Welfare Measurement and Policy Evaluation in a Dual-Market Locational Equilibrium

Transcription

1 Welfare Measurement and Polcy Evaluaton n a Dual-Market Locatonal Equlbrum Ncola V. Kumnoff Appled Economcs, Vrgna Tech 36 Hutcheson Hall (040) Blacksburg, VA 2406 Phone: Fax: kumnoff@vt.edu Abstract: Ths paper uses a model of sortng behavor across housng and labor markets n the San Francsco and Sacramento Consoldated Metropoltan Statstcal Areas to evaluate the dstrbutonal welfare mplcatons of Calforna s new standard for ambent ozone concentratons. The model depcts workng households who dffer n ther job sklls and n ther relatve preferences for multple publc goods makng a jont job-house choce among housng communtes and labor markets that dffer n the job opportuntes and publc goods they provde. Households reveal features of ther preferences through the locatons they choose, and these choces determne spatal varaton n the demand for housng and the supply of labor. A companon paper develops a structural estmator whch recovers preferences for publc goods from the observed sortng behavor of workng and retred households (Kumnoff [2007]). After combnng nformaton about preferences wth nformaton about the supply of housng and the demand for labor, the model of sortng behavor s used to smulate how wage rates, housng prces, and people s locaton choces would adjust to the ar qualty mprovements needed to meet Calforna s new standard. Convertng these results nto welfare measures suggests annualzed benefts range from $292 to $346 per household. These estmates are less than half the sze of approxmatons based on the standard practce of multplyng the average margnal wllngness-to-pay by the sze of the ozone reducton. March, 2008 Draft: Please do not cte I thank Jay Coggns, Paul Fackler, Ray Palmqust, Dan Phaneuf, Jaren Pope, and especally V. Kerry Smth for helpful comments and suggestons on ths research. I also thank semnar partcpants at the Unversty of Mnnesota. Support from the Natonal Scence Foundaton and the Vrgna Agrcultural Experment Staton s gratefully acknowledged.

2 I. Introducton More than 50 years ago, Charles Tebout (956) suggested that people sort themselves across space accordng to ther preferences for the publc goods that dfferentate urban neghborhoods. Ths smple proposton underles the tradtonal hedonc approach to estmatng the benefts from changes n publc goods. More recently, advances n sortng research have produced a new framework for polcy evaluaton whch combnes the nformaton provded by an equlbrum hedonc prce functon wth a formal descrpton of the choce process that explans how heterogeneous households sort themselves across dfferentated neghborhoods (Epple and Seg [999]; Bayer et al. [2007]). These equlbrum sortng models drectly manfest Tebout s logc. They use the propertes of market equlbra, together wth nformaton on households and ther locaton choces, to estmate structural parameters whch characterze heterogenety n preferences for local publc goods. The results can be used to develop theoretcally consstent predctons for the dstrbutonal welfare mplcatons of future polcy changes. Analyss s not lmted to margnal effects or a partal equlbrum settng. By characterzng the sortng process, the analyst can predct how households would adjust ther behavor n response to large-scale changes n publc goods or other amentes (Seg et al. [2004]). Understandng how people dffer n ther preferences s mportant for desgnng new polces and evaluatng ther mpacts. For example, Blnder and Rosen (985) demonstrate how nformaton about preference heterogenety can, n prncple, be used to desgn more effcent taxes on prvate goods. Equlbrum sortng models provde the means to mplement ther dea and extend t to consder polces whch target publc goods or envronmental amentes that affect people dfferently. Lkewse, to evaluate the welfare mplcatons of a new polcy whch affects people dfferently, the analyst must understand how people dffer n ther wllngness-topay for the assocated change n publc goods. Equally mportant for polcy evaluaton s the need to recognze that people may adjust ther behavor n response to large-scale changes. For example, Banzhaf and Walsh (forthcomng) fnd that when ndustral facltes whch emt toxc chemcals move nto a neghborhood, some resdents move out. When these facltes move out, new resdents move n. The prce adjustments needed to clear the housng market followng these shocks wll affect the welfare of homeowners and renters. Recent studes have demonstrated that shocks to spatally 2

3 delneated amentes such as cancer rsk (Davs [2004]), ar qualty (Chay and Greenstone [2005]), flood rsk (Pope [forthcomng]), and the presence of regstered sex offenders (Lnden and Rockoff [forthcomng]) can produce economcally sgnfcant changes n property values. The objectve of ths paper s to use a model of equlbrum sortng n Northern Calforna s two largest populaton centers, the San Francsco and Sacramento Consoldated Metropoltan Statstcal Areas, to evaluate the benefts from the state s new standard on ambent ozone concentratons. In May of 2006, Calforna reduced ts 8-hour ozone standard to parts per mllon. Meetng ths standard would requre a large change n the spatal dstrbuton of ar qualty n the study regon. Natural weather patterns lmt ozone accumulaton n the San Francsco Bay Area so that many of ts communtes already meet the new standard. Meanwhle, Sacramento s located n one of the four most polluted ar basns n the Unted States, and would requre ozone reductons of up to 28%. Ths change s suffcently large to expect that, f met, t may nfluence where some households decde to lve. Whle the San Francsco and Sacramento metropoltan areas are adjacent, ther major busness dstrcts are 80 to 20 mles apart far enough to lmt commutng. Thus, for workng households, movng to a new home may requre fndng a new job or adjustng to a dfferent commute. More generally, t s mportant to consder how labor markets nfluence the way households adjust to large-scale changes because hstorcal evdence on sortng behavor and recent survey data both suggest that job opportuntes may be the domnant factor n determnng where households choose to lve (Rhode and Strumpf [2003]). For example, the annual Amercan Housng Survey consstently reports proxmty to employment as the reason most frequently cted by households for choosng to lve n ther current neghborhood. The model developed n ths paper extends the equlbrum sortng framework from Epple and Seg (999) and Seg et al. (2004) to recognze that workng households make a jont job-house choce. In ths new dual-market framework, a locaton conveys a set of job opportuntes together wth local publc goods, whle workng households dffer n ther job sklls and n ther relatve preferences for those publc goods. A companon paper, Kumnoff (2007), develops a structural estmator whch recovers nformaton on job skll and preferences for publc goods from data on the characterstcs of workng households and ther locaton choces n both markets. The results from estmatng the model for the San Francsco-Sacramento regon 3

4 are used here to smulate how households, prces, and wages would adjust to the large-scale mprovements to ar qualty requred to meet Calforna s new ozone standard. The dual-market framework and Epple and Seg s model are both used to evaluate the dstrbuton of benefts from Calforna s new ozone standard. Movng to the dual-market framework ncreases beneft estmates by 55% for the average household. However, ths fgure aggregates over order-of-magntude dfferences for households n the communtes whch experence the largest reductons. The results also ndcate that approxmatons to welfare measures based on the standard practce of multplyng average margnal wllngness-to-pay by the sze of the change would overstate benefts by up to 336%. The remander of the paper s organzed as follows. Secton II develops a model of sortng behavor n the sprt of Tebout s orgnal model, and then generalzes t to recognze that workng households make a jont job-house choce. After formalzng the condtons for a dualmarket locatonal equlbrum, ths concept s compared to alternatve equlbrum concepts from the hedonc and sortng lteratures. Secton III develops a parametrc verson of the model and uses t to llustrate how assumptons about heterogenety n preferences and job opportuntes nfluence estmated welfare measures. Secton IV summarzes the data and results from estmatng the model for Northern Calforna and dscusses the parameter estmates used to calbrate the polcy smulaton. Secton V translates Calforna s new ozone standard nto a spatal dstrbuton of ar qualty for the polcy smulaton, and secton VI develops the general equlbrum model and nterprets the results. Fnally, secton VII summarzes the polcy mplcatons and provdes some concludng remarks. II. Characterzng a Dual-Market Locatonal Equlbrum To begn, dvde the urban landscape nto a fnte set of J housng communtes, each of whch dffers n ts prce of housng ( p ) and n ts provson of a vector of local publc goods, ( g ). j Publc goods are defned broadly to nclude servces produced from local taxes, such as school qualty and polce and fre protecton, as well as envronmental amentes such as ar qualty and access to open space. Households may dffer n the relatve mportance they assgn to each of these publc goods. To reflect ths heterogenety, let γ represent relatve preferences, and g ( γ ) j j represent the composte provson of publc goods n communty j as perceved by a γ type 4

5 household. All households are assumed to be prce-takers, to have perfect nformaton, and to be freely moble. Each one wll choose the communty that maxmzes ts utlty, gven ts ncome ( y ) and ts preferences (α ) for publc goods relatve to prvate goods. Utlty maxmzaton can be represented as a two-stage problem, where each household frst determnes the optmal quanttes of housng and numerare n every communty and then chooses the communty that maxmzes ts utlty. The frst stage s shown as equaton (). maxu ( h, b) [ g( γ ), h, b,α ] subject to ph = y b. () Condtonal on a communty, a household wll choose quanttes of housng (h) and a composte prvate good (b) to maxmze ts utlty subject to the budget constrant. Assumng households are free to purchase contnuous quanttes of housng at the market prce n each communty, preferences can be restated usng the ndrect utlty functon n (2). V [ α ] [ g( γ ), p, α, y] U g( γ ), h( g( γ ), p, α, y), y ph( g( γ ), p, α, y), =. (2) Each household wll choose the communty that provdes ts preferred bundle of publc goods, gven ts (exogenous) ncome and prces. Ths s Tebout sortng. To recognze that workng households face dfferentated job opportuntes, dvde the urban landscape along a second dmenson nto K labor markets that dffer n the wage pad to workers of each job skll. Wth J housng communtes and K labor markets, each (j,k) par represents a unque job-house combnaton, whch wll be descrbed as a locaton. Each locaton requres a specfc commute. For a household that commutes between j and k, w, represent wage earnngs less the value of tme spent commutng, where θ s a vector let ( θ ) j k descrbng the worker s job skll and ther shadow value of tme. Therefore, a workng household s total ncome can be represented by nw + ( θ ) w jk, ts exogenous non-wage ncome ( nw ) plus ts vrtual wage ncome. Holdng ther job locaton and nomnal wage fxed, a household can vary ther vrtual wage ncome by changng ther house locaton, whch changes ther commute tme. The k subscrpt on the wage functon recognzes that, condtonal on skll, a worker may be compensated dfferently n dfferent labor markets due to varaton n technology, regulaton, agglomeraton, or other factors whch affect labor demand. 5

6 Utlty maxmzaton s smlar to (2) except that households now choose both a home and a job. Equaton (3) formalzes ths problem for household. max jk [ g ( γ ), p, α y ], where y nw + w ( θ ) V, j j jk jk =. (3) jk A workng household wll choose the job-house combnaton that maxmzes ts utlty, recognzng that ts wage ncome wll be determned by that choce. For a retred household, y = nw, and the locaton choce problem reduces to the more famlar one of selectng a housng communty. Utlty maxmzaton s a necessary, but not suffcent, condton for the exstence of a locatonal equlbrum. A dual-market locatonal equlbrum must also be characterzed by vectors of housng prces and wage rates such that all markets clear and no household could mprove ts utlty by movng. These condtons are formalzed n (4). V H L [ g ( ), p, α, y ( θ )] V [ g ( γ ), p, α, y ( θ )], l m S k S j γ (4.A) j j jk l l lm, D [ p ] = H p, g, w, f (, γ, θ, nw) j j [ ] j D [ w p, g, f ( α, γ, θ, nw) ] = L [ w ( θ )] k α. (4.B),. (4.C) k k Equaton (4.A) smply says that every household chooses the locaton whch maxmzes ts utlty. These choces, n turn, determne spatal varaton n the demand for housng and the supply of labor. Equaton (4.B) provdes the market clearng condton for housng n communty j. Supply equals demand, and of course both depend on the prce of housng. In general, the demand for housng wll also depend on the characterstcs of communtes and job opportuntes whch nfluence where households choose to locate. Thus, the demand for housng depends on wages, local publc goods, and f ( α, γ, θ, nw), the jont densty of non-wage ncome, preferences, and job sklls n the populaton of households. Equaton (4.C) provdes a parallel equlbrum condton for labor market k. The supply of labor depends on the wages offered to workers, on the characterstcs of households, and on the characterstcs of communtes. The dual-market locatonal equlbrum n (4) combnes features of the equlbrum 6

7 concepts that underle models of Tebout sortng and nterregonal models of hedonc equlbra. As n the sortng lterature, households choose from a dscrete set of communtes accordng to ther heterogeneous preferences for local publc goods (e.g. Epple and Seg [999]; Bayer and Tmmns [2007]). As n the nterregonal hedonc lterature, workers may be compensated dfferently f they move between labor markets (e.g. Rosen [979]; Roback [982]). In addton to ntegratng these features, the equlbrum summarzed n (4) generalzes both lteratures to recognze that households may choose to lve n one labor market and work n another. Importantly, the ablty to commute expands the ways n whch households can adjust to a shock. They can move to a dfferent communty, as n the sortng lterature. They can change ther job and ther house smultaneously by movng to a dfferent labor market, as n the nterregonal hedonc lterature. Or they can choose to reman n the same communty (labor market) and commute to a dfferent labor market (communty). Fgure llustrates how ths spatal landscape (panel D) dffers from hedonc property value models (panel A), nterregonal hedonc models (panel B), and models of Tebout sortng (panel C). The theoretcal propertes of a dual-market locatonal equlbrum do not provde clear predctons for what we can expect to learn about the wllngness-to-pay for publc goods from hedonc rent and wage functons. Ths s because the model relaxes two key assumptons of the hedonc framework. Frst, households are not free to choose contnuous quanttes of every publc good. School qualty may vary dscretely from school dstrct to school dstrct, for example. Wthout contnuty we cannot nvoke the frst-order condtons from Rosen s (974) model to nterpret a partal dervatve of a hedonc rent functon as a measure of the wllngnessto-pay for a margnal change n a publc good. 2 Second, the key result from Roback s (982) nterregonal hedonc model that the full mplct prce of a publc good s measured by combnng rent and wage dfferentals reles on the assumpton that people lve and work n the same place. Commutng breaks the connecton between changes n publc goods, rents, and wages at a pont n space. For example, consder households who lve n communty A and work n communty B. An exogenous shock to A s ar qualty may be partly captalzed nto B s wages. 2 Bajar and Benkard (2005) provde a general dscusson of the mplcatons of dscrete and contnuous choce sets n hedonc models of dfferentated product markets and Bayer et al. (2007) provde addtonal ntuton for the connecton to structural models of sortng behavor. 7

8 Is commutng emprcally mportant? Interregonal hedonc applcatons typcally defne a locaton as a county (Blomqust et al. [988]; Chay and Greenstone [2005]) or as a metropoltan area (Roback [982]; Bayer et al. [2006]). 3 Accordng to year 2000 Census worker flow fles, 27% of U.S. workers lve n one county and work n another, and 0% of workers commute between prmary metropoltan statstcal areas (PMSA). These natonal shares seem suffcently large to warrant further nvestgaton. Moreover, natonal shares wll tend to underestmate commutng rates n hghly urbanzed areas such as Boston, Los Angeles, and San Francsco, whch have provded the settng for emprcal studes of Tebout sortng (Epple and Seg [999]; Seg et al. [2004]; Bayer et al. [2007]). For example, 9% of the workers who lve n the San Francsco consoldated metropoltan statstcal area commute between PMSAs n the regon. On average, these workers spend 06 mnutes commutng to and from work every day. If wage ncome were exogenous to job locaton, one would expect these workers to work closer to home. When households choose among a dscrete set of communtes and some households choose to commute between communtes, we cannot explot the results from Rosen (974) and Roback (982) to nterpret the partal dervatves of hedonc rent and wage functons as exact welfare measures for margnal changes n publc goods. Nevertheless, households behavor can reveal features of ther preferences whch make t possble to estmate the demand for publc goods, the demand for housng, and the supply of labor. To explot ths nformaton, we must be wllng to mpose some parametrc restrctons on the shape of a household s utlty functon. III. A Parametrc Representaton of Dual-Market Sortng A. Utlty Maxmzaton by Workng Households We wll assume that an ndvdual household s utlty can be represented by the followng CES functon: 3 Techncally, Roback (982) uses data from 98 U.S. ctes. However, these ctes are often defned n a way that effectvely aggregates over prmary metropoltan areas, such as the cty of San Francsco-Oakland, or they tend to be the central cty of a metropoltan area, such as Washngton D.C. 8

9 ρ ν η+ ρ ρ β y jk Pj V α ( ) exp exp jk = g +, (5) j ν η + where g j = γ g j γ N g N j + γ Nξ j, and yjk nw +θ wzk ( θ2t jk ) =. The frst term n the functon represents utlty from publc goods, and the second represents utlty from the prvate good component of housng. All households are assumed to share the same elastcty of substtuton between publc and prvate goods ( ρ ), and the same housng demand parameters: prce elastcty (η ), ncome elastcty (ν ), and demand ntercept ( β ). Households dffer n ther relatve preferences for a lnear ndex of publc goods provded by each communty. They dffer n the weghts they place on each publc good n the ndex ( γ,..., γ N ) and n ther overall preferences for publc goods relatve to prvate goods ( α ) ndex weghts are normalzed to sum to, whch allows α to be dentfed separately as a scalng parameter on the strength of preferences. 4 observable. The N th publc good ( g Nj j. The Of the N publc goods n the ndex, N- are = ξ ) s observed by households but not by the analyst. 5 A household s ncome s defned by the sum of ts exogenous non-wage ncome and wage ncome, less the value of tme spent commutng. The prmary earner of each household s assumed to possess sklls that qualfy them for a certan occupaton (e.g. accountant, constructon worker). Ths observable component of job skll s ndexed by z. In labor market k, the average wage for that occupaton s w zk. However, a worker s ablty to collect that wage f they were to move from ther current job depends on features of ther job skll, such as educaton, experence, and ablty. These features are reflected n a sngle heterogeneous parameter, θ, that represents each worker s labor market moblty wthn ther occupaton. For example, f θ s greater (less) than, the worker would earn more (less) than the average wage for ther occupaton f they were to move to a new labor market. The wage n each job locaton s also adjusted for requred 4 α s extraneous n the sense that t s only dentfed by a normalzaton to the weghts n the publc goods ndex. Nevertheless there are two reasons for ncludng t n the model. Frst, t helps to llustrate the connecton to Epple and Seg (999). Second, normalzng the weghts n the publc good ndex smplfes estmaton. 5 One can nterpret ξ as a theoretcally consstent ndex of M unobserved attrbutes as long as households share the same ndex weghts. Snce ξ s the only structural error, equaton (5) exemplfes the pure characterstcs approach to modelng the demand for a dfferentated product (Berry and Pakes [2007]). 9

10 commute tme. t jk s the rato of commute tme to work tme, and 2 θ represents the worker s shadow value of tme as a share of the wage rate. If θ 2 = 0, effectve wage ncome equals actual wage ncome. At the other extreme, f θ 2 =, the worker s shadow value of tme equals ther wage rate. The demand for housng and the supply of labor depend on all the parameters of the ndrect utlty functon. For each communty, the resdual demand for housng s calculated by aggregatng over the ndvdual demands of all the households who maxmze ther utlty by choosng to lve there. 6 ndvdual household s demand: Applyng Roy s Identty to (5) produces the followng expresson for an h = βp y. (6) η ν j To develop an expresson for market demand, let Ω jk denote the set of values for the heterogeneous parameters such that locaton jk maxmzes utlty, gven values for the housng demand parameters and the elastcty of substtuton, Ω { (, γ, θ ) : V jk ( β, η, ν, ρ ) Vlm ( β, η, ν, ρ ) l m} jk =, α, (7) and let I jk be an ndcator functon whch equals f household s preferences and sklls belong to the Ω jk set. Then the aggregate demand for housng n communty j can be wrtten as (8). H D j = k I [ nw + θ w ( θ t )] η ν jk βp j zk. (8) 2 jk The supply of labor can be defned analogously. Assumng workers each work 40-hour weeks, we can measure the labor supply n terms of the number of workers: 6 In ths model, housng s treated as a homogeneous commodty. Of course, housng s not homogenous. Its structural characterstcs (e.g. bedrooms, bathrooms, sqft.) vary wthn communtes, and these dfferences wll be reflected n observable sale prces. Ths can be addressed f structural characterstcs enter the drect utlty functon through a separable sub-functon that s HOD. Under ths restrcton, Seg et al. (2002) demonstrate that the equlbrum hedonc prce functon wll be separable n the structural characterstcs of houses and the effect of publc goods. In ths case, communty-specfc fxed effects estmated from a hedonc regresson can be used to construct a theoretcally-consstent ndex for the cost of consumng publc goods n each communty. 0

11 L I. (9) S k = j jk As n (4) the demand for housng and the supply of labor both depend on the dstrbuton of prces, wages, and local publc goods across the urban landscape, and on the dstrbuton of preferences, sklls, and ncome n the populaton of households. The parametrc specfcaton n (5)-(9) captures the key features of a dual-market locatonal equlbrum. Households wth heterogeneous preferences and sklls make a jont jobhouse choce and ther collectve behavor determnes spatal varaton n the supply of labor and the demand for housng. 7 The model also nests Epple and Seg (999) as a specal case. In ther model, ncome s exogenous to locaton choce, households have dentcal relatve preferences for publc goods, and the shape of the jont dstrbuton of ncome and preferences s assumed to be known. To recover ther specfcaton from (5) smply drop the job skll ( θ ) and tme cost ( θ 2 ) parameters, drop the subscrpts on γ,... γ, and assume f ( α, y) N ~lognormal. These restrctons smplfy estmaton, but they have the potental to nfluence polcy mplcatons. Kumnoff (2007) dscusses the dentfcaton of the model n (5)-(9) and develops an estmator whch recovers all the parameters of the ndrect utlty functon from nformaton on the sortng behavor of workng and retred households. He uses the estmator to decompose the extent to whch assumptons about preference heterogenety and job opportuntes nfluence estmates of the wllngness-to-pay for margnal changes n ar qualty. Estmates of margnal wllngness-to-pay are frequently used to develop frst-order approxmatons to the benefts from non-margnal changes n publc goods. The advantage of ths approach s that t s easy to mplement. The dsadvantage s that t s best suted to small changes. When the results from a margnal analyss are used to predct the effects of a large-scale change n publc polcy, the predctons can be extremely naccurate (Heckman et al. [997]). Ths s mportant because publc polces whch target ar qualty, school qualty, and other publc goods are usually ntended to acheve large changes over some subset of the target populaton. Recent applcatons have begun to consder ths ssue. Smth et al. (2004) use the Epple-Seg model to smulate the 7 To close the model we need to defne the supply of housng and the demand for labor. Nether s estmated n ths paper. The smulatons are mplemented under assumptons about ther elastctes. Walsh (2007) demonstrates how the estmaton of a land supply functon can be ntegrated nto an emprcal model of Tebout sortng.

12 general equlbrum adjustment process followng large mprovements to ar qualty n the Los Angeles ar basn, and Walsh (2007) consders large changes n the publc provson of open space n Wake County, North Carolna. Both studes report substantal dfferences n partal and general equlbrum welfare measures. However, the mgraton patterns whch drve these dfferences are based on the assumpton of zero movng costs. If movng to a new home requres acceptng a longer commute or a lower wage, the smulatons may exaggerate the magntude of mgraton and ts mpact on captalzaton rates. Furthermore, the drectons of mgraton reflect what each household perceves are ts opportuntes for spatal substtuton. Ths percepton stems from the assumed form of preference heterogenety. The next two subsectons llustrate how assumptons about heterogenety n preferences and job opportuntes nfluence what we learn about preferences and welfare measures from observed sortng behavor. B. Identfyng Preferences for Publc Goods from Equlbrum Sortng Behavor Gven a specfcaton for utlty and a defnton for the choce set, a household s observed locaton provdes set dentfcaton of ther preferences. In other words, ther choce mplctly defnes a set of values for the parameters of the utlty functon that descrbe how local publc goods contrbute to sortng behavor. To attach values from ths set to the populaton of households requres addtonal assumptons about the dstrbuton of each preference parameter. The ndrect utlty functon can be used together wth the data that descrbe the choce set to partton preference space nto regons that defne the set of values for the heterogeneous parameters capable of explanng each observed locaton choce. More precsely, applyng the revealed preference condtons n (4.A) to the ndrect utlty functon n (5) generates a system of nequaltes whch mplctly defne the Ω jk sets n (7). Ths process provdes a graphcal analog to Samuelson s (948) revealed preference logc by llustratng how a household s preferences are dentfed by the choces they make and by the choces they could have made, but dd not. To llustrate the dentfcaton logc, consder the populaton of retred households who choose among the communtes n table. In ths smple example, each communty dffers n only two publc goods, g and g 2, both of whch are observable. Gven values for the elastcty of substtuton and the housng demand parameters n (5), the revealed preference condton n (4.A) defnes 6 nequaltes. These can be solved to dentfy bounds on the sets of values for the 2

13 heterogeneous preference parameters, α, γ, and γ 2, whch are capable of explanng each household s observed choce. For example, wth β = 2, η =. 963, ν =. 75, ρ =. 0, and y = $50,000, preference space can be parttoned nto the four regons shown n fgure 2A. 8 A household wth preferences anywhere n regon choosng to lve n communty A, a household wth preferences n and so on. Ω A of the partton wll maxmze ts utlty by Ω B wll choose to lve n B, The borders whch separate ndvdual regons of the partton defne the values for α, γ, and γ 2, that would make a household exactly ndfferent between the correspondng communtes. Thus, the borders reflect substtuton patterns. 9 Communty B, for example, shares borders wth each of the other communtes. Consder a margnal ncrease n the prce of housng n B. Households that currently resde n B but have preferences on the border between B&D wll respond to the prce ncrease by movng to D. Lkewse, households on the borders between B&A and B&C wll move to communtes A and C. The partton reflects Tebout s (956) observaton that households reveal ther preferences for publc goods by the communtes they choose. Consder communtes A and D. Households n D must pay more for housng but are rewarded wth hgher provson of both publc goods. Therefore, condtonal on ncome, households who move from A to D must be wllng to decrease the sze of ther home n order to ncrease ther consumpton of publc goods. By makng ths choce, a household reveals relatvely strong preferences for publc goods, whch s reflected n a large value for α. Now consder B and C, two communtes wth smlar housng prces. Communty B provdes more of g and C provdes more of g 2. Therefore, a household s choce to lve n B (C) reveals t has relatvely strong preferences for g ( g 2 ), whch s reflected n a large value for γ ( γ 2 ). For workng households, the partton has two addtonal dmensons, θ and θ 2. Ths s dffcult to vsualze, but the ntuton for how job opportuntes nfluence the dentfcaton of preferences can be seen by consderng a scenaro where workng households who lve n 8 See Kumnoff (2008) for a step-by-step descrpton of the parttonng process. 9 The defnton of substtuton used here s defned as strong gross substtuton n Anderson, DePalma and Thsse (992), where k s a substtute for j ff h P > 0. k j 3

14 communty D earn a hgher wage, $50,500. The extra $500 could reflect a shorter commute to the same job or a new commute to a dfferent job. Fgure 2B llustrates how ths nformaton changes what we can nfer about preferences from sortng behavor. Notce that we lose some precson n our ablty to dentfy the preferences of households who lve n D. They may have chosen to lve there because t provdes access to a hgher-payng job, not because of ther preferences for the publc goods t provdes. By the same logc, the choce not to explot the job opportuntes provded by D ncreases the precson n our ablty to dentfy the preferences of households n B and C. Ths example demonstrates how nformaton on job opportuntes relaxes the strct connecton between locaton choces and preferences that forms the bass for emprcal models of Tebout sortng such as Epple and Seg (999) and Bayer et al. (2007). Assumptons about the form of preference heterogenety determne the dmensonalty of the partton. Suppose we restrct households to have dentcal relatve preferences for the two publc goods, as n Epple and Seg (999). If we fx the weghts n the publc goods ndex at ( γ ) ( 0.48, 0.52), 2 = γ, for example, fgure 2A reduces to a horzontal lne at γ Ths onedmensonal partton s reproduced n fgure 2C. Comparng ths wth the other two parttons llustrates how our assumptons about the choce set and the extent of preference heterogenety nfluence the sze and shape of the preference sets whch are capable of ratonalzng observed behavor. Ths s mportant because each polcy nterventon. Ω jk set corresponds to a range of welfare effects for a C. Measurng the Welfare Implcatons of a Polcy Interventon An ndvdual household s wllngness-to-pay for a margnal change (MWTP) n g can be derved from the ndrect utlty functon as follows: MWTP ν ρ V g y γ α g. (0) V Y V α g jk j ( g ) = = ρ ρ jk j Snce MWTP s a functon of preferences, each pont n the partton of preference space corresponds to a specfc MWTP. Suppose we want to evaluate the welfare mplcatons of a polcy whch wll margnally mprove g n communty C. The choce of C reveals only that 4

15 households lvng there have preferences somewhere n regon Ω C of the partton. Two extreme cases allow us to provde bounds for the MWTP. The frst case s where every household has preferences at the pont (**) n fgure 2A, whch corresponds to the lowest MWTP of any pont n Ω C. The opposte extreme s where every household has preferences at (*), whch corresponds to the hghest MWTP. Thus, [MWTP(**), MWTP(*)] spans the range of possble measures for ndvdual MWTP. The wder ths range the greater the senstvty of welfare effects to the dstrbutonal assumptons made n order to dentfy the densty of preferences wthn each regon of the partton. Comparng the three parttons n fgure 2 llustrates a type of bas/varance tradeoff faced by the analyst. Suppose the true model s characterzed by workng households makng a jont job-house choce based, n part, on ther heterogeneous preferences for multple publc goods. In ths case, estmatng an Epple-Seg type model of pure-tebout sortng, where ncome s treated as exogenous and relatve preferences are assumed to be dentcal, wll have two effects. It wll lead to based welfare measures and t wll decrease the senstvty of those welfare measures to dstrbutonal assumptons. Movng to the dual-market framework elmnates the restrctons that ntroduce bas, but the added dmensonalty of the Ω jk sets ncreases the scope for dstrbutonal assumptons to nfluence results. The economc mplcatons of ths tradeoff wll ncrease wth the sze of the change n g. The nformaton contaned n the partton of preference space can also be used to calculate exact partal equlbrum measures of the Hcksan wllngness-to-pay (WTP PE ) for large scale changes. Equaton () defnes ths measure for an ndvdual household, usng superscrpts to denote the perods before and after a change to the provson of publc goods n communty j. V 0 0 PE [ g ( γ ), p, α, y ( θ, w, t ) WTP ] = V [ g ( γ ), p, α, y ( θ, w, t )] j j jk zk jk. () j j jk zk jk WTP PE measures the amount of money that can be taken away from an ndvdual and leave them exactly as well off as they were before the change, holdng prces, wages, and locaton choces constant. Of course, a suffcently large shock to the provson of publc goods may nduce some 5

16 households to move. They may move to a new communty, they may choose a new job, or they may change both ther home and ther job. As households move, prces and wages may need to adjust n order to clear the housng and labor markets, and these adjustments wll feed back nto welfare measures. Equaton (2) defnes the ex post wllngness-to-pay for a change for a household that moves from locaton (j,k) to locaton (l,m). V GE [ g ( γ ), p, α, y ( θ, w, t ) WTP ] = V [ g ( γ ), p, α, y ( θ, w, t )] l l lm zm lm. (2) WTP GE measures the household s wllngness-to-pay for the change n publc goods at ts new locaton, after accountng for captalzaton of the qualty change nto housng prces and wage rates. Gven nformaton on the dstrbuton of preferences n the populaton of households, the model n (5)-(9) can be used to smulate the general equlbrum adjustment process, and solve for the prces, wages, and locaton choces that defne a new locatonal equlbrum. j j jk zk jk IV. A Model of Equlbrum Sortng n Northern Calforna Ths secton summarzes the data and results from usng the parametrc specfcaton from the prevous secton to estmate household preferences for ar qualty and school qualty from ther sortng behavor across housng and labor markets n Northern Calforna s two largest populaton centers the San Francsco and Sacramento Consoldated Metropoltan Statstcal Areas (CMSAs). A full descrpton of the data, estmator, and results s provded n a companon paper (Kumnoff [2007]). Here, the objectve s to hghlght the key features of the data and results whch are used to calbrate the subsequent polcy smulaton. A. Data The Sacramento-San Francsco regon contans about 9 mllon people, roughly 25% of the state s populaton and 3% of the U.S. populaton. Ths regon can be dvded nto 22 housng communtes and 8 work destnatons usng defntons for a communty and a work destnaton from the emprcal lteratures on Tebout sortng and nterregonal hedoncs. Specfcally, housng communtes are defned as unfed school dstrcts and work destnatons 6

17 are defned as Prmary Metropoltan Statstcal Areas (PMSA). 0 Fgure 3A shows how the regon s dvded nto eght PMSAs. The populaton s mostly concentrated around the San Francsco Bay and the cty of Sacramento, as seen by the densty of census tracts. The choce set used to estmate the model s defned as the top 268 communty-pmsa combnatons whch, together, account for 99% of the workng populaton. A workng household s job sklls are classfed accordng to the occupaton of ts prmary earner, usng the 22 categores n the Standard Occupatonal Classfcaton System (e.g. managers, healthcare support workers, etc.). 2 Retred households comprse an addtonal category. The data were generated n three steps. Frst, for each of the 268 locatons, dstrbutons of non-wage ncome by occupaton were generated from publcly avalable specal tabulatons of Census data. Then, for each communty, data were collected on the prce of housng and the provson of two publc goods, ar qualty and school qualty. Fnally, for all the potental job locatons assocated wth each communty, data were collected on the mean wage rate and mean commute tme for workers n each occupatonal category. The prce of housng n each communty ( p,..., p 22 ) was calculated from data on 540,642 ndvdual housng transactons compled from county Assessor records. These transactons represent most homes sold n the regon between 995 and Each record contans the actual sale prce and structural characterstcs of the home, ncludng the number of bedrooms, number of bathrooms, square feet, lot sze, and age. These data were used to calculate an ndex of housng prces usng the hedonc procedure descrbed n Seg et al. (2002). In short, ths procedure recovers a set of communty-specfc fxed effects, whle controllng for the relatonshp between the prce and structural characterstcs of a home. The fxed effects provde an ndex for the prce of housng as t reflects the cost of consumng publc goods. The fxed effects recovered from the regresson ndcate that housng n the most expensve communty costs 6.5 tmes as much as n the cheapest communty. After normalzng by the lowest prce, the ndex ranges from.00 n Sacramento s Grant Unon hgh 0 The Census Bureau descrbes a PMSA as a large urbanzed county or cluster of countes that demonstrate very strong nternal economc and socal lnks, n addton to close tes to other portons of the larger area [CMSA]. The crteron used to select locatons s that they must account for at least 500 workng households (0.02% of the workng populaton). Ths effectvely excluded multple-hour commutes between dstant locatons. 2 60% of marred couples n the study regon reported both the husband and wfe workng n 999. Whle a dualearner job search would be an nterestng extenson, t s not possble gven present data lmtatons. 7

18 school dstrct to 6.5 n San Francsco s second supervsoral dstrct. Overall, the dstrbuton s consstent wth the conventonal wsdom that the Bay Area s an expensve place to lve. The cheapest communtes are all located n the Sacramento PMSA, whle 24 of the 25 most expensve communtes are n the San Francsco and San Jose PMSAs. Ozone concentratons are used as a proxy for ar qualty because t s the chef component of urban smog whch, for households, s perhaps the most readly observable measure of ar qualty. The Calforna Ar Resources Board records hourly concentratons of ozone at montorng statons throughout the state. Fgure 3B overlays the locaton of 20 montorng statons on school dstrcts n the study regon. The exact measure used n ths analyss s the average of the top 30 -hour daly maxmum readngs (n parts per mllon) recorded at each montorng staton durng the course of a year. Households are assumed to be prmarly concerned wth ar qualty near ther home, not ther job. Under ths assumpton, communtyspecfc measures are constructed by frst assgnng to each house the ozone measure recorded at the nearest montorng staton, and then takng an average over all the houses n the communty. Then, to control for annual fluctuaton n ozone levels, the process was repeated for 999, 2000, and 200, and the results averaged. The fnal measure ranges from 0.03 (parts per mllon) n the hghest ar qualty communty to 0.06 n the lowest. Data on school qualty come from the Calforna Department of Educaton. The measure used n ths study s the Academc Performance Index (API), a composte ndex of standardzed test scores, weghted across all subjects and grade levels. For each communty, a three-year average API was constructed by weghtng the score of each school n the communty by ts number of students from The resultng measure ranges from 528 to 94. For each occupatonal category and PMSA, mean annual wages were obtaned from the Calforna Employment Development Department. 3 Wages can very substantally between PMSAs. Workers wth jobs n the constructon and excavaton category are pad 32% more n San Jose than n Sacramento, for example. Some of ths varaton may reflect local cost-oflvng adjustments n markets where housng s partcularly expensve, lke San Jose and San Francsco. The varaton may also reflect unobserved heterogenety n the mx of jobs wthn each category, or locaton-specfc attrbutes of jobs. 3 Wages nclude base pay, producton bonuses, tps, and cost-of-lvng adjustments, but exclude nonproducton bonuses, overtme pay and the value of benefts. 8

19 Fnally, data on the mean tme for every tract-to-tract commute were taken from the Census Transportaton Plannng Package specal tabulaton. These fgures were used to calculate the average one-way commute tme between each home communty and PMSA. It ranges from to 4 mnutes, wth a mean of 36 mnutes and a standard devaton of 9 mnutes. B. Estmaton Results The estmator developed n Kumnoff (2007) uses data on the characterstcs of households and ther locaton choces to recover the partton of preference space whch explans ther observed sortng behavor. Ths process uses the same type of nformaton as the GMM approach proposed by Seg et al (2004) and the maxmum lkelhood estmator n Bayer et al (2007). Unlke these methods, however, there s no need for a pror assumptons about the shape of the dstrbutons used to characterze heterogeneous preference parameters. Ths s accomplshed by dvdng the estmaton nto two stages, smlar to Bajar and Benkard (2005). The process begns by estmatng all the homogeneous parameters whch enter the utlty functon: β, η, ν, ρ, and ξ. The housng demand parameters are estmated from the emprcal analog to the demand functon n (6), and ρ and ξ,...,ξ 22 are recovered through an teratve process that selects values for these parameters whch match predcted and observed behavor. 4 Gven values for the homogeneous parameters, a Gbbs algorthm s used to draw a random sample of ponts from each cell of the partton of preference space. The algorthm samples unformly wthn each cell, effectvely tracng ts shape. Repeatng ths process for every cell generates a populaton of ponts whch, together, approxmate the partton of preference space. Workng households are assumed to choose among the 268 (dstrct, PMSA) locatons, recognzng that ther wages and commutes wll be determned by ther choce. Recall that ths model reduces to Epple and Seg (999) when the utlty functon n (5) s smplfed by droppng the job skll and tme cost parameters (,θ 2 assumng f (, y) θ ), droppng the subscrpts from ( γ,..., ) γ N, and α s lognormal. Estmatng ths sngle-market verson of the model provdes a 4 Pror to estmaton, the demand functon n (6) s multpled by prce n order to transform t nto an expendture functon whch can be estmated from quantles of the dstrbuton of ncome and housng expendtures n each communty. In ths case, the 25 th, 50 th, and 75 th quantles were used. 9

20 lnk to the exstng lterature and a baselne for comparson n the subsequent polcy smulaton. 5 Table 2 summarzes the resultng parameter estmates, whch are used to calbrate the smulaton n secton VI. Pont estmates are reported for the homogeneous parameters and means and standard devatons are reported the margnal dstrbuton of each heterogeneous parameter. Snce the dfferences between the two models do not affect β, η, and ν, the frst stage of the estmaton was only performed once. The resultng estmates for the prce elastcty ( ˆ η = 0.38) and ncome elastcty ( ˆ = 0.66) ν are typcal for the emprcal lterature on Tebout sortng. The negatve values for ρ ndcates the demand for publc goods s downward slopng. Whle the dual-market estmate s consderably larger n absolute magntude, both mply smlar values for the elastcty of substtuton between publc and prvate goods (0.89 and 0.98). 6 Estmates for ξ,...,ξ 22 are also very smlar between the two models. In general, ξ s negatvely correlated wth dstance to San Francsco Bay. Clmate, open space, and cultural amentes are three unobserved publc goods that seem lkely to nfluence ths result. The Bay Area has the mldest weather n the study regon, the most opportuntes for dnng and nghtlfe, and a large share of land n open space. Ths pattern s consstent wth Walsh (2007) who fnds open space to be an mportant determnant of where households choose to lve. In the sngle-market case, preference heterogenety s characterzed by the parameters whch defne f ( ln α, ln y). To recover preferences n the dual-market case, households were frst classfed accordng to 0 ncome bns reported n the Census data, and each household was assgned a level of ncome equal to the mdpont of ts bn. 7 Then the Gbbs algorthm was used to draw 000 ponts from each cell of the partton, condtonal on ncome. Ths translates to 60,08,000 ponts 000 ponts drawn from each of the 22 cells at each of the 0 ncome levels for retred households, plus 000 ponts drawn from each of the 268 cells for each of the 220 (occupaton, non-wage ncome) types of workng households. 8 The dual-market partton generalzes the revealed preference logc from Epple and Seg s model of pure Tebout sortng. Ths can be seen by comparng the preference sets 5 The frst stage of the estmaton s the same as n the dual-market case. The remanng parameters are recovered usng the smulated GMM approach from Seg et al. (2004), whch explots the (a pror) lognormalty assumpton. 6 The elastcty of substtuton s defned as: σ = ( ρ ). 7 Measured n thousands, the mdponts are: [ ]. 8 Ths followed a burn-n of 00 draws to reduce senstvty to startng values. 20

21 assgned to households n three communtes Pttsburg, Mlptas, and Sunol Glen. Of the three, Sunol Glen and Mlptas provde more of every publc good than Pttsburg. 9 Therefore, regardless of relatve preferences, every household wll perceve Pttsburg as provdng the lowest qualty bundle of publc goods. Gven ths unanmous orderng, a household s choce to lve n Pttsburg reveals that they have weaker preferences for publc goods (relatve to prvate goods) compared to households wth the same ncome n the other two communtes. Ths logc s reflected by the stratfcaton of households n panels A and B of fgure 4. Panel A presents the orderng of households n the sngle-market case and panel B presents the preference sets for retred households n the dual-market case. In both fgures, the preference sets for Sunol Glen and Mlptas le above the set for Pttsburg n the α dmenson. However, notce that retred households n Sunol Glen and Mlptas have overlappng ranges of values for α n the dualmarket case. Ths occurs because the two communtes are not strctly ordered by ther provson of publc goods. Sunol Glen has hgher qualty schools and Mlptas has cleaner ar. Thus, the choce between them helps to dentfy relatve preferences. Specfcally, households n Sunol Glen are revealed to have strctly hgher values for γ school γ ar. Ths s llustrated n panel C whch projects the preference sets from panel B nto γ space. Addng job destnatons to the choce set expands the borders of the preference sets. Intutvely, heterogenety n job skll and the opportunty cost of tme provde new ways to explan observed behavor. Ths can be seen by comparng fgure 4C wth the correspondng γ projecton for managers n 4D. Notce the strkng dfference between the preference sets assgned to workng and retred households n Mlptas. Mlptas has approxmately average values for ar and school qualty, whch helps to explan why retred households who choose to lve there are assgned smlar values for the weghts n the publc good ndex,.e. γ. ar γ school Meanwhle, ths rato can be much larger for managers who commute to San Jose. The reason s that San Jose s the hghest payng job destnaton and Mlptas offers one of the shortest commutes. Ths explans why managers wth strong preferences for ar qualty would choose to lve n Mlptas nstead of a dfferent communty wth cleaner ar. Fnally, the dual-market partton was translated nto a dstrbuton of preferences for the 9 Ther normalzed values for {ar, school, prce} are: Pttsburg {0.82, 0.79,.42}; Mlptas {0.96,.05, 2.6}; Sunol Glen {0.9,.20, 2.62}. Both models assgn hgher values of ξ to Mlptas and Sunol Glen than to Pttsburg. 2

22 polcy smulaton by samplng unformly over each cell of the partton accordng to the populaton of households n the correspondng locaton. 20 For example, the census data report 232 households wth a prmary earner n the archtecture and engneerng occupaton who lve n the Acalanes school dstrct, work n the Oakland PMSA, and have total ncome of $2,500. Therefore, 232 draws were chosen unformly from the regon of the partton that corresponds to ths household type. Ths process was repeated for every type so that the resultng dstrbutons represent all 3.2 mllon households n the study regon. The last fve columns of table 2 report the results. The mean value of θ 2 mples the shadow value of tme s approxmately 40% of the wage rate smlar to the rule-of-thumb (33%) used n the recreaton demand lterature (Phaneuf and Smth [2005]). The mean of θ suggests a hgh degree of geographc job specalzaton and/or a hgh job search cost. It mples the average worker would earn approxmately half of the market wage f they were to change job locatons. Estmates for α and γ are not drectly comparable between the two models n terms of magntude snce they correspond to dfferent estmates for ρ and ξ. Nevertheless, there s a strkng dfference between ther relatve values: γ γ s an order of magntude larger n the dual-market case. ar school Ths dfference wll affect how households react to mproved ar qualty n the polcy smulaton. V. Polcy Scenaro: Calforna s New Standard for Ground Level Ozone Due to concerns over the negatve health effects of ground-level ozone, the Envronmental Protecton Agency (EPA) recently establshed strcter standards for ambent ozone concentratons. The Phase 2 Ozone Rule fnalzed n November, 2005 dentfes nonattanment areas across the country that fal to meet the natonal 8-hour lmt on ambent ozone concentratons of 0.08 parts per mllon (ppm). These areas cover 8% of the countes n the Unted States. The Phase 2 Rule outlnes a set of correctve actons that must be taken by the states whch contan nonattanment areas. Frst, they must nstall abatement equpment that EPA consders to be reasonably avalable. Second, they must restrct constructon of new statonary sources of ozone precursors and restrct modfcatons to exstng sources. Fnally, states wth the most severe volatons may be requred to use cleaner-burnng reformulated gasolne. 20 Note that ths does not mply a unform dstrbuton of preferences n the populaton of households. 22

23 The four nonattanment areas wth the most severe volatons of the new standard are all located n Calforna: the Los Angeles Ar Basn, the Sacramento CMSA, Rversde County, and the San Joaqun Valley. These are the only four regons whch EPA desgnates as havng a severe or a serous problem. Calforna state offcals addressed ths problem n May, 2006 by adoptng an even strcter 8-hour standard of 0.07 ppm. Ths new standard s the focus of the polcy smulaton, whch asks the hypothetcal queston: what would households n the Sacramento-San Francsco regon be wllng-to-pay to attan the new 0.07 ppm ozone standard? There are two ssues whch must be addressed n order to defne the spatal dstrbuton of ozone n the attanment scenaro. Frst, the 8-hour lmt whch defnes the new attanment rule must be converted nto the same unts as the -hour measure of ozone concentratons used as a proxy for ar qualty durng the estmaton. The second ssue s that the mpled reducton n emssons of ozone precursors needed to meet the new standards n communtes wth low ar qualty would be lkely to spll over nto communtes wth hgh ar qualty. For example, 8-hr ozone levels n the western part of the San Francsco Bay Area already satsfy the new 0.07 ppm lmt. Ths s largely due to natural wnd currents that tend to push ozone toward the East Bay and nto Sacramento, contrbutng to ther ar qualty problems. Assumng ozone reductons are derved from new regulatons on emssons that apply throughout the regon, a reducton n ozone that would brng Sacramento nto attanment would stem partly from reduced emssons of ozone precursors n the San Francsco Bay Area. Snce wnd currents do not remove ozone from the Bay Area entrely, the decrease n emssons would lower ozone levels there as well. The spatal dstrbuton of ozone concentratons n the attanment scenaro was developed n two steps. Frst, data on 8-hr ozone were used to dentfy ndvdual montorng statons that volated the 0.07 ppm lmt durng the baselne years of the study perod ( ). For each of these montors, the reducton n 8-hr ozone requred to brng t nto attanment was translated nto the correspondng reducton n the -hour ozone measure that was used to defne ar qualty durng the estmaton. The second step was to estmate the hstorcal relatonshp between changes n ozone at nonattanment statons and changes n ozone at attanment statons. The resultng estmate was used together wth the ozone reductons requred at nonattanment statons to predct the correspondng reductons for attanment statons. Secton IV descrbed how the level of ar qualty n each communty was measured usng 23

24 a three-year average of the annual top 30 -hr daly maxmum ozone readngs. In contrast, Calforna s new ozone standard s based on a 3-year average of the 4 th hghest annual 8-hr ozone readng. To make the converson between the two measures, the reduced-form relatonshp between them was estmated usng annual data for each montorng staton n the study regon. Frst, the 8-hr measure was constructed for each montorng staton for Then, the - hr data were regressed on the 8-hr data. The results mply that a ppm reducton n the 8-hr measure corresponds to a.09 ppm reducton n the -hr measure. The coeffcent explaned almost all of the varaton n ozone concentratons (R 2 =.97). Next, for each nonattanment montor, the reducton n the 8-hr measure needed to brng that montor nto attanment was multpled by.09 to generate an estmate for the correspondng reducton n the -hr measure. Durng the second step of the process, annual data from 980 to 2003 were used to estmate the hstorcal relatonshp between ar qualty changes at attanment and nonattanment montors. Whle ozone concentratons have decreased steadly n the areas wth the lowest ar qualty, they have remaned farly flat n attanment regons. Fgure 5 llustrates ths trend, usng data from representatve montorng statons n Sacramento and Oakland. The relatvely flat trend for Oakland reflects the way weather n the San Francsco Bay lmts the senstvty of ozone concentratons to changes n precursor emssons. Regressng the annual change n the log of 8-hr ozone (ppb) at attanment montors on the annual change n 8-hr ozone at nonattanment montors ndcates we should expect a ppb decrease at the average nonattanment montor to be accompaned by a 0.06% decrease at the average attanment montor. Therefore, for the montorng statons that were n attanment of the new standards durng , the percentage ozone reducton n the attanment scenaro was estmated by multplyng the average change at nonattanment statons (-.6 ppb) by the regresson coeffcent (0.06%). Ths calculaton mples a 0.7% decrease at attanment montors. In comparson, ozone concentratons are predcted to decrease by 2% at the average nonattanment montor. Fnally, the -hr ozone levels predcted for the ndvdual montorng statons were used to produce communty-specfc measures of ar qualty, usng the same aggregaton procedure used to prepare the data for estmaton. Fgure 6 shows the dfference between the attanment scenaro and baselne ozone concentratons n Ar qualty mproves sgnfcantly for most communtes physcally located n the Sacramento and Yolo prmary metropoltan 24

25 statstcal areas, as well as for some communtes n Oakland and San Jose. In contrast, the ozone reductons are margnal for communtes n the San Francsco, Santa Cruz, and Santa Rosa PMSAs. Table 3 reports the average reducton over all the communtes n each PMSA, as well as the range of changes across the ndvdual communtes. The reductons range from 0.6% n the San Mateo Unon Hgh school dstrct (San Francsco PMSA) to 27.9% n the Black Oak Mne Unfed school dstrct (Sacramento PMSA). VI. General Equlbrum Smulaton Gven the dstrbuton of preferences recovered durng the estmaton, the task n ths secton s to solve for a new set of housng prces, wage rates, and locaton choces that satsfy the condtons for a locatonal equlbrum followng the ar qualty mprovement defned n the attanment scenaro. Ths can be done by usng the dstrbuton of preferences to smulate how households would respond to the shock. However, recall that the dstrbuton of preferences s not suffcent to fully characterze a locatonal equlbrum. Some addtonal nformaton must be provded. Part A of ths secton explans how each component of the smulaton was defned n order to close the model. Then parts B and C nterpret the smulaton results from the sngle-market and dual-market versons of the model. Fnally, part D compares the resultng welfare measures to the exstng lterature on the wllngness-to-pay for ar qualty. A. Components of the General Equlbrum Model In the lmt, all the attrbutes of a locaton may be endogenous and nterrelated n a general equlbrum. For example, n order to acheve EPA s Phase 2 ozone standard, frms may be requred to nstall new polluton abatement equpment at exstng facltes. These regulatory costs may affect the demand for labor f they lead to the closure of older facltes. Lkewse, f households respond to an ar qualty mprovement by adjustng ther commutng patterns, the correspondng change n vehcle mles traveled could alter the level of automoble emssons, whch would feed back nto the level of ar qualty. Whle these feedback effects are nterestng and potentally mportant, they are excluded from the present analyss n order to focus attenton on the mplcatons of preference heterogenety and the nteractons between housng and labor 25

26 markets. 2 Assumng the provson of publc goods s exogenous, the general equlbrum model has four sets of components: the supply and demand curves for housng n every communty and the supply and demand curves for labor n each PMSA. The housng demand and labor supply curves are mplctly defned by the jont dstrbuton of ncome and preferences that was estmated for the populaton of households n each verson of the model. Addtonal nformaton must be provded to defne the supply of housng and the demand for labor. In prevous work, the housng supply curves have been treated as perfectly nelastc (Smth et al. [2004]), calbrated usng a range of elastctes (Seg et al. [2004]), and estmated ndependently (Walsh [2007]). Here, the housng supply and labor demand are both treated as perfectly nelastc. Fnally, an assumpton s requred about who collects the captal gans (or losses) from changes n housng prces and wage rates. All the applcatons cted above treat households as renters and assume that changes n property values are absorbed by absentee landlords. The same assumpton s mantaned here and extended to the labor market. In other words, changes n profts that arse from adjustments to wage rates are assumed to be collected by the absentee owners of frms (.e. shareholders ). The decson to treat households as renters rather than homeowner/shareholders has potentally mportant welfare mplcatons. For example, suppose an mprovement n the qualty of a publc good rases housng prces. Ths would be strctly welfare mprovng for a retred homeowner. The qualty mprovement ncreases ther utlty and the ncrease n housng prces can not make them worse off. Lkewse, f the retred homeowner decdes to move, they collect the captal gans from the ncrease n the prce of ther home. In contrast, a retred renter lvng n the same communty wll experence a welfare loss f the ncrease n ther housng expendtures exceeds ther wllngness-to-pay for the qualty mprovement. Accordng to the 2000 Census of populaton and housng, 60% of the homes n the San Francsco-Sacramento regon are owner-occuped. B. Smulaton Results: Sngle-Market Model 2 Ferreyra (2007) and Walsh (2007) use structural parameter estmates from equlbrum sortng models to calbrate smulatons wth endogenous provson of school qualty (Ferreyra) and open space (Walsh). Unlke the present analyss, these studes treat wage ncome as exogenous and lmt the extent of preference heterogenety. 26

27 In the sngle-market case, the smulaton process s straghtforward. It begns by usng the estmaton results summarzed n table 2 to characterze the jont dstrbuton of ncome and preferences n the ntal equlbrum. Then the dstrbuton of publc goods s shocked by the ar qualty mprovement n the attanment scenaro. Followng ths shock, the challenge s to solve for the new utlty-maxmzng locaton choce made by every household, and a vector of housng prces that guarantees these choces equate the supply and demand for housng n every communty. The relatvely smple form of preference heterogenety n the sngle-market model allows ths problem to be formulated as a -dmensonal rootfndng problem, whch s easly solved usng the algorthm developed by Seg et al. (2004). 22 Table 4 reports the average changes n ozone, prces, and welfare for the attanment and nonattanment communtes n each PMSA. All welfare measures are based on households ntal locatons. For example, the $22 MWTP and $4 WTP GE for nonattanment communtes n Sacramento correspond to the households who started n those communtes, regardless of where they may have moved durng the smulaton. Not surprsngly, the table reflects the type of sortng behavor that underles the emprcal model and the estmator. On average, households who ntally chose to lve n nonattanment communtes have a lower average MWTP for mproved ar qualty ($27) than households who chose to lve n attanment communtes ($). The reverse s true for partal equlbrum welfare measures because nonattanment communtes experence much larger ozone reductons. These ar qualty mprovements make the (formerly) nonattanment communtes relatvely more desrable, nducng households to bd up ther rental prces, whch partly offsets welfare mprovements from the ozone reducton. Snce the smulaton framework s a closed model and there are no ncome effects, the 22 housng markets cannot clear smultaneously f housng prces ncrease everywhere. As more households move nto nonattanment communtes and the demand for housng decreases n ther ntal locatons, some prces must fall. The communtes wth relatvely small ar qualty mprovements are generally the ones wth prce decreases, addng to the welfare mprovement for current resdents. On average, rents n attanment communtes decrease by 0.54%, whch s 22 The key observaton s that f (, ln y) lnα can be used to defne a chan of households across communtes accordng to overall publc goods provson. One must solve for the prces mplctly defned by lnks n the chan that equate supply and demand n each communty. Ths problem can be defned recursvely;.e. the frst prce s modfed untl the housng market clears n the last communty. See the appendx for detals. 27

28 why WTP GE typcally exceeds WTP PE n these communtes. Table 5 hghlghts some of the dversty n welfare effects wthn the metro areas by comparng the results for 0 ndvdual communtes n the Oakland PMSA. Oakland provdes a convenent example because ts communtes span much of the range n housng prces and ar qualty n the ntal equlbrum. As expected, the relatvely large ozone reductons n Acalanes (-0.9%) and Lvermore Valley (4.6%) are accompaned by prce ncreases (0.2% and 0.6%). Lkewse, the relatvely small reductons n the remanng Oakland communtes lead to small decreases n the prce of housng. For example, although ozone concentratons drop by 0.7% n Alameda Cty, the much larger reductons n communtes lke Acalanes and Lvermore Valley make them more attractve, nducng some of the households n Alameda Cty to move there. Consequently, the prce of housng n Alameda Cty has to drop by -0.5% to clear the market. Table 5 also llustrates how a polcy that pursues envronmental justce can make renters worse off. 23 In the ntal equlbrum, Black Oak Mne has the second lowest prce of housng and the lowest ar qualty. People who ntally chose to lve there may have done so because they are ndfferent to ar qualty, or because they have low ncome. In ether case, the estmaton results mply these households have the lowest average MWTP for ar qualty ($4). They would prefer hgher ozone levels and nexpensve housng to the hgher prces that follow the ozone reducton. Consequently, ther welfare goes down when prces ncrease. Fnally, notce that the model depcts a large share of the populaton movng between communtes. In partcular, every household n Antoch, Castro Valley, Lvermore Valley, Pttsburg, Sunol Glen, and El Dorado moves to a dfferent communty durng the smulaton. Ths reflects changes to the poston of these communtes n the rankng by overall publc goods provson. For example, pror to the ar qualty mprovement, Antoch was ranked 23 rd by the publc goods ndex. The ozone reducton decreases ts rank to 2. Whle the rankng of communtes changes, households are stll strctly ordered accordng to ther (one-dmensonal) preferences for publc goods. The households who prevously lved n Antoch move to Travs and Vacavlle, the new 22 nd and 23 rd ranked communtes. These restrctve mgraton patterns help to explan why there s so lttle varaton n the welfare obtaned by movers relatve to non- 23 Accordng to the US Envronmental Protecton Agency, Envronmental justce s acheved when everyone, regardless of race, culture, or ncome, enjoys the same degree of protecton from envronmental and health hazards and equal access to the decson-makng process to have a healthy envronment n whch to lve, learn, and work. 28

29 movers. In addton to havng smlar preferences, they occupy communtes wth smlar provson of publc goods both before and after the ar qualty mprovement. C. Smulaton Results: Dual-Market Model *****Prelmnary***** Introducng labor markets and generalzng the depcton of preference heterogenety complcates the task of solvng for a locatonal equlbrum. Unlke the sngle-market case, there s no obvous way to sort households across communtes. Nevertheless, households can always be ranked accordng to the maxmum prce they would be wllng to pay to lve n any gven communty, condtonal on ther current utlty. Lkewse, workng households can be ranked accordng to the mnmum wage they would be wllng to accept to work n any gven labor market. These rankngs form the bass for an algorthm that teratvely adjusts housng prces and wage rates untl all markets clear smultaneously. The mechancs of the algorthm are descrbed n the appendx. Intutvely, t begns by askng: what s the maxmum prce that would clear each communty s housng market after ar qualty mproves? Ths prce s determned by solvng for every household s reservaton prce as a functon of ther current utlty, and then usng these prces to sort households nto the communty untl the aggregate demand for housng equals the supply. After updatng the utlty of movers, the process s repeated for every other communty and labor market. The prces (wages) from ths frst teraton provde an upper (lower) bound on the new equlbrum prces (wages). Subsequent rounds of adjustments decrease prces and ncrease wages untl all markets clear. Whle ths algorthm results n a new locatonal equlbrum, the process s computatonally ntensve. 24 To reduce the burden, the smulaton was performed usng a % sample of the populaton. Table 6 reports the average changes n prces, ncome, and welfare for each PMSA. The results dffer consderably from the sngle-market case. In partcular, average WTP GE ncreases from $28 to $845 n non-attanment communtes and decreases from $278 to $92 n attanment communtes. These dfferences can be explaned by four features whch dstngush the dualmarket smulaton: () greater dmensonalty n the dstrbuton of preferences, (2) cost-oflvng adjustments whch arse from nteracton between housng and labor markets, (3) job- 24 Wth the full set of 3.2 mllon households, the algorthm takes more than 2 weeks to converge. Wth a % sample, t converges n approxmately 24 hours. 29

30 related movng costs that lmt the geographc moblty of workng households, and (4) greater opportuntes for spatal substtuton mpled by the form of preference heterogenety. Each of these features s explaned before comparng the two sets of general equlbrum welfare measures. Movng to a dual-market framework tends to ncrease partal equlbrum welfare measures, especally n nonattanment communtes. Ths can be seen by comparng the estmates for MWTP and WTP PE n table 6 wth ther sngle-market counterparts n table 4. To help explan these aggregate outcomes, fgures 7A through 7B plot average MWTP n each communty aganst baselne ozone concentratons. Both models depct a smlar decreasng trend. Intutvely, all else held constant, the choce to lve n a communty wth cleaner ar reveals a hgher MWTP. 25 Lkewse, fgures 7C and 7D llustrate how WTP PE tends to ncrease n ozone concentratons snce communtes wth hgher ntal concentratons have larger reductons. Movng to the dual-market framework ncreases the varablty n these relatonshps by offerng alternatve explanatons for why households wth strong preferences for ar qualty would choose to lve n communtes wth hgh ozone concentratons. For example, the average MWTP n Sacramento Cty s $26 n the sngle-market case compared to $73 n the dual-market case. Whle Sacramento Cty has relatvely hgh ozone concentratons (86 ppb), workng households wth strong preferences for ar qualty may choose to lve there because t offers one of the shortest commutes to the Sacramento PMSA. The second dstngushng feature of the dual-market smulaton s that t predcts an ncrease n housng prces for every communty. The average ncrease s 6.0% n nonattanment communtes compared to 0.3% n attanment communtes. These ncreases are typcally accompaned by ncreases n wage rates that effectvely serve as cost-of-lvng adjustments. When the prce of housng ncreases n a nonattanment communty, workng households wth strong preferences for prvate goods (.e. low α ) seek to move to less expensve areas. Ths often requres movng to a new job n a dfferent PMSA. Therefore, n order to clear the labor markets that serve nonattanment communtes, wage rates have to ncrease to offset the hgher cost-of-lvng. Ths explans why the PMSAs wth the largest ozone reductons (Sacramento, 25 It s also true that households wth hgher ncomes tend to lve n communtes wth cleaner ar. Ths contrbutes to the predcted relatonshp between ar qualty and MWTP because, all else constant, MWTP s ncreasng n ncome. 30

31 Yolo) also have the largest wage adjustments, whereas wages are vrtually unchanged n San Jose and San Francsco whch are wthn commutng dstance to relatvely few nonattanment communtes. Now consder two facts: 9% of workers commute between PMSAs and half of the PMSAs contan both attanment and nonattanment communtes. Thus, the cost-of-lvng adjustments to wages n PMSAs wth hgh ozone concentratons also beneft workers who commute to attanment communtes elsewhere n the regon. The resultng ncome effects ncrease ther demand for housng whch, n turn, requres prces to ncrease n order to clear the housng markets n attanment communtes. The thrd factor whch contrbutes to the dfference between sngle and dual-market estmates for WTP GE s ther dfferent mplcatons for household moblty. As dscussed earler, allowng households to dffer n ther relatve preferences for publc goods means they perceve more opportuntes for spatal substtuton. Meanwhle, the dstrbuton of θ recovered durng the estmaton mples that the average worker would be pad less f they were to move to a dfferent labor market, whch effectvely lmts ther geographc moblty. Thus, workng households are less lkely to move far from ther job, but more lkely to perceve nearby communtes as potental substtutes for ther current locaton. Durng the smulaton, 24% of retred households moved to a dfferent communty compared to 3% of workng households. Meanwhle, only 0.2% of workng households changed jobs. Not surprsngly, the workers who change jobs have relatvely hgh values for θ. For movers, the mean value of θ s 0.94 compared to the populaton mean of Ths renforces the nterpretaton of θ as a job moblty parameter. Heterogenety n job moblty, nteractons between rent and wage adjustments, and the ncreased dmensonalty of preferences all nteract to ncrease the dversty n general equlbrum welfare measures. Ths can be seen by comparng the results for ndvdual communtes n table 7 wth the sngle-market results n table 5. In some communtes such as Antoch, Lvermore Valley, and Pttsburg, cost-of-lvng adjustments are not suffcent to compensate the average household for hgher rents, leadng to a net welfare loss. The opposte result apples to the average household n Berkeley, Dubln, and Sunol Glen. Furthermore, WTP GE can dffer substantally between households who move and those who do not. For example, consder El Dorado. In the ntal equlbrum t has the second lowest ozone 3

32 concentratons, the 5 th lowest prce of housng, and t requres a relatvely long commute to job destnatons n the Sacramento PMSA. Consequently, the estmaton results ndcate that households who lve there have a relatvely low WTP PE for mproved ar qualty. When rents ncrease n El Dorado followng the ozone reducton, the average resdent who chooses to stay there experences a net welfare loss. Meanwhle, the resdents who move experence a net welfare gan whch exceeds ther WTP PE. These households move to sx other communtes n the Sacramento PMSA, all of whch experence smaller prce ncreases. In contrast, the restrctons on preference heterogenety n the sngle-market verson of the model rule out ths type of dversty n mgraton patterns. Fgures 7E and 7F llustrate how the average WTP GE vares across communtes n each verson of the model. In the sngle-market case, communtes wth the hghest ntal ozone concentratons also tend to have the lowest average WTP GE. Ths s due to a combnaton of three factors. Frst, the households who lve n communtes wth the lowest ar qualty were assgned the lowest values for α y durng the estmaton. These households wll have the lowest per/unt WTP PE for the change. Second, communtes wth hgher ntal ozone concentratons have larger reductons n the attanment scenaro and, therefore, larger prce ncreases. For many households n nonattanment communtes, the welfare loss from the prce ncrease outweghs the welfare gan from the ozone reducton. Fnally, the strct orderng of households across communtes means they have few opportuntes to adjust to prce ncreases by movng. On average, a household that moves durng the smulaton locates n a new communty that dffers from ts ntal locaton by 0.6 places n the prce rankng. In the dual-market case, communtes wth the hghest ntal ozone concentratons tend to have the hghest average WTP GE, amd consderable varablty. Whle the prce ncreases n nonattanment communtes are much larger n the dual-market smulaton, so s the welfare gan from the ozone reducton. Ths s because, durng the estmaton process, the model recognzed that there may be some households n nonattanment communtes who have relatvely strong preferences for ar qualty and chose to lve there for other reasons. Furthermore, the cost-oflvng adjustments to wages do much to compensate workng households for the hgher prces. Fnally, snce households are not strctly ordered across communtes, they have more flexblty n how they adjust to the change. The average mover chooses a new locaton that dffers from ts 32

33 ntal communty by 3.3 places n the prce rankng. D. Interpretaton The smulaton results summarzed n tables 4 through 7 provde theoretcally consstent predctons for the dstrbutonal welfare mplcatons of Calforna s new ozone standard. The rchness of detal n these dstrbutons offers the potental to evaluate the standard based on numerous crtera whch matter to polcymakers. For example, by recoverng welfare effects for households that dffer by locaton, ncome, and occupaton, the model permts consderaton of the mplcatons for envronmental justce. But are ts predctons for general equlbrum adjustment relable? An deal way to answer ths queston would be to observe the behavor of ndvdual households both before and after an ar qualty mprovement and then compare ther actual mgraton patterns (and the ensung prce and wage adjustments) wth the predctons made by the model. Whle ths quas-expermental approach to model valdaton would provde helpful feedback, t s also extremely dffcult to mplement. It would requre trackng the populaton of households across space and tme, and solatng an ar qualty change whch s not confounded by changes n unobserved characterstcs of households and communtes. Identfyng quas-experments that meet these crtera and developng alternatve ways to evaluate the predctve power of the general equlbrum model are two mportant topcs for further research. 26 The remander of ths secton provdes some ntal feedback on the partal equlbrum verson of the model by comparng the estmates for MWTP to those from the exstng lterature on valung ar qualty changes. Measures of the wllngness-to-pay for reduced ozone concentratons are not drectly comparable wth MWTP estmates reported n much of the exstng lterature where ar qualty s typcally measured by partculate matter or by the number of days durng a year that ozone levels exceed state or federal standards. However, assumng that all of these measures are smply dfferent proxes for clean ar, they can be compared n terms of a common proportonate change. Convertng the range of values from the exstng lterature nto measures that would be equvalent to a margnal ( part-per-bllon) reducton n ambent ozone concentratons mples a 26 There s a growng lterature on structural model valdaton. Keane (forthcomng) provdes an overvew, and Provenchur and Bshop (2004), and Keane and Wolpn (2007) provde examples of emprcal valdaton exercses. 33

34 range from $7 to $54 year 2000 dollars (Seg et al. [2004]). The correspondng estmate from the sngle-market verson of the model was $80, compared to $40 n the dual-market case. The result that average MWTP ncreases when the choce set s expanded to nclude job opportuntes s consstent wth the early nterregonal hedonc lterature whch found that housng prces and wage rates both appear to reflect a substantal share of the mplct prce of envronmental amentes (e.g. Roback [982], Blomqust et al. [988]). The fact that the $80 and $40 estmates are both relatvely hgh could stem from methodologcal dfferences or smply from dfferences n the study regon. From a methodologcal perspectve, the closest comparson to the exstng lterature s to Seg et al s (2004) applcaton of the sngle-market verson of the model to Los Angeles n 990. They report an average MWTP of $66. However, the average level of ozone concentratons across the communtes n ther applcaton s 50 ppb, compared to a maxmum of 09 here. Moreover, medan ncome n the San Francsco CMSA s 35% hgher than n the Los Angeles CMSA. If Northern and Southern Calforna were consdered as part of the same choce set, the relatonshp between MWTP, ar qualty, and ncome would mply that households n San Francsco and Sacramento would tend to have a hgher MWTP than those n Los Angeles. Thus, estmates of the wllngness-to-pay for margnal changes from the dual-market model appear to be reasonably consstent wth the exstng lterature. VII. Polcy Implcatons Table 8 summarzes the estmaton and smulaton results by reportng the average per/household changes n rents, wages, and welfare. In the sngle-market case, accountng for general equlbrum adjustment produced an estmate for the average wllngness-to-pay of $230 compared to a partal equlbrum measure of $29. The dfference between them s manly due to a $4 decrease n annualzed expendtures on housng. Movng to the dual-market framework ncreased both the partal ($292) and the general equlbrum ($346) measures. Whle average rents and ncome both ncreased n the dual-market smulaton, the cost-of-lvng adjustments ($502) more than compensate the average workng household for the hgher rents ($438). To the extent that partal equlbrum measures fal to capture the gans from adjustment, they wll underestmate wllngness-to-pay. General equlbrum measures wll overestmate 34

35 these gans to the extent that they fal to fully model lmts to moblty. Treatng the partal and general equlbrum estmates from the sngle-market verson of the model as bounds and multplyng them by the number of households n the San Francsco-Sacramento area would mply that cumulatve annualzed benefts from Calforna s new standard on ground level ozone le between $0.4 and $0.73 bllon. Recognzng that households face dfferentated job opportuntes ncreases ths range to $0.93 to $.0 bllon. The welfare measures reported here dffer from the results that would be obtaned by followng the standard practce of multplyng an estmate for average MWTP by the sze of the mprovement. The mportance of ths dfference s llustrated n table 8 by presentng the results from three back of the envelope calculatons. All three calculatons multply average MWTP by a measure of the average ozone reducton. They dffer n how they aggregate the communtyspecfc ozone reductons to generate a regonal average. The frst calculaton takes a weghted average by the sze of each communty, measured n acres. Ths s denoted n the table as acre weghts. The second measure weghts each communty by ts populaton, and the thrd takes an arthmetc average of the ozone reductons over the 22 communtes. All three calculatons grossly overestmate wllngness-to-pay. They produce estmates whch are between 53% and 300% hgher than the general equlbrum measures n the sngle-market case and between 7% and 336% hgher n the dual-market case. The dfference between exact beneft measures and back-of-the-envelope calculatons based on average MWTP hghlghts the economc mportance of Charles Tebout s nsght for publc polcy evaluaton. That s, all else constant, households wth the weakest preferences for ar qualty and the lowest wllngness-to-pay for an mprovement wll choose to lve n the communtes wth the hghest ozone concentratons. Snce these communtes are the ones whch need the largest ozone reductons to meet the new standards, the aggregate benefts from the reducton are much smaller than f ar qualty were mproved unformly across the study regon. The opposte would be true f the largest ozone reductons were to occur n the communtes wth the hghest ar qualty. Ths logc apples generally to the evaluaton of new polces whch mpose standards on the provson of publc goods and envronmental amentes. 35

36 References Anderson, Smon P., André de Palma, and Jaques-Franços Thsse Dscrete Choce Theory of Product Dfferentaton. Cambrdge and London: The MIT Press. Bajar, Patrck and C. Laner Benkard "Demand Estmaton wth Heterogeneous Consumers and Unobserved Product Characterstcs: A Hedonc Approach." Journal of Poltcal Economy, 3(6): Banzhaf, H. Spencer and Randall P. Walsh. Forthcomng. "Do People Vote wth Ther Feet? An Emprcal Test of Tebout's Mechansm." Amercan Economc Revew. Bayer, Patrck, Fernando Ferrera, and Robert McMllan "A Unfed Framework for Measurng Preferences for Schools and Neghborhoods." Journal of Poltcal Economy, 5(4): Bayer, Patrck, Nathanel Keohane, and Chrstopher Tmmns "Mgraton and Hedonc Valuaton: The Case of Ar Qualty." NBER Workng Paper 206. Bayer, Patrck, Fernando Ferrera, and Robert McMllan "Tebout Sortng, Socal Multpler and the Demand for School Qualty." NBER Workng Paper 087. Berry, Steven and Arel Pakes "The Pure Characterstcs Demand Model." Internatonal Economc Revew, 48(4): Blnder, Alan S., and Harvey S. Rosen "Notches." Amercan Economc Revew, 75(4): Blomqust, Glenn C., Mark C. Berger, and John P. Hoehn "New Estmates of Qualty of Lfe n Urban Areas." Amercan Economc Revew, 78(): Chay, Kenneth Y., and Mchael Greenstone "Does Ar Qualty Matter? Evdence from the Housng Market." Journal of Poltcal Economy 3 (Aprl): Davs, Lucas "The Effect of Health Rsk on Housng Values: Evdence from a Cancer Cluster." Amercan Economc Revew 94 (December): Epple, Denns, and Holger Seg "Estmatng Equlbrum Models of Local Jursdcton." Journal of Poltcal Economy 07 (August): Ferreyra, Mara Marta "Estmatng the Effects of Prvate School Vouchers n Mult- Dstrct Economes." Amercan Economc Revew, 97(3): Heckman, James J., Lance Lochner, and Chrstopher Taber "General Equlbrum Treatment Effects: A Study of Tuton Polcy." Amercan Economc Revew, 88(2):

37 Keane, Mchael P. Forthcomng. "Structural vs. Atheoretc Approaches to Econometrcs." Journal of Econometrcs. Keane, Mchael P. and Kenneth I. Wolpn "Explorng the Usefulness of a Nonrandom Holdout Sample for Model Valdaton: Welfare Effects on Female Behavor." Internatonal Economc Revew, 48(4): Kumnoff, Ncola V Recoverng Preferences from a Dual-Market Locatonal Equlbrum. Mmeo. Kumnoff, Ncola V Decomposng the Structural Identfcaton of Non-Market Values. Vrgna Tech AAEC Workng Paper Lnden, Legh and Jonah E. Rockoff. forthcomng. "Estmates of the Impact of Crme Rsk on Property Values from Megan's Laws." Amercan Economc Revew. Phaneuf, Danel J. and V. Kerry Smth (2005): Recreaton Demand Models, n Handbook of Envronmental Economcs, Vol. II, ed. by K. Göran-Mäler and J. Vncent, Amsterdam: North Holland. Pope, Jaren C. Forthcomng. Do Seller Dsclosures Affect Property Values? Buyer Informaton and the Hedonc Model. Land Economcs. Provencher, Bll and Rchard C. Bshop "Does Accountng for Preference Heterogenety Improve the Forecastng of a Random Utlty Model? A Case Study." Journal of Envronmental Economcs and Management, 48(): Rhode, Paul W. and Koleman S. Strumpf "Assessng the Importance of Tebout Sortng: Local Heterogenety from 850 to 990." Amercan Economc Revew, 93(5): Roback, Jennfer "Wages, Rents, and the Qualty of Lfe." Journal of Poltcal Economy, 90(6): Rosen, Sherwn "Hedonc Prces and Implct Markets: Product Dfferentaton n Pure Competton." Journal of Poltcal Economy, 82(): Rosen, Sherwn "Wage-Based Indexes of Urban Qualty of Lfe," n Current Issues n Urban Economcs. P. Meszkowsk and M. Straszhem eds. Baltmore: John Hopkns Unversty Press. Samuelson, Paul A "Consumpton Theory n Terms of Revealed Preferences." Economca, 5(60): Seg, Holger, V. Kerry Smth, H. Spencer Banzhaf, and Randy Walsh "Estmatng the 37

38 General Equlbrum Benefts of Large Changes n Spatally Delneated Publc Goods." Internatonal Economc Revew 45 (November): Smth, V. Kerry, Holger Seg, H. Spencer Banzhaf, and Randy Walsh "General Equlbrum Benefts for Envronmental Improvements: Projected Ozone Reductons under EPA s Prospectve Analyss for the Los Angeles Ar Basn." Journal of Envronmental Economcs and Management, 47(3): Tebout, Charles M "A Pure Theory of Local Expendtures." Journal of Poltcal Economy 64 (October): Walsh, Randall L "Endogenous Open Space Amentes n a Locatonal Equlbrum." Journal of Urban Economcs, 6(2):

39 TABLE A HYPOTHETICAL CHOICE SET Communty Publc Goods g g 2 Prce A B C D NOTE. Hgher values for a publc good ndcate hgher qualty. TABLE 2 PARAMETER ESTIMATES: MEAN (STANDARD DEVIATION) USED IN POLICY SIMULATION Model β η ν ρ log (α) γ school γ ar θ θ Sngle-Market (0.75) Dual-Market (3.88) (0.20) (0.8) (0.28) (0.32) NOTE. The sngle-market verson of the model uses the specfcaton from Epple and Seg (999). In ths case, the weght on school qualty s normalzed to, and the jont lognormal dstrbuton of ncome and preferences s also characterzed by: μ. 0, σ. 78, and corr( α, ln y) =. 49. ln y = ln y = TABLE 3 DESCRIPTION OF THE ATTAINMENT SCENARIO, BY PMSA Prmary Metropoltan Statstcal Area Average Ozone Concentratons Baselne (ppb) Attanment (ppb) Change (%) communtes n PMSA () Changes n Indvdual Communtes nonattanment communtes () largest reducton (%) smallest reducton (%) Oakland Sacramento San Francsco San Jose Santa Cruz Santa Rosa Vallejo-Farfeld-Napa Yolo NOTE. Average ozone concentratons n a PMSA were calculated as a weghted average over the communtes n the PMSA, usng the total acreage of each communty as a weght. The measure of ozone n each communty s the average of the top 30 -hour ozone concentratons durng the course of a year. 39

40 TABLE 4 SINGLE-MARKET WELFARE MEASURES AND CAPITALIZATION RATES, BY PMSA Prmary Metropoltan Statstcal Area Mean Δ Ozone (%) Δ rent (%) Non-Attanment Communtes MWTP ($) WTP PE ($) WTP GE ($) Δ rent (%) Attanment Communtes MWTP ($) WTP PE ($) Oakland Sacramento San Francsco San Jose Santa Cruz Santa Rosa Vallejo-Farfeld-Napa Yolo All Communtes WTP GE ($) TABLE 5 SINGLE-MARKET WELFARE MEASURES AND CAPITALIZATION RATES, SELECTED COMMUNITIES Communty PMSA Ozone (ppb) Δ rent movers MWTP WTP PE WTP GE ($) Baselne Attanment % Δ (%) (%) ($) ($) movers nonmovers Acalanes Oakland Alameda Cty Oakland Albany Cty Oakland Antoch Oakland Berkeley Oakland Castro Valley Oakland Dubln Oakland Lvermore Valley Oakland Pttsburg Oakland Sunol Glen Oakland Black Oak Mne Sacramento El Dorado Sacramento Sacramento Cty Sacramento

41 PMSA TABLE 6 DUAL-MARKET WELFARE MEASURES AND CAPITALIZATION RATES, BY PMSA Mean Δ Ozone (%) Δ rent (%) Non-Attanment Communtes Δ nc (%) MWTP ($) WTP PE ($) WTP GE ($) Δ rent (%) Attanment Communtes Δ nc (%) MWTP ($) WTP PE ($) Oakland Sacramento ,075, San Francsco San Jose Santa Cruz Santa Rosa Vallejo-Farfeld-Napa Yolo ,296, All Communtes WTP GE ($) TABLE 7 DUAL-MARKET WELFARE MEASURES AND CAPITALIZATION RATES, SELECTED COMMUNITIES Communty PMSA Ozone (ppb) Δ rent Δ nc movers MWTP WTP PE WTP GE ($) Baselne Attanment % Δ (%) (%) (%) ($) ($) movers nonmovers Acalanes Oakland Alameda Cty Oakland Albany Cty Oakland Antoch Oakland Berkeley Oakland Castro Valley Oakland Dubln Oakland Lvermore Valley Oakland Pttsburg Oakland Sunol Glen Oakland Black Oak Mne Sacramento El Dorado Sacramento , Sacramento Cty Sacramento , TABLE 8 PER HOUSEHOLD WILLINGNESS-TO-PAY TO MEET CALIFORNIA S NEW OZONE STANDARD Equlbrum Concept MWTP acre weghts MWTP x Δ ozone pop weghts dstrct weghts WTP PE WTP GE Δ Rents Δ Income Sngle-Market Dual-Market 40, NOTE. In the acre weghts scenaro, ozone s measured as the average ozone reducton per acre. In the pop weghts scenaro, ozone s measured by frst assgnng each household the ozone reducton n ther home communty and then averagng over households. In the communty weghts scenaro, ozone s measured as an average over communtes. 4

42 42 A. Hedonc Property Value Model B. Interregonal Hedonc Model C. Tebout Sortng Model D. Dual-Market Equlbrum Sortng Model Locaton = house Provson of publc goods vares across ndvdual homes Wage ncome s exogenous to locaton choce Locaton = house Provson of publc goods vares across communtes Wage ncome s exogenous to locaton choce Locaton = house, work metro area Provson of publc goods vares across communtes Wage ncome s endogenous to locaton choce Some commutng between metro areas Locaton = metro area Provson of publc goods vares across metro areas Wage ncome s endogenous to locaton choce No commutng between metro areas * * * k = k = 4 k = 2 k = 3 * k = k = 2 k = 3 k = 4 j FIG. Depcton of the Urban Landscape n Four Alternatve Models of a Locatonal Equlbrum. Metropoltan areas are ndexed by k. Panel B llustrates how metropoltan areas consttute unque locatons n the nterregonal hedonc model. Panel A dsplays the locatons of ndvdual homes wthn each metro area. In panel C, the metro areas are dvded nto communtes. Fnally, n panel D the astersks represent central busness dstrcts and the arrows ndcate commutng patterns to work.

43 Ω B A. Partton for retred households wth y=$50, Ω A * Ω D 0.25 Ω C γ 0.00 ** α Ω B B. Partton for workng households wth y=$50,000 n communtes A,B,C, and y=$50,500 n communty D 0.50 Ω A Ω D 0.25 Ω C γ α C. Partton for retred household wth y=$50,000 and dentcal relatve preferences α 0.00 Ω A Ω B Ω C Ω D FIG 2. A Partton of Preference Space n Three Competng Models. All three parttons correspond to the hypothetcal choce set n Table. Panels A and B recognze that households may dffer n ther relatve preferences for publc goods and reflect the normalzaton thatγ + γ 2 =. In panel C, households are restrcted to have dentcal relatve preferences: ( γ ) ( 0.48, 0. 52)., γ 2 43

44 44 Sacramento Yolo Oakland San Jose Santa Rosa Vallejo- Farfeld- Napa San Francsco Santa Cruz A. Prmary Metro Areas & Census Tracts B. School Dstrcts & Ar Montorng Statons FIG 3. The San Francsco and Sacramento Consoldated Metropoltan Statstcal Areas α Pttsburg.43 Mlptas 2.92 Sunol Glen Pttsburg Mlptas Sunol Glen A. Sngle-Market B. Dual-Market, Retred Households C. Dual-Market, Retred Households D. Dual-Market, Managers FIG 4. Partton of Preference Space, Three Communtes