What Can We Learn From Hedonic Models Where Markets Are Dominated By Foreclosures? Abstract

Transcription

1 Wha Can We Learn From Hedonic Models Where Markes Are Dominaed By Foreclosures? N. Edward Colson Pennsylvania Sae Universiy and Jeffrey Zabel Tufs Universiy Draf: June 2012 Absrac Hedonic propery value models have been frequenly used o value environmenal ameniies (or dis-ameniies) since markes for hese goods (bads) do no usually exis. Typically, researchers cie Rosen s (1974) seminal work ha allows one o inerpre funcions of he hedonic regression coefficiens as he marginal willingness o pay (MWTP) for he environmenal good. This allows he resuls from he hedonic models o be used o evaluae he ne benefis from environmenal policies and acions such as cleaning up Superfund sies and improving air and waer qualiy. There are a number of assumpions needed for he Rosen resul o hold. However, under exreme circumsances in he housing marke, hese assumpions are unlikely o be realisic. Recen years have winessed such exreme circumsances, such as wild swings in housing prices, high levels of morgage defaul, and mos significanly, high levels of foreclosure. In his paper, we address he following quesion "How can we inerpre he coefficien esimaes for environmenal goods in hedonic propery value models where markes are dominaed by foreclosures?" The key poin is ha he Rosen framework for developing he hedonic model and inerpreing he coefficiens in his model as MWTP relies on an equilibrium assumpion ha is quesionable in oday s housing marke ha is dominaed by foreclosures. In order o evaluae he impac of foreclosures on he housing marke in general and more specifically on he inerpreaion of he coefficiens for environmenal variables in he hedonic model, we develop a disequilibrium model of he housing marke ha explicily accouns for foreclosures hrough heir impac on vacancies. We also raise issues having o do wih composiion bias in ho and cold markes and how his affecs he coefficiens in he hedonic model.

2 I. Inroducion Hedonic propery value models have been frequenly used o value environmenal ameniies (or dis-ameniies) since markes for hese goods (bads) do no usually exis. Typically, researchers cie Rosen s (1974) seminal work ha allows one o inerpre funcions of he hedonic regression coefficiens as he marginal willingness o pay (MWTP) for he environmenal good. This allows he resuls from he hedonic models o be used o evaluae he ne benefis from environmenal policies and acions such as cleaning up Superfund sies and improving air and waer qualiy. There are a number of assumpions needed for he Rosen resul o hold. However, under exreme circumsances in he housing marke, hese assumpions are unlikely o be realisic. Recen years have winessed such exreme circumsances, such as wild swings in housing prices, high levels of morgage defaul, and mos significanly, high levels of foreclosure. In his paper, we address he following quesion "How can we inerpre he coefficien esimaes for environmenal goods in hedonic propery value models where markes are dominaed by foreclosures?" Even when he marke is in equilibrium, here are problems wih he sandard hedonic model ha can resul in coefficien esimaes ha are biased esimaes of MWTP. In paricular, endogeneiy and omied variables bias plague early sudies ha aemp o esimae MWTP for environmenal goods. Recen sudies rely on more modern mehodologies o miigae hese biases. These include random experimens, insrumenal variables, regression disconinuiy, and he differencein-difference framework. The ypical applicaion of one of hese approaches in environmenal economics uses observaional daa ha varies boh spaially and emporally. In hese cases, i is a common assumpion ha he parameers (oher han he consan) are consan over ime. Barik (1988), among ohers, have poined ou ha when here is a large-scale change in an environmenal good, say, hrough he imposiion of air qualiy sandards, his assumpion is unlikely o hold since general equilibrium effecs due o residenial re-soring will shif he hedonic funcion. The impacs of larger-scale changes in environmenal qualiy are probably beer measured using recenly-developed soring models ha capure he general equilibrium effecs ha hese changes can engender (see Kuminoff e al. (2010) for an excellen review of hese models). For example, Smih e al. (2004) show ha he general equilibrium effecs can be quie differen han he parial equilibrium effecs from a marke-wide change in air qualiy in Los Angeles. Sill, when he impacs of changes in environmenal goods are very local, such as in he discovery and clean up of leaking underground sorage anks, he general equilibrium effecs will be relaively small and hence i is more reasonable o inerpre he hedonic coefficiens as MWTP. When he marke equilibrium does no change hen he hedonic esimaes provide an upper bound on he rue ne benefis since hey do no accoun for moving coss (Freeman 1993), hough even his resul has been quesioned (Kuminoff and Pope 2010). These issues aside, here are oher reasons o believe ha MTWP, iself, can change over ime and his can complicae how we use hedonic esimaes o evaluae he ne benefis from environmenal policies. Naional and urban business cycles can affec he supply and demand 1

3 for housing which will hen affec he housing marke oucomes ha are he basis for he hedonic equaion. These impacs are exacerbaed wih significan swings in he housing cycle such as wha has been experienced in he las decade. In paricular, housing demand is affeced by household income whose changes are ied o he business cycle. Furher, he increase in inequaliy has changed he shape of he income disribuion. The increase in he upper ail is one explanaion for Supersar ciies (Gyourko e al xxxx). Leamer (2007) has made he claim ha housing IS he business cycle. He shows ha residenial invesmen is a much beer predicor of recessions han business aciviy. Leamer s explanaion for he imporance of housing is ha house prices are sicky downward. Hence he reacion in he housing marke o excess supply (due o a drop in demand) is no a drop in price bu a drop in sales. The fall in sales leads o a decline in new housing supply and he commensurae drop in consrucion, finance, and real esae jobs. I is declines in volume ha leads declines in prices. I is clear ha he housing marke is no as liquid as oher asse markes and hence canno quickly re-equilibrae afer macroeconomic shocks push he marke ou of equilibrium. Houses are he larges purchase made by households and hence ransacions are no likely o be sponaneous. Houses are no divisible and heerogeneous characerisics and informaion asymmeries can make maching buyers and sellers more difficul. Brokers ac as inermediaries and his only adds o ransacion coss. DiPasquale and Wheaon (1994) find evidence ha he housing marke akes years o clear. Riddel (2004) also finds evidence ha housing marke exhibis long periods of disequilibrium. A key o prolonged marke disequilibrium, paricularly in a down marke, is he downward sickiness of house prices. There are numerous reasons for his downward sickiness. Leamer (2007) offers one: sellers valuaions of heir houses are based on recen comparable ransacions whereas buyers valuaions are based on heir ake on fuure values. So when he marke is ho and prices are rising, buyers value unis more han sellers and sales volume is high. Bu when he marke is cold, he opposie occurs. Sales only occur when sellers ge lucky and are mached wih a buyer wih a relaively high valuaion. As Leamer (2007) poins ou, wha are observed in a cold marke are sellers prices, no marke prices. Anoher explanaion is given by Genevose and Mayer (2001); owners are no (psychologically) willing o sell heir houses for less han hey paid for i; so called loss aversion. Kiel and Zabel (1999) offer a similar psychological mechanism o explain why new owners end o over-value heir homes more han owners who have been in heir homes for longer periods of ime; selfserving bias (Lowensein, Issacharoff, Camerer, and Babcock 1993) ha arises because he value ha new owners place on heir house reflecs heir perceived abiliies in bargaining in he housing marke. In paricular, new owners would no be inclined o believe ha heir home is worh less han hey paid for i since his would indicae hey had been duped by he marke. I is exacly in a down marke, when buyers valuaions are falling, ha new owners are relucan o drop heir valuaions below he recen price hey paid for heir home. One sign ha he marke is no in equilibrium is a large number of vacancies. Vacancy raes above he naural rae (ha arises from housing search) are an indicaion of excess housing supply. The recen downurn in he housing marke has led o an unprecedened number of 2

4 foreclosures a he naional level ha has push he vacancy rae in many housing markes above he naural rae. This has resuled in a sae of housing marke disequilibrium which violaes one of he key assumpions underlying he Rosen framework. The analysis of how he housing cycle affecs he hedonic funcion is he goal of his sudy. We will pay paricular aenion o he role ha foreclosures play in deermining marke oucomes and hence he marke hedonic. Finally, he composiion of ransacions ha are used o esimae he hedonic can affec he esimaes of he hedonic parameers. This composiion bias is known o be an issue when generaing house price indices bu i may also affec he esimaes of MWTP for environmenal goods as well. This is paricularly relevan in he conex of he recen housing downurn, as he sale of foreclosed properies has significanly impaced he composiion bias of ransaced unis. In he case of a large number of foreclosures, one migh be emped o hrow ou foreclosed sales. We invesigae how his affecs he inerpreaion of hedonic regression coefficiens. Anoher relaed issue is ha coefficien esimaes can be affeced by he housing cycle; ha is esimaed implici prices of housing characerisics can vary across he cycle. This ies ino he lieraure on ho and cold markes and hin markes in paricular. We invesigae his issue as well. The key poin is ha he Rosen framework for developing he hedonic model and inerpreing he coefficiens in his model as MWTP relies on an equilibrium assumpion ha is quesionable in oday s housing marke ha is dominaed by foreclosures. In order o evaluae he impac of foreclosures on he housing marke in general and more specifically on he inerpreaion of he coefficiens for environmenal variables in he hedonic model, we develop a disequilibrium model of he housing marke ha explicily accouns for foreclosures hrough heir impac on vacancies. We also raise issues having o do wih composiion bias in ho and cold markes and how his affecs he coefficiens in he hedonic model. The resuls of his analysis will have imporan implicaions for he evaluaion of he benefis of environmenal goods and hence he economic efficiency of policies ha affec he provision of environmenal goods. For example, here is a large lieraure ha uses hedonic models o esimae he benefis from cleaning up Superfund sies (e.g. Kiel and Williams (2007), Greensone and Gallagher (2008), and Gamper-Rabindran and Timmons (2011)). Given our findings, we will provide a re-inerpreaion of hese resuls. Finally, we will come back o he iniial issue of foreclosures and review he laes lieraure on esimaing he MWTP for environmenal goods and provide a criical inerpreaion of hese resuls. II. The Rosen Framework of Hedonic Prices in Spaial Equilibrium The basis of he Rosen model is he pricing of a heerogeneous good wih muliple characerisics. The problem is cas in characerisic space where consumers and producers of he good decide where o locae based on heir opimal oucomes from uiliy and profi maximizaion. Hence we can hink of each poin in he characerisic space as a specific good; ha is he heerogeneous good wih a specific se of characerisics. 3

5 This framework lends iself quie naurally o he residenial locaion decision whereby individuals choose over a se of housing unis locaed across a housing marke. The choice of a paricular spaial locaion resuls in housing services ha emanae from he srucural characerisics ha comprise he housing uni and from he local public goods and oher spaial ameniies ha are associaed from his locaion. Furher, producers or housing developers (assumed o be owners of undeveloped land) are also making decisions abou when o build and wha specific srucure o consruc in his housing marke. The oucome of hese opimizing decisions, under a se of assumpions, will resul in an equilibrium hedonic price funcion. This funcion can be used o deermine he implici prices of he srucural and neighborhood characerisics. The ineres in environmenal economics is he pricing of local environmenal (dis)ameniies such as hazardous wase sies and air and waer qualiy. Based on he soluions o he consumer and producer maximizaion problems, he equilibrium hedonic price schedule p(z) represens a se of angencies beween consumer bid funcions and producer offer funcions. Rosen shows ha under hese equilibrium condiions ha he coefficiens corresponding o he housing characerisics in he hedonic equaion can be inerpreed as consumers marginal willingness o pay for hese characerisics. One issue is ha Rosen doesn disinguish beween srucural characerisics, s and neighborhood characerisics, n. A disinguishing facor is ha he amoun of s is deermined by he developer whereas, o a cerain exen, n is no. The laer migh require a Tiebou-ype framework o produce a similar resul as Rosen derived; he hedonic funcion can be used o esimae MWTP for hese goods. Tiebou s (1956) main poin is ha local public goods ha are provided by he local jurisdicion can be efficienly allocaed wihou federal involvemen because households will reveal heir rue preferences for hese goods by choosing where o live heir choice of residence will reflec he oucome of an opimizaion problem ha is similar o wha occurs for privae goods. Hence local public goods should be capialized ino house prices and he general Rosen resul holds ha he marginal valuaion of he local public goods will reflec consumer marginal willingness o pay for hese goods. Hedonic valuaion of environmenal commodiies is based on his model. If he funcion were known, we could ake he derivaive of p(z) wih respec o environmenal characerisic z i and claim, on he basis of eiher (1) or (3) ha his derivaive represens he willingness o pay for z i, and on ha basis cos-benefi analysis of some environmenal improvemen can be underaken. Of course p(z) is no known and mus be esimaed from daa. There are wo ses of issues which hen arise: firs he hedonic funcion is based on boh he bid and offer funcions and he poins on he hedonic are due o facors ha affec boh consumers and producers. This inroduces a classic simulaneous equaions problem in he esimaion of p(z). Bu, as Palmquis (1991) poins ou Alhough i is imporan o include boh consumer and producer behavior when describing he marke, for many environmenal issues he criical informaion is conained on he consumer side of he marke. Forunaely, i is ofen possible o focus on he equilibrium price schedule and on consumers decisions. In hese cases, ignoring he producer side does no creae heoreical or economeric problems. (Palmquis, p80) 4

6 This is because housing supply is dominaed by an exising sock which is fixed in place by hisorical circumsances. On his accoun he above model of builder/supplier decisions can be replaced by one in which consumers are mached wih a given disribuion of z (Epple 1987). Environmenal goods in his model are simply one more elemen of z which consumers ake as given. Even on his assumpion of fixed supply, a second issue arises, which is ha absen full informaion on boh he disribuion of z and consumer ase and income, he funcional form of p(z) canno be deermined from he model. As Epple (1987) poins ou p(z) can be eiher concave or convex a some value z*, depending on he densiies of y, α, and z in he neighborhood of z* 1. j p Esimaes of p(z) herefore mus be esimaed from regression analysis, where he dependen variable is he price of he house and he independen variables are he z s which are given some nonlinear funcional form. This funcional form is generally aken o be one ha fis he daa well, since (o repea) he heory gives no guidance. In any case, wih he parameers of p(z) esimaed, derivaives can be calculaed and cos-benefi analysis underaken. To ake a common example, i is ofen assumed (again, because he fi of he regression is good) ha he hedonic funcion akes he form: lnp i 0 j X ij j u i (1) where p i is he price of he i h uni a ime and X ij is he value of characerisic j for uni i a ime. In his case, he hedonic price of he j h characerisic in period is j p where p is he average price a ime. This paricular funcional form highlighs wo ways in which he hedonic price can vary over ime: (1) he overall price of housing can vary; (2) he parameer associaed wih he environmenal characerisic can vary over ime. While oher funcional forms will require differen calculaions of hedonic prices, hese basic principles generally sill apply. Now consider he price of his characerisic as ime passes, paricularly in ligh of he evens of 2007 and beyond. The housing marke of his era can be characerized by hree phenomena: 1. A fall in he general price of housing 2. A fall in he frequency of rading so-called cold housing marke 3. An increase in he number of foreclosures and vacancies in general and in paricularly so in cerain neighborhoods. The quesion hen is wheher hese phenomena have an effec on eiher has an effec on price j or p. Clearly 1. III. Foreclosures, Vacancy Raes, and he Housing Marke 1 Perhaps a foonoe here explaining ha even if everyhing here were solved you would usually only have a local approximaion o willingness o pay and ha for real cos-benefi analysis o ake place you would need o esimae he bid funcions a la Kiel and Zabel or Coulson and Bond. 5

7 The housing crisis of 2007 and going forward has led, as noed, o a large increase in foreclosed properies. This has generaed real effecs in he housing marke, among which is a noable increase in housing vacancy raes. Figure 1 displays hisorical rends in wha he Census calls ownership vacancy raes for he period for he US as a whole and for four seleced saes: Florida, Nevada, Ohio, and Pennsylvania. Noe firs ha he U.S. rae was more or less consan beween 1 and 2 percen unil he ime of he crisis, whereupon i basically doubled o nearly 2 percen beween 2005 and However he changes in his rae were quie heerogenous across saes. The firs wo, Florida and Nevada, were widely regarded as ceners of he housing bubble and is deflaion in he key years. The vacancy raes displayed in Figure 1 reflec his. These saes vacancy raes were, hough above he naional average, quie sable unil 2005, whereupon hey rose dramaically, o above 5 percen in This is widely viewed as being he resul of homeowners leaving heir propery in he wake of defaul and foreclosure evens 3. This inerpreaion is reinforced by examining he vacancy rend for Ohio, whose residens were also severely hi by foreclosures. Ohio had a lower han average vacancy rae for much of he pre-crisis period bu beginning even in 2004 had a srong upsurge in vacancies which lef i well above average a he end of he period. By conras, Pennsylvania which had a raher less severe foreclosure crisis, did no experience a rise in vacancies during he crisis period. One las poin o noe is ha all of he saes, and he US generally, experienced a downurn in he vacancy rae in The sable behavior of vacancy raes over ime (a leas up unil he recen crisis), and in paricular he fac ha raes are persisenly greaer han zero suggess ha even in equilibrium i is opimal for vacancy raes o be greaer han zero. This posiive equilibrium rae has been dubbed he naural vacancy rae, and is congruen wih he noion ha search and maching in housing markes is cosly, given he heerogeneous housing sock (Arno, 1989, Wheaon, 1990). The naural vacancy rae has been confirmed by Smih and Rosen (1983). I can vary across housing markes as i is affeced by facors ha affec he cos of holding vacan unis, search coss, ransacion coss and credi marke imperfecions. Gabriel and Nohaf (1998) esimae he naural vacancy raes for for 16 MSAs. They show ha hese raes depend on he change in rener occupied housing unis, rens (level), he variabiliy in rens, he percen minoriy, and he change in populaion. If a homeowner chooses o keep a uni vacan raher han selling in response o an offer, his is a decision o hold a real opion. Tha is, when he owner of a vacan uni decides o keep a uni vacan raher han selling i a he curren marke price, his is because she believes ha waiing is worhwhile. Waiing is more worhwhile if prices are expeced o increase and if he volailiy of housing invesmen reurns is larger (Rosen and Smih). These ideas can be made more precise wih a simple model, similar in spiri o Wheaon (1990) and o models of he naural unemploymen rae (e.g. Wrigh, 1986). Suppose here is a sock of 2 This is he vacancy rae for single family and condominium unis, and is disinguished from he renal vacancy raes derived from aparmen buildings and is radiionally several percenage poins greaer han he owner rae. The source is hp:// 3 See Malloy and Shan (2012); O Donnell and Coulson (2012) 6

8 housing of populaion normalized o uniy. A any poin in ime some fracion of hem, v are vacan. Owners of vacan propery pos an asking ren, r a, and awai offers. They receive one offer per period, which has probabiliy p(r a ) of being from a (poenial) buyer wih an offer ren greaer han r a (i.e. p(.) is he cumulaive disribuion funcion of offer rens). Owners of occupied unis (who may hemselves be he occupiers) dis-aach from heir unis (and make hem vacan) wih probabiliy α. This is because of desired locaion change or, in he case of Wheaon (1990), demand for a differen ype of housing srucure. Whaever he reason, hese unis also become vacan and receive an offer immediaely, from he save disribuion. Thus, in ime, vacancies can exis for wo reasons. Firs, here are unis ha were vacan in -1, and did no receive a sufficienly high offer. The mass of hese is 1 pr v. Second, here are newly vacan unis which also did no receive a sufficienly high offer. The mass of hese is α1 pr 1 v. Therefore he law of moion for vacancies is v 1 pra v -1 1 pra 1 v -1 e (2) where e represens shocks o vacancies arising from eiher source. The fac ha boh p(.) and α are beween zero and one suggess ha v is a saionary AR(1) process wih firs order coefficien 1 1 and a long run equilibrium or naural vacancy rae, v*, of v* 1 pra 1 pr pr a a On his inerpreaion, posiive shocks will have persisen effecs and higher han average vacancy raes will persis for some ime, bu in he end, vacancy raes will ulimaely reurn o heir equilibrium level. The increase in vacancies due o foreclosures, on his accoun, is a large shock o he second source of vacancies which has pushed he vacancy rae above he naural rae and his has resuled in disequilibrium in he housing marke. Therefore, and imporanly, he effec of he foreclosure crisis is o only emporarily raise vacancy raes, which will reurn o heir long run naural raes in due ime. While he simple model above leaves ou he role of housing price and quaniy adjusmen in he face of all hese new vacancies, i is inuiive (hough no mahemaically sraighforward) o augmen he model accordingly. Gabriel and Nohaf (1988), following Rosen and Smih (1985), in heir invesigaion of renal vacancy raes, posi ha v * v u R = g (4) where g > 0 and u is a random error erm. Thus rens rise when he marke is shor of vacan unis, and vice-versa, as is naural. Noe ha such a ren-adjusmen model complicaes he dynamics of equaion (2) since i suggess ha he AR(1) coefficien is ime-varying, bu we (3) 7

9 ignore ha here. In any case, he persisence of vacancies in (4) causes he sign of g o be posiive. We can exend Gabriel and Nohaf o owner-occupied housing in wo ways: (1) we can argue ha propery prices are he presen discouned value of fuure rens, so ha even a emporary increase in rens should have an effec on prices, especially if he effec, hough emporary, is persisen and (2) we can argue ha a similar price-adjusmen dynamic applies o ownership propery. Since he variabiliy of rens is less han he variabiliy of prices (Sinai and Souleles, 2005) he laer inerpreaion may be preferable. III.1 A Disequilibrium Model of he Housing Marke We now develop a srucural model of he housing marke ha allows for disequilibrium where he vacancy rae falls ou naurally as an error correcion mechanism. This builds on models developed by DiPasquale and Wheaon (1994), Follain and Velez (1995), and, in paricular, Hwang and Quigley (2006). S S D D We firs specify demand and supply equaions for housing Q P, X and P, X S D Given ha he housing marke is in (long run) equilibrium, Q Q Q Q., Q S and Q D, will S D likely be coinegraed wih coinegraing parameer equal o 1. Tha is Q Q V is I(0). * N Following he discussion of he naural vacancy rae, V V V is he error correcion N mechanism where V is he naural rae. Furher, o make he relaionship wih foreclosures * clear, V is specified as a funcion of foreclosures, f, V * f. The error correcion model for inverse demand is p q 1 v 2 * -1 f f 3 x 4 d p 5-1 where lower case leers indicae logs, and x d includes he user-cos of housing, rens, income, he number of households and employmen. I is expeced ha α 2 < 0; if v -1 * > 0 hen here is excess supply of housing and prices will decrease and vice versa. Noe ha he number of foreclosures also eners by iself in he model. Tha is, hey are viewed as a local disameniy which direcly affecs he demand for housing. Hence i is expeced ha α 3 < 0. p - 1 is included by specifying a parial adjusmen mechanism for prices. Noe ha q is essenially (he log of) new housing supply 1 2 * -1 f q p v x q (6) 3 s x s includes inpu prices, financing coss, average ime on he marke (TOM), and local regulaions. I is expeced ha 2 < 0, a rise in vacancies above he naural rae will reduce he 4-1 s d (5) 8

10 supply of new housing. The lag of q is included by specifying a parial adjusmen mechanism for new housing supply. Economic condiions can indirecly affec new housing supply hrough p. Tha is, as economic condiions worsen, prices will fall and his will reduce supply given ha 1 > 0. Following Topel and Rosen (1988), we include TOM in x S. They noe ha ineres raes should only affec supply hrough demand-side effecs on prices. Bu if increases in he ineres rae lead o a drop in demand and prices are sicky downward hen houses are likely o spend more ime on he marke. In fac, Topel and Rosen find ha TOM has a large effec on new supply. They poin ou ha TOM is poenially endogenous bu IV resuls differ lile from OLS. In essence, TOM is a very similar means for capuring marke disequilibrium as is vacancies. The lengh of ime a uni is vacan is clearly par of TOM for ha uni. Bu TOM does no appear o fall ou naurally as an error correcion mechanism as do vacancies (should be included as a lag?) To complee he sysem, he vacancy equaion is modeled as a funcion of foreclosures and v p q f x v (7) * x v will include he expecaion and variance of fuure price changes, E(p +1 ) and V(p +1 ). * I is expeced ha γ 1 < 0, γ 2 > 0, and γ 3 > 0. The lag of v -1 is included by specifying a parial adjusmen mechanism for new housing supply. Since Leamer poins ou ha he business cycle is really a housing volume cycle, how can we inroduce sales volume ino he model? Follain and Velez include i (acually he urnover rae) as one of he equaions in heir srucural model of he housing marke. They also include i in he supply equaion. They claim o find he anomalous resul ha he urnover rae is negaively correlaed wih price bu his migh no acually be surprising given ha Leamer show ha volume leads price so ha volume urns down before price does. The urnover rae is clearly relaed o TOM as a higher TOM means a lower urnover rae. v 5 * -1 v III.2 Ho and Cold Markes Now consider again he housing and foreclosure crisis as a shock o boh prices and vacancies. There is no only a house price decline, bu also an increase in vacancies due o he defaul and foreclosure process. Wha models like Hwang and Quigley s empirically demonsrae is ha he inerconnecedness of hese variables exacerbaes he effecs of hese shocks, bu ha neverheless he effecs on price are only emporary. Anoher srand of lieraure akes a slighly differen approach. Krainer (2001) noes ha wheher a marke is ho or cold can have profound effecs on he price and vacancy raes in a marke. To summarize his model, in a ho marke, sellers are able o (and wan o) sell houses quickly, hus vacancy raes are low and prices are high. Since hese quaniies depend on he 9

11 sae of naure here is nohing ha drives vacancy raes back o heir naural values. These ideas are amplified in Novy-Marx (2009) who noes ha addiional enry by buyers is induced when markes are ho, because he value of enry increases. This raises prices, and reduces vacancy, even more, exacerbaing he values of hese fundamenals. The opposie of course is rue in hese models during cold markes, when buyer enry is low, prices fall, illiquidiy and vacancies increase. Thus o he exen ha hedonic prices depend on housing prices, he recen crisis will cause a fall in hedonic prices, and i is possible ha his is a more permanen sae of naure for ha housing marke. Chernobai and Chernobai (2012) noe ha buyer heerogeneiy exiss in hese markes. They caegorize buyers ino long- and shor-erm buyers, and noe ha shor-erm buyers are more likely o buy low qualiy unis han long-erm buyers (because he coss of aaching hemselves o he low qualiy uni are lower). The auhors do no disinguish beween ho and cold markes, nor apply he qualiy heerogeneiy of housing o environmenal goods in paricular, one can neverheless assume ha people who buy houses in areas wih negaive environmenal aribues are more likely o be shor erm buyers. Transacion raes will herefore be higher in hese areas and he hedonic price of environmenal aribues is likely o be higher han i would be if his buyer selecion did no exis (i.e. in a marke where buyers and sellers are randomly mached). A cold marke is cold, herefore, because hese shor erm buyers are he ones who have lef he marke. The price of housing falls in all markes, bu he price in low-qualiy (i.e. wih negaive environmenal aribues) areas will fall farher ha is, he hedonic price of environmenal commodiies falls. Long-erm buyers, who now dominae he marke, have less desire o live near a superfund sie. Thus no only P falls in a cold marke, bu β does as well. The resul of his analysis of he housing marke is ha he marke is ofen in a sae of disequilibrium where down markes are characerized by excess supply ha is due o downward sicky prices. The recen experience of excess supply is exacerbaed by he increased foreclosures. The marke has been slow o reurn o an equilibrium ha requires prices o fall enough o bring vacancies back o heir naural rae. When he marke is in disequilibrium, he marke price is no likely o be equal o MTWP. The acual price will depend on he bargaining power of he buyers and sellers. This is displayed in Figure 2. The boom line is, in periods of disequilibrium, inerpreing coefficiens in he hedonic as MTWP for a paricular characerisic is quesionable. A bes, one should view hese coefficiens as capializaion effecs and no as MWTP. One key indicaor ha he marke is in disequilibrium, as characerized by excess supply, is a large increase in he number of foreclosures as is currenly exhibied in many U.S. housing markes. IV. Economeric Model The goal of he paper is o assess wha we can learn from hedonic models when he marke is dominaed by foreclosures. So we now move from he srucural model of he housing marke o he hedonic funcion. 10

12 Assume one housing marke ha consiss of N unis. N ransacions are observed every period = 1,,T. The general economeric specificaion of he hedonic model is p i g(x, u ; ) (8) i i where p i is he ransacion price for uni i in period, X i is a vecor of housing characerisics (srucural and neighborhood), and u i is a sochasic error erm ha needs no be i.i.d. bu, for now, assume E[u i z i ] = 0. is a parameer vecor ha is allowed o vary over ime. This will allow for he price of housing o vary over ime (i.e. ime-varying inercep) as well as he coefficiens for he individual componens of X i. In paricular, as our developmen and discussion of he disequilibrium model of he housing marke shows, no only will he marke equilibrium vary over he housing cycle bu he ransiion beween equilibriums will be drawn ou. This will lead o changes in over ime. A ypical funcional form is a log-linear model ha allows for nonlinear relaionships beween he elemens of X i and ln(p). lnp i 0 X i u i (9) where some of he elemens of X i could be binary or squares of oher variables. Then he hedonic price for characerisic j is j p where his price is evaluaed a he mean of p in period. Given ha prices will change over he housing cycle, he price for characerisic j will also change over he housing cycle unless j increases by he same percenage ha p declines such ha p is consan. j Of ineres o environmenal economiss are he coss of residing near hazardous wase sies, landfills, incineraors, nuclear power plans, indusrial faciliies and commercial sies such as gas saions and waer and air qualiy. Oher environmenal goods are acually ameniies such as open space in he form of parks or welands. Bu hese can also have negaive impacs on house prices as he exisence of open space can impose resricions on developmen. A classic example is he imposiion of criical habia designaion for endangered species. When he characerisic of ineres is one of hese environmenal goods or some oher neighborhood characerisic, geing accurae esimaes of he corresponding hedonic price is complicaed by he likely presence of omied variables and/or endogeneiy bias. Modern mehods ha aemp o miigae hese biases usually require panel daa in order o mimic he reamen/conrol framework of randomized experimens where oucomes are compared before and afer he reamen is adminisered. When he reamen is a large-scale change in an environmenal good, he hedonic price for ha good will likely change as he marke reequilibraes. This is rue even if he housing marke is oherwise sable. Kuminoff and Pope (2011) show ha his can make i paricularly difficul o accuraely esimae MWTP. 11

13 A common assumpion in hedonic models is ha is consan over ime. As we know from he lieraure on aggregaion bias, he esimaed value for will be some kind of average (hough Kuminoff and Pope (2011) show ha even his is no necessarily he case) of he s. Furher, o ge an esimae of he hedonic price, i is common o muliply he esimaed value of by p. Boh of hese acions will disor he acual hedonic price a a given poin in ime. So here are wo quesions: (1) Suppose one hough ha he price of air polluion was consan over he cycle. In a semilog funcion does his imply ha bea(air polluion) rises as P falls during a downurn.? (2) If no, can we make recommendaions for funcional forms and/or esimaion pracices ha provide beer, more robus, esimaes of hedonic prices a various poins in he cycle? Jaren Pope and Nick Kuminoff have oulined a series of bes pracices ha address he second quesion. They show in Kuminoff and Pope (2010) ha he Box-Cox specificaion is preferable in many circumsances. The problem of how o inerpre he esimaed hedonic price under hese condiions is even more complex when he marke is in disequilibrium. Again, he boom line is ha i is likely o be a srech o inerpre he esimaed hedonic price as MWTP for he environmenal good. IV.1 Adding Foreclosures o he Hedonic Model Now inroduce foreclosures ino he model. Foreclosed houses are likely o sell a lower prices han non-foreclosed unis boh because financial insiuions have an incenive o sell hem quickly because hey do no collec rens while vacan unis and because hese unis are subjec o vandalism (bu is his differen han oher vacan properies?) and because foreclosed properies are likely o no have received proper mainenance during he foreclosure process. This migh indicae ha foreclosed properies ha sell can be included wih jus he addiion of a dummy for foreclosures or wih some oher characerisics such as ime vacan. lnp i 0 z i f i u i where f i is a binary indicaor ha he propery is foreclosed. A recen paper ha looks a how foreclosed properies affec house prices is Campbell, Giglio, and Pahak (2011, henceforh CGP). They esimae a hedonic equaion using ransacion daa for Massachuses for 1987 o CGP s esimae of is , , and for singlefamily, muli-family, and condos. I could also be he case ha he coefficiens are differen for foreclosed unis. lnp i 0 z i f i z i f i u i 12

14 in his case allowing for separae coefficiens for foreclosures is he same as dropping hem from he sample. CGP find ha here is a larger discoun for foreclosed properies ha are found in low qualiy census racs and larger when he srucure is worh less. They claim ha his resul may be due o greaer vandalism in lower qualiy neighborhoods and fixed coss of proecion ha jusify larger proporional discouns on cheaper houses. Foreclosed properies can also affec he prices of nearby properies. So a he leas, we need o modify he model for non-foreclosed properies o accoun for his affec p i g z 1i,..., z ki, f i d i, u i ; where f i (d i ) is he number of foreclosures wihin disance d i of uni i a ime. CGP find ha an addiional foreclosure ha is 0.05 miles away causes prices o fall by abou 1 percen. Using similar daa, Gerardi, Rosenbla, Willen, and Yao (2012) find ha properies wihin 1/16 of a mile of (1) a seriously delinquen propery, (2) a bank-owned propery, (3) a propery sold by he bank in he las year and (4) a propery sold by he bank more han a year ago sell a 2.8%, 3.3%, 2.4% and -0.2% discouns, respecively. The auhors claim ha he bes explanaion for he discoun is he reduced invesmen by owners of disressed properies. V. Analysis of Empirical Sudies ha esimae Hedonic Prices for Environmenal Goods V.1 Noise Polluion Consisen daa of he ype ha is recommended o ge bes esimaes of hedonic prices for environmenal goods is quie difficul o assemble. We can obain some inuiion from measudies of he hedonic prices of environmenal goods. This evidence has more cross-secional variaion han ime variaion, bu he evidence conained here can sill be quie informaive. Take, for example, he sudies of aircraf noise gahered for he mea-analysis of Nelson (2004). Nelson repors, for each of hese sudies boh he average propery price and he hedonic price of one decibel of aircraf noise, expressed as a percenage of propery value- he calls his he NDI%. In he case of he semilog hedonic funcion his would be simply he hedonic parameer β, and for he linear funcional form i would be he parameer value divided by he average propery price 4. We conver his hedonic valuaion o price levels by convering back o marginal prices (i.e. muliplying NDI% by he average propery value in he sample). As i happens, he sudies used by Nelson encompass wo disinc periods of analysis. The firs se uses propery daa from he period 1969 hrough 1971 and he second draws from 1980 o Because of he differences beween hese wo periods i is pruden o analyze hem separaely, so Figures 3 and 4 provide scaer plos of he relaionship beween he hedonic price of aircraf noise and he average housing price, for each of he wo periods. Wihin each period here is a clear posiive relaionship beween he wo. I may be hough ha his is a produc of including he price iself in he calculaion of he hedonic price, bu his is no he case In a more rigorous (mea)- regression analysis, Nelson finds ha ha he NDI% iself is posiively relaed o sales price. 4 We exclude a few Canadian sudies and hose which use ren raher han sales price as he variable of ineres. 13

15 Would his posiive relaionship beween housing prices and hedonic prices apply o ime series variaion wihin a given marke? There is no reason o hink no. Willingness o pay for everyhing, including environmenal ameniies, will be higher when he economy is in a boom phase, and lower during recessions; environmenal commodiies are presumably normal goods. In addiion, he above analyses sugges ha his will be he case simply because of he ypes of buyers who ener and exi a differen phases of he cycle. MORE TO COME HERE. VI Conclusion 14

16 References Arno, Richard Housing Vacancies, Thin Markes, and Idiosyncraic Tases, Journal of Real Esae Finance and Economics, 2, Campbell, John, Sefano Giglio, and Parag Pahak Forced Sales and House Prices, American Economic Review 101(5): Chay, Kenneh and Michael Greensone Does Air Qualiy Maer? Evidence from he Housing Marke, Journal of Poliical Economy, Chernobai and Chernobai (2012) DiPasquale, Denise and William C. Wheaon Housing Marke Dynamics and he Fuure of Housing Prices, Journal of Urban Economics, 35, Follain, James, and Orawin Velz Incorporaing he Number of Exising Home Sales ino a Srucural Model of he Marke for Owner-Occupied Housing, Journal of Housing Economics, 4, Gabriel, Suar and Frank Nohaf Renal housing markes and he naural vacancy rae, Journal of he American Real Esae and Urban Economics Associaion 16: Gamper-Rabindran, S. and C. Timmins Valuing he Benefis of Superfund Sie Remediaion: Three Approaches o Measuring Localized Exernaliies, NBER Working Paper No Genesove, David, and Chrisopher J. Mayer Equiy and Time o Sale in he Real Esae Marke. American Economic Review, 87(3): Genesove, David, and Chrisopher J. Mayer Loss Aversion and Seller Behavior: Evidence from he Housing Marke. Quarerly Journal of Economics, 116(4): Gerardi, Krisopher, Eric Rosenbla, Paul Willen, and Vincen Yao Foreclosure Exernaliies: Some New Evidence, Fed Working Paper Greensone, M. and J. Gallagher Does Hazardous Wase Maer? Evidence from he Housing Marke and he Superfund Program, The Quarerly Journal of Economics 123(3): Guren, A. and T. McQuade, How Do Foreclosures Exacerbae Housing Downurns? unpublished mimeo, Harvard Universiy. Harding, John P., Eric Rosenbla, and Vincen W. Yao The foreclosure discoun: Myh or realiy? Journal of Urban Economics 74:

17 Hwang, Min, and John M. Quigley Economic Fundamenals in Local Housing Markes: Evidence from U.S. Meropolian Regions. Journal of Regional Science 46(3): Kiel, Kaherine A. and M. Williams The Impac of Superfund Sies on Local Propery Values: Are all sies he same? Journal of Urban Economics 61: Kiel, Kaherine A. and Jeffrey E. Zabel The Accuracy of Owner Provided House Values: The American Housing Survey, Real Esae Economics, he Journal of he American Real Esae and Urban Economics Associaion 27: Krainer, J A heory of liquidiy in residenial real esae markes, Journal of Urban Economics 49: Kuminoff, Nicolai V., Chrisopher F. Parmeer, and Jaren C. Pope Which Hedonic Models Can We Trus o Recover he Marginal Willingness o Pay for Environmenal Ameniies? Journal of Environmenal Economics and Managemen, 60(3), Kuminoff, Nicolai V. and Abdul S. Jarrah A New Approach o Compuing Hedonic Equilibria and Invesigaing he Properies of Locaional Soring Models. Journal of Urban Economics, 67(3): Kuminoff, Nicolai V. and Jaren C. Pope The Value of Residenial Land and Srucures during he Grea Housing Boom and Bus, draf Ocober Kuminoff, Nicolai V. and Jaren C. Pope A Novel Approach o Idenifying Hedonic Demand Parameers, draf June. Kuminoff, Nicolai V. and Jaren C. Pope Rosen Bias in he Willingness o Pay for Nonmarke Goods, draf Sepember. Kuminoff, Nicolai V., V. Kerry Smih, and Chrisopher Timmins The New Economics of Equilibrium Soring and Is Transformaional Role for Policy Evaluaion. NBER Working Paper # Leamer, Edward, 2007, Housing IS he Business Cycle, NBER Working Paper # Lowensein, G.S., S. Issacharoff, C. Camerer, and L. Babcock Self-Serving Assessmens of Fairness and Prerail Bargaining, Journal of Legal Sudies 22: Mayer, Chrisopher J A Model of Negoiaed Sales Applied o Real Esae Aucions. Journal of Urban Economics, 38(1): Mayer, Chrisopher J Assessing he Performance of Real Esae Aucions. Real Esae Economics, 26(1): Mian, Aif, Amir Sufi, and Francesco Trebbi Foreclosures, House Prices, and he 16

18 Real Economy, NBER Working Paper No Ngai, L. Rachel and Silvana Tenreyro Ho and Cold Seasons in he Housing Marke, Cenre for Economic Performance Discussion Paper No Novy-Marx, Rober Ho and Cold Markes, Real Esae Economics, 37(1): Palmquis, Raymond Hedonic Mehods in Braden, John B., and Charles D. Kolsad, eds., Measuring he Demand for Environmenal Qualiy, Norh Holland, 1991, Riddel, Mary Housing-marke disequilibrium: an examinaion of housing-marke price and sock dynamics , Journal of Housing Economics 13: Rosen, Kenneh T., and Lawrence B. Smih The Price Adjusmen Process and he Naural Vacancy Rae, American Economic Review, 73, Sieg, H., V.K. Smih, H.S. Banzhaf and R.Walsh Inerjurisdicional Housing Prices in Locaional Equilibrium. Journal of Urban Economics 52: Sinai, T. and Souleles, N. 2005, Owner-Occupaion as a Hedge Agains Ren Risk Quarerly Journal of Economics, 120: Sein, Jeremy Prices and Trading Volume in he Housing Marke: A Model wih Down-Paymen Effecs, Quarerly Journal of Economics 110(2): Tiebou, Charles A Pure Theory of Public Expendiures, Journal of Poliical Economy Topel, Rober, and Sherwin Rosen Housing Invesmen in he Unied Saes, Journal of Poliical Economy 96(4): Wheaon, William C Vacancy, Search, and Prices in a Housing Marke Maching Model, Journal of Poliical Economy, 98,

19 Figure 1 Owner vacancy raes, US and seleced saes, year Unied Saes Pennsylvania Florida Ohio Nevada 18

20 Figure 2 House Price Excess Supply Supply P P E Demand Q D Q E Q S Housing Quaniy 19

21 Figure 3 Hedonic price of 1 decibel airpor noise Hedonic price of airpor noise vs. house price: Sudies conduced Sample average house price 20

22 Figure 4 Hedonic price of 1 decibel airpor noise Hedonic price of airpor noise vs. house price: Sudies conduced Sample average house price 21

23 Appendix 1: General Equilibrium Model 1: Rosen Model Define z = (z 1,z 2,,z k ) o be a vecor of n housing characerisics. The good is compleely deermined by his vecor of characerisics. Hence z corresponds o a specific good in he full R k produc space. Furher, p(z) is he price associaed wih his vecor of characerisics ha corresponds o a specific elemen in his produc space. p(z) is deermined by marke clearing condiions: he amoun supplied a each poin in he produc space mus equal he amoun demanded by consumers choosing o locae here. Thus p is he house price observed in marke ransacions, while he markes for individual z s are no, bu mus be inferred from he marke for houses. Given ha each z i is a good and no a bad, p(z) is coninuously increasing in each z i and is assumed o have coninuous second derivaives. p(z) is no assumed o have any specific funcional form and can clearly be nonlinear in is argumens. I is assumed ha he marke is no hin. Tha is, i is assumed ha here is a coninuous specrum of producs so ha he choice se is coninuous. Consumers: I is assumed ha consumers purchase only one uni of he produc ha is locaed in he goods space. The consumer s uiliy funcion is U(x, z 1,z 2,,z k; α) where x is all oher goods and he price of x is se o one and α is a ase parameer. U( ) is assumed o be sricly concave. Consumers maximize uiliy subjec o he budge consrain: y = x + p(z) where y is income. The firs-order condiions are p U z i p i i 1,..., k z i U (1) x Thus p i, he derivaive of he hedonic price funcion, can be inerpreed as he price of z, he implici housing characerisic. Noe ha his comes from he usual equivalence beween he raio of prices and he marginal rae of subsiuion beween any wo commodiies. Anoher way o express his problem is in erms of he bid funcion B(z 1,z 2, z k ;u 0,y,α) ha is defined implicily hrough he indirec uiliy funcion U y B, z1,..., z k ; u 0 (2) where B( ) is he expendiure a consumer is willing o pay for z = (z 1,z 2,,z k ) a a given uiliy u 0 and income level y. Taking derivaes of (2) resuls in B U z 1 i B i 0, B u 0, and B y 1 z i U x U (3) x 22

24 B i is he marginal rae of subsiuion beween z i and income (given ha he price of x is 1). This is he consumer s marginal value of z i (given u 0 and y). The bid funcion is increasing in z i ; consumers value more z i over less. I can be shown ha he second derivaive is negaive so ha he increase in how much a consumer will spend for a marginal increase in z i declines in z i ; a sandard resul in consumer heory. Noe ha from equaions (1) and (3), i follows ha he marginal bid is equaed o he marginal price: p i = B i. Uiliy is maximized when B(z *; u*, y) = p(z *) and B i (z*; u*,y) = p i (z*), i = 1,..., k, where z* and u* are opimal values. Thus he opimal value for z occurs where he wo surfaces p(z) and B(z; u*,y) are angen o each oher. This opimal oucome is condiional on y and α ha are assumed o have he join disribuion funcion F(y,α). Then he populaion equilibrium is characerized by a se of bid funcions whose envelope is he marke hedonic funcion. Producers: To simplify he analysis, i is assumed ha each z is produced separaely wih no join producion or spillovers. Hence each firm produces one produc z. Le M(z) denoe he number of unis of z ha are produced. I is assumed ha each firm akes he hedonic price funcion as given and maximizes profi (M,z) = Mp(z) - C(M, z; ) where C(M, z; ) is he cos funcion ha is he oucome of minimizing coss subjec o he producion echnology ha is a funcion of M, z, and oher inpu facors. represens facors ha vary across firms such as inpu prices and producion funcion parameers. Assume C is convex wih C(0, z) = 0 and C M and C zi > 0. The firs-order condiions are M, z; i 1,..., k and p(z) C M, z; p i C z i These firs-order condiions indicae ha he marginal revenue from an addiional uni of each aribue ha is sold equals he marginal cos of producing ha uni. Furhermore, he amoun of z produced is deermined up o he poin where he revenue p(z) equals he marginal cos of producion, evaluaed a z*. Analogous o he consumer s problem, his can be expressed in erms of he offer funcion O(z 1,...,z k ; 0, ) indicaing he prices he firm is willing o accep on producs defined by differen levels of he z i s a fixed profi 0 and opimal M. O(z 1,...,z k ; 0, ) is deermined by solving ou for M in he following wo-equaion sysem and hence solving for O( ) in erms of z, 0, and 0 M, z M Oz; 0, CM, z; (5) and Oz; 0, C M M, z; (6) By differeniaing equaions (5) and (6), one obains M (4) O z i C z 1 i 0 and O 0 (7) M M 23