New empirical evidence on heteroscedasticity in hedonic housing models

Journal of Housing Economics 13 (2004) 136–153

www.elsevier.com/locate/jhe

New empirical evidence on heteroscedasticityin hedonic housing models�

Simon Stevenson¤

Centre for Real Estate Research, Michael SmurWt Graduate School of Business, University College Dublin, Carysfort Avenue, Blackrock, County Dublin, Ireland

Received 12 January 2004

Abstract

This paper re-examines the issue of heteroscedasticity in hedonic house price models. Thepaper uses data for Boston, which has a high average age of dwelling. The results largely sup-port previous Wndings with evidence of heteroscedasticity with respect to the age of dwelling.The iterative GLS correction, speciWed in terms of age, eliminates all heteroscedasticity at bothaggregate and disaggregate levels. However, tests for heteroscedasticity with respect to livingarea show that the GLS models report signiWcant Wndings. In addition, a more general EGLSapproach does not even eradicate heteroscedasticity with respect to age. Evidence is presentedthat would support the estimation of hedonic models at a disaggregate level. It is hypothesisedthat this is due a greater level of homogeneity in the sample at a submarket level, leading to areduction in reported heteroscedasticity with respect to both age and living area. 2004 Elsevier Inc. All rights reserved.

1. Introduction

This paper aims to provide further empirical evidence as to the degree and causesof heteroscedasticity in the estimation of hedonic house price models. The wide-

� The author extends his thanks to Caitriona O’Brien for research assistance and also to the editor, twoanonymous referees, participants at the 2003 American Real Estate Society Annual Conference and semi-nar participants at the National University of Singapore for comments on an earlier draft of this paper.

¤ Fax: +353-1-283-5482.E-mail address: [email protected].

1051-1377/$ - see front matter 2004 Elsevier Inc. All rights reserved.doi:10.1016/j.jhe.2004.04.004

mail to : [email protected]

S. Stevenson / Journal of Housing Economics 13 (2004) 136–153 137

spread use of hedonic based models in both housing research and in the provision ofhouse price indices, means that estimation problems are a primary concern. Hetero-scedasticity occurs when the variances of the error term in the model are not equal; ineVect each residual term is being drawn from a diVerent distribution. Homoscedastic-ity is one of the main underlying assumptions of the standard ordinary least squares(OLS) approach that is used to estimate hedonic based models. The violation of thisassumption can not only lead to changes in the estimated standard errors of thecoeYcients, but also to the value of the coeYcients themselves. A number of studieshave found that one of the primary causes of heteroscedasticity in hedonic models ofhousing dynamics is the age of the properties. This is in part due to the fact that asproperties age renovations become more likely. However, the timing of these renova-tions will not only diVer between dwellings, but in addition, exact data on renova-tions are generally unavailable in data sets used in empirical analysis. Therefore, noformal account can be taken of the impact of age. In addition, older properties mayalso obtain what Goodman and Thibodeau (1995) refer to as vintage eVects, in whichthe age of the property signiWcantly increases the value of the property. However, theinterlinkage between this increase in value beyond a certain age, and the variable inthe quality of the property may result in a non-linear relationship between age andvalue. It is argued that while prices may drop initially, the price starts to rise at a cer-tain point but due to the variability in the quality of older of properties this mayresult in an increasing variance in the residuals as dwelling age increases.

Goodman and Thibodeau (1995, 1997) provide initial evidence that dwelling age isa primary cause of heteroscedasticity. Using data for Dallas they utilize an iterativegeneralized least squares (GLS) procedure to examine whether the heteroscedasticityin the hedonic estimates is related to dwelling age. The authors Wnd evidence of heter-oscedasticity in the overall sample, and in half of the submarkets they examine. Theyalso Wnd that the GLS approach they adopted resulted in improved estimates. Good-man and Thibodeau (1998) extend this analysis to examine the impact of dwelling ageon repeat sale indices, rather than the hedonic indices analysed in the previous papers.Fletcher et al. (2000a) extend the above papers to examine the impact of variablesother than age on heteroscedasticity. As the authors note, if correction is made to onlyone variable this may actually worsen the estimation. Using UK data they Wnd thatthe external area of the property also causes heteroscedasticity in the hedonic estima-tion. The rationale behind the use of area is that as properties increase in size there is agreater potential for diVerences in design and the quality of the Wttings in the prop-erty. These potential diVerences can therefore lead to increased variation in prices.

This current paper examines heteroscedasticity in hedonic models using data forBoston. The choice of Boston is deliberate due to the relative age of the properties inthe city. The Goodman and Thibodeau (1995, 1997) papers use data for Dallas,which does not have a high percentage of vintage properties. In contrast the averageage of the properties in the Boston sample is 75 years. This should allow an examina-tion of whether heteroscedasticity brought about by age factors, can be handled inthe same way in a city with a wider spread of dwelling age. The primary methodolog-ical approach is that proposed in the Goodman and Thibodeau (1995, 1997) papers.Tests are also undertaken using a more general EGLS correction approach. The

138 S. Stevenson / Journal of Housing Economics 13 (2004) 136–153

paper also examines whether other factors, such as area, also contribute to hetero-scedasticity. As with the Goodman and Thibodeau (1997) analysis of Dallas, the cur-rent paper also separates the analysis by location as well as looking at the entireMSA. This issue is important for a number of reasons. First, as Goodman andThibodeau (1997) show, substantial variation can be observed across the submarketsexamined, in terms of both the level of heteroscedasticity present and the eVective-ness of a GLS approach in eliminating it. Second, a number of studies have show thatmore eYcient hedonic estimates can be made at a submarket level. Fletcher et al.(2000b) and Berry et al. (2003) show that the signiWcant improvements can beobtained by estimating hedonic models on a disaggregated basis.

2. Hedonic speciWcation and OLS and GLS estimation

This paper uses data for Boston for the period 1995–2000, with a total number of6441 observations. The data were obtained from First American Real Estate Solu-tions. The property speciWc variables used in the analysis include land area, livingarea, number of bedrooms and bathrooms, a pool dummy, a dummy variable forparking facilities, and a dummy concerned with external construction. Time andlocational dummy variables are also included. The time dummies are based on theyear of the transaction, while Boston is divided into 13 separate submarkets. For thetime dummy variables, 1995 is excluded with coeYcients for the years 1996–2000,while Allston is the excluded submarket.1 With regard to external construction thedwellings were divided into four types, which were Aluminium, Brick, Stone, andWood, with Aluminium being excluded.

Initially, standard hedonic models are estimated with tests then undertaken withrespect to heteroscedasticity. All of the hedonic models are estimated in semi-logform. The initial estimates, reported in Table 1, include the T-statistics from both theoriginal speciWcation and re-run using the White correction. Table 2 reports theresults from an alternative speciWcation that attempts to control for some of the ageaVects by including squared and cubed age as well as age itself. In both cases themajority of the variables are signiWcant at conventional levels and are of the expectedsign. The main exceptions are the dummy variables for the number of stories andwhether the house has a swimming pool. In the case of the pool dummy this may bedue to the small number of properties in the sample that have a pool. Basement areais also insigniWcant in both models as perhaps surprisingly is the number ofbedrooms. As can be seen the use of the Hansen–White correction does lead tochanges in the signiWcance of a number of variables. In addition, in the majority ofcases the corrected standard errors are higher, leading to lower T-statistics, indicatingthat heteroscedasticity may be present. The importance of age can be observed from

1 The submarkets used in this study are largely distinct communities within the Boston area. They arenot necessarily political jurisdictions but rather well-known areas. The Boston area used consists of anamalgamation of areas and it should be noted contains a lower number of single family homes than manyof the other submarkets used.


the reported coeYcients in both of the alternative speciWcations. In the initial speciW-cation the age variable is signiWcant and signed negatively, indicating that as ageincreases the value of the dwelling decreases. The addition of the squared and cubedterms, as reported in Table 2, see both of these variables being reported as signiWcant,indicating that the relationship between dwelling price and age is not linear.

Two alternative methods of testing for heteroscedasticity are used in this paperwith respect to age. The Wrst is the Glejser test, which regresses age against theabsolute value of the residuals from the hedonic model. The second is similar to thatused in the Goodman and Thibodeau (1995, 1997) papers and uses the squared andcubed age variables in addition to age itself as the independent variables in the asimilar manner to the Glejser test. In both cases the Hansen–White correction is used

Table 1Initial OLS hedonic estimates

Note. This table details the coeYcients, original T-statistics and Hansen–White T-statistics for the ini-tial semi-log hedonic model for the entire Boston MSA. * indicates signiWcant at a 10% level, ** at a 5%level, and *** at 1% level.

Variable CoeYcient T-Statistic White’s T-statistic

Constant 7.6253 42.14*** 35.99***

Age ¡0.9408E¡03 ¡3.923*** ¡4.015***

Living area 0.3690 9.115*** 7.879***

Basement area 0.0014 0.0363 0.0338Total land area 0.1465 9.710*** 8.505***

Number of rooms 0.0708 1.604 1.486Number of bedrooms ¡0.0107 ¡0.3712 ¡0.2984Number of bathrooms 0.1308 6.172*** 5.395***

Pool dummy 0.0589 0.7055 1.369Number of stories 0.0033 0.1731 0.1367Parking dummy 0.0626 3.770*** 4.497***

Brick exterior wall dummy 0.1997 7.884*** 6.583***

Stone exterior wall dummy 0.1278 2.509** 2.280**

Wood exterior wall dummy 0.0607 5.033*** 5.450***

1996 Dummy 0.1014 4.796*** 4.283***

1997 Dummy 0.2010 10.15*** 9.129***

1998 Dummy 0.3587 18.21*** 16.47***

1999 Dummy 0.4872 25.000*** 21.91***

2000 Dummy 0.7347 36.80*** 35.26***

Boston 1.3337 20.97*** 16.98***

Brighton 0.2271 4.013*** 4.920***

Charlestown 0.5856 9.888*** 10.03***

Dorchester ¡0.3787 ¡7.497*** ¡8.353***

East Boston ¡0.3382 ¡5.713*** ¡6.125***

Hyde Park ¡0.1963 ¡3.775*** ¡4.224***

Jamaica Plain 0.1649 3.080*** 3.185***

Mattapan ¡0.4526 ¡8.429*** ¡9.070***

Roslingdale ¡0.0809 ¡1.580 ¡1.799*

Roxbury ¡0.6955 ¡11.24*** 8.185***

South Boston 0.0858 1.505 1.599West Roxbury 0.1292 2.536** 2.892***

R2 adjusted 0.6277


to estimate the standard errors. The results from the two tests are reported in Table 3and in both cases indicate that heteroscedasticity is present. In the case of the Glejsertest both the initial and adjusted T-statistics with respect to age are highly signiWcant.With regard to what Goodman and Thibodeau (1995, 1997) refer to as the absoluteresidual model, all three age variables are signiWcant and the F-test to examine jointsigniWcance is also signiWcant at conventional levels.

Two alternative approaches are adopted in the correction of heteroscedasticity.The Wrst is the same methodology as Goodman and Thibodeau (1995, 1997), which isbased on the iterative GLS approach proposed by Davidian and Carroll (1987). The

Table 2OLS hedonic estimates with cubic age speciWcation

Note. This table details the coeYcients, original T-statistics, and Hansen–White T-statistics for theaggregate hedonic model with the inclusion of squared and cubic age variables. * indicates signiWcant at a10% level, ** at a 5% level, and *** at 1% level.

Variable CoeYcient T-Statistic White’s T-statistic

Constant 7.5507 41.06*** 34.31***

Age 0.2350E¡02 1.620 1.224Age squared ¡0.6672E¡04 ¡3.670*** ¡2.543**

Age cubed 0.3201E¡06 4.862*** 3.085***

Living area 0.3962 9.774*** 8.392***

Basement area ¡0.0128 ¡0.3386 ¡0.3156Total land area 0.1396 9.267*** 8.118***

Number of rooms 0.0807 1.834* 1.699*

Number of bedrooms ¡0.0089 ¡0.3102 ¡0.2497Number of bathrooms 0.1176 5.512*** 4.853***

Pool dummy 0.0470 0.5645 1.069Number of stories 0.0082 0.4369 0.3459Parking dummy 0.0519 3.118*** 3.969***

Brick exterior wall dummy 0.1974 7.811*** 6.531***

Stone exterior wall dummy 0.1351 2.662*** 2.401**

Wood exterior wall dummy 0.0593 4.936*** 5.328***

1996 Dummy 0.1036 5.107*** 4.408***

1997 Dummy 0.2038 10.33*** 9.272***

1998 Dummy 0.3590 18.31*** 16.56***

1999 Dummy 0.4893 25.21*** 22.05***

2000 Dummy 0.7381 37.11*** 35.47***

Boston 1.2858 20.15*** 16.30***

Brighton 0.2223 3.942*** 4.805***

Charlestown 0.5482 9.143*** 9.176***

Dorchester ¡0.3839 ¡7.631*** ¡8.465***

East Boston ¡0.3381 ¡5.736*** ¡6.131***

Hyde Park ¡0.2106 ¡4.062*** ¡4.526***

Jamaica Plain 0.1541 2.886*** 2.965***

Mattapan ¡0.4645 ¡8.672*** ¡9.250***

Roslingdale ¡0.0892 ¡1.747* ¡1.979**

Roxbury ¡0.7001 ¡11.35*** ¡8.838***

South Boston 0.0848 1.492 1.576West Roxbury 0.1191 2.344** 2.656***

R2 adjusted 0.6333


initial OLS model is re-estimated with weighted least squares using the reciprocals ofthe normalised predicted values from the absolute residual model. This iterative pro-cedure is repeated until the largest change in any of the parameters is less than 0.0001.This model is therefore based explicitly on the framework that the heteroscedasticitypresent is due to the age factor. The second approach is a general EGLS correction.This form is used due to the Wndings of Fletcher et al. (2000a) in Wnding that hetero-scedasticity may be caused by variables other than age. In their study they illustratethat heteroscedasticity may be induced by the area of the property. The EGLSapproach therefore does not assume that heteroscedasticity is caused by a single spec-iWed variable. Rather, the model uses the residuals from the original speciWcation.

The corrected hedonic model is displayed in Table 4. It can be seen that theapproach does have the desired aVect of reducing the standard errors of the majorityof the hedonic coeYcients, however, this is more evident with the iterative age speciWcform than with the EGLS. In order to compare the diVerent models, implied depreca-tion rates with respect to age are displayed in Fig. 1. A couple of key issues stand outwith respect to the depreciation rates. The Wrst concerns the fact that the EGLSprovides consistently higher Wgures than the other models. The second is related to

Table 3Glejser heteroscedasticity tests on age

Note. This table details results for two alternative tests for heteroscedasticity with respect to age. (A)The results from the Glejser test. The Glejser test has age as the independent variable and the residualsfrom the aggregate hedonic model including the squared and cubic age terms as the dependent variable.(B) The results from the absolute residual model to test for heteroscedasticity with respect to age. The testhas age, squared age, and cubed age as the independent variables and the residuals from the aggregatehedonic model including the squared and cubic age terms as the dependent variable. * indicates signiWcantat a 10% level, ** at a 5% level, and *** at 1% level.

� �

(A) Glejser testsGlejser test on original

speciWcation0.1369 0.1428e¡02

T-Statistic 12.06*** 10.24***

White’s T-statistic 12.15*** 9.613***

Glejser test on cubic age speciWcation

0.1387 0.1394E¡02

T-Statistic 12.27*** 10.05***


� �1 �2 �3 R2 F

(B) Absolute residual modelTests on original

speciWcation 0.2513 ¡0.3389E¡02 0.5399E¡04 ¡0.1684E¡06 0.0238 10.4352***

T-Statistic 9.566*** ¡3.244*** 4.247*** ¡3.614***

White’s T-statistic 9.006*** ¡3.175*** 4.362*** ¡3.906***

Tests on cubic age speciWcation 0.2340 ¡0.2624E¡02 0.4507E¡04 ¡0.1407E¡06 0.0217 6.2946**

T-Statistic 8.947*** ¡2.523** 3.560*** ¡3.032***

White’s T-statistic 7.501*** ¡1.928* 2.520** ¡2.003**


the fact that the implied rates are relatively low. The results extend to an age of 100;with the Wgures implying that century old properties only sell for around 90% of newhomes. This low level of depreciation may be in part due to the nature of the Bostonmarket and the high average age of properties in the area.

Table 5 reports the absolute residual heteroscedasticity tests for the two GLSspeciWcations. For the iterative GLS it can be seen that none of the age variables are

Table 4GLS hedonic estimates

Note. This table reports the results for the iterative GLS aggregate hedonic model proposed by Good-man and Thibodeau (1995) and an EGLS speciWcation. * indicates signiWcant at a 10% level, ** at a 5%level, and *** at 1% level.

Variable GLS EGLS

CoeYcient T-Statistic CoeYcient T-Statistic

Constant 7.3834 37.68*** 7.5507 25.99***

Age 0.1100E¡02 0.8286 0.4149E¡02 2.062*

Age squared ¡0.4036E¡04 ¡2.479** ¡0.8072E¡04 ¡3.226***

Age cubed 0.1903E¡06 3.364*** 0.3436E¡06 3.870***

Living area 0.2889 6.088*** 0.3962 10.33***

Basement area ¡0.1020 ¡2.264** ¡0.0128 ¡0.3579Total land area 0.1430 9.607*** 0.1396 9.797***

Number of rooms 0.0550 1.254 0.0807 1.939*

Number of bedrooms ¡0.0038 ¡0.1350 ¡0.0089 ¡0.3279Number of bathrooms 0.0931 4.335*** 0.1176 5.828***

Pool dummy 0.0592 0.7822 0.0470 0.5968Number of stories 0.0132 0.6951 0.0082 0.4619Parking dummy 0.0538 3.527*** 0.0520 3.296***

Brick exterior wall dummy

0.1797 7.096*** 0.1974 8.257***

Stone exterior wall dummy

0.1211 2.373** 0.1351 2.814***

Wood exterior wall dummy

0.0550 4.747*** 0.0593 5.219***

1996 Dummy 0.0969 4.963*** 0.1036 5.399***

1997 Dummy 0.1919 10.09*** 0.2038 10.92***

1998 Dummy 0.3394 17.89*** 0.3590 19.35***

1999 Dummy 0.4658 24.81*** 0.4893 26.65***

2000 Dummy 0.7126 36.94*** 0.7381 39.23***

Boston 1.2826 19.17*** 1.2858 21.30***

Brighton 0.2276 3.960*** 0.2223 4.167***

Charlestown 0.5672 8.999*** 0.5482 9.666***

Dorchester ¡0.3662 ¡7.056*** ¡0.3839 ¡8.067***

East Boston ¡0.3156 ¡5.208*** ¡0.3381 ¡6.064Hyde Park ¡0.1971 ¡3.721*** ¡0.2106 ¡4.295***

Jamaica Plain 0.1781 3.261*** 0.1541 3.051***

Mattapan ¡0.4613 ¡8.466*** ¡0.4645 ¡9.168***

Roslingdale ¡0.0830 ¡1.585 ¡0.0892 ¡1.847*

Roxbury ¡0.6804 ¡10.55*** ¡0.7001 ¡12.000***

South Boston 0.0933 1.576 0.0848 1.5777West Roxbury 0.1260 2.418** 0.1191 2.478**

R2 adjusted 0.6114 0.6333


signiWcant at conventional levels, and the F-statistic testing for joint signiWcance isalso not signiWcant. These results appear to conWrm the Wndings of Goodman andThibodeau (1995, 1997) with the elimination of heteroscedasticity from thehedonic model through the use of the iterative GLS approach. However, in termsof the EGLS speciWcation, all of the coeYcients are signiWcant at a 99% level,while the F-statistic is signiWcant at a 90% level. Therefore, while the age speciWciterative framework does succeed in eliminating age-induced heteroscedasticity

Fig. 1. Depreciation rates with respect to age. Note. This Wgure reports the implied depreciation rates fromthe four hedonic models. The Wrst OLS model is that incorporating only age, while the second includes thesquared and cubed terms in addition.

Table 5Absolute residual model for GLS speciWcation

Note. This table details results from the absolute residual model to test for heteroscedasticity withrespect to age for the aggregate GLS hedonic models. The test has age, squared age, and cubed age as theindependent variables and the residuals from the aggregate hedonic model including the squared andcubic age terms as the dependent variable. * indicates signiWcant at a 10% level, ** at a 5% level, and *** at1% level.

� �1 �2 �3 R2 F

(A) GLS estimation0.2383 ¡0.1468E¡02 0.2290E¡04 ¡0.6540E¡07 0.0058 1.3038

T-Statistic 9.301*** ¡1.441 1.847* ¡1.439White’s T-statistic 7.666*** ¡1.146 1.417 ¡1.062

(B) EGLS estimation0.6238 ¡0.6995E¡02 0.1204E¡03 ¡0.3750E¡06 0.0223 3.6839*

T-Statistic 8.947*** ¡2.523** 3.560*** ¡3.032***

White’s T-statistic 7.501*** ¡1.928* 2.520** ¡2.003**


from the hedonic model, this is not the case with the EGLS. This would indicatethat the more speciWc correction is more robust and eYcient in eVectively handlingthe age factor. These Wndings are contrary to those reported by Fletcher et al.(2000a), who found that a general EGLS correction did eliminate age related heter-oscedasticity.

3. Analysis of living area

The previous empirical analysis concentrated on the issue of age related hetero-scedasticity. Fletcher et al. (2000a) argue heteroscedasticity may also be caused byfactors such as the living area of the property. The paper argues that, as the size of adwelling increases there is a greater potential for divergence in the design, quality,and repair of the property. Such eVects, as with age, may induce heteroscedasticity inhedonic models. The authors also argue that if a correction that is speciWcally aimedat one potential cause of heteroscedasticity is used, this may actually worsen the esti-mates and may not necessarily eliminate all forms of heteroscedasticity. Therefore,while the iterative GLS has been shown to successfully handle age related heterosced-asticity, this may not guarantee it eVectively correcting for heteroscedasticity causedby other variables.

Tests for heteroscedasticity due to the eVect of area are run for both the originalOLS model and for the two GLS corrections. Table 6 reports the tests for the aggre-gate model. In addition to the Glejser test, the Park test is also used in this case. Thistest regresses the log of area on the log of the squared residuals of the appropriatehedonic model. Both the Glejser and Park tests show signiWcant evidence of hetero-scedasticity in relation to the property’s living area. This is the case in the both theoriginal OLS speciWcation and both of the GLS hedonic models. Indeed, there is nonoticeable change in the level of the signiWcance observed between the three. Thiswould support the Wndings of Fletcher et al. (2000a) in that more than age may causeheteroscedasticity and the correction of heteroscedasticity purely in terms of age maynot necessarily remove all forms of it. However, as with the tests with respect to age,the EGLS speciWcation also does not adequately correct for heteroscedasticity withrespect to living area, with signiWcant results again reported. This again is contrary tothe Wndings of Fletcher et al. (2000a) with regard to their Wndings concerning thesuitability of a general EGLS correction framework.

4. Submarket analysis

Previous studies of hedonic models have observed a number of key issues in rela-tionship to whether the model is estimated on an aggregate or disaggregated basis.The Goodman and Thibodeau (1997) results indicate substantial variation in thelevel of heteroscedasticity present in submarkets and also the eVectiveness of theGLS approach in eliminating it. In addition, as mentioned in Section 1, a number ofpapers have also shown that estimating hedonic models at a disaggregate level can


result in more eYcient estimates.2 In order to further examine the aggregate anddisaggregate estimates the Chow test is used to compare the residual sum of squareerrors of the metropolitan level model and the 13 submarket models. The Chow testresults in an F-statistic of 7.2651, which is signiWcant at a 1% level, indicating moreeYcient estimation at a submarket level.

This section of the paper tests for the presence of heteroscedasticity in each of the 13submarkets examined. In each case tests are performed on the original OLS and thecorrected GLS speciWcations. In the submarket hedonic models the locational dummiesare naturally removed. In addition, in a number of submarkets some of the dummyvariables were removed due to the lack of any dwellings that displayed these character-istics. An example of this is the swimming pool dummy. In addition to those papersthat have explicitly examined the issue of estimation a large literature has developed

2 See, for example, Fletcher et al. (2000b) and Berry et al. (2003).

Table 6OLS heteroscedasticity tests on living area

Note. This table reports the results of the Glejser and Park tests for heteroscedasticity with respect toliving area for the OLS, GLS, and EGLS aggregate hedonic models. The Glejser test has age as the inde-pendent variable and the residuals from the aggregate hedonic model including the squared and cubic ageterms as the dependent variable. The Park test uses the log of living area as the independent and the log ofthe squared residuals as the dependent variable. * indicates signiWcant at a 10% level, ** at a 5% level, and*** at 1% level.

� �

(A) Heteroscedasticity tests on original cubic age speciWcationGlejser test on living area ¡0.5518 0.1086

T-Statistic ¡6.084*** 8.782***

White’s T-statistic ¡4.977*** 7.134***

Park test on living area ¡9.6072 0.7691T-Statistic ¡13.49*** 7.919***


(B) Heteroscedasticity tests on GLS speciWcationGlejser test on living area 0.1497 0.5283E¡04

T-Statistic 13.46*** 8.474***




(C) Heteroscedasticity tests on EGLS speciWcationGlejser test on living area ¡1.4709 0.2894

T-Statistic ¡6.084*** 8.782***





which has examined the identiWcation of submarkets.3 However, Bourassa et al. (2003)illustrate that for the purposes of mass appraisal the use of standard geographic deWni-tions generally deWne suitable submarkets and that statistical techniques such as clusteranalysis and principal components analysis are not necessarily required.

Tables 7 and 8 report the heteroscedasticity tests with respect to age for the initialOLS speciWcation and the two GLS forms. Table 7 details the Glejser test results for theOLS speciWcation, while Table 8 reports the results for the absolute residual model forall three speciWcations. The two GLS speciWcations were estimated in the same manneras with the aggregated model. It is immediately evident that while heteroscedasticitywas signiWcantly present in the OLS aggregate model, there are a limited number ofsubmarkets for which signiWcant Wndings are observed. For the Glejser test signiWcantWhite T-statistics are reported for only three of the submarkets; Dorchester, East Bos-ton, and South Boston. For all remaining submarkets there is no evidence of hetero-scedasticity. Likewise, Table 8 reports only limited signiWcant Wndings. In this casesigniWcant F-statistics are reported for Hyde Park and Roslingdale. These Wndings maybe due to potential similarity in age proWle at a submarket level, leading to reduced var-iation in age. The results would also appear to support the existing evidence as to theattractiveness of modelling hedonic equations at a disaggregated level.

Table 8 also reports the heteroscedasticity tests for the submarkets after the imple-mentation of the GLS procedures. As can be seen all evidence of heteroscedasticity isremoved in the case of the iterative GLS speciWcation. This further supports the useof the Goodman and Thibodeau (1995, 1997) iterative GLS approach in addressingheteroscedasticity with respect to age. As with the aggregate model, all evidence ofheteroscedasticity is eliminated using this correction. However, as previouslyreported with regard to the aggregate tests, the EGLS speciWcation does not fullyeradicate such heteroscedasticity. While heteroscedasticity is removed for the Rosl-ingdale submarket, a signiWcant F-statistic is still reported for Hyde Park, whileJamaica Plain also reports signiWcant Wndings. In this last case the original OLS didnot report such Wndings. These results therefore cast further doubt on an EGLSspeciWcation is addressing a speciWc form of heteroscedasticity.

In addition to the tests with respect to age, submarket tests are also conductedwith respect to living area and are reported in Table 9. The table reports the Glejserand Park tests for both the OLS and GLS versions of the model. As with the hetero-scedasticity tests with respect to age it is noticeable that the majority of the OLSsubmarket models do not display any evidence of heteroscedasticity. As hypothesisedearlier in the paper, this may be due to the homogeneous nature of submarkets withless variation in the type, age, and quality of the properties in the sample. In compar-ison, the aggregate model is examining the entire Boston area and would thus containfar greater variation in the characteristics of the dwellings in the data set. For theOLS speciWcation only West Roxbury reports signiWcant coeYcients for both theGlejser and Park tests, while only three other markets, Dorchester, Hyde Park, andRoslingdale display any evidence with the Hansen–White adjusted T-statistics for

3 See, for example, Adair et al. (1996), MacLennan and Tu (1996), Hoesli et al. (1997), Watkins (1999),and Bourassa et al. (1999).


Table 7Glejser heteroscedasticity tests for submarkets

Note. This table details results from the Glejser test for heteroscedasticity with respect to age for eachof the OLS models for the submarkets. The Glejser test has age as the independent variable and theresiduals from the aggregate hedonic model including the squared and cubic age terms as the dependentvariable. * indicates signiWcant at a 10% level, ** at a 5% level, and *** at 1% level.

� �

Allston 0.1841 0.3734E¡03T-Statistic 1.257 0.2290White’s T-statistic 2.340** 0.4007

Boston 0.5718 ¡0.1429E¡02T-Statistic 3.551*** ¡0.9656White’s T-statistic 4.305*** ¡1.219

Brighton 0.2066 ¡0.6142E¡03T-Statistic 3.678*** ¡0.7743White’s T-statistic 2.729*** ¡0.6414

Charlestown 0.3166 ¡0.3820E¡03T-Statistic 5.927*** ¡0.8206White’s T-statistic 8.102*** ¡1.1370

Dorchester 0.1992 0.9781E¡03T-Statistic 5.027*** 1.971**

White’s T-statistic 6.145*** 2.264**

East Boston 0.0828 0.2435E¡02T-Statistic 0.7483 1.857*

White’s T-statistic 1.099 2.434**

Hyde Park 0.1058 0.1339E¡02T-Statistic 3.139*** 2.011**

White’s T-statistic 2.913*** 1.631

Jamaica Plain 0.1727 0.1451E¡02T-Statistic 2.687*** 1.519White’s T-statistic 2.110** 1.095

Mattapan 0.3615 ¡0.1699E¡02T-Statistic 5.374*** ¡1.526White’s T-statistic 3.554*** ¡1.081

Roslingdale 0.1779 0.9556E¡04T-Statistic 6.468*** 0.2243White’s T-statistic 7.312*** 0.2636

Roxbury 0.2787 0.1003E¡02T-Statistic 1.647 0.5733White’s T-statistic 2.290** 0.7935

South Boston 0.1365 0.1545E¡02T-Statistic 2.027** 2.212**


West Roxbury 0.1545 ¡0.1554E¡04T-Statistic 8.765*** ¡0.0512White’s T-statistic 10.55*** ¡0.0603


Table 8Absolute residual model for submarkets

Note. This table details results from the absolute residual model to test for heteroscedasticity withrespect to age for the submarket hedonic models. The test has age, squared age, and cubed age as the inde-pendent variables and the residuals from the aggregate hedonic model including the squared and cubic ageterms as the dependent variable. (A) The results with respect to the OLS estimation, (B) the GLS results,while (C) the EGLS Wndings. * indicates signiWcant at a 10% level, ** at a 5% level, and *** at 1% level.

� �1 �2 �3 R2 F

(A) OLS estimationAllston ¡0.7159 0.0369 ¡0.4508E¡03 0.1739E¡05 ¡0.0300 0.2460Boston 0.1191 0.4962E¡02 0.8420E¡05 ¡0.2514E¡06 0.0022 0.1957Brighton ¡0.1473E¡01 0.1484E¡01 ¡0.3022E¡03 0.1779E¡05 ¡0.0019 1.8667Charlestown 0.2441*** 0.2331E¡02 ¡0.3509E¡05 0.1079E¡06 0.0147 0.2439Dorchester 0.1904** 0.4274 ¡0.9063E¡04 0.6047E¡06 0.0028 0.7747East Boston 0.1210 ¡0.8618E¡03 0.6796E¡04 ¡0.3955E¡06 0.0031 0.3548Hyde Park 0.2929*** ¡0.1313E¡01* 0.3014E¡03** ¡0.1813E¡05 0.0133 5.9506**

Jamaica Plain 0.7080*** ¡0.1818E¡01 0.1449E¡03 0.2109E¡06 0.0572 0.8864Mattapan 0.6452*** ¡0.1635E¡01 0.2015E¡03 ¡0.7108E¡06 0.0152 1.1496Roslingdale 0.2462*** ¡0.7155E¡02* 0.1757E¡03* ¡0.1186E¡05* ¡0.0003 3.0206*

Roxbury 0.1050 0.1431E¡01 ¡0.1903E¡03 0.7433E¡06 ¡0.0137 0.5892South Boston 0.4531E¡01 0.8968E¡02 ¡0.9519E¡04 0.3046E¡06 0.0159 0.3772West Roxbury 0.1526*** ¡0.8602E¡03 0.3591E¡04 ¡0.3318E¡06 ¡0.0024 0.0758

(B) GLS estimationAllston 0.0275 0.2787E¡02 ¡0.9272E¡05 ¡0.3065E¡07 ¡0.0389 0.0031Boston ¡0.3175 0.2494E¡01 ¡0.3148E¡03 0.1289E¡05 0.0257 1.4885Brighton 0.0475 0.5409E¡02 ¡0.1043E¡03 0.6591E¡06 ¡0.0089 0.4706Charlestown 0.0824** 0.2874E¡02 ¡0.4049E¡04 0.1563E¡06 ¡0.0144 0.7778Dorchester 0.2317*** 0.2018E¡02 ¡0.4638E¡04 0.3307E¡06 ¡0.0010 0.1671East Boston 0.1259 ¡0.1856E¡02 0.7731E¡04 ¡0.4817E¡06 ¡0.0061 0.0361Hyde Park 0.1963 0.8522E¡02 ¡0.3209E¡03 0.2689E¡05 0.0097 1.8044Jamaica Plain 0.3224 0.1914E¡02 ¡0.2742E¡03 0.2848E¡05 0.0158 0.3384E¡02Mattapan 0.5071*** ¡0.1043E¡01 0.1241E¡03 ¡0.4064E¡06 0.0024 0.6628Roslingdale 0.1006 ¡0.4563E¡02 0.1525E¡03 ¡0.1215E¡05 ¡0.0026 0.4359Roxbury 0.2231* 0.1859E¡02 0.2355E¡04 ¡0.2826E¡06 ¡0.0198 0.0137South Boston 0.1489* 0.9271E¡03 0.2131E¡04 ¡0.2048E¡06 ¡0.0027 0.6607E¡02West Roxbury 0.1522 0.3027E¡02 ¡0.1095E¡03 0.9252E¡06 0.0002 0.8852

(C) EGLS estimationAllston ¡0.0685 0.3537E¡02 ¡0.4318E¡04 0.1665E¡06 0.0141 0.3620Boston 1.9188** ¡0.4927E¡01 0.3926E¡03 0.5716E¡06 0.0655 0.8864Brighton ¡0.7172E¡01 0.7225E¡01 ¡0.1471E¡02 0.8658E¡05 0.0141 1.8336Charlestown 0.7472*** 0.7136E¡02 ¡0.1074E¡04 ¡0.3304E¡06 0.0297 0.1341Dorchester 0.4707*** 0.1057E¡01 ¡0.2241E¡03 0.1495E¡05 0.0065 0.4440East Boston 0.1588E¡01 ¡0.1131E¡03 0.8921E¡05 ¡0.5192E¡07 0.0240 0.3548E¡02Hyde Park 0.6816*** ¡0.0306** 0.7013E¡03** ¡0.4218E¡05 0.0173 3.7089*

Jamaica Plain 1.9188** ¡0.4927E¡01 0.3926E¡03 0.5716E¡06 0.0655 2.7720*

Mattapan 1.6523*** ¡0.4187E¡01 0.5160E¡03 ¡0.1821E¡05 0.0241 1.8263Roslingdale 0.1038*** ¡0.3016E¡02* 0.7406E¡04* ¡0.4998E¡06* 0.0037 2.2917Roxbury 0.1530 0.2085E¡01 ¡0.2773E¡03 0.1083E¡05 0.0106 0.4497South Boston 0.9375E¡02 0.1856E¡02 ¡0.1970E¡04 0.6303E¡07 0.0292 0.5817West Roxbury 0.6372*** ¡0.3593E¡02 0.1500E¡03 ¡0.1386E¡05 0.0005 0.0512


Table 9Living area heteroscedasticity tests for submarkets

OLS estimation GLS estimation EGLS estimation

� � � � � �

(A) AllstonGlejser test on living

area0.1820 0.1993E¡04 0.1854 ¡0.8689E¡04 ¡0.1030 0.4177E¡02

T-Statistic 1.403 0.2765 1.761* ¡0.1486 ¡0.1171 0.3535White’s T-statistic 1.706* 0.2918 2.100** ¡0.1523 ¡0.1316 0.3890

Park test on living area

63.567 ¡9.3191 ¡0.6482 0.0963 61.493 ¡9.6789

T-Statistic 1.666* ¡1.818* ¡0.6796 0.7519 1.562 ¡1.830*

White’s T-statistic 1.203 ¡1.290 ¡0.6926 0.7441 1.121 ¡1.289

(B) BostonGlejser test on living

area0.4341 ¡0.6009E¡05 0.3485 0.8476E¡06 1.4847 ¡0.8291E¡01

T-Statistic 7.716*** ¡0.3148 6.829*** 0.0489 1.725* ¡0.7505White’s T-statistic 7.250*** ¡0.3203 6.845*** 0.0549 1.401 ¡0.6162


¡2.2988 0.0312E¡01 ¡3.5109 0.7579E¡01 ¡0.9039 ¡0.3116E¡01

T-Statistic ¡0.8702 ¡0.0919 ¡1.1334 0.2244 ¡0.3422 ¡0.0919White’s T-statistic ¡0.9276 ¡0.0987 ¡1.229 0.2048 ¡0.3647 ¡0.0987

(C) BrightonGlejser test on living

area0.1768 ¡0.7788E¡05 0.1302 0.1016E¡04 1.8074 ¡0.1376

T-Statistic 3.912*** ¡0.2860 3.726*** 0.4826 1.079 ¡0.6012White’s T-statistic 3.297*** ¡0.2783 3.368*** 0.4905 0.8895 ¡0.5060


¡4.7794 0.3672E¡01 ¡9.5099 0.6621 ¡1.6139 0.0367

T-Statistic ¡1.272 0.0716 ¡2.699*** 1.376 ¡0.4295 0.0716White’s T-statistic ¡1.474 0.0831 ¡2.990*** 1.538 ¡0.4978 0.0831

(D) CharlestownGlejser test on living

area0.3272 ¡0.3099E¡04 0.2800 ¡0.1802E¡04 1.7097 ¡0.1179

T-Statistic 6.764*** ¡1.154 6.414*** ¡0.7436 1.678* ¡0.8522White’s T-statistic 0.2774 ¡1.192 6.599*** ¡0.7852 1.577 ¡0.8132


1.8813 ¡0.7609 ¡0.4937 ¡0.4627 4.1229 ¡0.7615

T-Statistic 0.2774 ¡0.8262 ¡0.0726 ¡0.5009 0.6070 ¡0.8257White’s T-statistic 0.5235 ¡1.465 ¡0.1274 ¡0.8269 1.146 ¡1.465-

(E) DorchesterGlejser test on living

area0.1807 0.5179e¡04 0.2456 0.1627e¡04 ¡0.7618 0.1936

T-Statistic 5.772*** 3.194*** 7.853*** 1.004 ¡1.269 2.401**

White’s T-statistic 5.068*** 2.599*** 6.986*** 0.8642 ¡0.9984 1.879*


Table 9 (continued)


� � � � � �


¡5.9962 0.3062 ¡4.0178 0.4592E¡01 ¡4.1853 0.3062

T-Statistic ¡3.098*** 1.178 ¡2.126** 0.1809 ¡2.163** 1.178White’s T-statistic ¡3.058*** 1.155 ¡2.036** 0.1736 ¡2.134** 1.155

(F) East BostonGlejser test on living

area0.3866 ¡0.7571E¡04 0.2801 ¡0.4559E¡04 0.1450 ¡0.0150

T-Statistic 4.108*** ¡1.164 3.821*** ¡0.9003 1.665* ¡1.241White’s T-statistic 3.688*** ¡1.074 3.372*** ¡0.7954 1.488 ¡1.116


01.1827 ¡0.4599 ¡3.1567 ¡0.2746 ¡5.1935 ¡0.4671

T-Statistic ¡0.0780 ¡0.2182 ¡0.1963 ¡0.1228 ¡0.3421 ¡0.2213White’s T-statistic 0.1304 ¡0.3702 ¡0.3346 ¡0.2122 ¡0.5731 ¡0.3762

(G) Hyde ParkGlejser test on living

area0.0237 0.1138E¡03 0.1226 0.4554E¡04 ¡1.8270 0.3118

T-Statistic 0.5342 3.408*** 3.005*** 1.481 ¡2.435** 2.963***

White’s T-statistic 0.3912 2.304** 2.435** 1.158 ¡2.004** 2.412**


¡9.0451 0.5861 ¡3.2674 ¡0.2024 ¡7.2825 0.5756

T-Statistic ¡2.651*** 1.225 ¡0.9563 0.673 ¡2.118** 1.193White’s T-statistic ¡1.863* 0.8481 ¡0.6656 ¡0.772 ¡1.480 0.8219

(H) Jamaica PlainGlejser test on living

area0.1633 0.5820E¡04 0.4560 0.1351E¡04 ¡1.5045 0.3000

T-Statistic 2.952*** 1.978** 4.258*** 0.2370 ¡1.328 1.966**

White’s T-statistic 2.828*** 1.626 4.933*** 0.2798 ¡1.231 1.787*


¡6.0649 0.3107 ¡1.5441 ¡0.1756 ¡4.0710 0.3107

T-Statistic ¡2.131** 0.8108 ¡0.4943 ¡0.4174 ¡1.430 0.8108White’s T-statistic ¡2.247** 0.8484 ¡0.5219 ¡0.4385 ¡1.508 0.8484

(I) MattapanGlejser test on living

area0.3270 ¡0.4589E¡04 0.0263 0.9072E¡04 2.6541 ¡0.2749

T-Statistic 4.267*** ¡0.8589 0.5928 2.943*** 1.826* ¡1.362White’s T-statistic 3.778*** ¡0.8181 0.3671 1.791* 1.582 ¡1.193


¡1.6573 ¡0.2841 ¡13.923 1.2286 0.2236 ¡0.2841

T-Statistic ¡0.4785 ¡0.5908 ¡3.712*** 2.360** 0.0646 ¡0.5908White’s T-statistic ¡0.4881 ¡0.6061 ¡3.391*** 2.162** 0.0659 ¡0.6061

(J) RoslingdaleGlejser test on living

area0.1587 0.1729E¡04 0.1371 0.1627E¡03 0.0178 0.8234E¡02

T-Statistic 4.405*** 0.7143 1.884* 3.328*** 0.1673 0.5609White’s T-statistic 3.809*** 0.6391 1.739* 2.917*** 0.1365 0.4602


Note. This table reports the results of the Glejser and Park tests for heteroscedasticity with respect toliving area for the submarket OLS, GLS and EGLS hedonic models. The Glejser test has area as the inde-pendent variable and the residuals from the aggregate hedonic model including the squared and cubic ageterms as the dependent variable. The Park test uses the log of living area as the independent and the log ofthe squared residuals as the dependent variable. * indicates signiWcant at a 10% level, ** at a 5% level, and*** at 1% level.

either of the tests. It is interesting that all of these submarkets also initially displayedevidence of heteroscedasticity with respect to age. This may provide further evidenceas to a possible issue with regard to the divergence in Wndings at an aggregate and dis-aggregate level, namely the level of diversity of the properties in each market.

Table 9 also reports the two tests using the GLS hedonic models for each of thesubmarkets. As with the aggregate tests the GLS procedure appears to correct for

Table 9 (continued)


� � � � � �


¡10.006 0.76592 ¡15.709 1.6476 ¡11.734 0.7659

T-Statistic ¡4.039*** 2.240** ¡6.118*** 4.845*** ¡4.736*** 2.240**

White’s T-statistic ¡4.095*** 2.281** ¡5.769*** 4.588*** ¡4.802*** 2.281**

(K) RoxburyGlejser test on living

area0.1542 0.1199E¡03 0.1622 0.1039E¡03 ¡1.3629 0.2567

T-Statistic 1.463 2.226** 1.674* 2.098** ¡1.369 1.918*

White’s T-statistic 1.026 1.294 1.178 1.227 ¡1.091 1.486


¡6.9905 0.5339 ¡3.1205 ¡0.6302E¡01 ¡1.1432 ¡0.2247

T-Statistic ¡1.898* 1.078 ¡0.3210 ¡0.0482 ¡0.1150 0.1681White’s T-statistic ¡2.043** 1.154 ¡0.5095 ¡0.0719 ¡0.1912 ¡0.2602

(L) South BostonGlejser test on living

area0.2648 0.9910E¡05 0.2300 0.5959E¡05 0.4727E¡01 0.1460E¡02

T-Statistic 4.611*** 0.2741 4.793*** 0.1973 0.5700 0.1279White’s T-statistic 4.372*** 0.2732 4.462*** 0.1925 0.5848 0.1324


¡9.3495 0.7739 ¡9.1154 0.6937 ¡12.380 0.7584

T-Statistic ¡1.344 0.8081 ¡1.335 0.7381 ¡1.820* 0.8098White’s T-statistic ¡1.794* 1.133 ¡1.744* 1.005 ¡2.424** 1.132

(M) West RoxburyGlejser test on living

area0.1021 0.3667E¡04 0.1002 0.3678E¡04 ¡1.0215 0.2305

T-Statistic 4.747*** 2.486** 4.744*** 2.538** ¡1.531 2.495**

White’s T-statistic 4.771*** 2.385** 4.665*** 2.392** ¡1.429 2.315**


¡9.8465 0.6994 ¡8.4563 0.5026 ¡6.9876 0.6994

T-Statistic ¡4.615*** 2.367** ¡3.974*** 1.705* ¡3.275*** 2.367**

White’s T-statistic ¡4.289*** 2.201** ¡3.929*** 1.681* ¡3.044*** 2.201**


little of the heteroscedasticity concerned with area. The results for West Roxburyfor both of the tests and both of the speciWcations remain signiWcant, while for theGlejser test for Roslingdale, which was not signiWcant initially, is so with the iterativeGLS model. The Park test for Roslingdale remains signiWcant in each case.

In the case of both Dorchester and Hyde Park, which reported signiWcant Glejsertest statistics with the OLS, while this signiWcance is removed with the iterative GLS,it remains with respect to the EGLS speciWcation for both markets. In addition, forthe Mattapan submarket, while no evidence was reported of heteroscedasticity withrespect to living area with the OLS model, it is when the iterative GLS is used, forboth the Glejser and Park tests.

5. Conclusion

This paper has re-examined the issue of heteroscedasticity in hedonic models usingdata for Boston. The aggregate results largely support previous studies, with signiW-cant evidence of age related heteroscedasticity reported when the standard OLSapproach is used. The iterative GLS correction, which speciWes age as the primarycause of heteroscedasticity, does eliminate all heteroscedasticity from the aggregatehedonic model. However, tests examining possible heteroscedasticity induces by vari-ability in the living area of the properties report signiWcant Wndings, even with theiterative correction. A more general EGLS speciWcation is also tested. However, theresults indicate that in the case of both age and living area the EGLS does not eradi-cate all evidence of heteroscedasticity. The results provide evidence that the estima-tion of hedonic models at a disaggregated level may provide more eYcient estimates.The majority of the initial submarket OLS models do not display evidence of hetero-scedasticity, with respect to either age or area. It is hypothesised that this may be dueto less variation in the dwellings in terms of their characteristics leading to a morehomogeneous sample. In addition, Chow tests also support the view that moreeYcient estimates are obtained using the disaggregated data.

References

Adair, A.S., Berry, J.N., McGreal, S., 1996. Hedonic modelling, housing submarkets and residential valua-tions. J. Property Res. 13, 67–83.

Berry, J., McGreal, S., Stevenson, S., Webb, J., Young, J., 2003. Estimation of apartment submarkets. J.Real Estate Res. 25, 159–170.

Bourassa, S.C., Hamelink, F., Hoesli, M., MacGregor, B.D., 1999. DeWning housing submarkets. J. Hous-ing Econ. 8, 160–183.

Bourassa, S.C., Hoesli, M., Peng, V.S., 2003. Do housing submarkets really matter?. J. Housing Econ. 12,12–28.

Davidian, M., Carroll, R., 1987. Variance function estimation. J. Am. Statistical Assoc. 82, 1079–1091.Fletcher, M., Gallimore, P., Mangan, J., 2000a. Heteroscedasticity in hedonic house price models. J. Prop-

erty Res. 17, 93–108.Fletcher, M., Gallimore, P., Mangan, J., 2000b. The modelling of housing submarkets. Journal of Property

Investment and Finance 18, 473–487.


Goodman, A., Thibodeau, T., 1995. Dwelling age heteroscedasticity in hedonic house price equations. J.Housing Res. 6, 25–42.

Goodman, A., Thibodeau, T., 1997. Dwelling age heteroscedasticity in hedonic house price equations: anextension. J. Housing Res. 8, 299–317.

Goodman, A., Thibodeau, T., 1998. Dwelling age heteroscedasticity in repeat sales house price equations.Real Estate Econ. 26, 151–171.

Hoesli, M., Thion, B., Watkins, C., 1997. A Hedonic investigation of the rental value of apartments in cen-tral bordeaux. J. Property Res. 14, 15–26.

MacLennan, D., Tu, Y., 1996. Economic perspectives on the structure of local housing systems. HousingStud. 11, 387–406.

Watkins, C., 1999. Property valuation and the structure of urban housing markets. Journal of PropertyInvestment and Finance 17, 157–175.

Documents

New empirical evidence on heteroscedasticity in hedonic housing models