In terurban Wage and Rent differences: the Value of AirQua lity an d Crime in Chile.∗byFelipe Vásquez La vínDepa rtm ent of Agricultural and Resou rce Econom ics, University of Califo rnia ,Berkeley, 311 Giannini Hall.∗I am grateful to Maximilian Auffhammer, Sofia Villas-Boas, Rui Huang, James Manley andSusan Stratton for their useful comments on the draft version of this paper. I would like to blamethem for any errors which remain but m y good manners compel me to absolv e them of any guiltand take full responsibility myself.1AbstractIn this article I exa m ine th e existe nce of compensating differentials in the housing andlabor markets using data from a national survey in Ch ile. Contrasting with earlierliterature I consider the simultaneous c ha racter of decisions made b y individual inboth th e labor and housing market. Emphasis is placed in the joint estimatio n of bothwage and ren t equations taking into account the correlation bet ween the error termsin these two equations. A first round of estimations includes an OLS, a SURE and asimultaneous Tobit model. I tested the endogeneity of some amenities of interest usinga Hausma n test. T h e hypothesis of endogeneity can not be rejected. Th erefore theestimations are corrected for endogeneity using 2SLS and 3SLS. Finally I computedwelfaremeasuresfortwoofthemostimportantproblemsnowadaysinChile,crimeand air pollution. Results show that i) incremen ts in crime rate or air pollution ha v ea negativ e impact in welfar e and ii) welfa re measu res estimates and their varian ce arehighly biased when the simultaneity is not considered.21IntroductionAs an extension of the theory of compensating wage differen tials, hedonic w age theorypostulates that when w orkers have the same productivit y and the market is perfectlycompetitiv e, differences in w ages will reflect d ifferences in the no n-wage c h aracteristicsof the jobs. In particular, different levels of ame nities, ceteris paribus, should bereflected in the gap of equilibrium w ages obtained by otherwise “equal jobs andworkers” (Rosen 1979, 1986).These amenities include ch aracteristics that are completely exogenous to the eco-nomic agen ts suc h as climate components (precipitation, temperature, humidity, etc),as well as other c hara cteristics that are a result of the agents’ decisions such as urbancondition s and enviro nmental qualit y. When an individua l ch ooses a place to liv e orw ork, he or she indirectly affects other aspects of the communit y such as populationdensity, average education and income, n umber of cars in the location, etc. In thesame w ay, when firms make location decisions, they also affect some c haracteristicsof the neighborhood through emissions to the en viron m ent, labor demand , etc.In particular I an ticipat e that conditions like air quality and crime rates generatea wage differen tial among different locations, to the exten t that these c har acteristicsvary among regions. Th us in places where environm ental conditions are considered tobe better one would expect that, all other factors equal, w ages should be permanentlylo wer than in those regions where conditions are considered to be w orse. This is the3essence of the theory of hedonic wag es.This idea can be traced bac k to hedonic price theory, which looks at the di ffer-ences in housing prices to obtain a welfare measure associated with an environmen ta lamen ity. In this literature, the value of an environmental amenity can be appro x-imated through the estimation of a cross section price equation, which can be afunction of location specific amenities (sa y air pollution and crime), house and otherneighborhood characteristics. Studies that specific ally address the effect of air qualityon housing prices are Ridker and Henning (1967), Anderson and Croc ker (1971), Free-man (1971, 1974) and Sm ith and Dey ak (1975); crime has been studied by Roback(1982) and Deller et al. (2001) among others.In equilibrium the marg inal imp licit price for the amenity will equate the con-sume rs’ m arg inal willingness to pay, and hence the derivativ e of the housing pricefunction with respect to the en vironm ental amenit y can be interpreted as its marg inal(implicit) price (Rosen, 1974; Freeman, 1979; Palmquist, 1991).One difference between hedonic wage and price theory is that while for propertyvalue models the derivative of the price function with respect to the en viro nmentalamen ity can be in ter p reted as the marginal price for this ame nity, this is no longerso in the wage model. The reason is that from the worker’s perspective the housingand job decisions are connected. Generally, a decision to mo ve to a job in anothercit y will be at the same time a decision to change residence to that city. But, if an4environmental amenity does have an effect on the job and housing location charac-teristics, then these decisions will not be independent. For examp le if the prospectof living and w orking in a clean env iro n ment increases the desirab ility of a job in acertain city, proba bly the dema n d for housing services will be high in this cit y andtherefore housing ren ts will also be high. Thus the worker should consider the trade-off betweenhavinga“better”jobandpayingamoreexpensiverent. Thisiswhythejob and housing decisions are modeled together in the form al hedonic wage models(Rosen, 1979; M arin and Psac h aropoulos, 1982; Robac k , 1988; Hoehn et al. 1987).The princ ipal result of this procedure is that the marginal willing ne ss to pay for ahigher enviro nm ental qualit y will depend on both the willingness to accept a lowerwage and the willingness to spend more on housing (Freeman, 2003).From an estimation perspectiv e one should model at least a two-equation systemwith a w age and a housing price equation. Since Roback (1982) developed the modelfor t wo simultaneous equation systems, man y authors have applied it to estimatethe value of some enviro nm ental amen ities. Nevertheless, most of them ha ve totallyignored the possible correlation between the error terms in these equations. Theusual practice has been to estimate two separate equations, one equation for wageand another for rent, using OLS or some nonlinear Box-Co x transformation. Someexamples of this kind of applications include papers b y Robac k (1982, 1989), Hoehnet al. (1987, 1988), and Deller and Ottem (2001) amon g others. Clark and Kahn5(1988) calculate a willingness to pay function