Intraurban variation in the price of housing

JOURNAL

OF

URRAN

ECONOMICS

lntraurban

6,

464-479

Variation

in the

Experiment

Received

August

Price

R.

JACKSOS~

Station,

Georgia

Institute

1, 1977;

revised

January

JEERY Engineering

( 1979)

of Housing

of Technology 3, 1978

Theoretical models of spatial consumer behavior assume the existence of a housing price surface that increases with accessibility. It is often hypothesized that inadequate accessibility measures are responsible for the failure of most empirical studies to support this premise. A general accessibility measure consisting of a double power series in Cartesian coordinates is developed and shown to represent a general formulation of traditional accessibility measures. This formulation is incorporated in a hedonic price regression model, and the model is estimated using census tract data for the city of Milwaukee. The hedonic prices are then used to construct intraurban housing price indexes. The results of this study provide strong support for the existence of the presumed price surface. A comparison of this new hedonic price model with traditional models suggests that the double power series formulation is a superior representation of accessibility.

Theoretical models of spatial consumer behavior have been widely used tp study the structure of the urban economy and to explore the spatial implications of congestion, pollution, and many other contemporary urban problems (see, for example, [la, 13, 17, 18-J). Spatial equilibrium in these models is based on the premise that housing price varies directly with accessibility.2 Furthermore, a stable solution requires that price increase at an increasing rate with accessibility. The existence of such a price gradient has implications not only for the usefulness of these theoretical models but also for the resolution of many pract’ical policy issues. For example, the theoretical models suggest t(hat observed blackwhite rent differentials may exist in part because of the more accessible 1 I am indebted to Roger Blair, David Kaserman, Jerry Milliman, John Sturrock, and John Trimble for helpful comments on previous drafts of this paper. 2 Although theoretical models traditionally consider only workplace accessibility, all important trip destinations contribute to the accessibility advantage of any site. The term accessibility, as used in this study, refers to the locational advantage created by all trip destinations. 464 0094-1190/79/040464-16$02.00/O Copyright All rights

0 1979 by Academic Press, of reproduction in any form

Inc. reserved.

VARIATION

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HOI’SINC

465

location of black housing. If so, t’he portion of observed black-white rent differentials attributable to discrimination can be determined only by netting out the accessibility-related housing price differential. A review of previous empirical studies provides no consensus on the magnitude or even the existence of intraurban housing price variat’ion. Occasionally results are reported suggesting considerable price variation, [S, 91.” More often, however, empirical studies fail to find a statjistically significant relationship between accessibility and price [5, 7, 11, 14, 151. Several recent studies have even reported statistically significant accessibility influences of the wrong sign [l, 31. These conflicting results are often att’ributed to the inadequacy of traditional accessibility measures. The purpose of this study is to develop a general measure of accessibility and to apply this measure in an empirical study of intraurban housing price variation. The results suggest that frequently used accessibility measures are inadequate and that sizeable variation in housing prices does occur within the urban housing market. The remainder of this paper is organized as follows. Section I develops a new hedonic regression model that differs from t’raditional models by incorporating a double power series to represent accessibility. Estimation results are presented and intraurban housing price indexes are developed for the city of Milwaukee in the second and third sections. A brief comparison of the power series and traditional hedonic price regression results in Sect’ion IV supports the hypothesis of traditional accessibility measure inadequacies. Section V summarizes the analysis. I. A NEW

HEDONIC REGRESSION OF URBAN RENTS

MODEL

A hedonic price regression model is used in t’his section to isolate the influence of accessibility on the price of housing in Milwaukee. The model estimated here differs from existing hedonic regression models of the housing market in that a new, more general functional form is used to represent accessibility. Traditional accessibility measures based on distance to the central business district (CBD) or distance to work centers weighted by employment (accessibility indexes) are likely to provide disappointing results in most housing market applications. Accessibility is determined by the spatial distribution of work places, shopping centers, schools, and other trip destinations as well as the transportation network. Although one might expect an underlying trend in the accessibilit’y surface to exist, 3 This study focuses on accessibility-related variations in the price of housing services ; consequently, variations in dwelling-unit and neighborhood attributes influence the quantity of housing services and not the price.

466

JERRY

R. JACKSON

empirical specification of such a trend is difficult because complex interacts to determine the accessibility of any location. The accessibility trend can be represented as

A = f(X, Y>,

forces

(1)

where X and Y are Cartesian coordinates. (1) represents the empirical relationship between accessibility and location. If the function, f, were known, one could determine the level of accessibility at location (Xi, YJ by evaluating the accessibility functionf(X;, YJ. Under this specification, effects of all important accessibility influences (i.e., the distribution of workplace, shopping, school location, etc.) are implicitly captured in the function, f. This general specification of the empirical relationship between location and accessibility forms the basis for the accessibility measure employed in this study. To implement this approach, we take a Taylor series expansion of f(X, Y) around the midpoint of the Cartesian coordinate system. This yields A = f(X,

Y) = ~0.0 + ul,oX + uo,lY + al,lXY

+

u2,0X2

+

uo,2Y2

+. . . + u,,,oX” + uo,nYn + R, = 2 2 uk ixkYj k-0 j-0 ’ + RR, k + j 6 11, (2) where a’s represent the function and its partial derivatives evaluated at (0, 0), n represents t’he polynomial degree, and R, is a remainder. The remainder exists because it may not be possible to transform f(X, Y) exactly into an nth degree polynomial form.4 The general form of t’he hedonic price regression model estimat’ed in the next sect,ion is

R = b, + blX + b,N + ba(A)L + u,

(3

where R is monthly rent, X and N represent vectors of structure and neighborhood characteristics, and L is quantity of land; bl and b2 represent hedonic price vectors of structure and neighborhood attributes, &(A) represents the price of land as a function of accessibility, and u is a stochastic disturbance term. According to this specification, hedonic prices of structure and neighborhood characteristics are considered spatially constant ; however, the price of land varies spatially as a result of demand for more accessible sites. This model formulation is consistent with theories of urban land value which hold that accessibility advantages 4 The double This technique for a bibliography

power series representation of a surface is called trend surface analysis. has been used extensively in geology. See Krumbein and Graybill [lo] and survey of trend surface analysis.

VARIATION

IN

THE

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OF

467

HOUSIXG

are capitalized in the land price. Under this specificat’ion, the contribution of accessibility to dwelling unit rent is directly related to the quantit’y of land and is not treated as a lump sum.5 The funct.ional dependence of land price on accessibility and the double power series represent’ation of accessibilit’y yields a double power series representation of land price.6 Thus, the polynomial hedonic price regression model can be written as R = 6, + blS + bzN + 5 k=l

II.

ESTIMATION PRICE

2 a!+Xkyj.L

-k %

lc+j
j=l

OF THE POLYNOMIAL REGRESSION MODEL

(4)

HEDONIC

The coefficients of the hedonic regression model, (4), are estimated for the city of Milwaukee using census tract data as the basic unit of observation. Variables included in the regression model are identified in in Table 1. Average census tract’ rent’, AVRENT, is defined as AVRENT

=

0.012.MV.m

+ R.n

m + n

2

(3

where MV and R are median census tract dwelling unit value and rent, respectively ; m is the number of owner-occupied dwelling units and n is the number of rental units in the census tract 0.012 is a conversion factor used to impute rent from dwelling unit value.’ 5 The issue addressed here relates to the manner in which accessibility affects per unit land values. If the accessibility influence depends on the size of the lot, then the interaction specification given in (3) is preferred. If, on the other hand, accessibility influences the value of residential lots regardless of lot size, then a lump-sum treatment is appropriate. King [S] describes the rather naive implications of the lump sum accessibility specification. The choice between interaction and lump-sum specifications for neighborhood effects is less clear cut. A rather detailed examination by Kain and Quigley [7], however, suggests the lump-sum treatment in (3). 6 The general function dependence of 63 on A can be represented as a Taylor series approximation so that

63(A) = aa + cd + azAZ + asA +

. . + anA” + R,,

(7)

terms are defined as before. Substituting the polynomial form of A in (2) for each in (7) and collecting terms yields an expression similar in form to (2). 7 This value for the conversion factor was derived from estimates provided by Shelton’s [16] study on the relationship between rent and dwelling unit value. It is not generally recognized that an inappropriate value-rent conversion factor in the traditional rent measure, (5), may bias the estimated hedonic prices. The extent of the bias depends on the size of the factor error and the correlation between each attribute and MTr. (I-PRENT). Experiments with other values of the conversion factor (including the commonly quoted rule-of-thumb, 0.01) indicate a possible problem only for our where

A term

468

JERRY R. JACKSON

Four variables are used to capture the variation in rent caused by variations in the structural characteristics of dwelling units. hIDRMS and PGTIBATH measure the size of the dwelling unit. Both variables should be positively related to housing expenditure. AVGAGE reflects the obsolescenceof dwelling units. PBLT40 is included to reflect technical change such as new heating and cooling systems which were not available when older units were constructed. The signs of coefficients on AVGAGE and PBLT40 are expect’ed to be negative. Neighborhood characteristics encompass attributes which influence the rent of dwelling units but are not related to accessibility or the structure. Three binary variables are included in the regression model to capture the influence of neighborhood racial composition. The coefficient on WBOUND is expected to be negat’ive reflecting whites’ desires to live in all-white neighborhoods.* Coefficients on BBOUND and BINT are also expected to be negative reflecting the excess supply of black housing resulting from a large white outmigration [S]. The relative magnitude of negative coefficients on BBOUND and BINT is uncertain. If a black preference for integrated neighborhoods predominates, rents should be greater in black boundary census tracts (BBOUND) ; on the other hand, t’he social flux accompanying a transition neighborhood may result in a rent premium for locations in the black interior (BITT). The next four neighborhood characteristics can be considered nuisance and employment cent’er externalities. PEXPWAY and PRAIL are calculated by dividing linear dist’ance of express\vay and railroad routes in each census tract by the census tract land area. Rail and expressway influences are expected to negatively affect rents primarily because of the associated noise pollution. The air pollution variable, PAR70, is a measure of the concent’ration of part’iculate matter for 1970. EMPD2 is total manufacturing employment, in t’housands, in plants of over 100 employees located within a a-mile radius of the midpoint of the census tract. This variable is included to represent the disamenities which accompany proximity to employment centers. PAR70 and EhIPD2 are expected to negatively influence rent. The remaining neighborhood variables in Table 1 reflect the social character of each census tract. TRANG is the number of households who have moved to exist’ing homes in the census tract from 1965 to 1970 estimate of consumer valuation of PRENT, the percent of renters residing in the census tract. In particular, reasonable values of the conversion factor yield coeflicients on the accessibility terms that vary only in the third significant decimal place. Since our conclusions and results are focused on the influence of accessibility, this potential problem can be ignored. 8 This specification is suggested by the “customer preference” hypothesis of racial housing price differences. See King and hlieskowski [9] for a review of this and other hypotheses which attempt to explain race-related price differentials.

VARIATION

IN THE

PRICE

OF HOUSING

TABLE 1 Hedonic Index Variable Definition Variable variable AVRENT Structure characteristics MDRMS AVGAGE PGTIBATH PBLT40

469

.-__-

Description

Source

Dependent

Neighborhood characteristics WBOUND BBOUND BINT PEXPWAY PRAIL PAR70 EMPDZ TRANG PINMIG PPMEQ PRENT Land characteristics AVLS AVLS*X AVLS*Y AVLS*Y4

Average census tract rent Median Average Percent Percent

1

roomsa age of housing units of units with more than one bath of units built before 1940

Binary variable designating >50/0 and 6 33% black Binary variable designating >33yo and 6 90% black Binary variable designationg >90% black Expressway distance divided by land area Rail distance divided by land area Suspended particulates for midpoint of census tract Employment within a 2 mile radius Percent of population moved in last 5 years Percent of population moved from outside SMSA in last 5 years Neighborhood homogeneity measure Percent of housing units being rented

1 1 1 2, 3 2, 3 4 5, 6 1 1 1 1

Average lot size Average lot size and location interaction term Average lot size and location interaction term

2, 3 2, 3

Average lot size and location interaction term

2, 3

2, 3

a Unless noted otherwise variables refer to census tract values. Sources. 1 U.S. Bureau of the Census, Census of Population and Housing: 1970, Census Tract, Final Report PHC(l)-131, Milwaukee, Wisconsin SMSA. * Census Tract Map, issued with source 1. 3 Mobile Travel Map, Rand McNally and Company, 1974 edition. 4 Prospectus for a Regional Air Quality Maintenance Planning Program, Southeastern Wisconsin Regional Planning Commission, 1974 (preliminary version). 5 ClassiJied Directory of Wisconsin Manufacturers, 1970, Milwaukee, Wisconsin Manufacturers Association. 6 Unemployment Compensation Employers by Location and Type of Business, March 1970, Wisconsin Department of Industry, Labor and Human Relations, State of Wisconsin.

470

JERRY

R. JACKSON

divided by the number of existing homes. This variable measures social st’ability of the neighborhood. il neighborhood characterized by a large portion of transient,s is expected to negatively influence rents. PINRIIG is the percent of the census tract population who have moved to the census tract from outside t’he SMSA in t#he preceding 5 years. This variable is included to capture t’he rent inflation in areas attractive t,o inmigrants. A neighborhood social homogeneity variable (PPMEQ) is constructed by calculating the squared difference between the percent of labor force engaged in professional and managerial occupations for the census tract and the Milwaukee average of 17.75. The value of this variable increases as t’he neighborhood becomes more homogeneous; a positive influence on rent is expected. PRENT is the percent’ of census tract dwelling units which are rented. Analyses by Sweeny [19] and others leads us to expect a negative coefficient on PRENT. Local public services such as school qualit,y, fire protection, and police protection are not included in the hedonic equation because the study area incorporates only one municipalit#y.g The influence of these effects is, therefore, captured in the intercept. Residential land area in each census tract is derived by measuring total land area from the 1970 SMSA census t’ract’ map and subtracting nonresidential land area est’imated from land-use maps. AVLS is determined by dividing residential land area by number of housing unit’s. AVLS and the remaining explanatory variables in Table 1 represent the lot sizcaccessibility interaction terms. A number of t#he original 218 Mil\vaukee census tract,s had to be eliminated from the sample because of problems encountered in constructing AVLS. The estimation of residential land area was particularly subject to error in sparsely populated census tracts and tract’s wit#h a large amount of manufacturing activity. After eliminating census tracts for which it was impossible accurately t’o estimate resident,ial land area, 147 observations remained in the sample. An understanding of the geomet’ric interpretation of the power series polynomial is helpful in selecting the appropriate degree of the approximating polynomial. The value of the polynomial can be visualized as t,he height of a surface above the point (X, Y). If the land-price surface (i.e., &(A)) can be closely approximated by a plane, then the planar representation of the polynomial (the first three terms given in (2)) should be used in the regression model. A quadrat’ic approximation (the first six terms of (2)) represents a surface with a single maximum value for accessibility. More complex surfaces with multiple peaks can be repre9 It is assumed that different provision of these services.

parts

of PIIilwaukcc

are not discriminated

against

in the

VARIATION

IN

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PRICE

OF

HOl‘SIh-IG

471

sented by increasing the degree of the approximating polynomial. Since the maximum number of extrema which can be represented by cubic, quartic, and quintic polynomials are 4, 9, and 16 respectively, one should be able to represent most accessibility surfaces satisfactorily without having to include an unmanageable number of polynomial terms.‘” The model was estimated using quadratic, cubic, quartic, and quintic accessibility polynomials. Two crit,eria were used to determine the preferred degree of the polynomial used to approximate accessibility. The first consist,s of examining regression models of different polynomial degrees to determine the point at’ which the change in the sum of squares due to the regression indicates that additional polynomial terms do not add significantly to the explanatory power of the model. The F-statistic for differences in proceeding from a first to second degree equahion, from a second to a third and so on indicates t’hat the fourt’h degree model is preferred. The second criterion used t,o determine the accessibility polynomial degree is examination of the residuals for spat’ial autocorrelation. Residuals may display discernable spa&l patterns either because of specification error or because the regression model should have an aut80regressive structure. l1 If a polynomial of too low degree is est’imated, this misspecification can be expected to result’ in spatial autocorrelation of the residuals. If spat’ial autocorrelation appears when the F test described above indicates stopping the search, it is prudent to estimate models of several higher degrees. If however spatial autocorrelation disa,ppears at the same time that the F test indicates the insignificance of added polynomial terms, it is reasonable t#o stop t’he search for a satisfact’ory approximating polynomial. Residual maps were examined visually for discernable spatial patterns. Although statistics for testing for the presence of spatial autocorrelation have been developed, their application is difficult and much less meaningful when applied to irregularly spaced dat,a. Our examination of residuals indicates that moving from a third to fourth degree model removes the presence of discernable spatial autocorrelation. The coefficients of t,he preferred quartic polynomial regression model are presented in Table 2. Except for the coefficient of TRANG, which is not significantly different from zero at a 5y0 significance level, all of t’he coefficient,s for structure and neighborhood variables are of the expected sign. Coefficients on PGTIBATH and PBLT40, the only structural attributes that demonstrate a significant influence on monthly rent, lo The number of terms required by the second through 6, 10, 15, and 21 respectively. I1 See Fisher [4] for an example of a spatial autoregressive [2] for a discussion of spatial autocorrelation.

fifth

degree

model.

polynomial See Cliff

are

and Ord

JERRY

472

R. JACKSON TABLE

Hedonic

Price

2

Regression

Equation

Variable

Coefficient

t-Value

Variable

Coefficient

C MDRMS AVGAGE PGTIBATH PBLT40 WBOUND BBOUND BINT PEXPWAY PRAIL PAR70 EMPD2 TRANG PINMIG PPMEQ PRENT R= = 0.9683 Standard error

209.86 2.100 -0.4376 1.020* -0.3612* - 14.996 -34.63b -21.71* -2643a -328.5 - 1.473 -0.6703b 25.97 1.376b 0.02828 -1.226*

6.97 0.6626 0.9444 5.427 2.155 4.561 7.513 4.259 1.951 0.3617 0.6911 3.171 1.503 5.776 1.764 8.813

AVLS AVLS*Y AVLS*X AVLS*YX AVLS*Y2 AVLS*X2 AVLS*Y3 AVLS*Y2X AVLS*YX2 AVLS*X3 L AVLS*Y=X= AVLS*YaX AVLS*XsY AVLS*Y* AVLS*X4

5.302* 0.09419 -1.002 0.1350 -0.1884* -0.4176” -0.001574 0.05428a 0.09359 0.1138 0.03102* 0.003971 0.005757 0.002629” 0.002085

of the regression

n,b = coefficient

estimates

t-Value 3.474 0.4192 1.929 1.124 2.578 2.062 0.2833 2.233 1.737 1.787 3.348 0.9638 0.4412 2.159 1.255

= 10.06

which

are significant

at the 0.05 and 0.01 level,

respectively.

indicate that estimated average census tract rents in Milwaukee vary by as much as $79 and $17 because of variation in dwelling unit size (PGTlBATH) and dwelling unit age (PBLT40) respectively.‘? Census tract variation in percent’ of units older t#han 30 years yields estimated rent variations of $35. The influence of neighborhood racial composit’ion causes estimated monthly rents to vary by as much as $35. The decline in rents observed as one moves from the white interior to the white boundary (WBOUND) and from the black interior (BINT) to the black boundary (BBOUND) is consistent with the findings of King and filieszkowski [9] in their detailed study of race-related differentials. The lower rent in black areas relative to white areas supports our hypot’hesis of an excess supply of black housing. An expressway influence (PEXPWAY) in t#he census t’ract cont’ributes to a rent variation of up to $59 while employment center externalities (EAIPD2) decrease estimated rents in our Milwaukee sample by as much as $22. The coefficient of PINJIIG indicates that rent inflation caused by inmigration may increase average census tract rents by as much as $85. Variat,ions in neighborhood social homogeneity result in 12 Average

census

tract

rent

(AVREKT)

is $144.

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rent differentials of up to $43. Finally, census t,ract variation in PRENT contribut’es to rent variations as high as $109. Alt’hough regression coefficients on RIDRMS, AVGAGE, PRAIL, PARiO, and TRANG were not significantly different from zero at the 957, confidence level, estimated coefficients represent plausible rent variation across Milwaukee census tracts. The coefficient’s of primary interest in this study are of t’he locat’ionaverage lot size interact.ion terms. Of the 15 polynomial coefficients, six are significantly different from zero at t,he 57c significance level and nine are significant at the 10% level. Unfortunat8ely, the polynomial accessibility model specified in this study prohibit,s t#he direct examination of the relationship between accessibility and the price of housing because accessibility influences arc reflected in the coefficient estimates of all of t’he polynomial t’erms. It, is relatively easy, however, to construct locational price indexes to measure the quantitative influence of accessibilit,y 011 the price of housing. III.

THE

RELATIVE

PRICE

OF HOUSING

SERVICES

The implicit prices from the hedonic regression equation derived in the last section can now be used to estimate the relative price of housing services for each census tract. Implicit prices of neighborhood and structural characteristics are considered spatially const’ant ; however, the price of land varies spatially as a result, of the demand for more accessible sites. Examinat#ion of the accessibility-related price of land, ha(A), reveals a plateau comprised of eleven contiguous census tracts in the western portion of Milwaukee which is suitable as a reference location. This 3-square-mile area represents t’he most accessible location in Milwaukee ; the eleven tract averages of attributes and land prices are used as base values in the construction of price indexes. Laspeyres and Paasche indexes were construct,ed for use in this study. While absolute values of the indexes differ, relative variations in the price surface were nearly identical. E’or simplicity we present the average of these two indexes in the contour map in Fig. 1. The price surface plateau is located in a fairly central location with respect to manufact’uring employment location (see Pig. 2). Prices drop off in all directions but increase again as one moves in a northeasterly direction approaching the University of Wisconsin-Milwaukee and the manufacturing center in northeastern >Iilwaukee. The contour lines appear to follow a fairly regular concentric pattern as predictled by the simple spatial theory of consumer behavior ; however, the distortion caused by uneven employment distribution and the express-

474

JERRY

R. JACKSON

MILWAUKEE

FIG.

1. Milwaukee

price

surface

contour

nmp.

way system is clearly evident. The heavy manufacturing activity in West Milwaukee pulls t’he cont80ur lines in that direction. The outermost contour line is nearly L-shaped as a result of the expressway that passes through Milwaukee on the South and West sides. High-speed expressway commut’ing makes many locations along the expressway equally desirable from an accessibility viewpoint’. The northern segment, of this outer contour line dips back toward the center of the city following t#he terminal stretch of expressway in that area. While the location of the CBD does appear to influence the price contours, the generally assumed predominance of t’he CBD location is certainly not’ evident. Figure 1 suggests considerable intraurban price variation. Areas approximat’ely 2 miles away from the high price plateau exhibit a price difference of about 5y0. ,4 variation of about 15% is indicated for census tracts locat,ed at the city boundaries. In terms of the mean 1970 monthly

VARIATION

IN

Milwaukee rent (AVRENT) $7.22 and $21.65. The pract’ical advant’age depends to a large extent’ variation exhibit#ed in Fig. 1. can be determined by test’ing Ho: against the alternative

THE

PRICE

OF

475

HOUSING

of $144 these rent differences

amount

of the double power series formulat’ion on the statistical significance of the price The significance of the spatial price variation the null hypothesis 2 l’s,& i=l

i=l

l’ibZi

= 1,

hypothesis

MILWAUKEE

to

COUNTY

FIG. 2. Milwaukee expressway system represents location of 1000 manufacturing

\

and jobs.

employment

locations.

Each

rectangle

JERRY

476

R. JACKSON

where Zi = land, neighborhood, and structural characteristics at’ t)he base location or alternative location depending on whether the Laspeyres or Paasche index is being tested ; Pib = price of characteristics at the base location; and Pi = price of characteristics at the current location. Rejection of the null hypothesis in favor of the alternative hypothesis indicates that the estimated price index is significantly different from 1, which is the base price of housing services. Substituting the hedonic regression equation (4) with current attribute prices in the numerat’or and base location prices in the denominator allows us to reformulate the null hypot,heses as a linear combination of regression coefficients. That is, Ho:

W’B

= 0,

where w’ = [o,o”‘o(x - x,)(YYb)(xY - &Yb)“‘(Y4 xb, Yb = base location Cartesian coordinates, and B = the full vector of hedonic prices.

-

17b4)],

The appropriate test statistic is calculated for each census tract [20, p. 138). Examination of these test statistics indicates that rent variation of more than about 3y0 is st#atistically significant at t’he 5y0 significance level.13 Approximately three-fourths of the land area of Milwaukee contains dwelling units whose prices differ significant’ly from t’he base locat’ion price. IV.

A CORII’ARISOIV TRADITIONAL

OF’ POLYKVOMIAI, MEASURES

AXD

The ability of traditional hedonic price regression models to capture the accessibility-related housing price variat’ion in Milwaukee has implications both for the value of the double power series accessibility specification and for the reconciliation of conflicting evidence on housing price variation. If the tradit’ional measures fail to successfully capture accessibility advantage of different locations in Milwaukee, then it can be argued that the double power series accessibility formulation appears to overcome the deficiencies in traditional measures and that conflicting evidence from past studies probably arises because of specification difficulties. la Paasche

and Lmpeyres

indexes

yield

identical

test statistics.

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Our best efforts at estimating (3) wit,h A represented by various transformations of distance to the central business district (DCBD) or by an accessibility index failed t’o provide acceptable empirical results.14 These traditional measures included DCBD, l/DCBD, log of DCBD, quadratic form in DCBD, and an accessibility index of form

A i = 5 Ei/dijy, j=l where

Ai = value of the index for location Ej = employment at’ locationj, d,j = distance from location i to.j,

i,

y = parameter of the index, and n = number of employment locations. The parameter, 7, was allowed to vary from 0.5 to 2.0 in increments of 0.5. All of these traditional measures resulted in either implausible relationships (e.g., positive rent gradients) or insignificant influences on rent. While only reestimation of a large number of exist’ing hedonic price regression models can conclusively demonstrate the superiority of our new general accessibility measure, the results of this analysis for Milwaukee strongly suggest that future hedonic price studies consider the double power series formulat’ion of accessibility. V. SUMMARY

,4ND

CONCLUSIONS

Theoretical models of spatial consumer behavior assume the existence of a housing price surface that increases at an increasing rate with accessibility. A review of existing empirical studies casts serious doubt on t#he validity of this assumption. It is often hypothesized that t.his lack of evidence results primarily from poor measures of accessibility used in these studies. A general accessibility measure is developed in this study and incorporated in a hedonic regression model. Accessibility is specified as an nth degree double power series in X and Y coordinates. Hedonic prices are then used to construct price indexes of the relative price of housing for different locations in Milwaukee. Analysis of the price surfaces indicates that considerable price variation does occur within urban housing markets. For Milwaukee, this variation is on the order of 15%. A test is developed to examine t’he statistical significance of this price variat’ion. The results of this test indicate that the price I4Space are available

limitations from

prohibited presentation the author on request.

of these

results

; detailed

regression

results

478

JERRY

R. JACKSON

indexes exhibit statistically significant variation when t’he price changes by about 3y0 from the reference value. The results of this study have implications for future theoretical and empirical research on the urban housing market. The empirical verification of the theoretically implied price gradient provides strong evidence on the existence of the presumed price surface. The success of the double power series accessibility specification in capturing accessibility rents along with the failure of traditional accessibility measures suggest t’hat this new formation represents a superior empirical representation of accessibility. REFEREXCES 1. Brian J. L. Berry, “Ghetto Expansion and Single-Family Housing Prices : Chicago, 1968-1972,” Journal of Urban Economics, 3,397-223 (1976). 2. Andrew D. Cliff and Keith Ord, 1973, Spatial Autocorrelation, London: Pion Limited. 3. Charles B. Daniels, “The Influence of Racial Segregation on Housing Prices,” Journal of Urban Economics, 2, 105-122 (1975). 4. Walter D. Fisher, “Econometric Estimation with Spat,ial Dependence,” Regional and Urban Economics, 1, 1940 (1971). “Determinants of Real Estate Values,” 5. D. M. Grether and Peter Mieszkowski, Journal of Urban Economics, 1, 127-146 (1974). 6. Robert A. Haugen and James Heins, “A Market Separation Theory of Rent DifferQuarterly Journal of Economics, 83, 660-672 entials in Metropolitan Areas,” (1969). 7. John J. Kain and John M. Quigley, “Measuring the Value of Housing Quality,” Journal of the American Statistical Association, 65, 532-548 (1970). 8. A. Thomas King, Property Taxes, Amenities, and Residential Land Vu&s (Cambridge: Ballinger Publishing Company (1973). 9. A. Thomas King and Peter Mieszkowski, “Racial Price Discrimination, Segregation, and the Price of Housing,” Journal of Political Economy, 81, 590-606 (1973). 10. W. C. Krumbein and F. A. Graybill, 1965, An Introduction to Statistical Models in Geology, New York : McGraw-Hill Book Co. 11. Victoria Lapham, “Do Blacks Pay hlore for Housing ?” Journal of Political Economy, 79, 1244-1257 (1971). 12. Richard F. Muth, Cities and Housing (Chicago: University of Chicago Press, 1969). 13. Yitzhak Oron, David Pines, and Eytan Sheshinksi, “Optimum vs. Equilibrium Land Use and Congestion Toll,” The Bell Journal of Economics and Management Science, 4, 619-636 (1973). 14. Henry 0. Pollakowski, “Local Public Services and Residential Choice,” Institute for Economic Research Discussion Paper Number 74-1, University of Washington, 1974. 15. Ronald G. Ridker and John A. Henning, “The Determinants of Residential Property Values with Special Reference to Air Pollution,” The Review of Economics and Statistics, 49, 246-257 (1967). 16. John P. Shelton, “The Cost of Renting Versus Owining a Home,” Land Economics, 44, 59-72 (1968).

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PRICE

OF

HOUSING

$79

17. Robert Solow, “Congestion Cost and the Use of Land for Streets,” 7% Ijell Journal of Economics and Manageme& Science, 4, 602-618 (1973). 18. James P. Bucker, “Transport Improvements, Commuting Costs, and Residential Location,” Journal of Urban Economics, 2, 123-143 (1975). 19. James L. Sweeny, ‘LHousing Unit Maintenance and Model of Tenure,” Journal of Economic Theory, 8, 111-138 (1974). 20. Henri Theil, Principles of Econometrics (h’ew York: John Wiley and Sons, Inc., 1971).