Harrison Rubinfeld

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JOURNAL OF ESVIRONMEN TAL ECONOMICS AND MANAGEMEN T 5, 81-102 (1978)

Hedonic Housing Prices and the Demand for Clean Air1DAVID HARRISON, Jn.

Departmen t of City and Regi onal P lanni ng, Harvard Uniuersity, Camb ridge, MassachusettsAKD

DANIEL L. RUBINFELDDepartment of Economics and Institute of Public Policy Studies, The University of Michi gan;

National Bureau of Economic Research, Camb ridge, Massachusetts

Received December 22, 1976This paper investigates the metho dologic al problems associated with the use of

housing market data to measure the willingne ss to pay for clean air. With the useof a hedonic housing price model and data for the Boston metropolitan area, quanti-tative estimates of the willingne ss to pay for air quality improvements are generated.Marg inal air pollu tion damages (as revealed in the housing market) are found toincrease with the level of air pollu tion and with household income. The results arerelatively sensitive to the specification of the hedonic housing price equatio n, butinsensitive to the specification of the air quality dema nd equatio n.

I. INTRODUCTIONExpressing the benefits of reduced urban air pollution concentrations in

monetary terms is a diff icult task, despite the fact that the general nature of thebenefits is reasonably well established. Several attempts have been made toutilize economic analys is to estimate the dollar benefits of air quality improve-ments. One approach is to proxy willingness to pay by measuring either theadded cost to society from increased air pollution, or equivalently the reducedcosts associated with air quality improvement. A second technique infers willing-

1 This research was supported by the Natio nal Bureau of Economic Research. Al l statisticalanalyses were performed on the NBE R Center for Com putatio nal Researchs TROLL System.We wish to thank m embers of the NBE R for their technical advice; Wil liam Apgar, A. MyrickFreeman, Gregory Ingram, John Kain , Robert McDonald, and two anonymous referees forhelpfu l comments on earlier drafts; Gary Fauth, Gregory Ingram, Eugen e Kroch, RobertMcDon ald, and Ann Schnare for providing data used in this study; and Laxmi Rao of theNBE R for providing helpfu l research assistance.

2 Studies have documented the damages which high concentrations of air pollutants imposeon huma n health, on vegetation, on various materials and fibers, a nd on the aesthetic ele-ments of urban living. While urban residents perceive some of the dama ge, such as eyeirritation, hazy skies, and dirty pa int, other damag e is only evident to trained researchers.For a summary of these dama ge studies, see Harrison [q].

s This approach has been used in a number of studies to evaluate the costs of air pollu-tion to plants, materials, or human health. For example , Lave and Seskin [I91 used statisticalestimates of the effect of air pollu tion on morbidity and mortality rates to compute increasesin health costs and decreases in earning capacity attributed to higher air pollution levels.

810095-0696/78/0051-0081$02.00/0Copyright 0 197 8 by Academic Press, Inc.All rights of reproduction in any form reserved.


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82 HARRISON AND RUBINFELDness to pay for better air quality from an analysis of the housing market, on thepresumption that individuals wil l pay more for a unit located in an area withgood air quality than for an otherwise identical unit located in an area withpoor air quality.4This paper investigates the methodological problems associated with thehousing market approach. While several studies have used this methodology toestimate the demand for air quality improvements, they have paid little atten-tion to the sensi tivity of the results to the assumptions embedded in the pro-cedures.5 Using data for the Boston housing market, we generate quantitativeestimates of the willingness to pay for air quality improvements and test thesensitivity of these results to alternative specifications of the basic buildingblocks in the procedure. Our data base is superior to others because it containsa large number of neighborhood variables (necessary to isolate the independentinfluence of air pollution) and more reliable air pollution data.Section II of this paper describes the four-step procedural model which is thebasis of our empirical investigations. The first step is to estimate a hedonichousing value equation with air pollution as one housing attribute; the secondstep is to calculate each households willingness to pay for a marginal changein air pollution from the hedonic housing value equation; the third step is toestimate a marginal willingness-to-pay function for households in the urban area,a function that i s analogous to a demand curve for clean air ; and the fourthstep is to use the willingness-to-pay function, along with estimates of air pollu-tion concentrations before and after pollution controls, to calculate the per house-hold dollar benefits of the control strategy. Section III gives empirical resultsfor different specifications of the housing value equation, and Section IV pre-sents the corresponding results for various specifications of the marginal willing-ness-to-pay function. Section V illustrates the average dollar benefits of thefederal automobile emission control program to Boston area residents, emphasiz-ing the sensi tivity of the average benefit figure to alternative specifications ofthe housing value and willingness-to-pay functions.

II. THE PROCEDURAL MODELIn this section we present a procedural model for measuring the willingnessto pay for improvements in air quality. Our model is based on a theoretical

structure which assumes that households consider the level of air pollution aswell as the quantity and quality of housing and other neighborhood charac-terist ics in making their housing choices. Housing value differentials then providethe starting point for estimating households willingness to pay for reductionsin air pollutant concentrations. Since the issues associated with the theoreticalconstruct used here have been considered in detail in other papers, we presentthe theory in only rudimentary form. 6 Some of the important underlying assump-tions are noted, but we refer the reader to the cited literature for further details.

*We stress that housing market studies of this type at best can only ascertain thosebenefits which are perceived by households. It is clear that individua ls are not aware of allpotent ial health hazards associated with air pollu tion and are often ignorant of the degree towhich the air they breathe is pollut ed.

5 Housing price studies which have investigated the willingne ss to pay for clear air in-clude [l, 10, 22, 27, and 351.

6 The most com plete treatment of the theoretical issues is in [28].


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THE DEMAN D FOR CLEAN AIR 83Our theoretical model assumes that individual households maximize a utility

functionu(x:,h) (2.1)subject to the budget constraint

Y =x+p(h) + T (2.2)where :

x = quantity of composite private goods, whose price is set equal to oneh = (h,;.., h,) is a bundle of housing attributes, including accessibili ty,structure and neighborhood characteristics, and air pollutionconcentrations,y = annual money income,p(h) = housing (or hedonic) price function, andT = money cost of transportation.

Our specification of the utility function (2.1) implies that housing is appropri-ately viewed as a bundle of attributes, rather than as a single commodity. Tosimplify our discussion we shall arbitrarily associate the first housing attribute,hl, with a single measure of air pollution and label it a. In order to apply thecalculus to the utility maximization problem for the household we assume thatU is stric tly concave with regard to the various housing attributes (when viewedas goods rather than bads).8The first step in our procedural model is to specify the hedonic housing valuefunction, p(h). The p(h) f unction translates a vector of housing attributes ateach location into a price which influences the decisions of both suppliers anddemanders of housing attributes .Q Implicit in this description of the hedonichousing function are the following important assumptions:

(1) Al l consumers accurately perceive the characteristics represented bythe vector h at every location.(2) There is sufficient variation in h so that the function p(h) is continuous,with continuous first and second partial derivatives.(3) The market is in short-run equilibrium.

7 For some applications of the hedonic approach to the analysis of housing deman d, see[4, 12-15, 17, 22, and 321. For more genera l discussions of the hedonic approach to consumerdemand, see [8, 17, 20, and 281.

s We could have generalized the specification of the utility function to allow for the house-hold production of housing services from the housing attributes, but we chose not to do so.Such a generaliz ation adds an addit ional complic ation which is not necessary for our pur-poses; but it would make explicit the fact that housing price differe ntials may arise fromdifferences in household consumption technologies as wel l as from differences in householdstastes for housing attributes. For some insightf ul discussions of the relevance of householdproduction theory for the problems of estimati ng hedonic price functions, see [17, 21, 22, 26,and 311.

9 We have chosen to write the theoretical mod el in terms of annua l rental prices, althoug hour empiric al work uses housing values (capitalized streams of annua l rental prices) inconformity with other studies. Conceptually, rental prices are more appropriate because theyreflect the markets current valuation of housing attributes. Housing values, on the otherhand, reflect the markets expectations about future as wel l as present housing conditions.


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84 HARRISON AND RUBINFELD(4) Spatial variations in housing characteristics ( including air pollution)are capitalized into differentials in housing prices.IO

Note that the p(h) relationship between housing attributes and house pricesneed not be linear. Nonlinearities may exist in part because the market may notbe in long-run equilibrium-unlike the attributes of less durable commodities,housing attributes cannot be untied and repackaged to produce an arbitrary setof attributes at all locations. For example, a nonlinear relationship observed inan hedonic equation between the number of rooms and housing value may inpart reflect disequilibrium supply conditions and in part reflect varying marginalbenefits from extra increments of interior space. Similar conditions may hold forair pollution and other neighborhood attributes. In fact, supply conditions aremore complex for neighborhood characteristics than for structural attributessince there is no long-run neighborhood attribute s~~pply price equivalent to theconstruction cost for rooms and other structural components.The second procedural step, calculating each households willingness to payfor a marginal change in air pollution, follows from the first order condition forutility maximization (when Eq. (2.1) is maximized subject to Eq. (2.2) ) withrespect to the air pollution attribute, a. This first order condition is given belowas Eq. (2.3):

dfT/d(-a) dp(h)w, (IL) = --__ = -~--- =d ,:/& 8(-a) pu II) (2.3)Equation (2.3) states that in equilibrium the households amlual willingness to payfor a small improvement in air quality [ W,( h) ] is equal to the increased cost[p,(h)] incurred in purchasing (or renting) a different house with identicalattributes except for a marginal improvement in air quality. Thus the secondstep consists of calculating the derivatives of the hedonic housing price equationwith respect to the air pollution attribute, i.e., @I( h)/cY( -u). Calculated sepa-rately for each household, this derivative is an estimate of W,(h), the house-holds willingness to pay for a marginal improvement in air pollution.To determine each households willingness to pay for nonmarginal improve-ments in air quality we need to estimate the relationship between the air pollu-tion level and marginal willingness to pay, i.e., the W,(h) schedule.11 Estimat-ing the W,(h) schedule is the third step in the procedural model. The W,(h)function is estimated in our model by regressing households marginal valuations(the derivatives calculated in the second step for each household) on air pollu-

10 A competitive market is not sufficient to guarantee that differentials in air quality wil lbe capitalized into housing prices. For example , full capitalizati on may not take place in amod el in which there are endogenous labor markets (see Polinsky and Rubi nfeld [24] and[25] for details). An excess supply of undisting uishable low- pollutio n areas may also preventfull capitaliza tion of air pollu tion differences.

11 The schedule we seek is the inverse of the compensated dema nd curve for the airquality attribute (see [Sl). It can be conceptualized by considering the follo wing experi-ment. Let the level of utility attained by the household in equilibrium be fixed. Then fix thehouseholds location, its consumption of the composite good, and all housing attributes otherthan air quality. The total willin gness to pay for a given decrease in air pollu tion is themaximum amount of income the household is willing to give up to keep the decreased levelof air pollu tion. W,(h), the marg inal willingne ss to pay for decreases in air pollu tion con-centration, is equal to the derivative of the total willingness-to-pay function with respect toair pollu tion concentration.


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THE DEMAN D FOR CLEAN AIR 85tion concentration and other variables (household income, for example) whichmay cause the demand for cleaner air to shift. Section IV presents results forseveral specifications of the W,(h) function as well as the results of estimatingthe W,(h) function from alternative hedonic housing value equations.Before estimating the marginal willingness-to-pay function, we must askwhether it is possible to identify W,(h) f rom the available housing market data.This is a classic identification problem, since one can imagine a supply as wellas a demand function for each housing attribute at every location. However, inthe case of air pollution it seems reasonable to assume that the supply is eitherexogenously fixed or at least unresponsive to changes in household tastes, sothat variations in the level of air pollution over space allow us to identify infor-mation about households demand for clean air.12 Thus, we proceed under theassumption that it is possible to identify households willingness to pay for cleanair from the housing market data.The fourth and final step in evaluating the dollar benefits of a scheme toimprove urban air quality is to use the willingness-to-pay schedule to place adollar value on physical improvements in air quality estimated by a meteorologi-cal airshed model. In Section V we perform such an exercise and estimate thedollar benefits of the federal automobile emission control strategy in the Bostonmetropolitan area. Estimates of pollutant concentrations both with and withoutfederal automobile emission controls were obtained from a meteorological modelof the Boston airshed. The per household willingness to pay for substantialreductions in air pollution can be calculated for households at each location byintegrating W, ( h ) f rom the old concentration to the new air pollution concen-tration. Since the dependent variable in the first step hedonic equation is housingvalue, the integral of willingness to pay is an estimate of the capitalized valueof the air quality improvement to each household. To obtain an annual value adiscount rate must be applied.

The example in Section V compares results in terms of the average annualdollar benefits per household, which is calculated as a weighted average of thedollar benefits for households in each of the geographic areas (census tracts)used in the estimation procedure. Comparing average benefit figures illustratesthe sensitivity of the final results to alternative specifications of the hedonichousing value function and of the willingness-to-pay function, the two empiricalbuilding blocks in our procedural model of benefit estimation. The specificationsused in the example and explanations of their derivations are presented belowin Section III (housing value equation) and Section IV (willingness-to-payequation).

III. HOUSING VALUE EQUATIONThis study utilizes data for census tracts in the Boston Standard Metropolitan

Statist ical Area (SMSA) in 1970. Following the example of most studies of thiskind, we focus on the owner market. Thus, the dependent variable in our housingequation is the median value of the owner-occupied homes in the census tract.

12Our empirical estimates test for the importance of possible supply shifts, and we con-clude that they have a minor influence on benefit estimates.

13 There is some controversy about the proper dependen t variable in a housing valueequatio n. See, for example, Wieand [351 who argues that the correct depende nt variable isthe unit price of housing, proxied by housing value per unit of land.


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86 HARRISON AND RUBINFELDThe independent variables in the equation include two structural attribute vari-ables, eight neighborhood variables, two accessib ility variables, and one airpollution variable. The pollution variable used in the empirical estimates is theconcentration of nitrogen oxides (NOX). The NOX variable is used to proxyair quality since the air pollution variables in our data base are so highly corre-lated that specifying their independent impacts on housing values in the BostonSMSA would be extremely difficult .I4 Descriptions of the data we employed andfull results of our estimation of the equation are given in the Appendix.

One of the major objectives in estimating the hedonic housing equation wasto determine the best fitting functional form. Comparing models with eithermedian value of owner-occupied homes (MV) or Log( MV) as the dependentvariable, we found that the semilog version provided a slightly better fit. UsingLog( MV) as the dependent variable, we concentrated on estimating a nonlinearterm in NOX; i.e., we included NOXp in the equation, where p is an unknownparameter. Determining the proper exponent on NOX in the housing valueequation is important because different exponents imply different patterns of theinfluence of air pollution on housing values and thus different patterns for thewillingness to pay for air quality improvements.

The statistical fit in the equation was best when p was set equal to 2.0, i.e.,when NOX2 was in the equation. I5 This basic equation (see Table VII in theAppendix) is used in the remainder of the paper to generate estimates of thewillingness to pay for air pollution reduction. The equation conforms well toour a priori expectations about the influence of each variable on median housingvalues. Virtually all coefficients have the expected sign and are statis tically sig-nificant.lG The high R2 (0.81) indicates that the variables in the equation accountfor much of the variation in median housing values observed in the BostonSMSA in 197O.l The NOX variable has a negative sign and is highly significant.

14 Air pollut ant variables are often not so highly correlated. There are two likely reasonswhy we observed a high correlation between NOX and particulates (PART), the othermajor air pollut ant we hypothesized would influe nce housing values. First, whil e in manyurban areas NOX is primarily an autom obile polluta nt and PART is a stationary source pol-lutant, in Boston only 79,388 tons out of an estimated 201,743 tons of NOX emissions wereaccounted for by autom obile emissions. Since the stationary source emitters of both NOXand PART tend to be in central city zones, the result is a high correlation between the twovariables, which is not observed in urban areas in which automotiv e emissions account forthe bulk of total NOX em issions. Second, the true correlation between NOX and PART issomewhat overstated because the TASS IM mod el generates data for 122 zones, not 506census tracts. Translating zonal data into census tract da ta tends to overstate the correlationbecause relatively more census tracts are located in center city zones in which PART andNOX levels tend to be most hig hly correlated.

15 The exponent was estimated by performing a grid search over alternative parametervalues for p in the term NOX*-l/( p - 1). The usefulness of this particular transformation ofthe NOX variable is described in Box and Cox [3] and in Kme nta [16, pp. 467-4681. Thevalue for p was estimated by a grid search rather than by direct nonline ar estimati on be-cause of computational difficulties we encountered with the nonlinear estimation method.

16 There are some exceptions. For exampl e, the AGE variable is positive and statisticallyinsignifican t, probably because in Boston AGE does not correlate closely with housing quality(since many older units are of high quality).

17 We were concerned that multic ollinearit y amon g neighborh ood, accessibility, and airquality variables migh t be a problem . (The simp le correlations among variables appear inTable VI.) In fact, we did find that when both NOX and particulate concentration (PART)appear in the same equation , collinearity does become serious. In some specifications with


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THE DEMAN D FOR CLEAN AIR 87Assessing the quantitative importance of the NOX coefficient ( -0.0064) requiressome calculation because, with the nonlinear specification, the change in housingvalue resulting from a one pphm (part per hundred million) change in NOXconcentration depends upon the level of NOX and the levels of the other ex-planatory variables. When NOX and the other variables take on their meanvalues, the change in median housing values from a one pphm change in NOXis 1613.l*We also estimated the same housing value equation substituting PART forNOX (see Table VII). The coefficient of PART4 is negative and statis tically verysignificantl In addition, the coefficients of the nonpollution variables are vir-tually the same with PART or NOX in the equation, adding credence to theview that the various pollution variables are reflecting households aversion topollution generally rather than to individual pollutants.While NOX was determined to be the superior NOX term, the nonlinearleast squares grid search suggested that we could not place great confidence inthe precise exponent of 2.?OBecause of the distinct possibility that the true valuefor p is some value other than 2, our later uses of the housing value equationinclude results for exponents of the NOX variable ranging from 1.0 (the linearsemilog form) to 3.0. As an additional test of the sensitivity of the results to non-linearities in NOX, we estimated an equation including both log( NOX) andlog (NOX) , the first two terms in a Taylor series approximation to NOXP, andone including both NOX and NOX2. Most of the coefficient estimates were notsubstantially different from those in the basic equation with NOX? as the soleair pollution term. The application in Section V provides comparisons of benefitestimates when these other formulations are used.The basic equation was substantially unchanged when corrected for hetero-scedasticity. Because our empirical analysis is based on census tract data ratherthan individual observations we anticipated that heteroscedasticity might be a

both NOX and PART appearing, the coefficient on NOX became positive. However, theproblem is simplified if one is willing to alter the specification to include a single pollutantmeasure. To test for the presence of multicollinearity with a single pollutant measure, weexperimente d to see whether the use of ridge regression techniques migh t alter our parameterestimates (they did not). In additi on, we did a singular value decomposition of the matrixof explanatory variable data as described in Belsley and Kle ma [21. The singular value de-compositio n is a numerica l analysis technique which is useful for determ ining the extent towhich there are linear dependencies amon g the columns of the explanatory variable matrix.Specifically, the Nxk matrix X is decomposed as X = UZV, where Z: is a diago nal matrixwhose diagonal elements (called singular values) are the square roots of the eigenvalues ofXX . Low singular values imply near linear dependencies and thus a severe multicollinear ityproblem. The relatively high values we obtained indicated that multicollinearity does notpermit a serious problem in estimating the housing value equation,

18 We were also concerned about the sensitivity of the mod el parameters to the data,Tests of this kind, which involve reestimating the mod el w ithout one or more data points, aredescribed in detai l in Welsch [341. In general, the coefficient on NOX is quite ins ensitive tothe omission of indiv idual or small groups of data points.

19 The nonline ar estimati on procedure using PA RT results in an exponent of 4.0, and thusthe equatio n listed in Table VII for PART uses PART 4 as the variable.

20 Because we used a grid search estima tion procedure, we were not able to determ ine anexact standard error for p. However, by using a standard nonline ar estimati on routine andan initial estimate of p = 2, we were able to approximate the asymptotic standard error of pas being equal to 1.3.


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88 HARRISON AND RUBINFELDproblem. To test for heteroscedasticity we applied a Park-Glejser procedure tothe basic equation. On this basis we rejected the null hypothesis of homoscedas-ticity at the 5% levelzl To correct for heteroscedasticity we reestimated thehousing value equation using weighted least squares; the result is presented inTable VII. Most of the coefficients were essentially unchanged, with the coeffi-cient on NOX falling in absolute value from -0.0064 to -0.0058. The examplein Section V includes results which account for this heteroscedasticity correctionin the housing value equation.Changes in the specification of the nonpollution variables in the housing valueequation did change the results substantially. When the two accessib ility vari-ables, weighted distance to Boston area employment centers (DZS) and theindex of accessibi lity to radial highways (RAD) were deleted; the coefficient ofNOX changed from -0.0064 to -0.0036. Because concentrations of NOX inBoston are higher in areas closest to the major employment centers and radialhighways, deleting DZS and RAD from the equation tends to reduce the mea-sured impact of NOX concentrations on housing values. The coefficient of NOXwith DZS and RAD omitted reflects both the disadvantages of greater NOXconcentrations and the advantages of greater accessibility . It is, therefore, sub-stantially biased. The same specification bias occurs when proportion of thepopulation that is lower status (LSTAT) is deleted from the equation, exceptthat the direction of bias is the opposite. The coefficient of NOX changes from-0.0064 to -0.0081 when LSTAT is eliminated. Deleting LSTAT tends tocredit NOX concentration with some of the neighborhood disamenities resultingfrom a high proportion of lower status households. These alternative specifica-tions illustrate the dangers of interpreting coefficients in poorly specified equa-tions. We discuss the quantitative impact of the specification differences on thecalculated willingness to pay for improved air quality in Section V.

IV. WILLINGNESS-TO-PAY EQUATIONBy calculating the derivative of the housing value equation with respect toNOX (the second step in our procedural model), we obtain information on the

amount of money that households would be willing to pay for small reductions inair pollution levels in their census tracts. As discussed in Section II, th is infor-mation is used in the third step to estimate a schedule relating willingness topay for marginal improvements to the level of air pollution and other variables.Table I presents five formulations of the willingness-to-pay equation, all basedon the basic housing value equation. The first two equations assume a linearrelationship between the willingness to pay for a marginal change in NOX con-centration and the NOX level, household income (ZNC), and (in Eq. (4.2) )persons per dwelling unit (PDU). The other three equations postulate a log-logrelationship.

21 We regressed the logarit hm of the square of the residuals against the logarith m of totaldwe lling units in a linear regression. The intercept of -1.54 was insignifican t, but the slopeof -0.48 was significant at the 5% level (the t value was -2.44 ). This test is described in16, 7, and 231.

22 Our willingness-to-pay equations are estimated using ordinary least squares under theassumption that the supply of air poll ution is perfectly inelastic at each location. This assump-tion is reasonab e in terms of short-run crosssection analysis, but may be suspect in a longerrun context. To test the sensitivity of our results to the potent ial simultanei ty problem caused


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THE DEM AND FO R CL EAN A I R 89

Willingness t,o Pay for Air Pollutiou Iteduct,ion Based on Nonlinear Housing Value Equation

Linear Equations* II-(4.1) w = - 1040 + 209 NOS + 12.1 zsc 0.5(4.2) W = -581 + 1X9 SOS + 12.4 ISC - 119,s PDl: 0.55

Log-log Eqrlat.ions*(4.3) log l+- = 1.08 + 0.57 log NOY + 1.00 log ISC 0.w(4.4) log W = 1.05 + 0.78 log NOX + 1.01 log ZSC - 0.24 log PDlJ 0.64(4.5) log w = 2.20 + 0.9 7 log 1VOX + O.SO log I.\TC - 0.03 (Yl) (log I\TOX)

- 0.07 (Y2) (log ,VOX) 0.64* All coeficient,s are significant at the 0.01 level.a W = marg inal willingne ss to pay ($) ; ArOX = nitrogen oxides concentration in pphm;

INC = household income in hundreds of dollars; PDU = persons per dwelling unit; Yl = 1when 95 >_ ZNC > 130, 0 otherwise; Y2 = 1 when ISC 2 130, 0 otherwise.

The relationship between marginal willingness to pay, NOX level and house-hold income implied by these results is depicted graphically in Fig. 1 for Eq.(4.3). The three curves illustrate the marginal willingness to pay as a functionof NOX level for three income levels, low ( 8500 per year), medium ( 11,500per year), and high ( 15,000 per year). The positive slope for all curves impliesthat households perceive at least some damages from air pollution to be greaterat higher pollution levels. Thus the willingness to pay for marginal reductionsis greater as pollution levels increase. Moreover, these differences seem to besubstantial for the NOX levels existing in Boston census tracts in 1970, wherethe average NOX level ranges from approximately 3 pphm to 9 pphm. Forexample, a middle-income household earning 11,500 per year would be willingto pay roughly 800 for a 1 pphm improvement in NOX when the NOX level is3 pphm, while the willingness-to-pay figure would jump to approximately 2200when the NOX level is 9 pphm. Figure 1 also shows that the willingness to payfor a marginal improvement in NOX concentration is greater for households inhigher income groups.The straight line at 2052 illustrates the willingness-to-pay curve implic it ina simple linear housing value equation (i.e., with hlV as the dependent variableand NOX in the equation) in which households are assullied to place the samedollar value on a 1 pphm improvement in NOX regardless of the existing levelof air pollution and their income level. Our results suggest that the assumptionof a constant will ingness to pay is unwarranted. Indeed, it appears that the total-by a less than perfectly inelastic supply of air pollu tion, we estimated the willingness-to-payequatio n using two-stage least squares, with INDUS , PDU (possible supply variables) andZNC appearin g in the first stage reduced form equation. The two-stage least squares esti-mate of the pollution elasticity fell to 0.70, while the income elasticity fell to 0.93. Thesechanges in elasticity had littl e impact on the nonm arginal benefit calculations described in thenext section. We also tested the log-log w illingness-to-pay equatio n for heteroscedasticity byapplying the Park-Glejser test described in the previous section. After rejecting the nullhypothesis at the 5% level, we reestimated the willingness-to-pay equatio n using weighte dleast squares. The weighted least squares equati on was log (W) = 0.91 + 0.96 log (NOX) +1.01 log (INC ), with all parameters significant at the 1% level. We report the impact ofthis adjustme nt on estimated benefits in the follow ing section.


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90 HARRISON AND RUBINFELDwillingness to pay for air pollution reduction varies a great deal depending uponthe existing air pollution levels in the urban area and the income profile of thepopulation.

Figure 1 also indicates that the premium that high income households are pre-pared to pay rises as the NOX level increases. At low NOX levels (3 pphm),the differential for households earning 11,500 compared to households earning8500 is only 200. But at high NOX levels (9 pphm), the differential is about700. Equation (4.5) includes a test of the hypothesis that households in differentincome groups have different elasticities of willingness to pay with respect toNOX levels. Dummy variable interaction terms are presented for middle incomehouseholds ( 9500 to 13,090) and high income households (over 13,000). Thenegative coefficients on both interaction terms imply that the elasticity of willing-ness to pay with respect to NOX level is 0.97 for the low income group, 0.94 forhouseholds in the median income group, and 0.90 for households in the highincome group.23 The larger willingness-to-pay elast icity for lower income house-holds suggests that as air pollution is reduced (other things equal), the marginalvaluation of air quality improvements declines more rapidly for lower incomehouseholds than for middle-income and high-income households.*

V. AN ILLUSTRATION: THE WILLINGNESS TO PAY FORFEDERAL AUTOMOBILE EMISSION CONTROLSTo illustrate the fourth and final step of our procedural model, this sectionestimates the housing value benefits associated with a program to improveBoston area air quality. Specifical ly, we consider the benefits from the federal

automobile emission control strategy, in which the federal government estab-lished tailpipe emission standards for new cars beginning in model year 1971.These emission standards became increasing ly stringent up to the 1978 yearmodel, when a roughly 90% reduction from the 1970 levels is mandated fornitrogen oxides, hydrocarbons, and carbon monoxide.The purpose of this illustration is not to determine the precise dollar figure forbenefits from this control strategy. Rather, it is to illustrate the sensitivity of thebenefit figure to different specifications of the housing value and willingness-to-pay equations. Much greater care would be necessary to separate out the inde-pendent influence of the automobile pollutants from the overall air pollution inthe Boston area in order to estimate with confidence the precise dollar value ofthe federal automobile emission control program.?

23 These elasticities are statistically different from each other at the 5% level.24 We do not present any results in which housing attributes other than air quality appear

in the willingness-to-pay equatio n. We found that the inclusion of other housing attributes hadvery littl e effect on our estimates of the willingne ss to pay for nonm argina l changes in airquality. However, it is possible that some housing attributes are complementary to (or sub-stitutable with) reduced air pollu tion so that households consuming greater (lesser) quan-tities of those attributes would be wil ling to pay more (less) for NOX improvements. Forexample , we tested the hypothesis that air quality and the number of rooms (RM) are com-plimentary, and the results c onfirmed the hypothesis (all t tests were highly significant):

log W = 0.71 + 0.81 log (NOX) + 0.78 log (INC) + 0.84 log (RM).25 It is difficult to say with assurance whether our benefit figures are overestimates or

underestimates of the true dollar value that Boston households place on the air quality im-provements generated by stringent auto controls. Benefits may be overestimated because the


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THE DEMAN D FOR CLEAN AIR 91W(S)

2500

2000

1500

1000

500

0 1 2 3 4 5 6 7 8 9 10NOX (PPHM)

FIG. 1. Willingness to pay for 1 pphm improvem ent in NOX concentration, by NOX levelfor households in three income levels (log-log version).

The physical changes in NOX concentrations in each of the 506 Boston SMSAcensus tracts were calculated for 1990 using the Transportation and Air ShedSimulation Model (TASSIM ), 26 The average dollar value of these physicalimprovements in NOX concentration depends upon the amount each householdis willing to pay for the physica l improvement they experience.27 The resultsgiven in Sections III and IV for the first three steps permit us to estimate theaverage dollar value under various assumptions about the function relatinghousing values to NOX concentration and other variables, and the function re-lating willingness to pay for marginal changes in NOX to the NOX level andvarious household characteristics. The full range of potential estimates of averagedollar benefits calculated in the fourth step can be visualized as a matrix withNOX variable may reflect the disbenefits associated with particulates and other nonauto pol-lutants. Note that our calcuations do not assume any reduction in nonauto sources of NOX(the physical changes in NOX predicted from auto controls are relatively small because of thelarge contribution of other NOX sources in the Boston airshed), and thus the auto benefits arenot overstated for that reason. A uto benefits may be understated because the value of re-ducing carbon monoxid e and hydrocarbon emissions may not be taken into account andbecause the full dollar b enefits of the auto emission control strategy includes some benefitswhich are not likely to be reflected in housing prices.

20 For a description of the TAS SIM mod el, see Ingram and Fauth [ll]. The estimates of1990 NOX concentrations in Boston subareas were obtain ed in TASS IM by substituting theemissions characteristics of the 1990 controlled fleet for the 1970 fleet emissions figures usedin the basic run. The physical benefits of the federal autom obile emission program are thensimply the difference between NOX concentrations in 1970 and 1990.

27 Our calculations assume that households are only wil ling to pay for air quality improve-ments in their residence tract. So me household members may also experience benefits in othertracts, where they work, shop, or visit.


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92 HARRISON AND RUBINFELDthe rows corresponding to different formulations of the housing value equationand the columns corresponding to different formulations of the willingness-to-pay equation. However, it is not necessary to present the full matrix of estimatesto gain an appreciation of the sensitivity of the results to alternative specificationsof the two building block equations.

Table II presents average annual benefits per household for four formulationsof the housing value equation and two versions of the willingness-to-pay equa-tion. The largest estimate of average household benefits ( 118) is derived froma linear housing value equatiomZx This is the specification often employed inprevious housing value studies. The linear equation contains the implic it assump-tion that every unit reduction in NOX concentration is valued identically by allhouseholds. The willingnes-to-pay function for all households is then a horizontalline at the unit price for NOX estimated by the linear housing value equation(see Fig. 1, where W = 2050).The other results reported in Table II are equations based on a semilog specif i-cation of the housing value equation (which inherently allows for variations inmarginal willingness to pay) that differ in the exponent assigned to NOX. Thebenefit estimate in which we place the greatest confidence is obtained from thesemilog housing value equation with the exponent of NOX equal to 2 (the basicequation) and the log-log willingness-to-pay equation. This combination yieldsa benefit estimate of 83 per household per year, approximately 30% below thefigure based on a linear housing value equation.? This 83 estimate takes intoaccount the fact that households willingness to pay for marginal reductions inair pollution may vary with the pollution concentration (a movement along thewillingness-to-pay curve; see Fig. l), as well as with household income (a shiftin the willingness-to-pay curve). The benefit estimate of 92 given in the secondcolumn indicates that if one were to allow willingness to pay to vary by tractbut not be systematically related to the level of pollution and income (i.e.,neglect the willingness-to-pay function), benefits would be overestimated byapproximately 11%.Calculating average benefit figures for the entire SMSA ignores variations inaverage benefits enjoyed by subgroups of the population classif ied by income,race, and other variables. To illustrate the distributional information that our

2s The formula used to calculate annua l benefits per household in 1990 for the linearspecification is:

where: AB = average annua l benefits per household (in dollars) from emission controls;HHt = number of households in census tract i; 4 NOXb = improvem ent in NOX concentra-tions in tract i in 1990 compared to 1970; a, = coefficient of NOX from linear housing valueequatio n; N = number of census tracts in sample (N = 506). Divid ing average benefits by10, imply ing a discount rate of 1070, yields an estimate of average annua l benefits.

20 The average dollar value is calculated as in the previous footnote, except that averagebenefit per household, B,, is substituted for the product (A NOXl) (a,). BI is calculated asfollows :


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THE DEMAN D FOR CLEAN AIR 93TABLE II

Average Annual Benefits per Household in Bost,on SMS A From Change in X0X Levels due toAutomobile Emission Controls : Based on Different Housing Value Equat,ions

Housing vahleequat,ion

Willingness-to-Pay equationAssume Assume W

11 = j(XOX, ISC) constant,(log-log version)

Linear $118.00Semi log (P = 1) $101.26 105.26Semi log (P = 2) 83.00 92.03Semi log (P = 3) 59.17 78.32

model can generate, we estimated the average benefits for three income classes.3oWe found that low income households received the highest benefit ( 93), whilehigh income households had the lowest average benefit ( 71). Low incomehouseholds receive the greatest dollar benefit because they live in highly pol-luted areas that experience the greatest reduction in pollution from auto emissioncontrols.The remaining results in Table II are tests of the sensitivity of benefits to theexponent of NOX in the housing value equation. Altering the exponent on theair pollution term from 2.0 yields markedly different average benefit figures.Average benefits are greatest for the semilog case (among the three values listedin Table II) when the exponent is put at 1.0, i.e., when NOX is entered in theequation. For the case when the log-log willingness-to-pay equation is used togenerate average benefits, average benefits increase from 83 to 101 when theexponent changes from 2.0 to 1.0. This change represents a 22% increase inaverage benefits. The change is just as dramatic when the exponent is assumedto be 3.0 rather than 2.0. Average benefits decline from their baseline value of83 to only 59, a 299, drop. Since we estimated a standard error of 1.3 on theexponent of 2.0 for NOX, we conclude that the true value for average benefitsin this case could easily range from approximately 60 per year to over 100per year, depending upon which specification of the NOX variable is the trueone.We also tested for the sensitivity of average benefits per household to differentspecifications of the willingness-to-pay function when the basic housing valueequation was used. These results (not reported here) indicate that the choiceof a specific willingness-to-pay function does not greatly influence the averagebenefit figure. For example, when the linear rather than the log-log version ofthe willingness-to-pay equation with NOX and ZNC is used, average benefitsonly increase from 83 to 84.

A great many other specifications of the housing value equation are possible,To explore the sensitivity of the average benefit figures to different housing valueequations, we calculated average benefit figures using a single willingness-to-payequation (the log-log version with NOX and ZNC) and several versions of the~10 ncome groups were based on the follow ing classification of census tracts by average

household income: low income: = $13,000 per year.


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94 HARRISON AND RUBINFELDTABLE III

Annu al Benefits per Household-Sensitivity to Alternate Specificationsand Various Statistical Problemsa

Annual benefitsper household ($)

I. Housing price specifications(1) Basic (s emilog, with NOX2)(2) Delete DIS and RAD(3) Delete LSTA T(4) Add NOX(5) Substitute log (NOX) and (log NOX)2(6) Income submarkets(7) Distance submarkets(8) Low status submarkets

II. Statistical Corrections(9) Heteroscedasticity in housing value equatio n 76.03

(10) Heteroscedasticity in willingness-to-pay equati on 84.07(11) Simultaneity in willingness-to-pay equation 82.31

83.0047.08

104.6478.5265.1359.8449.3575.65

a Unless otherwise indicated, all figures are based on the log-log specification of the willingness-to-pay equatio n : log W = f[log (NOX), log @NC)].

* This figure is based on the linear specification of the willingness-to-pay equatio n.

housing value equation. These results are listed in Table III. The baseline figureis 83, which is the average benefit obtained using the basic housing valueequation.The first experiment consisted of deleting some variables from the basicequation. Average benefits proved to be very sensitive to these experiments.When the two accessibil ity variables DIS and RAD were omitted from thespecification, average benefits fell from 83 to 47. This decrease occurs becausewhen DZS and RAD are omitted from the equation, some of the advantages of

greater accessibility cancel out the disadvantages of higher NOX concentrations.Therefore, the benefits of reduced pollutant concentrations appear smaller. Thesame confusion occurs when LSTAT is deleted from the equation, except thatomitting LSTAT increases the calculated average benefits from 83 to 105.When LSTAT is not in the equation, the empirical results attribute to high NOXlevels some of the perceived disbenefits of being in an area with large propor-tions of lower status households. These results show that the benefits of reducedair pollution concentration may be substantially overestimated or underestimatedif the equation used to describe the structure of the housing market is misspeci-fied. One should be particularly suspicious of estimates of dollar benefits fromair pollution reductions which are based on formulations omitting importantneighborhood and accessibi lity variables which are like ly to be quite highlycorrelated with air pollution.

The second experiment reported in Table III is to modify the housing valueequation by including other nonlinear functional relationships for NOX. Includ-ing both NOX and NOX in the housing value equation somewhat decreases theaverage benefits, although the decline is not very great (from 83 to 79). Amore substantial decrease occurs when log NOX and (log NOX) are substituted


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THE DEM AND FO R CL EAN A I R 95for NOP in the equation. Average benefits in that case decline to 65.31 Theseresults provide additional evidence of the sensitivity of the average benefitmeasure to the form in which air pollution influences housing values.

The next three estimates in Table III [ (6)) (7), and (S)] provide the resultsof experiments which assume that the Boston SMSA housing market is actuallya series of distinct submarkets. The aggregative census tract data used in thisstudy do not allow us to calculate average benefits for detailed specifications ofhousing submarkets. However, we tested for the variations in the averagebenefits when submarkets were postulated based on household income (threecategories: low income, medium income, and high income), on accessibility to em-ployment (two categories: accessible, not accessible), and on socioeconomic status(two categories: high status, low status). The average benefits were calculatedfor the submarket cases by estimating separate housing market equations (thebasic equation), using the results to estimate a single willingness-to-pay func-tion to calculate household benefits for each tract in the various submarkets,and then calculating average benefits from the Boston SMSA as a whole. Whilethe specifications of the submarkets in these experiments are crude, the results inTable III indicate that the presence of submarkets may decrease average benefitssubstantially. In the most extreme case, when two submarkets are defined interms of accessibi lity to major employment centers, the average benefits fallfrom 83 to 49. The 49 figure represents approximately a SO(b decline from the118 estimate based on the linear housing value equation.

The final estimates of average benefits in Table III reflect corrections forheteroscedasticity in the housing value equation and heteroscedasticity andsimultaneity in the willingness-to-pay equation. The average benefit figures inTable III indicate that correcting for these possible statistical problems has arelatively small effect on the estimate of average benefits, although the averagebenefit figure does decline to 76 when a correction is made in the housingvalue equation.

VI. CONCLUSIONMost empirical studies which attempt to measure the willingness to pay for

cleaner air from housing value differentials (such as Ridker and Henning [27] )estimate a hedonic equation in which housing values are regressed against pol-lution levels as well as other housing attributes. Freeman [5] and Small [30]have argued that the benefit estimation procedure used by Ridker and Henningand others is correct for valuing marginal improvements in air quality, But inusing these regression results to estimate the total benefits arising from a non-marginal improvement in air quality, Ridker and Henning and other researchersimplicitly assume that the value placed on a marginal improvement in air pollu-tion concentration is independent of the level of air pollution and independent

~1 This $65 figure is based on a linear rather than a log-log version of the willingness-to-pay equatio n (because a log-lo g formul ation could not be estimated), so the $65 figure is notdirectly comparable to the $83 figure. However, our results clearly indicate that the func-tiona l form of the willingness-to-pay equati on has a smal l influence on average benefits.

:( Our attempts to define submarkets based on cross-classifications of several variables (thepercent Black popula tion in the census tract, the average tract income, the accessibility of thetract to employ ment centers, and the scl~ool quality in the tract) faile d because many of thevariables were constant or nearly constant with in the s&markets. This result is a function ofusing average values for census tracts rather than indiv idual observations on households.


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96 HARRISON AND RUBINFELD

Variable1 dependent

MVStructural

RM

AGE

NeighborhoodB

LSTAT

GRIM

IIVDUS

TAX

TABLIS IVVariables used in the Housing Value I


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Variable I )efinition

I TRAl IO

CHAS

Accessibilil.,vDIS

II AD

Air PollutionA~O_Y

PAM

THE DEMAN D FOR CLEAN AIR 97TAHLK IV-Continuctl

Source---__

Pupil-teacher rat,io by t,own school district. Measures Massachuaet ts Dept. ofprtblic sector benefits in each town. The relation of the 15ducation (IQ71 -1 QTB)pupil&teac her rat,io to school quality is not entirelyclear, although a low ratio should imply each studentreceives more indivi dual att,ention. We expect the signon PTlIA710 to be negative.Charles River dummy : = 1 if tract bounds the Charles 1970 U. S. CensusIliver; =0 if ot,herwise. CHAS captrues the ameni ties Tract nuapsof a riverside locsation and (1111s the coeflicient shouldbe positive.

Weighted distances to five employ ment centers in the Srhnare CJQ]Boston region. According to t,raditio nal theories ofurban land rent gradients, housing values should behigher near employ ment renters. DZS is entered inlogarith m form; the expected sign is negative.Index of accessibility to radial highways. The highway 3lIT I3osiorr Pr,ojert,access index was calculated on a town b:lsis. Goodroad acress variables are needed so that allto pollut ionvariables do not capture the location al advantages ofroadways. IZAD captures other sorts of location al ad-vantages besides nearness to workplace. 1~ is enteredin logarithm ic form ; the experted sign is positive.

Nitrogen oxide concentrat ions in pphm (annual aver- TASS IRLage concentrat,ion in parts per hundred mill ion).Part,iculat,e concentrations in mg/hcm3 (annual aver- TASS Intage concerrtt,ation in milligr ~ams per hrmdred crtbicmeters). -

Slmunary Statistics for Housing Valu e Equation Variables

Variable Mean Sl)


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98 HARRISON AND RUBINFELDof household income and tastes. This is equivalent to assuming a linear dlamagefunction for air pollution that is identical for all households.The four-step estimation procedure used in this study allows us to concludethat marginal air pollution damages, at least as revealed in the housing market;increase with the level of air pollution and increase with the level of householdincome. By taking expl icit account of these variations by estimating a willingness-to-pay function, we find that the improper use of marginal valuation estimatesto calculate the benefits of nonmarginal improvements causes benefits to beoverstated by approximately 3070.In the process of using our model to estimate households willingness t? pay,we found that the valuation placed on a marginal improvement in air quality isquite sensitive to the specification of the hedonic housing value equation. Withplausible specifications of the relationship among air pollution, housing attributes,and housing values, aggregate benefit estimates may be reduced as much as 60%below the figure based on a constant marginal valuation. In contrast, the benefitestimates were found to be insensit ive to the specification of the willingness-to-pay function. Neither modifying the functional form nor changing the specificvariables included in the equation had a significant effect on the dollar value ofbenefits in the example we considered.

APPENDIX: RESULTS FOR THE HOUSING VALUE EQUATIONMost of the empirical results for the housing value equation are based on a

common specification, as given in Eq. (A.l).log (MV) = al + azRM* + asAG& + aa log (DIS) + us log (RAD) + aeTAX

+ a7PTRATI0 + a8(B - 0.63)2 + aglog (LSTAT) + a&RIM+allZN + allINDUS + a&HAS + algNOXP + e (Al)

The study uses data for census tracts in the Boston Standard Metropolitan Sta-tistical Area (SMSA) in 1970. With tracts containing no housing units or com-prised entirely of institutions excluded, the Boston sample contains 506 censustracts. The definition of each variable, its expected sign, the data source, and thefunctional form in which each enters are indicated in Table IV. The samplemeans and standard deviations are reported in Table V, and the simple corre-lations among variables are given in Table VI.The data on 1970 air pollution concentrations used in this study were ob-tained from a meteorological model of the Boston air shed, the Transportationand Air Shed Simulation (TASSIM ) Model developed by Gregory Ingram andothers.33 The TASSIM model generates surfaces of mean air pollutant concen-trations for the Boston SMSA which are then adjusted (or calibrated) usingregression equations which compare TASSIM output to monitoring data.4 Nine-

33 The TASSIM Model is described in [ll].34 It is likely that individua ls are sensitive to variations in pollu tion levels as wel l as annua l

means. For any averaging period, Larsen [18] found that the readings over 1 year were dis-tributed log-norm ally, a distribution with two parameters (mean and variance). Thus, airpollu tion exposure at any given housing site would be completely described if the mean andvariance for the years readings were included. Not includ ing the variance in our housingvalue equatio n migh t bias our results, altho ugh the strong correlations between momen ts ofthe frequence distribution suggests that the bias is not very great. Both Anderson andCracker [I] and Wieand [35] reported that their results were not changed when othermoments were added to the housing value equation.


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T

V

Simpe

Coeao

amo

Vae

Av

RX

AGE

DIS

RAD

TXPTRATO

B

JSAT

CRId

ZN

INDUSCHASPART

SOS

INC

_~

3

10

RM

07

10

E

AGE

-03

-02

10

DIS

03

02

-07

10

5

RAD

-03

-02

04

-05

10

3

TX

-04

-02

05

-06

09

10

PTRATO

-05

-03

02

-02

04

04

10

2

B

-03

-00

02

-02

04

04

01

1o

LSTT

-07

-06

06

-05

04

05

03

03

10

GRIM

-03

-02

03

-04

06

05

02

03

04

10

E

Z

03

03

-05

05

-03

-03

-03

-01

-04

-02

10

5

JNDUS

-04

-03

06

-07

06

07

03

03

06

04

-05

10

L

CHAS

01

00

00

-00

-00

-00

-01

-00

-00

-00

-00

00

10

s

PART

-04

-03

07

-08

05

06

02

02

06

04

-05

07

00

10

NOX

-04

-03

07

-08

06

06

01

03

05

04

-05

07

00

09

Io

INC

08

06

-05

04

-04

-05

-04

-03

-07

-03

04

-05

00

-05

-05

1o


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100

Variable

Dependent;ConstantRL WAGELog (DIS)Log (RAD)TAXPTRATIO(Z3 - 0.63)2

Log (STAT)C R Z M%:\TI NDUSCHASNOXPPART=PPR2

HARRISON AND RUBINFELD

TABLE VIIHousing Valu e Eyust,ionsc

Basic equationEqnation 1

Log (MV)9.76

(65.22)0.0063(4.83)

8.98 x lot5(1.7)

--o.lY(-5.73)0.096

(5.00)-4.20 X lO-

( - 3.43)-0.031

(-6.21)0.36

(3.53)-0.37

(- 14.84)-0.012

(-9.53)8.03 x 10-S

(0.16)2.41 x lo-

(0.10)0.088

(2.75)-0.0064(-5.64)

2

0.81a t statistics are in parentheses,

Basic equat,ionweighted

least squaresIGluation 2Log wn9.66

(66.91)0.0057(4.53)

1.26 X lO+(0.25)-0.20(-6.21)

0.107(5.94)

-3.53 x lo-( - 3.09)

-0.030(-6.25)

0.43(4.01)

-0.38(- 16.24)

-0.014( - 8.00)

2.82 x 10-d(0.58)

-2.22 x 10-4(-0.10)

0.090(2.92)

-0.0058C-5.27)

2

Equation :3

Log (MV)9.75

(71.46)0.0061

(1.75)-8.78 x 10-S

(-0.17)-0.21(-6.53)

0.082(4.43)

-3.98 X lo-*(-3.35)

-0.033( - 6.85)

0.44(4.48)

-0.35(-14.39)

-0.011(-9.26)

4.25 x 10-b(0.86)

9.05 x 10-4(0.40)0.067

(2.07)

-0.051( - 7.99)

40.82

teen stations monitor NOX and 18 monitor particulates. The fits of the calibrationequations are quite good, the explained variance being 51% for the NOXequation and 84% for the PART equation.3535 Other housing value studies have not used a meteor ological mod el to derive air polluta nt

concentrations but instead have obtaine d air pollu tion data for census tracts by extrapolatingdata from a relatively small number of monito ring stations. Ridker and Henn ing [27], Ander-son and Cracker [l], and Wieand [35] 11 used St. Louis air pollu tion data derived from iso-pleth maps which were based on a maximum of 41 monitoring stations; Anderson andCracker also used simila r data from Washington, D. C., and Kansas City, although the numberof monito ring stations was not given. N elson [22] used Washington, D. C. data derived frombetween 9 and 26 mc&toring stations.


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THE DEMAN D FOR CLEAN AIR 101Table VII gives the results of estimating Eq. (A.1) with NOXP in the equation,

where p is a parameter to be estimated. This is the basic equation used in thepaper as the starting point for judging the sensi tivity of the results to alternativespecifications of the housing value equation. Table VII also contains the resultsof estimating the same housing value equation using weighted least squares andsubstituting PART for NOX.

REFERENCES1. R. J. Anderson and T. D. Cracker, Air pollu tion and residential property values, Urb.

Stud. 8, 171-180 ( 1971).2. D. A. Belsley and V. C. Klem a, Detecting and assessing the problems caused by multi-

collinearity: A use of the singular-value decomposi tion, Working Paper NO. 66,Natio nal Burea u of Economic Research, Cam bridge, Mass. (December 1974).

3. G. E. P. Box and D. R. Cox, An analysis of transfomration, I. Roy. Sta.S. 26, 211-243(1964).

4. D. B. Diam ond, Income and residential location in urban areas, University of Chicago,Chicago, Ill. (December 1975).

5. A. M. Freeman, On estima ting air pollu tion control benefits from land value studies,J. En&r. Mana g. 1, 74-83 (May 1974).

6. H. Glesjer, A new test of heteroscedasticity, 1. Am. Stat. A. 64, 316-323, ( 1969).7. S. M. Goldfel d and R. E. Quandt, Nonlinear Methods in Econometrics, North-Hollan d,

Amsterdam, Holland ( 1972).8. Z. Griliches, Introduction: Hedonic prices revisited, in Price Indexes and Quality Change

(Griliches, Ed.), Harvard University Press, Cambr idge, Mass. ( 1971).9. D. Harrison, Jr., Who Pays for Clean Air: The Cost and Benefi t Distribution of FederalAutomobile Emission Standards, Ballinger, Cambridge, Mass. ( 1975).

10. D. Harrison, Jr., and R. N. McDona ld, Willingness to pay in Boston and Los Angelesfor a reduction in automob ile-relat ed pollutants, in A Report by the Coordi natingCom mittee on Air Quality Studies (Nation al Academy of Sciences), prepared for theComm ittee on Public Works, U. S. Senate, Volum e IV: The Costs and Benefits ofAuto mob ile Emissio n Control, U. S. Government Printin g O ffice, Washington, D. C.( Septem ber 1974).

11. G. K. Ingram and G. R. Fauth, TASSIM: A Transportation and Air Shed Simulatio nModel, Final Report to the U. S. Departme nt of Transportation, Natio nal TechnicalInformatio n Service, Spring field, Va. (May 1974).

12. J. F. Kai n and J. M. Quigley, Measuring the value of housing quality, J. Amer. Stat. A.,65, 532-548 (May 1970).

13. J. F. Kain and J. M. Quigley, Housing Markets and Racial Discrim ination: A Micro-economic Analysis, Natio nal Bureau of Economic Research, New York, NY ( 1975).

14. A. King , The dema nd for housing: A Lancasterian approach, University of Maryland,Coll ege Park, Md. (January 1975).

15. A. Kin g and P. Mieszkowski, Racial discrim ination, segregation, and the price of housing,.I. Poli t. Econ. 81, 590-606 (May/June 1973).

16. J. Kme nta, Elements of Econometrics, Macm illan, New York, NY ( 1971).17. K. J. Lancaster, New approach to consumer theory, J. P&t. Econ. 74, 132-157 (April

1966 ) .18. R. I. Larsen, A mathe matical mod el for relating air quality measurements to air quality

standards, U. S. Environm ental Protection Agency, Washington, D. C., Report AP-89(November 1971).

IQ. L. B. Lave and E. P. Seskin, Air pollution and human health, Science, 169, 723-733(August 21, 1970).20. R. E. B. Lucas, Hedonic price functions, Econ. Inq. XIII, 2, 157-178 (June 1975).

21. J. Muellbauer, Household production theory, quality, and the hedonic technique, Amer.&on. Rev. 64, 977-993 (December 1974),

22. J. P. Nelson, Reside ntial choices, hedonic prices, and urban air quality, J, UrI7. Econ.(forthcoming).


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