods. For reasons discussed inChapter 2, prices in these neighborhoods may differ from those prevail-ing outside the ghetto. However, we hypothesize that whites and blackspay the same prices within these neighborhoods.hi

Table 8-2 shows the estimated coefficients for the 567 rental unitsand the 267 owner-occupied single-family homes in the city for thelinear, semilog, and log-log specifications. In the semilog models, thedependent variable, rent or market value, is expressed in logarithmicform. In the log-log models, the following variables are also expressed aslogarithms: interior and exterior quality, age, parcel area, first-floor area,quality of adjacent units and block face, median schooling, miles fromthe CBD, school quality and crimes. There is very little differenceamong the six equations in terms of overall goodness of fit; all six explaina very large proportion of the variation in the dependent variables. If thenumber of statistically significant coefficients (t ratios significant at the.05 level) is used as the criterion, there is, again, little basis for preferringone equation over another, although, by this standard, the semilogequation for owners and the semilog and log-log equations for renters areslightly better. Since neither the semilog nor the log-log specificationshows a clear superiority, our discussion of the results emphasizes thelinear form because of its simpler interpretation.

Despite some important differences, the parameter estimatesobtained for the five unit-quality variables are generally consistentamong equations, generally conforming to a priori expectations. Theleast consistent results are obtained for the exterior-quality variable,which has a negative sign in all three owner equations. Its coefficient is,

11Because of the intense segregation in U.S. cities, the practical difference may besmall. For a study that uses race of the occupant rather than a neighborhood variable, i.e.,ghetto, see King and Mieszkowski, "Estimate of Racial Discrimination," and our discus-sion in Chapter 3.


however, smaller than its standard error in every case. The negative signmay be due to multicollinearity; for single detached units, interior andexterior quality may simply be too highly correlated.

Except for the unanticipated negative sign obtained for exteriorquality in the owner equations, the coefficients in Table 8-2 indicate thathouseholds pay substantially more for higher-quality units. For example,the linear equation for renters indicates that they will pay about $1.31 permonth for an additional unit of interior quality, $4.77 per month for anadditional unit of exterior quality, $3.09 per month for hot water, $4.44per month for central heating, and $.29 per month for an additional yearof newness.

The semilog and log-log models suggest even higher valuations ofhot water and central heating. Coefficients of the semilog model suggestthat units with hot water and central heating rent for 25 percent and 13percent more, respectively, than otherwise comparable units. It is likelythat these variables act as more general measures of dwelling-unitquality, and that the estimates reflect this.

Central heating and hot water are not included in the owner models,and as noted previously, the coefficient of exterior quality is smaller thanits standard error. However, the coefficient of interior quality, which issignificant at the .10 level, indicates that owners will pay $8.18 per month($818 in value) for an additional unit of interior quality. Newness is evenmore valuable in the owner than in the renter submarket; owners willpay $1.00 ($100 in value) for a year of newness as compared wit!1 anoutlay of only $.29 by renters. The average owner-occupied structure inthe city sample is fifty years old; thus, the results in Table 8-2 indicatethat a new unit would sell for $5,000 more than an otherwise comparableunit of average age.

The size variables are generally highly significant and have thecorrect sign. The coefficient of number of rooms, expressed in loga-rithms in all six equations, indicates in the additive equation for rentersthat a prospective renter would have to pay about $9.18 more per monthfor a three-room unit than for a comparable two-room unit, but only anadditional $11.56 to obtain a five-room unit rather than one consisting ofthree rooms. A similar progression exists for owner-occupied units; asix-room unit costs about $1,007 more than a comparable three-roomunit, but an eight-room unit costs only $418 more than one consisting ofsix rooms. In comparing the rooms coefficients of the renter and ownerequations, it is essential to remember that the owner equation includesfirst-floor area, particularly since it is hard to imagine adding a roomwithout increasing the floor area. If an added room measured only tenfeet by ten feet, it would add $634 to the value of the unit through thefloor-area coefficient. The semilog models indicate that rents increase by


37 percent with each additional room, while the value of single-familyhouses increases by 26 percent with each additional room, floor-areabeing held constant.

Neighborhood characteristics include several measures of residen-tial quality that are external to the sampled property. All share thedistinctive feature that the owners of individual properties cannot bythemselves change their level. Instead, such changes require the aggre-gation of individual location and investment decisions, governmentaction, or both. Yet these external factors strongly influence the locationdecisions of individual households and the market valuation of individualproperties. Most previous studies of urban housing markets have beenbased on aggregate data such as census-tract statistics, or on nationalprobability samples, which lack information on neighborhood character-istics. As a consequence, few of these studies have considered theinfluence of the quality of nearby properties on property values, onhousing consumption, and on the quality of an individual property. Theestimates in Table 8-2 provide some indication of the relative importanceof these aspects of residential quality.

It is apparent from Table 8-2 that the condition of adjacent andnearby properties has a substantial effect on the market value of sampleproperties. Variables which describe the physical condition of adjacentand nearby properties appear to have nearly as large an influence on thevalue of sample properties as the interior- and exterior-condition varia-bles. For example, in the renter additive equation, the sum of thecoefficients of adjacent and block-face variables is $5.57 per month,whereas the sum of the coefficients of the interior- and exterior-qualityvariables is $6.08. The condition of adjacent properties and the blockface appears to have an even larger effect on the value of owner-occupied single detached properties. The sum of the coefficients of theadjacent and block-face variables in the additive equation is $11.96, ascompared with only $3.55 for the interior- and exterior-quality variables.Because of the serious collinearity between the interior- and exterior-quality indexes for single detached units, this comparison may be some-what misleading. When exterior quality is omitted from the additivevalue equation for the entire sample, the coefficient of interior qualityincreases to $12.41, while the coefficients of block and adjacent qualitybecome $6.05 and $4.70, respectively.

In addition to these measures of the condition of nearby dwellingunits, the surrogate for neighborhood prestige (median schooling ofresidents of the census tract) is positive and larger than its standard errorin all six equations, differing from zero at the 1 percent level in all butone. The additive models indicate that a rental unit located in a censustract where the median adult has only completed the eighth grade will


rent for $5.90 less per month than an otherwise identical rental unitlocated in a census tract where the median adult has completed the tenthgrade. If the unit in question is owner-occupied, it will have a marketvalue $2,982 less than a comparable unit in a tract with a medianeducational level two years greater. The largest neighborhood-prestigeeffects are obtained for the multiplicative model; a 1 percent change inmedian schooling produced a change in house values of about 1 percentand a change in rents of almost 1/2 percent.

The results obtained for the school-quality and crime variables areonly suggestive of the importance of these public services. The coeffi-cient of the neighborhood crime index is smaller than its standard errorin all of the equations and has the wrong sign in two of the six. Theresults for the coefficient of school quality are somewhat better. Thesehave the correct signs and are larger than their standard errors in all sixequations. Taken at face value, the results of the additive model indicatethat renters are willing to pay $2.76 more per month for units served byneighborhood schools where students average one year better inachievement. The semilog and log-log specifications suggest somewhatlarger effects. From the frequent references to school quality and crimein discussions of how households make residential choices and of howthe urban housing market operates, stronger school and crime effectsmight have been anticipated.12

For a number of reasons, however, part of the influence of betterschools on value may be represented by dwelling-unit and neighbor-hood-quality variables. There is reason to believe that there is consider-able error in the school-quality measurement. As a result, since meanschool achievement is highly correlated with the indexes of residentialquality, the residential variables may be proxying the effects of schoolquality.13 Moreover, if better schools attract households with higherincomes, which spend more on housing maintenance, part of thesemeasured effects of dwelling-unit and neighborhood quality are logicallyindistinguishable from school quality.

Even more acute problems are encountered in attempting to mea-sure neighborhood public safety. Inclusion of a neighborhood crimeindex in the model is more a statement of good intentions than a seriouseffort to confront the conceptual and measurement problems of quanti-fying the perceived safety of a neighborhood. The index of neighborhood

t2Oates, "Effects of Property Taxes."'3For a discussion of this problem see Eric A. Hanushek and John F. Kain, "On the

Value of Educational Opportunity as a Guide to Public Policy" in On Equality of Educa-tional Opportunity, Frederick Mosteller and Daniel P. Moynihan, eds. (New York: Ran-dom House, 1972).


crime used in the analysis is also highly correlated with the indexes ofresidential quality.

A final reason for anticipating weak school and crime effects is theabsence of suburban properties. The largest variation in school qualityand level of criminal activity is found not within the city of St. Louis butrather between the city and its suburbs.

Theories of urban spatial structure place considerable emphasis onaccessibility to the center as a determinant of housing value. The resultsin Table 8-2 provide very weak evidence of an accessibility gradient. Inonly two of the six equations in Table 8-2 does the coefficient of distancefrom the CBD exceed its standard error, and it is negative in all but oneequation. There are several, not necessarily inconsistent explanationsfor the relatively poor performance of the accessibility variable. Themost reasonable is that the relationship between accessibility and rentand value is more complex than can be embodied in any of the simplefunctional forms included in Table 8-2. In particular, as we have indi-cated in Chapter 2, the location rent surfaces for various attributes, orbundles of attributes, probably vary. Moreover, the estimates in Table 8-2 are heavily influenced by ghetto properties, and we made the point inChapter 3 that accessibility considerations play only a minor role indetermining the market value of such properties. Subsequent analyseswill provide support for both of these contentions.

Of the variables specific to the renter model, all but two of thestructure-type dummies and all but one of the tenancy-terms variablesare significant at the .05 level in the additive model. All structure-typedummies in the semilog equations, and all but the rooming-housedummy in the log-log equations, are significant at the .05 level. Of thetenancy-terms variables, only the "no water" and "no furniture" vari-ables fail to pass this test. The regression coefficients for the duration-of-occupancy variable are small—a monthly rent discount of only $.25for each year of occupancy in the additive model and .4 percent per yeardiscount in the semilog and log-log models—but they are highly signifi-cant. These small differences presumably capture a lagged adjustmentof monthly rent. Landlords are less likely to raise rents when theirproperties are occupied by stable tenants than when there is a change inOccupancy.

A different landlord-tenant interaction may be responsible for therelatively large coefficient of the owner-in-building variable. The addi-tive model suggests that this discount amounts to $4.37 per month, whilein the semilog model it amounts to about 7 percent of monthly rent and inthe log-log model to about 6 percent. The lower rents for units withresident landlords may result from less sophistication and professional-ism on the part of these smaller operators, or they may reflect different


tenant-selection policies. When the owner lives on the property, he mayselect tenants more carefully to achieve lower vacancy rates and lowermaintenance and repair costs. The critical impact of these factors on theprofitability of rental properties has been emphasized in other studies.'4

The findings also suggest that standardized dwelling units locatedinside the ghetto are somewhat more expensive than those outside, aconclusion which is consistent with Ridker and Henning's study of St.Louis and with other investigations of housing-market discrimination.'5The coefficient of proportion white is negative in all six equations.However, its level of significance is exceedingly low in the regression forowner-occupied housing. For renters, in the additive equation, t = 1.743;in the semilog, t = 1.127; and in the log-log, t = 1.649. Taken at facevalue, the coefficients in the linear model indicate that a comparablerenter unit costs 6.3 percent more in an "all-black" area than in an "all-white" area. The estimated differences from the semilog and log-logmodels are 3.8 percent and 5.7 percent respectively. For owner-occu-pied units, the three models imply that comparable units cost 1.0 percent(from the linear form), 3.8 percent (from the semilog form) or 4.2 percent(from the log-log form) more in an "all-black" than in an "all-white"area of the central city.

Although the negative signs for the proportion-white variables inTable 8-2 are consistent with the findings of discrimination markups inmost earlier studies of housing-market discrimination, serious questionsmay be raised about the specifications used for both the owner and rentalmodels.16 If housing-market discrimination exists, it is doubtful that itseffects can be represented by a uniform percentage markup on all typesof housing. The phenomenon is undoubtedly far more complex—withthe effects of discrimination more or less strongly evident in varioussubmarkets defined by quality and structure type. It should also beremembered that the equations in Table 8-2 are estimated for citydwelling units only. Yet, it is clear that for most households—particu-larly, white households—the relevant housing market is the entire met-ropolitan area. In the following section, the small suburban sample isadded, and the effect of racial discrimination on housing prices isconsidered more fully.

14Muth, Cities and Housing; George Stemlieb, The Tenement Landlord (NewBrunswick, N.J.: The Urban Studies Center, Rutgers, 1966).

'5Muth, Cities and Housing; King and Mieszkowski, "An Estimate of Racial Dis-crimination"; Stengel, "Price Discrimination"; Chester Rapkin, "Price DiscriminationAgainst Negroes in Rental Housing Market" in Essays in Urban Land Economics (LosAngeles and Berkeley: University of California Press, 1966); David H. Karlen, "RacialIntegration and Property Values in Chicago" (Urban Economics Report No. 7, Universityof Chicago, April 1968); Ridker and Henning, "Determinants of Residential PropertyValues."

16See citations in note 15.


THE VALUE OF HOUSING ATTRIBUTES INSIDE ANDOUTSIDE THE GHETTO

In Chapter 3 we asserted that the most useful analytical way ofrepresenting the effects of racial discrimination in urban housing marketsis to postulate the existence of two relatively independent submarkets:the ghetto and the remainder of the metropolitan area. These twomarkets are interrelated in a variety of ways, but there are significantbarriers between them. The ghetto and nonghetto housing markets areorganized by different institutions and have different information net-works. Housing prices in the two markets must bear a relation to eachother, but this relationship need not be uniform for different types ofhousing. The two submarkets differ in terms of the composition of theirhousing stocks, the sources of the supply, and the extent and composi-tion of demand.

Blacks limit their search for housing—or are restricted by discrimi-natory practices and lack of information—to a few geographically con-tiguous neighborhoods that are designated by custom and practice forblack occupancy. Whites are free to live anywhere in the metropolitanarea, but for a variety of reasons (i.e., prejudice, an unwillingness to bethe only whites in the neighborhood, or the existence of better orcheaper housing outside the ghetto) they generally reside beyond theconfines of the ghetto.

The rent and value equations presented in Table 8-2 tend to corrob-orate earlier studies that have suggested the presence of a discrimina-tion markup. Our estimates and those obtained in earlier studies assumethat the structure of relative prices for the various housing attributes isthe same for properties located inside and outside the ghetto, i.e., thatthe samples of ghetto and nonghetto properties are homogeneous. Thisassumption of homogeneity is, however, inconsistent with the positionthat the ghetto and nonghetto housing markets are separate. Aitnoughsubstantial differences in the prices of comparable ghetto and nonghettoproperties at the boundaries of the ghetto are unlikely to persist for longperiods of time, prices in the interior of the ghetto may differ substan-tially from prices in the interior of the white housing market. Unfortu-nately, our sample is not extensive enough to test all hypotheses aboutthe structure of housing-attribute prices inside and outside the ghetto.Nonetheless, some crude tests of sample homogeneity between ghettoand nonghetto properties are possible.

Shown in Table 8-3 are three separate regression estimates of themarket value of housing attributes for owner- and renter-occupied prop-erties, depending on whether they are located inside or outside theghetto. The estimates in Table 8-3 aI.l employ an additive specification;comparable estimates for a semiog specification are presented in Table

0

TA

BLE

8-3

Line

ar S

peci

ficat

ions

of

Ren

t and

Val

ue E

quat

ions

for

Ghe

tto a

nd N

ongh

etto

Uni

ts

Ren

ters Non

ghet

to

Ow

ners Non

ghet

to

Var

iabl

esG

hetto

City

All

Ghe

ttoC

ityA

ll

— .4

8

4.23

2

7.76

'—

.17

6.73

1

6.75

'6.

95k

1.41

— 3

91

6.99

'

5.08

10.0

3214

.831

2.78

—1.

84

.06

— 3

71—

.661

Dw

ellin

g qu

ality

Inte

rior

Ext

erio

rH

ot w

ater

Cen

tral

hea

ting

Age

—1.

16'

Size R

oom

s20

.24'

26.5

0'30

.08'

—15

.44

30.8

3'B

aths

7.38

'13

.36'

13.7

2'11

.522

Floo

r ar

ea5.

16'

5.94

'Pa

rcel

are

a—

.26

•741

Nei

ghbo

rhoo

dA

djac

ent u

nits

1.26

1.22

9.08

Blo

ck f

ace

5.24

'1.

908.

50.6

1M

edia

n sc

hool

ing

3.61

'4.

171

2.68

'26

.83'

10.0

2'M

iles

from

CB

D—

1.78

'—

.99

1.89

'—

6.08

—1.

76Sc

hool

qua

lity

.32

3•35

4—

2.96

9472

Cri

me

—.0

0.0

1.1

0

—.8

5'

49.0

8'16

.26'

10.6

0'

2.31 .2

1—

3.68

'

NO

TE

: Tab

le n

otes

indi

cate

sig

nifi

canc

e of

t ra

tios

1>.0

1.2>

.05.

.10.

for

coef

fici

ents

(tw

o-ta

iled

test

).

1\)

4t r

atio

gre

ater

than

1.0

.

Stru

ctur

e ty

peSi

ngle

det

ache

d4•

374

Dup

lex

1.14

16.1

8'18

.24'

Row

hou

se2.

875.

27A

part

men

t7.

651

—1.

192.

33Fl

at4.

25R

oom

ing

hous

e7.

61T

enan

cy te

rms

No

heat

—9.

25'

—7.

54'

No

wat

er—

.97

No

furn

iture

No

appl

ianc

es—

6.97

'—

—16

.17'

Ow

ner

in b

uild

ing

—1.

79—

7.20

'6.

55'

Yea

rs o

f oc

cupa

ncy

— .1

62—

.241

— .2

31

Con

stan

t—

11.8

7—

18.2

87.

32—

102.

0037

4R

2.7

243

.749

.781

.859

.683

.715

Num

ber

of o

bser

vatio

ns31

425

327

988

178

313


8-4. The first and fourth equations in both tables present estimates of themarket value of individual housing attributes for properties located in theghetto. For these analyses, the ghetto is defined as consisting of allcensus tracts that were at least 85 percent black in 1967. The second andfifth equations in Tables 8-3 and 8-4 provide estimates of the marketvalue of housing attributes for central-city renter- and owner-occupiedproperties located outside the ghetto, i.e., for central-city propertieslocated in census tracts more than 85 percent white in 1967. The thirdand sixth equations provide estimates for all nonghetto properties,including an additional 26 renter-occupied and 136 owner-occupied prop-erties in St. Louis County. Addition of these suburban properties signifi-cantly increases the sample size, particularly for owner-occupied singledetached units. More important, it makes the nonghetto sample muchmore representative of the nonghetto housing market in the St. Louismetropolitan area. High-value properties and the best neighborhoods arestill underrepresented in the sample, but the effects of adding thesesuburban units to the sample are large. With 136 additional suburbanproperties, the mean value of single-family detached units increases byover $2,000, from $15,309 for the city nonghetto sample to $17,456 forthe entire nonghetto sample.

Except for the omission of the school and crime variables from theentire nonghetto sample, the equations estimated for the two nonghettosamples are identical. It is evident from Tables 8-3 and 8-4 that theestimated attribute prices for ghetto and nonghetto properties are verydifferent. For example, the linear equation suggests that city nonghettorenters pay an estimated $6.73 per month for an increment of interiorcondition; when suburban renter properties are added, an even higherestimate—$6.99 per month—is obtained. For rental properties in theghetto,. the coefficient of interior condition is negative— —$.48 permonth—although smaller than its standard error. Similarly, an addi-tional unit of exterior condition has an estimated value of only $2.68 inthe ghetto as compared with an estimated value of $6.75 for central-citynonghetto properties, and $5.39 for the combined nonghetto sample. Thepremium paid for central heating in the ghetto is, however, quite large:$7.76 for the ghetto compared with $1.41 for the city nonghetto sample,and $.06 for the entire nonghetto sample.

In contrast, most types of neighborhood quality appear to be moreexpensive inside the ghetto than outside. The sum of the adjacent-unitand block-face condition variables is $6.92 per month for ghetto rentalunits, as compared with only $3.16 for central-city nonghetto rentalunits, and $4.14 for all nonghetto rental units. The coefficient of medianschooling is $3.61 for the ghetto, $4.17 for the city nonghetto, and $2.68for the entire nonghetto. The coefficient of school quality is ten times as


TABLE 8-4Semilog Specifications of Rent and Value Equations for Ghetto and NonghettoUnits

NOTE: Table notes indicate significance of z ratios for coefficients (two-tailed test).1> .01.2> .05.

.10.4t ratio greater than 1.0.

Renters Qwners

Nonghetto Nonghetto

Variables Ghetto City All Ghetto City All

Dwelling qualityInterior —.003 .0722 .0631 .106'

Exterior .022 •Ø454 .084 .021 .028Hot water .2 13' .491' .482'Central heating .153' .088' .093'

— .002' — .005' — .0051 — .007' — .0081 — .0061

SizeRooms •357' .410' .421' .277' •3991

Baths .1051 .1352 .020 .059'Floor area .029' .038' .034'Parcel area — .002 .002 .019' .000

NeighborhoodAdjacent units •Ø374

Block face •Ø791 .013 .024 .021 .020 .0412

Median schooling .126' .063' .006Miles from CBD —.002 —.006 .020' .011 — — .022'School quality .006 •Ø552 .022Crime .000 — .000 — .000 — .000

Structure typeSingle detached .1172 •Ø974

Duplex .068 .2551 .262'

Row house .041 . .056Apartment .154' .038 .058Flat .129'Rooming house .1961 —.540' — .500'

Tenancy termsNo heat — .137' —.161' —.142'

No water —.011 —.033 —.017

No furniture — — —.133'

No appliances —.

Owner in building —.105' —.091'Years of occupancy — .0041 — .005' — .004'

Constant 2.671' 2.675' 3.032' 7.9151 7.890' 8.67'R2 .741 .771 .795 .690 .744 .748


large for the city nonghetto as for the ghetto. For rental properties,additional rooms, larger parcels, and additional baths all appear moreexpensive in the ghetto than outside.

Similar results are obtained for the owner models. 'The combinedinterior- and exterior-condition coefficients are larger for nonghetto thanfor ghetto properties. When exterior quality is omitted from the entirenonghetto value equation, the monthly cost of interior quality becomes$11.58 as compared with $10.99 for each unit of block quality and $3.52for each unit of adjacent-unit quality. By comparison, although few ofthe neighborhood quality variables are statistically significant, theircoefficients are uniformly larger for ghetto than for nonghetto properties.The sole exception is school quality, which has a negative coefficient inthe ghetto equation. In the city nonghetto model, the coefficient ofschool quality, which is significant at the .10 level, indicates that St.Louis homeowners are willing to pay nearly a thousand dollars more fora dwelling located in a neighborhood served by public schools thataverage one grade better on standardized achievement tests.

The results obtained for the size variables in the ghetto regressionsare bizarre. The coefficient of the logarithm of the number of rooms inthe additive model is actually negative, although smaller than its stan-dard error. In the semilog model, it is positive with a t ratio of 1.4 and avalue of .16. This coefficient is only about half as large as that obtained inthe city nonghetto equation, .28. Similarly, the other principal sizemeasure, first-floor area, has a value of .04 in the nonghetto equation, ascontrasted with a value of .03 in the ghetto semilog equation.

We believe that the inconsistent results for the ghetto rent and valuemodels result from the limited range of some housing attributes availablethere. For example, since ghetto schools are almost uniformly bad, it isnot surprising that the coefficient of school quality is small, often incor-rect in sign, and always smaller than its standard error in the ghetto valueand rent equations. We suspect many of the differences in attributeprices for ghetto and nonghetto properties are explained by supplylimitations of this kind.

Analyses in subsequent chapters will indicate that some combina-tion of price discrimination, the unavailability of certain types of housingin the ghetto, and real or imagined limitations on the ability of blackhouseholds to locate outside the ghetto distort black housing patterns.Even so, it is instructive to ask what the average black household wouldhave to pay in order to obtain its current housing bundle outside theghetto. Rent would be $49.37 versus $55.90, and the average owner-occupied unit could be purchased for $835 less ($12,319 versus $13,154).

In general, omitting ghetto properties from the sample seems toimprove the parameter estimates obtained in the value and rent equa-


tions, bringing them into closer correspondence with our a priori expec-tations about the structure of housing prices. One exception is providedby the distance-from-the-CBD variable. For the additive owner equa-tions, the coefficient of distance from the CBD is smaller than itsstandard error but negative for all three samples. In the additive rentermodels, however, the coefficient of distance from the CBD is negativeand significant at the 5 percent level for the ghetto. It is negative butsmaller than its standard error for city nonghetto properties, while beingpositive and significant at the 1 percent level in the full nonghettosample. This reversal with the addition of the relatively few suburbanobservations may reflect unmeasured higher quality in much suburbanrental housing or an actual inversion of the location-rent gradient forrental units. Such an inversion of the usual rent gradient could reflect anequilibrium excess supply of some types of rental units at centrallocations or a temporary excess demand for certain types of rental unitsat some suburban locations. The same reversal is evident in the semilogequations; for all nonghetto properties the price of rental housingincreases as distance from the CBD increases. Neither the owner norrenter semilog equations provide evidence that the price of ghettoproperties declines with distance from the CBD.

This question is only slightly different from that addressed in theanalysis of Table 8-2, where it was estimated that the average rentalproperty in the sample costs 4 to 6 percent more in an "all-black" than inan "all-white" area. However, we now acknowledge possible differ-ences in the structure of relative prices in the ghetto and in the nonghettohousing markets.

Estimates of the cost of purchasing the average ghetto owner andrenter properties outside the ghetto are obtained by solving the non-ghetto rent and value equations using the_average characteristics ofghetto properties. Conversely, estimates of the costs of purchasing theaverage nonghetto property inside the ghetto are obtained by solving theghetto equations using the average characteristics of nonghetto pro-perties.

Table 8-5 summarizes these calculations, in terms of percentagedifferences, for the stratified models for both owner and renter proper-ties. For example, the average monthly rent of ghetto units in the sampleis $55.90. Using the linear equation for nonghetto properties in the city(Table 8-3, column 2), the monthly rent of a dwelling unit with thesesame characteristics is estimated to be $50.09; thus the estimatedmarkup on ghetto properties is 11.6 percent. For the same comparison,the coefficients of the semilog model (Table 8-4, column 2) provide anestimated markup of 17.8 percent for a property with the averagecharacteristics of ghetto rental units, i.e., this property is 17.8 percent


TABLE 8-5Estimated Ghetto Markups for Housing Bundles from Stratified Models(percent)

Linear Semilog Log-Log

Rental bundles:Average ghetto housing bundle

In city nonghetto 11.6 17.8 19.1In entire sample nonghetto 13.7 9.2 10.0

Average city nonghetto housingbundle

In city ghetto 12.5 1.3 2.1Average nonghetto housing

bundle (entire sample)In city ghetto 6.9 2.5 1.6

Owner bundles:Average ghetto housing bundle

In city nonghetto 5.2 5.1 6.1In entire sample nonghetto 0.8 0.8 3.2

Average city nonghetto bundle .

In city ghetto 1.7 3.3 8.2Average nonghetto sample

(entire sample)In city ghetto 19.2 30.2 51.4

more expensive in the ghetto than in the rest of the central city. Using alog-log specification (not shown in Tables .8-3 and 8-4), the percentagedifference is estimated to be 19.1 percent.

When the estimates are computed using the coefficients from theentire nonghetto sample, we are, of course, unable to include the valueof schools and crimes in the comparisons. Using the entire nonghettosample, the estimates of ghetto markups are slightly lower, in the rangeof 9 to 14 percent.

The monthly rent of the average city nonghetto property is $68.09.Using the coefficients of the linear equation for ghetto properties (Table8-3, column 1), the estimated rent in the ghetto for a dwelling unit withthese characteristics is $76.63; thus the estimated markup is 12.5 per-cent. The estimated markups using the coefficients of the semilog andlog-log models are much smaller.

The fourth line of Table 8-5 presents the estimated markups basedon the characteristics of the average nonghetto rental property in theentire sample. Again, because information on the incidence of crime and


the quality of schools is unavailable outside of the central city, we areunable to include these important attributes in the comparisons.

The latter part of the table presents the estimated ghetto markupsfor owner-occupied properties.

For several reasons, we have more confidence in the estimates ofghetto markups presented in lines 1 and 5 of Table 8-5. These calcula-tions are based on the regressions estimated for, the city nonghettoproperties; thus, they include differences in the value of the schools andthe neighborhood crimes associated With each unit. The regressionresults estimated for nonghetto properties also appear to have fewerproblems with collinearity, since there is substantially more variation inthe independent variables.

This analysis suggests that the ghetto markup for rental propertiesmay be on the order of 12 percent, and for owner-occupied properties itmay be on the order of 5 percent.

The table, however, provides estimates for rental properties rangingbetween 1 and 19 percent; for owner-occupied properties, the estimatesrange between 1 and 51 percent. It is worth noting that in none of thesecomparisons is a comparable property estimated to be cheaper in theghetto housing market than in the nonghetto market.

STRATIFICATION BY DWELLING-UNIT SIZE

As we mentioned at the beginning of this chapter, we are not fullysatisfied with the functional forms used in the regression estimates. Wedoubt that any of them adequately represents the kinds ofjointness andinterdependence in attribute prices that characterize urban housing mar-kets. In many respects, additive specification is the least satisfactory. Itassumes that the price of each attribute is independent, and that thevalue of the complete bundle is the simple sum of the prices of theindividual attributes, weighted by the quantities of each. This impliesthat households pay a certain amount for each room regardless of itscondition or quality, a certain amount for dwelling-unit quality regard-less of the dwelling-unit size, and a fixed dollar amount for quantities ofeach neighborhood characteristic.

These strong additivity assumptions might be tenable if there wereno jointness in the production of the various attributes, if all housingmarkets were in long-run equilibrium, and if all attributes were producedin competitive markets. Unfortunately, in practice, none of these condi-tions is satisfied. Many attributes have a clear jointness in production,many others are not provided by competitive firms, and we anticipaterather large departures from long-run equilibrium. As a result of these


factors, there may be large spatial quasi rents on individual attributes oron particular bundles of attributes. The independence assumption isparticularly offensive in the case of variables measuring dwelling-unitsize and quality, since there are technological reasons for expecting thecost of producing dwelling-unit quality to depend on the size of thedwelling unit.

The semilogarithmic and logarithmic specifications are more plausi-ble than the additive model in this respect, since, in both, the paymentfor a particular attribute depends on the levels of the remaining attri-butes. For example, in the semilogarithmic model, the payment for aunit of a particular attribute is assumed to be proportional to the level ofthe remaining attributes. Thus, in the example cited previously, themarket value of dwelling-unit quality depends on the size of the dwellingunit; in fact, it is proportional to the base cost. An increase in dwelling-unit quality by one unit increases the cost of the dwelling unit by Xpercent. If housing bundles included only dwelling-unit size and qualityvariables, the semilog form of the equation might be a reasonablysatisfactory representation. However, there is little justification forrequiring that payments for neighborhood quality be proportional topayments for dwelling-unit size and quality, and even less justificationfor requiring the payment for dwelling-unit quality to be dependent onthe level of neighborhood quality. The logarithmic form of the modelembodies a similar, but even stronger, interaction among the paymentsfor individual attributes.

The semilog and log-log forms have the desirable property of allow-ing some interactions among the payments for individual attributes. Butthe permitted interactions are of a highly specific nature; and in one wayor another, each fails to correspond to our prior expectations about thestructure of attribute prices. For this reason, we now present an alterna-tive specification of the rent and value models that allows a fullerinteraction between dwelling-unit size and the several measures of qual-ity. To estimate these alternative models, we stratify the renter andowner samples by the number of rooms and obtain separate additiveequations for each size of dwelling unit. This procedure allows thepayment for each of the remaining attributes to vary with dwelling-unitsize. However, unlike the semilog and multiplicative forms of the pooledequations, these payments need not vary uniformly with changes in size.

The advantages obtained from stratifying the' equations by numberof rooms should not obscure the fact that there are also disadvantages tothis procedure. The most obvious is the substantial reduction in samplesize. The largest sample, five-room owner-occupied units, includes only125 observations and several samples have less than 50 observations.


Still another serious consequence of stratification is a reduction in thevariance of both the dependent and explanatory variables. These reduc-tions in sample variance create a number of statistical difficulties. Due tocollinearity among variables and reduced variance in many variables inthe stratified samples, it is not possible to obtain meaningful coefficientestimates for many of the variables that were statistically significant inthe pooled model. To obtain estimates for the subsamples based on thenumber of rooms, it was necessary to prune the value and rent equationssubstantially by omitting obviously nonsignificant variables and thosetoo highly correlated with other included ones.

The reduction in sample variance is exacerbated by yet anotherproblem. As the data in Tables 8-6 and 8-7 illustrate, virtually all of theremaining housing attributes are systematically related to the number ofrooms in the dwelling-unit. Moreover, for each size category, units in theghetto are systematically inferior in both dwelling-unit and neighborhoodquality to units located outside the ghetto. The positive relationshipbetween size and quality is quite regular for three-, fou•r-, and five-roomrental units, and for four-, five-, six-, and seven-room owner units. Thelargest and smallest rental units, however, conform less well to thispattern, possibly because the sample sizes are quite small. An importantconsequence of the association between dwelling-unit size and otherhousing attributes is that part of the effects on price of both omitted andincluded housing attributes may be reflected in the intercepts of thestratified equations.

As we have previously noted, the more serious problems of multi-collinearity and smaller sample sizes of the stratified regressions made itnecessary to omit a number of explanatory variables from these equa-tions. This was accomplished by excluding explanatory variables withsmall standard deviations and those with very low t ratios in trialregressions. However, three variables of particular theoretical interest—miles from the CBD, neighborhood prestige, and percent white—wereretained until the last iteration. This procedure produced the similar, butstill nonuniform equations, shown in Table 8-8. Although equations wereobtained for the entire sample, for the ghetto sample, and for the non-ghetto, only the equations for nonghetto properties for the owner cate-gories and for three out of five of the renter categories are shown inTable 8-8.

Owing to the lack of uniformity among the equations in Table 8-8, itis hard to generalize about them. Still, some interesting patterns areevident. Because of the strong interest that has centered on accessibilityin analyses of the housing market, all of the equations in Table 8-8include distance from the central business district. The results obtained

TA

BLE

8-6

Mea

ns o

f Hou

sing

Attr

ibut

es b

y N

umbe

r of

Roo

ms

for

Ren

ters

of G

hetto

and

All

Non

ghet

toP

rope

rtie

s

Var

iabl

es

Ghe

tto(R

oom

s)N

ongh

etto

(R

oom

s)

1—2

34

56—

81—

23

45

6-8

Uni

t qua

lity

and

size

Inte

rior

3.52

3.56

3.66

3.64

3.53

3.95

4.02

4.11

4.25

3.83

Ext

erio

r2.

292.

082.

242.

262.

102.

832.

632.

772.

832.

62H

ot w

ater

.82

.74

.91

.93

.94

.89

.96

.99

.98

.94

Cen

tral

hea

ting

.65

.44

.70

.80

.71

.67

.59

.88

.85

.94

Age

61.4

165

.98

61.6

164

.89

71.7

144

.78

55.9

947

.29

45.9

054

.41

Bat

hs.9

5.9

5.9

91.

021.

32.8

3.9

81.

011.

061.

06Pa

rcel

are

a15

.60

18.8

717

.95

23.4

028

.54

7.89

15.6

020

.22

30.9

35.6

4N

eigh

borh

ood

Adj

acen

t uni

ts2.

572.

362.

582.

682.

373.

503.

093.

363.

433.

32B

lock

fac

e2.

532.

372.

542.

592.

483.

333.

313.

473.

543.

35M

edia

n sc

hool

ing

8.69

8.67

8.88

9.13

8.88

9.22

8.88

9.50

9.6

9.44

Prop

ortio

n w

hite

17.7

618

.58

13.4

213

.18

11.1

099

.71

99.9

499

.72

99.5

199

.01

Mile

s fr

om C

BD

2.46

2.58

3.13

3.36

3.16

5.04

3.43

4.35

5.06

4.25

Ren

t47

.56

47.5

460

.44

68.2

464

.64

61.4

459

.27

76.4

187

.92

90.0

0N

umbe

r of

obs

erva

tions

3411

982

4631

108

9648

17

r.') 0

N)

N)

TA

BLE

8-7

Mea

ns o

f Hou

sing

Attr

ibut

es b

yN

umbe

r of

Roo

ms

for

Ow

ners

of G

hetto

and

All

Non

ghet

to P

rope

rtie

s

Var

iabl

es

Ghe

tto

(Roo

ms)

Non

ghe

tto (

Roo

ms)

45

67

8—12

45

67

8—12

Uni

t qua

lity

and

size

Inte

rior

3.79

3.99

4.04

4.32

3.95

4.25

4.52

4.62

4.63

4.64

Ext

erio

r2.

462.

582.

502.

792.

502.

913.

073.

083.

153.

11

Hot

wat

er.8

9.9

5.9

41.

001.

00.9

31.

001.

001.

001.

00

Cen

tral

hea

ting

.74

.85

.88

.91

1.00

.91

1.00

.97

1.00

1.00

Age

64.2

162

.35

64.0

663

.46

64.1

843

.32

29.5

531

.19

31.7

133

.93

Bat

hs.9

51.

001.

181.

001.

88.9

81.

051.

311.

531.

93

Floo

r ar

ea8.

828.

449.

0610

.74

10.1

58.

7410

.46

10.8

013

.27

15.5

3

Parc

el a

rea

29.3

435

.79

38.4

243

.06

52.4

446

.52

90.7

973

.18

111.

1622

7.50

Nei

ghbo

rhoo

dA

djac

ent u

nits

2.68

2.62

2.88

3.00

2.85

3.45

3.70

3.82

4.01

3.85

Blo

ck f

ace

2.63

2.75

2.82

3.09

2.88

3.28

3.78

3.94

4.13

4.13

Med

ian

scho

olin

g8.

778.

968.

949.

169.

569.

7610

.09

10.5

210

.60

10.2

1

Prop

ortio

n w

hite

18.6

76.

1414

.56

15.9

85.

6299

.68

99.4

999

.31

99.2

599

.31

Mile

s fr

om C

BD

3.20

3.40

3.39

3.69

4.34

6.00

7.40

8.14

8.60

7.88

Val

ue (

dolla

rs)

10,2

9210

,805

11,6

9514

,733

14,9

0512

,416

16,1

7617

,044

21,1

7028

,113

Num

ber

of o

bser

vatio

ns19

2017

1756

125

6238

30

TA

BLE

8-8

Ren

t and

Val

ue E

quat

ions

by

Num

ber

of R

oom

s fo

r A

ll N

ongh

etto

Pro

pert

ies

Ren

ters

(R

oom

s)O

wne

rs (

Roo

ms)

Var

iabl

es3

45

45

67

8—12

Uni

t qua

lity

and

size

Inte

rior

5.36

222

.592

7.64

75.0

82

Ext

erio

r4.

652

10.7

71

Hot

wat

er14

.811

11.3

3C

entr

al h

eatin

g9.

18'

—3.

73A

ge—

.32'

_•53

1_.

292

—.9

8'—

1.13

'_•

951

Roo

ms

11.8

6B

aths

9.25

Floo

r ar

ea7,

91'

4.61

14.

75'

8.66

'19

.30'

Parc

el a

rea

12.1

2—

2.89

.26

Stru

ctur

e ty

peSi

ngle

det

ache

d5.

84A

part

men

t_6

.162

4.87

_11.

162

Flat

N)

N)

rs.

Nei

ghbo

rhoo

dA

djac

ent u

nits

11.2

2'7.

78—

.62

14.9

0

Blo

ck f

ace

12.1

7'M

edia

n sc

hool

ing

—2.

224.

70'

3.99

.48

—.9

77•

Ø44

Mile

s fr

om C

BD

—.2

44.

13'

.65

—3.

01'

—6.

44k

Ten

ancy

term

sN

o he

at_1

6.28

1_1

2.91

1_l

0.49

2N

o w

ater

—3.

72k

No

furn

iture

_I0.

482

—17

.39'

No

appl

ianc

es—

16.2

4'—

13.7

7'_1

3.72

2

Ow

ner

in b

uild

ing

—17

.09'

Yea

rs o

f oc

cupa

ncy

—.1

0

Con

stan

t63

.09'

108.

9.1

—14

.67

—4,

349

7,43

06,

609

6,87

5—

14,5

50

R2

.864

.808

.884

.621

.541

.539

.759

.842

Deg

rees

of

free

dom

9482

3647

117

5429

23

Num

ber

of o

bser

vatio

ns10

896

4856

125

6238

30.

NO

TE

: Tab

le n

otes

indi

cate

sig

nifi

canc

e of

t ra

tios

for

coef

fici

ents

(tw

o-ta

iled

test

).1>

.01.

2>.0

5..1

0.4t

rat

io g

reat

er th

an 1

.0.


for the three rental equations in Table 8-8 are inconsistent with the pricerelationships predicted by monocentric theories of urban spatial struc-ture but generally confirm the results obtained for the nonghetto rentalequations in Tables 8-3 and 8-4. For the stratified nonghetto rentalequations, two of the three distance coefficients are positive, but onlyone, that for four-room apartments, is greater than its standard error.This coefficient is quite large, however, and is significant at the .01 level.The average four-room nonghetto unit in the sample is located 4.4 milesfrom the CBD, and the sample standard deviation is 2.7 miles. Thus, aunit one standard deviation closer to the center (1.7 miles from the CBD)would rent for $22.30 less than an otherwise comparable four-room unitone standard deviation toward the periphery (7.1 miles from the CBD).

In contrast to the results for rental units, the coefficients of thevariable of distance from the central business district in the ownerequations provide rather consistent evidence of declining location rentswith distance from the CBD. The coefficient of miles from the CBD isnegative for all room size categories and varies in magnitude from a lowof $3.01 per mile per month to $6.44 per mile per month ($301 and $644per mile in value). The pooled owner equation for all nonghetto proper-ties also has a negative coefficient, but it is smaller than its standarderror and is only about one-fifth as large as the smallest estimate of agradient obtained for individual room equations. This suggests that thereare different value gradients for the different size structures, a result thatis consistent with Straszheim's findings for San Francisco.17 As a result,pooling these units of different size produces a misspecification thatobscures the presence of any gradient. The gradients for five- and six-room units are quite similar. Interestingly enough, it is evident fromTable 8-7 that the average five-room unit has as much floor area as theaverage six-room unit. Both, however, have more square footage thanfour-room units and are smaller than either seven-room units or eight-to twelve-room units.

The other interesting result shown in Table 8-9 is the very differentpattern of significant coefficients for the neighborhood and dwelling-unitquality variables in the renter equations. None of the neighborhoodquality variables consistently affects the rent of four- and five-roomunits. However, both interior and exterior dwelling quality have largeand statistically significant coefficients in the three-room equation, andthe coefficient of exterior quality is large and statistically significant inthe four-room equation. By contrast, nearly opposite results areobtained for five-room units. Of the five measures of dwelling-unitquality, only structure age is larger than its standard error in the five-room equation, but all the coefficients of adjacent quality, block quality,

17Straszheim, Econometric Analysis.

TA

BLE

8-9

Add

itive

Ren

t and

Val

ueE

quat

ions

by N

umbe

r of

Roo

ms

for

All

Non

ghet

to P

rope

rtie

s

Var

iabl

es

Ren

ters

(R

oom

s)O

wne

rs (

Roo

ms)

1—2

34

56—

84

56

78—

12

Uni

t qua

lity

and

size

Inte

rior

18.2

2212

.562

13.6

868

.682

Ext

erio

r—

11.8

310

.912

6.53

8.73

Age

—.8

9—

.82'

—1.

14'

Floo

r ar

ea8.

85'

4.64

'4.

671

954'

18.3

71

Nei

ghbo

rhoo

dA

djac

ent u

nits

8.77

—1.

776.

59B

lock

fac

e5.

87—

.54

15.6

82—

.20

Mile

s fr

om C

BD

—3.

00'

—5.

35

Ten

ancy

term

sN

o he

at4.

53—

16.O

P—

4.23

No

furn

iture

—43

.18

1.73

120.

972

No

appl

ianc

es—

6.64

—14

.56'

Con

stan

t10

0.7'

120.

0111

.67

57.1

396

.47

R'

.842

.785

.740

.752

.764

.602

.534

.538

.749

.826

Deg

rees

of

free

dom

210

189

4110

5011

956

3224

Num

ber

of o

bser

vatio

ns9

108

9648

1756

125

6238

30

NO

TE

: Tab

le n

otes

indi

cate

sig

nifi

canc

e of

t ra

tios

for

coef

fici

ents

(tw

o-ta

iled

test

).1>

.01.

2>.0

5.'>

.10.

4t r

atio

gre

ater

than

1.0

.


and median schooling are significant at the 1 percent level and quitelarge. These results suggest further that the markets for small and largemultifamily units are quite distinct; a different configuration of attri-butes command market prices for larger multifamily units than forsmaller multifamily units.

In spite of this and other evidence of heterogeneity in the structureof prices for rental and owner units of different sizes, equations includingan identical set of explanatory variables for unit-size categories areshown in Table 8-9.

The rental equations include two dwelling-unit quality variables,exterior quality and age; one measure of neighborhood quality, blockquality; and three contract-rent corrections. The owner equationsinclude two measures of dwelling-unit quality, interior quality and struc-ture age; first-floor area; the quality of adjacent units; and distance fromthe CBD. Although equations for the largest and smallest rental units areincluded in Table 8-9, not much confidence can be placed in thembecause of the small sample sizes (only nine properties for one- and two-room rental units and seventeen properties for six- to eight-room units).

The identical form of the equation reported in Table 8-9 facilitatescomparisons among the equations for different room size classes. Nearlyall of the coefficients in the stratified equations have the anticipatedsigns, though many of the coefficients are not statistically significant.The few sign reversals that do occur are for very small samples, thelargest and smallest rental units; and, therefore, do not represent impor-tant exceptions. Age of structure appears in both the rental and ownerequations and is highly significant statistically in nearly all equations. Inthe rental sample, the age coefficient varies from forty-four cents permonth for each year of age for three-room units to over a dollar permonth for six- to eight-room units. There is no clear progression by unitsize, suggesting important deviations from long-run equilibrium. In theowner equation, the age coefficient varies from a low of $.93 per monthfor each year of age for six-room units to a high of $7.49 per month foreach year for the largest owner-occupied units. The latter figure cannotbe considered very reliable since it is based on only thirty observationsand is smaller than its standard error. Except for this estimate for thelargest units, all of the newness premiums for age vary within a narrowrange. If it can be assumed that age measures a uniform dimension ofquality for the various size units, this result is somewhat inconsistentwith the view that the St. Louis housing market is in long-run equilib-rium. Except for the eight- to twelve-room equation, the age coefficientsfor the stratified owner equations are of approximately the same magni-tude as are obtained for the comparable pooled equation in Table 8-3; thepremiums for newness for the stratified rental equations in Table 8-9,


however, are generally larger than those obtained in the comparablepooled equations in Table 8-3.

The coefficients of both exterior quality and block quality in thestratified renter equations vary substantially in terms of both statisticalsignificance and magnitude, and no simple pattern is evident by roomsize. However, the tendency observed in Table 8-8 for dwelling qualityto be a more important determinant of value for smaller units and forneighborhood quality to be a more important determinant of value forfive-room units is supported by the estimates in Table 8-9.

Except for the largest owner units, the coefficients of interiorquality vary within a fairly narrow range. Again, as with structure age,there is no noticeable tendency for the premium for dwelling-unit qualityto increase with room size. This may result from errors of measurementof the dwelling-unit quality variable, from misspecification, or fromdifferences in the structure of house values for units of different size.Resolution of this important question must await further research withimproved measurements and larger, more representative, samples. Simi-larly, the premium for adjacent-unit quality is quite different among unitsof different size and fails to exhibit an obvious regularity by size.

The stratification by room size is designed to standardize the sampleproperties by dwelling-unit size; however, it is evident that the proper-ties included in each of the room size classifications are not actuallyhomogeneous in terms of size. The inclusion of first-floor area in theowner equations then provides a measure of this variation in dwelling-unit size within room size categories. The significant variation in first-floor area for units of the same room size is clearly evident from therelatively large standard deviations of first-floor area within room sizecategories. The standard deviation of first-floor area which, not sur-prisingly, increases with the number of rooms, is 226 square feet for thesmallest units and 642 square feet for the largest, with a marked increasebetween six and seven rooms. Evidently, then, there is considerableoverlap in dwelling-unit size as measured by floor area among the roomsize categories. For example, the average first-floor area of five- and six-room units is nearly the same— 1,047 square feet and 1,080 square feet,respectively. Since the standard deviations of first-floor area for five- andsix-room units are 231 square feet and 354 square feet, it is obvious thatmany five-room units are larger than many six-room units when mea-sured by first-floor area.

The coefficients of the floor-area variable in the owner equations areall statistically significant at the 1 percent level and vary widely from oneroom size to another. The most similar estimates are obtained for five-and six-room units, which may be quite close substitutes. Both smallerunits—four-room—and larger ones—seven-room and from eight- to


twelve-room—are considerably more expensive per square foot of addi-tional floor area. These differences in unit cost per square foot mayeither be evidence of different quasi rents on units of uniform qualitywithin a room size class, or may reflect some of the previously men-tioned differences in dwelling unit and neighborhood quality among theroom size classes. Further research is needed to obtain more definitiveanswers to these questions.

The explanatory power of the individual equations in Table 8-8 isless in many cases than that of the comparable pooled equation in Table8-3. However, the more interactive specification of the rent and valueequations shown in Table 8-9 provides a marginally better explanation ofthe variation in rents and values than the single equation in Table 8-3.When the variance due to the stratification by room size is added to thevariance explained by the independent variables included in each equa-tion in Table 8-9, the overall explained variance is .798 for renters and.795 for owners.

SUMMARY

Housing choices, both as to type and location, reflect decisions byurban households to purchase a wide variety of heterogeneous attri-butes, including both quantitative and qualitative aspects of dwellingunits, structures, neighborhoods, and public services. This chapter hasprovided a detailed analysis of the market prices of these housingattributes.

Based upon detailed information gathered for each dwelling unit, wehave analyzed the market prices of bundles of housing services definedto include both quantitative attributes of the units themselves and quali-tative features of the structure, the parcel, and the immediate neighbor-hood. The results suggest that, for both owner-occupied and rental units,variations in the level of these attributes are systematically related tomarket prices. Besides attributes that measure dwelling-unit size (num-ber of rooms, baths, parcel area, first-floor area), the quality of dwellingunits, of parcels, and of the block face, and neighborhood prestige are allreflected in housing prices. It is worth emphasizing that many of theattributes of a heterogeneous housing stock, for example structure typeand lot size in built-up areas, are extremely durable and are expensive tomodify. Other attributes, for example, heighborhood ôharacteristics, arenot supplied by firms at all.

The analysis of attribute prices also considers, in a limited way, theinfluence of good schools and safe neighborhoods upon housing values


and rents. The results indicate that even within the central city, dwellingunits served by better schools command higher prices.

The results of our analyses for both renter and owner-occupiedproperties indicate that structures of attribute prices differ betweenproperties located in the ghetto and those located outside of it. In part,these differences reflect the limited choice of housing attributes availablein the ghetto housing market. For example, the premium for betterquality neighborhood schools is estimated to be about $4.85 (per monthfor an additional year of achievement on standardized tests) outside theghetto. This premium is not observed for ghetto properties, largelybecause the schools servicing these properties are uniformly bad.

When the sample of nonghetto properties is expanded to include theimportant suburban alternatives facing white households, the rent andvalue equations explain more of the variation in housing prices. Theanalysis of the combined city-suburban sample is limited, however, bythe absence of any information regarding suburban public services.

For the pooled sample of ghetto and nonghetto properties, theresults suggest that similar units cost 4 to 6 percent more in an all-blackthan in an all-white neighborhood. For the comparisons between sub-markets, the results suggest that a rental unit with the characteristics ofthe average ghetto unit would rent for 12 to 19 percent more in the ghettothan in the nonghetto portion of the housing market; for owner-occupiedunits, the discrimination markup is estimated to be 5 to 6 percent. Forexample, from the linear model, a representative rental unit in the ghettocosts about $70 a year ($5.80 a month) more than in the unrestricted(nonghetto) portion of the city housing stock. A representative owner-occupied unit in the ghetto would cost $651 less outside.

The analysis concludes by estimating value and rent relationshipsfor nonghetto properties separately for units of varying size (as mea-sured by numbers of rooms). Despite the reduction in the variation ofhousing attributes when the sample is stratified, the results indicate thatthere are important interaction effects between payments for size andother housing attributes. For example, the premium for newness appearsto vary with dwelling-unit size, though the relationship is a complex one.

In addition, the employment-accessibility variable used in the anal-ysis (miles from CBD) is more often significantly different from zero inthe stratified models for owners than in the pooled models. One implica-tion is that simple monocentric analyses, which ignore the existence ofresidential capital, fail to take into account some important tradeoffswhich are considered by households in choosing a residential location,and which are reflected in market prices. Moreover, employment acces-sibility is systematically related to other important housing attributes,


which themselves vary spatially. More detailed analyses of the accessi-bility measures, using both miles from CBD and more generalizedgravity-model measures of accessibility to employment or retail activity,indicate that the interaction of accessibility and the spatial distribution ofexisting hoqsing attributes deserves more attention in analyses of urbanspatial structure.

the value of housing attributes

Documents