Measuring the Value of Housing Quality John F. Kain; John M. Quigley Journal of the American Statistical Association, Vol. 65, No. 330. (Jun., 1970), pp. 532-548. Stable URL: http://links.jstor.org/sici?sici=0162-1459%28197006%2965%3A330%3C532%3AMTVOHQ%3E2.0.CO%3B2-G Journal of the American Statistical Association is currently published by American Statistical Association.

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/astata.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.

The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact [email protected].

http://www.jstor.org Mon Sep 24 21:16:22 2007

@ Journal of the American Statistical Association June 1970, Volume 65, Number 330 Applications Section

Measuring the Value of Housing Quality JOHN F. KAlN and JOHN M. QUIGLEY* Based on an extensive sample of individual dwelling units, this article estimates the market value, or the implicit prices, of specific aspects of the bundles of residential services consumed by urban households. Quantitative estimates were obtained by regressing market price of owner- and renter-occupied dwelling units on measures of the qualitative and quantitative dimensions of the housing bundle. The measures of residential quality associated with individual dwelling units were obtained by using factor analysis to aggregate some 39 indexes of the quality of narrowly defined aspects of the dwelling units, structures, parcels, and micro-neighborhoods. The analysis indicates t h a t the quality of the bundle of residential services has about as much effect on the price of housing as such objective aspects as the number of rooms, number of bathrooms, and lot size. The analysis also confirms the influence of neighborhood schools on the value of residential properties and indicates that rental properties in the ghetto may be systematically more expensive than those located outside of the ghetto.

1. INTRODUCTION

I n buying housing, families jointly purchase a wide variety of services a t a particular location. These include a certain number of square feet of living space, different kinds of rooms, a particular structure type, an address, accessibility to employment, a neighborhood environment, a set of neighbors, and a diverse collection of public and quasipublic services including schools, garbage collection, and police protection. Several published studies have tried to obtain statistical estimates of the individual contribution of these specific attributes to the total payments (rent or purchase price) for residential services. For example, Ridlier and Henning used census tract data to estimate the effect of variables such as air pollution, accessibility to dom-ntown, school quality, and substandardness on the average value of single-family homes [ 2 3 ] . Similar analyses have been published by Muth, Oates, Pendelton, and others [$, 10, 19, 20, 21, 221. All these attempts to estimate the market value of specific attributes of the bundle of residential services are deficient because they fail to represent adcquately the complexity of residential service bundles, because they lack adequate measures of residential quality or rely exclusively on aggregate (published census tract) data. This article seeks to correct these deficiencies by using information for individual dwelling units, by more completely describing the * J o h n F. Kain is professor of economics, Harvard University, and senior staff member, National Bureau of Economic Research. John hi. Quigley is Ph.D. candidate in economics, I-Iarvard University, and research associate, National Bureau of Economic Research. This article is based on research performed by the autl~orsfor Alan PI. Voorhees and Associates under contract t o the St. Louis Co~nrnllnityRenewal Program. The authors would like to thank Walter E. Hansen of Alan Voorhees and Associates for his frequent advice and sugicestions; Iioland K. hlcFarland of the St. Louis Community Renewal Program, slipen-isor of the data collrction; Eugene Wilhelm, who performed long hours in processing the large and complex data files used in the analysis; and Stephen IIendenon, Thomaa H. Tietenberg, a n d Robert C . Wilburn. who offered many constnlctive s~lggestionsfor the analppi8 Thev are alao grateful t o Jane E. Kenworthy for her editorial assistance.

Measuring the Value of Housing Quality

533

bundles of residential services, and in particular by seriously trying to measure their physical and environmental quality. Quantitative value estimates of individual attributes of the bundle of residential services are obtained by regressing market price (value for owneroccupied dwellings and monthly rent for renter-occupied dwellings) on the individual quality and quantity measures. The coefficients for individual variables then measure the market value of varying amounts of each attribute. If the housing market could be assumed to be in long-run equilibrium, this would be a fairly unanzbiguous measure since it would also be equal to the supply price of adding an increment of that attribute to the bundles. However, given the importance of stocks in the housing market, substantial departures from longrun equilibrium may be expected. Even so, knowledge of the market value of specific attributes of the bundles of residential services is of considerable theoretical interest and is valuable for many kinds of public and private decisions. For example, market value estimates of residential quality, obtained from earlier regressions, were used to obtain lower-bound estimates of the benefits of urban renewal programs [12]. Similarly, models of this kind would be of enormous value to appraisers in estimating the market value of real estate for tax and other purposes. The coefficients may also be considered as weights in a hedonic price index [3, 51. I n the September 1969 JASA, John C. Musgrave describes Census Bureau research to develop such an index for new single-family homes [16]. If the various measures of quality used here could be reproduced over time, it should be possible to develop similar indexes for the housing stock. This article provides a partial test of the importance and feasibility of such an effort. 2. MEASUREMENT OF RESIDENTIAL QUALITY

Difficulty in measuring the physical and environmental quality of the dwelling unit and surrounding residential environment is perhaps the most vexing problem encountered in evaluating the several attributes of bundles of residential services. These problems are so serious that the Bureau of the Census omitted all measures of dwelling unit quality from the 1970 housing census. Evaluations of the quality of sample dwelling units, structures, and blocks used in this study were obtained from three separate surveys of approximately 1,500 households and dwelling units in the city of St. Louis completed in the summer of 1967.' I n the first survey, interviewers were instructed to rate the quality of particular aspects of each dwelling unit, e.g., the walls, on a scale ranging between 1 ("excellent condition") and 5 ("requires replacement"). A second survey, conducted by city building inspectors, provided quality ratings for specific aspects of the exterior of each sample structure and parcel and of those on either side of the sample dwelling. Building inspectors also rated aspects of the quality of the block face (both sides of the street) on which the sample dwelling units were located, recorded the presence of specific adverse 1 The sample consisted of 1,526 houaehold addresses selected randomly within the city. Of this sample, 205 units were vacant; nonresponses and refusals further reduced the sample aize to 1,103. The sample design and seleoted tsbulationa of the raw data are discussed in [24].

534

Journal of the American Statistical Association, June 1970

environmental influences, such as noise, smohe, heavy traffic, and ~loxious odors, and estimated the extent of nonresidential activity on the sample Lloclis. These surveys provided 39 variables indicating the physical or visual quality of the bundle of residential services, including seven measures of the quality of dwelling units (e.g., condition of floors, windows, walls, levels of houselieeping, etc.), seven measures of the quality of the structure and parcel (e.g., condition of drives and wallts, landscaping, structure exterior, etc.), eight measures of the quality of adjacent properties (e.g., condition of structures, parcels, etc.), and 17 variables pertaining to the residential quality of specific aspects of the block face (e.g., condition of street, percent of nonresidential use, etc.). Detailed quality judgments about many conlporients of the bundle of residential services were obtained on the premise that individual interviewers and building inspectors xvould provide more corlsisteiit and precise evaluations of narrowly defined individual components than they could about broader aggregates. A second premise was that subsequent statistical aggregation of many separate judgments would provide more consistent and meaningful quality measuree than the subjective aggregation implicit in obtaining overall quality judgments from individual evaluator^.^ Although this procedure reduced the danger of interviem-ers' inconsistent and arbitrary aggregation, it created the corollary problem of h o ~ vto reduce the 39 separate quality measures to a more manageable number. I t would have been possible to include all 39 variables in the regressions with the remaining attributes of the residential services bundles. But, besides the statistical problems, such as n~ulticollinearityand the loss of degrees of freedom, which would arise from doing so, there is reason to believe that both the n~arlietand individual households evaluate residential quality in terms of fewer broader aggregates. Two different methods of aggregation were used in constructing these composite quality variables, with generally consistent results. The first set of composite quality indexes were simple, unweighted means of the individual quality measurements for the dwelling unit, the structure, the adjacent structures, and the block face. The second set, used in the regressions reported here, were derived from the original 39 variables by factor analysis. Since there is no way of unambiguously determining the appropriate number of factors, four-, five-, and six-factor representations of the 39 quality variables were computed and evaluated. The five-factor solution, summarized in Table 1, accounts for 60 percent of the variance among the 39 original variables and seems to provide the most meaningful description of the quality dimensions of the bundles of residential services. Each of the five factors appears to represent a separable and intuitively meaningful quality dimension of the bundles. The first factor accounts for 38.8 percent of the total variance of the original correlation matrix and loads heavily on 17 variables describing the overall condition of the structure and parcel, amount and quality of landscaping, I n designing the survey we cmsidered and rejected the techniqae developed by the Committee on the Hygiene of Housing of the An~ericanPublic Health Association. T h e -4PHA technique, used in many cities, involves a field survey of individual dwelling units. Many items are recorded for each dwelling and penalty scores are assigned t o each item which falls below a certain standard. These penalty points are then sumlned t o obtain a "dwelling score," which represents the overall quality of the dwelling [ z ] .

535

Measuring the Value of Housing Quality

Table I .

FACTOR LOADINGS O N INDIVIDUAL QUALITY VARlABlES -.

Variable

Factor 1

Dwelling unit Overall structural condition General housekeeping Condition of ceilings Condition of walls Condition of floors Condition of lighting Condition of windows

--

8 9 10 11 12 13 14

Structure and parcel Condition of structure exterior Overall parcel condition Quality of exterior Parcel landscaping Trash on parcel Nuisances affecting parcel Condition of drives and walks

.74 .72 .52 .56 .65

15 16 17 18 19 20 21 22

Adjacent structures and parcels Condition of structures Condition of parcels Structural quality of poorer Structural quality of better Parcel quality of poorer Parcel quality of better Nuisances affecting adjacent properties Sample relative to adjacent properties

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Block face Neighborhood problems Percent residential Percent commercial and residential Percent vacant Percent in poor condition Percent in fair condition Percent in good condition Block landscaping Trash on block Condition of sidewalk Condition of street Condition of curbs Amount of commercial traffic Nuisances affecting block Condition of alleyways Cleanliness of alleyways Overall block condition

1 2 3 4 5 6 7

2

3

4

6

-

-

-

.57

NOTE: -indicates standardized factor loading less than .5.

cleanliness of the parcel and block face, and condition of the streets, walks and driveways (Table 1).I n other words, the index appears to measure the overall quality of the exterior physical environment. For this reason, it is termed "Basic Residential Quality" (BRQ). The second factor, ('Dwelling Unit Quality" (DUQ), representing both the

536

Journal of the American Statistical Association, June 1970

structural condition and housekeeping inside the sample dwelling unit, accounts for an additional 8.2 percent of the variance in the original correlation matrix. All seven variables with factor loadings of more than .5 for DUQ refer to the interior of the dwelling unit and were obtained by the interviewers as part of the home interview survey. This raises the possibility that the differences in the indexes may be the result of different evaluators rather than independent quality dimensions. However, the relatively large number of home interviewers reduces this danger. The third factor, "Quality of Proximate Properties" (QPP), which explains an additional 6.0 percent of the total variance, amplifies the BRQ index by specifically accounting for the cleanliness, landscaping, and condition of nearby properties. The fourth factor, "Nonresidential Use" (NU), measures the presence and effect of commercial and industrial land uses in the immediate vicinity and accounts for another 4.2 percent of the total variance. It undoubtedly represents the effect of nonphysical characteristics such as noise, smoke, and traffic as well as the proportion of property on the block devoted to nonresidential use. The variables with factor loadings of more than .5 are micro-neighborhood or block-face variables. The fifth factor, "Average Structure Quality" (ASQ), adds another 3.2 percent to the explained variance and loads heavily on only two variables, measures of the average quality of structures on the block face as a whole. Besides the measures of residential quality, home interviewers obtained much information about characteristics of the occupants, objective characteristics of the dwelling units (e.g., number of rooms and bathrooms in a unit and whether it had hot water and central heating), and rent or value of the unit. Data on other aspects of the bundle of residential services, such as quality of neighborhood schools, incidence of crime, age of the structure, and various measures of accessibility were obtained from public records. These extensive data permitted us to estimate the market value of both quantitative and qualitative attributes of the bundle of residential services. Because of the lack of comparability between price data for rental and owner-occupied units, separate models were estimated for rental and owner submarkets. Also, because the small suburban subsample is incomplete in some important respects, separate models were estimated for the city and for the entire sample. 3. THE CITY EQUATIONS

Though the owner and renter equations are generally comparable, there are some differences. The renter equation is considerably more complicated and includes 25 explanatory variables compared with 15 for the owner model. Both the owner and renter equations include five quality indexes, number of rooms, number of bathrooms, age of structure, parcel area (parcel area per dwelling in the case of multi-family units), distance to central business district, median schooling of adults in the census tract, estimated percentage white of the census tract population in 1967, mean achievement levels of the neighbor-

Measuring the Value of Housing Quality

537

hood public school, and an index of the neighborhood level of criminal activity in the neighborhood.3 Besides these common variables, the renter equation contains six dummy variables for structure type, four dummy variables describing the rental terms (whether the rent includes payment for heat, water, furniture, and major appliances), two dummy variables indicating whether the dwelling unit has central heating and hot water, a variable indicating the duration of tenant occupancy, and a dummy variable indicating whether the owner lives in the same building. The only variable included in the owner-occupied model not in the rental model is first floor area, a surrogate for total floor area. It would have been desirable to include total floor area in the renter model as well, but it was unavailable; and first floor area, used in the owner model, is not' meaningful for multi-family structures. The owner equations are limited to single-family units because there is no adequate way of imputing an appropriate share of the value of owner-occupied, multi-family dwelling units to each dwelling unit. The four contract rent corrections and the owner-in-building and years-rented variables are not applicable to owner-occupied structures. The dummy variables representing both hot water and central heat are omitted from the owner sample because almost no single-family, owner-occupied structures included in the sample lack hot water and central heat. Although more complex specifications involving quality-quantity interactions were investigated, most of the estimation relied on linear or semi-logarithmic models. (In one instance an independent variable was transformed to logarithms as well.) For the renter models, the linear specification fit the data better; for the owner models, the semi-log form provided better results. Table 2 shows the estimated coefficients for the 579 rental units and the 275 owneroccupied, single-family homes in the city. The results obtained for the five quality indexes are particularly interesting. I n the renter model, the basic residential quantity, dwelling unit quality, and average structure quality variables are statistically significant. The coefficient for basic residential quality is almost six times its standard error; more importantly, the magnitude of the coefficients indicates that the rental market values these dimensions of residential quality very highly. Basic residential quality has an estimated value of $7.22 per unit. Dwelling unit quality is valued a t $4.02 per unit and average structure quality, a t $2.80 per unit. If they are 8 The percentagewhite variable is different from that used in earlier drafts of this article, which relied on data from the 1960 population census. The variable used here, the "estimated percent white" in the census tract in 1967, is based solely on the sample data. The sample size ia uncomfortably small, but the estimated 1967 percentage a p pea= to provide a better definition of the ghetto's boundaries than did the 1960 census tract data. All equations have been reestimated using the 1967 estimate in place of the 1960 census tract statistic, with generally improved results. Results using the 1960 racial composition variable are available in an earlier draft of this article [13]. Each sample was located within the appropriate public school district, and the average eighth-grade math achievement score for the public school servicing that district was recorded. This exam, given to all public school students in the eighth grade, measures student performance in school-year equivalents. The police department in the city of St. Louis maintains crime statistics for small geographical areas of approximately equal size. Sample dwelling units were matched with these areas, known as "Pauley Blocks," and the number of major crimes (felonies) reported for each was used as the index of criminal activity.

538

Journal of the American Statistical Association, June 1970

Table 2. REGRESSION EQUATIONS FOR CITY RENTER AND OWNER MARKETS Variable

Renter coeficient

Owner coeficient

Basic residential quality Dwelling unit quality Quality of proximate properties Nonresidential usage Average structure quality Proportion white in census tract Median schooling of adults in census tract Public school achievement Number of major crimes Age of structure Number of rooms (natural log.) Number of bathrooms Parcel area (hundreds of sq. ft.) First floor area (hundreds of sq. ft.) Single detached Duplex Row Apartment Rooming house Flat No heat included in rent No water included in rent No major appliances included in rent No furniture included in rent Hot water Central heat Duration of occupancy (years) Owner in building Constant

R Observations Significant at .05 level. Significant at .01 level. NOTE: With the exception of the dummy variables for structure type, the relevant tests are one-tailed.

a

added together, the five quality coefficients total $18.43. The mean value of contract rent for the sample is $63.19 with a standard deviation of $27.71. Thus, these aspects of residential quality account for a significant portion of monthly rent. The table also indicates that households purchasing single-family units place a high value on some of these quality dimensions. The coefficients indicate that property owners will pay over $1,400 more for an otherwise comparable property that is one standard deviation better than average in terms of basic residential quality, and they will pay over $750 more for a structure one standard deviation unit better in terms of dwelling unit quality. Neither the quality of proximate properties nor average structure quality has a coefficient that is statistically different from zero. The final index of quality (nonresidential use), evaluated a t the sample mean, suggests that a buyer of a single-family house would pay $850 more for a house one unit better than average. Sixteen other coefficients are significant a t the five percent level in the renter

Measuring the Value of Housing Quality

539

equation; an additional five variables are significant in the owner equation. Also highly significant is the number of rooms in the renter equation: the difference between a two- and three-room unit is $10.17; the difference between a four- and a five-room unit is $5.87. Dwellings with hot water rent for $4.89 more per month than cold-water flats, and central heating increases rent by $4.59 per month (the effect of dwelling-unit size and quality being held constant). For owners, the coefficient for the number of rooms indicates that a six-room house costs $550 more than a five-room house with the same floor area, and a nine-room house costs $400 more than an otherwise identical eight-room house. Age of structure is also strongly related to monthly rent and housing value. The results suggest that a new structure will sell for $3,150 more than an otherwise identical one that is 25 years old, i\!lonthly rent decreases by about $2.82 per month for each increase of ten years in age of structure. Since the average rental structure is nearly 60 years old, age has a considerable effect on monthly rent. It is worth emphasizing that this difference remains after the effects of the five indexes of quality and the presence or absence of central heating and hot water have been accounted for. This strong age effect is probably attributable to further differences in quality or style not accounted for by other variables. The surrogate for neighborhood prestige (median schooling of residents of the census tract) is statistically significant in both models. The coefficients indicate that an otherwise identical bundle located in a census tract in which the median adult has only completed the eighth grade will rent for $5.24 less per month than one located in a census tract where the median adult has completed the tenth grade; if owner-occupied, it will have a market value of $1,900 less. For owners, the lot-size and floor-area variables are statistically significant. The coefficients suggest that a 600-square-foot house can be purchased for $2,900 less than an otherwise identical 1200-square-foot house; a house on a 10,000-square-foot lot would cost $4,300 more than an identical unit located on a 5000-square-foot lot. Of those variables specific to the renter model, three of the dummy variables representing structure type are significant, as well as three of the contract rent corrections. For renters, duration of occupancy and whether or not the owner lives in the building are also highly significant. Although the regression coefficient for the duration-of-occupancy variable is small-only 27 cents per year of occupancy-it is highly significant. It is likely that this small difference measures a lagged adjustment of monthly rent. Landlords are less likely to raise rents when their properties are occupied by stable tenants than when the properties change occupancy. A different landlord-tenant interaction may be responsible for the larger and highly significant coefficient of the owner-in-building variable. The lower rents for units with resident landlords may result either from less sophistication and professionalism on the part of these smaller operators, or they may be due to different policies for selecting tenants. When the owner lives on the property, he may select tenants more carefully to achieve lower vacancy rates and lower

540

Journal of the American Statistical Association, June 1970

maintenance and repair costs. The critical impact of these factors on the profitability of rental properties has been emphasized in other studies [17, 261. The findings also suggest that standardized dwelling units located inside the ghetto may be somewhat more expensive than those outside, a finding consistent with Ridker and Henning's study of St. Louis and with other investigations of housing market discrimination. The coefficient for racial composition is statistically significant a t the five percent level in the rental equation and is approximately equal to its standard error in the owner equation. Taken a t face value the coefficient in the renter (owner) model indicates that a comparable unit in an "all-white" area would cost eight percent (five percent) less than one located in an "all-black" area. Although the ghetto markups indicated by estimates in Table 2 are consistent with most studies of housing market discrimination, serious questions may be raised about the specifications used for both the owner and rental models [8, 17, 19, 23, 24). If housing market discrimination exists, it is doubtful that its effects can be represented merely by an intercept shift. The phenomenon may be far more complex-with discrimination more or less strongly evident in various submarlrets defined by quality and structure type [lo]. To test one such hypothesis, separate equations were estimated for rental units located inside and outside the ghetto. When the coefficients of these stratified models were applied to the mean values of the explanatory variables for units in the two submarkets, the results indicated that the average ghetto unit would rent for about two percent less in all-white city neighborhoods, but the average nonghetto unit would rent for ten percent more in the ghetto. Moreover, as we have shown in another article, price discrimination may be only one of the adverse consequences of housing market discrimination [14]. The virtual unavailability of certain kinds of housing inside the ghetto and the difficulties Negroes experience in obtaining housing outside the ghetto a t any price may be more important. I n evaluating these results, it should also be remembered that the equations in Table 1 are estimated for city dwelling units only. Yet it is clear that for most households, particularly whites, the relevant housing market is the entire metropolitan area. The accessibility measure, miles from the CBD, is insignificant for both tenure types.4 This result is a t variance with most economic theories of residential location, which would predict the price of a standardized bundle of residential services to decline with distance from the city center [I, 7, 9, 11, 15, 17, 18, 271. The fault could be inadequate standardization, improper specification of the equations, the measure of accessibility used, or existing theories that fail to consider effects of such important factors as stocks or housing market discrimination. The results obtained for the school-quality and crime variables are somewhat disappointing, but hardly surprising. Stronger school and crime effects might have been anticipated given the frequent references to school quality and An employment-accessibility index (based on auto driving times), obtained from the EaseWest Gateway Transportation Study, was also used with no better results.

Measuring the Value of Housing Quality

54 1

crime in discussions of how households make residential choices and how the urban housing market operates [21]. For several reasons, part of the influence of better schools on value may be represented by the residential-quality variables. Mean school achievement is highly correlated with the indexes of residential quality. There is reason to believe that school quality is measured with considerable error. If so, the residential variables may be proxying the effects of school quality [6]. Moreover, if better schools attract higher income households, who spend more on housing maintenance, part of these measured effects of residential quality are logically the result of school quality. Further evidence of the effect of school quality on monthly rents was obtained by estimating separate regressions for properties located inside and outside the ghetto. Ghetto schools are uniformly bad. The standard deviation of school quality is only half as large for rental properties in the ghetto as for those located outside the ghetto. It is not surprising, therefore, that an insignificant school-quality coefficient was obtained in a separate ghetto regression, while the coefficient in the nonghetto stratification was larger ($5.05 versus $2.63 per month) than that obtained for the entire rental sample. Measurement problems are even more acute in obtaining an adequate measure of neighborhood public safety. Including a neighborhood crime index in the model is more a statement of good intentions than any serious effort to come to grips with the conceptual and measurement problems of defining a neighborhood's perceived safety. The index of neighborhood crime used in the analysis is also highly correlated with the indexes of residential quality. A final reason for anticipating weak school and crime effects is that the sample was restricted to the city of St. Louis. The largest variation in school quality and level of criminal activity is found not within the city but rather between the city of St. Louis and its suburbs. 4. EXPANDING THE SAMPLE

Although the data and the empirical results represent a significant improvement over previous studies, the analysis is deficient in several important respects. Perhaps its most serious shortcoming is the lack of information on suburban alternatives. For most households the relevant housing market is the entire region, and much of the variation in the bundles of residential services is in the suburban part of the market. Legal and budget limitations on the data collection program precluded a large-scale sample of suburban households; however, nearly comparable data were obtained for 26 suburban rental units and 136 suburban owner-occupied, single-family units. These observations differ from those used in estimating the city equations in only two respects; no information was available on school quality or neighborhood crime. These omissions are particularly unfortunate since, as noted previously, variation in these services between the central city and the suburbs is probably far greater than variation within the city.*Even so, the small increment to the sample appears to add appreciably to the sample information. Table 3 shows the renter model for the entire sample of central-city and

Journal of the American Statistical Association, June 1970

542

Table 3. REGRESSION EQUATIONS FOR RENTER MODEL WITH

SUBUXBAN OBSERVATIONS, SCHOOL AND CRIME VARIABLES DELETED

-

Variable

Including St. I,o~ria L'ounty

-

City only

Basic residential quality Dwelling unit quality Quality of proximate properties Nonresidential usage Average structure quality Proportion white in census tract Median schooling of adult,s in cellsus tract Age of structure Number of rooms ( n a t l ~ r alog) l Number of bathrooms Parcel area (hundreds of sq. f t . ) Single detached Duplex Row Apartment Rooming house Flat No heat included in rent No water included in rent No major appliances included i r l rerlt No furniture included in rent Hot water Central heat D u ~ a t i o nof occuparicy (years) Owner in building Niles from CBD County dummy Constant

R2 Observations

" Significant a t

.05 level. Significant a t .O1 level. NOTE: Wit11 the exception of the dummy variable. for structure type, the relevant tests are one-tailed.

suburball units. The variables for school achievement and neighborhood criniirlal activity are deleted, and the variable "distance from CBD" had been replaced by a dummy variable with a value of 1 for the county observat i o n ~ For . ~ comparison, the table also shows the coefficients for the city renter model when the school and crime variables are deleted. The most striking difference when the model is reestiniated for the entire metropolitan area is the increase in the significance of the coefficients. Of the 25 variables conlmon to both specifications of the renter model, 21 have larger t-values. illoreover, both the rrlagnitude and the significarlce of the quality variables' coefficients are greater for the more representative sample. When the crime and school variables are deleted from the city model, the magnitude and significance of the quality variables similarly increa~es.Thi:, i11dicate;lthat there j .As in the previous nlodr,ls, several auteaccessibility indexes were tested with reuults 110 better than those reported above.

Measuring the Value of Housing Quality Table 4.

543

REGRESSION EQUATIONS FOR OWNER MODEL WITH SUBURBAN OBSERVATIONS, SCHOOL AND CRIME VARIABLES DELETED

Including St. Louis County

Variable

City only

Basic residential quality Dwelling unit quality Quality of proximate properties Nonresidential usage Average structure q ~ ~ a l i t p Proportion n-hite in census tract Median schooling of adults in census tract, Age of structure N~imberof rooms (natural log) Number of bathrooms Parcel area (hundreds of sq. ft.) First floor area (hundreds of sq. ft.) hliles from central business district County dummy Constant

R2

077

Observations

0 7:3 275

411 --

S~gnificanta t .05 level. Sigmficant at .0l level. NOTE: I U relevant tests are

.--- -.

- .

-

one-tailed.

is some interrelationship between the five indexes of residential quality and the level of these public services within the city.6 Aside from the differences in the coefficients of the quality variables, the largest changes in regression coefficients are observed for the racial-composition variable. These changes in the magnitudes of the regression coefficients indicate that dm-ellingunits in the ghetto are somewhat more expensive than other units when differences in public services are accounted for. However, this measured price difference between ghetto and nonghetto units disappears when the differences in the quality of schools and other services are not acrounted for. When the owner models are reestimated incorporating the 136 county observations, similar results are obtained. Estiniates of the semi-log value model for the city and for the larger sample are presented in Table 4. I n both the linear and semi-logarithmic forms, the t-values and the magnitude of the quality variables increase when the county observations are added. The significance of all seven remaining variables common to both equations also increases. 5. QUANTITY-QUALITY RELATIONSHIPS

One important difference between the renter and owner models described previously is the way in which residential quality and dwelling-unit size are interrelated. I n the renter models, total monthly rent is computed by simply Further analysis and discussion of this interrelationsl~ipis contained in 1121.

Journal of the American Statistical Association, June 1970

544

adding premiums for higher residential quality to payments for the dwelling units' objective characteristics. This specification assumes that the premium for residential quality is the same regardless of dwelling unit size. The semi-log specification used for owner models is only slightly more flexible. It requires that the premium for higher quality be proportional to the payment for size (number of rooms). The market values of owner-occupied units of various sizes a t different quality levels are illustrated in Figure 1. With the remaining variables evaluated a t their sample means, a four-room unit one standard deviation better than average in terms of basic residential and Figure 7 .

VALUE OF OWNER-OCCUPIED HOMES AT AlTERNATlVE

LEVELS OF QUALITY AND SIZE

NUMBER OF

ROOMS

dwelling unit quality (i.e., index values of 1.0 versus index values of zero) costs $2,100 more than one of average quality. For a nine-room unit, the extra quality costs about $2,500 more. This incremental payment for higher quality is the same proportion, approximately 22 percent, of the payment for dwelling-unit size. These features of both the renter and owner models are disquieting. Although it seems plausible that the premium for higher quality should increase as dwelling-unit size increases, there is no persuasive reason why it should be a constant fraction of payments for dwelling-unit size. The constant payment for quality regardless of size is even less satisfactory. To test other hypotheses about the interrelation between payments for quantity and for quality, several alternative specifications were estimated in which additional terms were included to represent the joint effect of quality and quantity on monthly rent or market value. I n general, the resulting estimates were almost indistinguishable from the simpler linear and semi-log-

545

Measuring the Value of Housing Quality

arithmic models. The coefficients of the remaining variables were virtually the same for a11 of these alternative specifications. To illustrate these alternative specifications, the renter model for the entire sample (Table 3), summarized in (5.1), was reestimated to include variables representing the joint effects of the quality variables and the size (number of rooms) of the units. The alternative estimate, summarized in (5.2), includes two interaction terms: the product of the logarithm of the number of rooms (log R) with the Basic Residential Quality index (BRQ) and with the Dwelling Unit Quality (DUQ) index. Because the quality indexes have mean values of zero and admit negative values, a constant was added to the index scores.

V

=

$32.93 f $8.48 BRQ f $5.14 DUQ

+ $25.00 log R

R2 = .7503 V = $28.77 - $0.51 BRQ - $1.49 DUQ - $6.03 log R

4- $6.91[(BRQ f 3.00) slog R] + $4.78 [(DUQ

(5.1)

(5.2)

+ 3.00) .log R]

R2 = -7606 The regression coefficients of all other variables, represented by the constant terms, are within ten percent of those shown in Table 3, and R 2 is about one percent larger. The t-values for the coefficients of the interaction variables are 4.04 and 2.86, respectively; the t-values of the other three coefficients in (5.2) are considerably smaller than 1.0. Thus, the more elaborate specification fits the data only marginally better than the simple additive one. Nevertheless, it represents a substantially different relationship between quantity and quality. The premium for higher quality units increases with the size of the dwelling-unit; it is not proportional to the payment for dwelling-unit size. For example, according to (5.2), the difference between the cost of a three-room unit with basic residential and dwelling unit quality one standard deviation better than average (i.e., index values of 1.00) and the cost of an average-quality unit (index values of 0.00) of the same size is $10.85. For a five-room unit, the difference in monthly rent a t comparable quality Ievels is $16.89. The simple additive specification indicates that the same quality premium is $13.62 regardless of dwelling-unit size. Figure 2 illustrates monthly rent of dwelling units of various sizes a t different levels of quality for both formulations of the model (assuming average values for the remaining explanatory variables). Within the range of data used in this analysis, there is little basis for choosing among these alternative specifications empirically. A priori, i t might be argued that the second specification is more reasonable, but even within the limits of the fairly substantial data base used here, the simple additive specification performs about as well. Understanding the nature of the urban housing market requires a better grasp of these kinds of interrelationships. The difficulty of establishing which model is more "correct" merely illustrates the urgent need for performing similar analyses for larger and more representative samples of data.

Journal of the American Statistical Association, June 1970

Figure 2.

MONTHLY RENT AT ALTERNATIVE LEVELS O F QUALITY AND SIZE P 0+

/

4 0 0 0

- Additive Specification

I

------ Multiplicative Specification

NUMBER OF ROOMS 6. CONCLUSION

This article clearly illustrates the complexity of the bundle of residential services consumed by households and, by implication, the inadequacy of so much previous empirical and theoretical work on urban housing markets. Moreover, it clearly indicates the value of more complete bodies of survey data in developing a better understanding of housing markets. The research findings emphasize the complexity of the bundle of residential services and the importance of residential quality. The quality of a bundle of residential services has at least as much effect on its price as such quantitative aspects as number of rooms, number of bathrooms, and lot size. For example, the monthly rent of a dwelling unit one standard deviation larger than average

Measuring the Value of Housing Quality

547

as measured by number of rooms, number of bathrooms, and lot size, is about $16 more than that of an average unit. On the other hand, the additional rent for a unit one standard deviation better than average in basic residential quality and dwelling unit quality is more than $13. The article also provides some weak confirmation of the influence of neighborhood schools on the value of residential properties and indicates that rental properties in the ghetto may be more expensive than those in all-white areas. I n these and other respects, the research is hampered by the inadequate sample of suburban properties. Thus, though this analysis represents a substantial improvement over previous studies, the development of truly useful models will require collecting still larger and more extensive bodies of data. I n particular, examination of the entire metropolitan housing market is crucial. REFERENCES [I] Alonso, William, Location and Land Use, Cambridge: Harvard University Press, 1964. [2] American Public Health Association, Committee on the Hygiene of Housing, An Appraisal Method for Measuring The Quality of Housing, P a r t 1, New York, 1945. [dl Bailey, Martin J. and Muth, Richard F., "A Regression Method for Real Estate Price Index Construction," Journal of the American Statistical Association, 58 (1963), 933-42. [4] Brigham, Eugene F., "The Determinants of Residential Land Vr~lues,"Land Economics, 41 (1965), 325-34. [5] Griliches, Zvi, "Hedonic Price Indexes Revisited: Some Notes on the State of the Art," 1967 Business and Economics Statistics Section Proceedings of the American Statistical Association, 1967. [6] Hanushek, Eric A. and Kain, John F., "On the Value of Equality of Educational Opportunity as a Guide to Public Policy," in Frederick Mosteller and Daniel P. Moynihan, eds., On Equality of Educational Opportunity, New Yorlr: Random House, 1970 (forthcoming). [7] Harris, R. N. S., Tolley, G. S., and Harrell, C., "The Residence Site Choice," Review of Economics and Statistics, 50 (1968), 241-7. [8] Haugen, Robert A. and Heins, A. Jones, "A Market Separation Theory of Rent Differentials in Metropolitan Areas," The Quarterly Journal of Economics, November 1969, 660-72. [9] Hoover, Edgar M. and Vernon, Raymond, Anatomy of a Metropolis, Cambridge: Harvard University Press, 1959. [lo] Kain, John F., "Effect of Housing Market Segregation on Urban Development," 1969 Conference Proceedings, United States Savings and Loan League, Chicago, May 7-9, 1969. [Ill , ('The Journey-to-Work as a Determinant of Residential Location," Papers and Proceedings of the Regional Science Association, 9 (1962), 137-51. , and Quigley, John M., "Evaluating the Quality of the Residential Environ[I21 ment," Environment and Planning, 2 (1969). , "Measuring the Quality and Cost of Housing Services," Harvard Program on 1131 Regional and Urban Economics, Discussion Paper No. 54, July 1969. 1141 , "Housing Market Discrimination, Homeownership, and Savings Behavior," Harvard Program o n Regional and Urban Economics, Discussion Paper No. 58, January 1970. [15] Mills, Edwin S., ('An Aggregative Model of Resource Allocation in a Metropolitan Area," American Economic Review, May 1967, 197-211. I161 Musgrave, John C., "The Measurement of Price Changes in Construction," Journal of the American Statistical Association, 64 (1969), 771-86.

548

Journal of the American Statistical Association, June 1970

1171 Muth, Richard F., Cities and HousCng, Chicago: University of Chicago Press, 1969. 1181 , "Economic Change and Rural-Urban Conversations," Econo?netrica, 29 (1961), 1-23. 1191 , "The Variation of Population Density and its Components in South Chicago," Papers and Proceedings of the Regional Science Association, 15 (1965), 173-83. [20] Nourse, Hugh O., "The Effect of Air Pollution on House Values," Land Economics, 43 (1967), 181-9. [21] Oates, Wallace E., "The Effects of Property Taxes and Property Values: An Empirical Study of Tax Capitalization and the Tiebout Hypothesis," Journal of Political Economy, 77 (1969), 957-71. 1221 Pendleton, W. C., "The Value of Highway Accessibility," Unpublished Ph.D. dissertation, Department of Economics, University of Chicago, 1962. [23] Rapkin, Chester, "Price Discriminat,ion Against Negroes in the Rental Housing hfarket," in Essays i n Urban Land Economics, Los Angeles: Real Estate Research Program, University of California, 1966, 333-45. 1241 Ridker, Ronald G. and Henning, John A., "The Determinants of Residential Property Values with Special References to Air Pollution," The Review of Economics and Statistics, 49 (1967), 246-57. 1251 St. Louis City Plan Commission, by Alan M. Voorhees and Associates, Inc., Technical Report: Residential Blight Analysis, McLean, Va., 1969). [26] Sternlieb, George, The Tenement Landlord, New Brunswick: Urban Studies Center, Rutgers, The State University, 1966. 1271 Wingo, Lowdon, Jr., Transportation and Urban Land, Washington, D. C.: Resources for the Future, Inc., 1961.