Edward L. Glaeser Harvard University and NBER. and. Joseph Gyourko * University of Pennsylvania and NBER. December 15, 2006, Preliminary Draft

Transcription

1 HOUSING DYNAMICS by Edwad L. Glaese Havad Univesiy and NBER and Joseph Gyouko * Univesiy of Pennsylvania and NBER Deembe 5, 006, Peliminay Daf Absa The key sylized fas of he housing make ae posiive seial oelaion of pie hanges a one yea fequenies and mean evesion ove longe peiods, song pesisene in onsuion, and highly volaile pies and onsuion levels wihin makes. We alibae a dynami model of housing in he spaial equilibium adiion of Rosen and Robak o see whehe suh a model an geneae hese fas. Wih easonable paamee values, his model eadily explains he mean evesion of pies ove five yea peiods, bu anno explain he obseved posiive seial oelaion a highe fequenies. The model pedis he posiive seial oelaion of new onsuion ha we see in he daa and he volailiy of boh pies and quaniies in he ypial make, bu no he volailiy of he naion s moe exeme makes. The song seial oelaion in annual house pie hanges and he high volailiy of pies in oasal makes ae he wo bigges housing make puzzles. Moe eseah is needed o deemine whehe measuemen eo-elaed daa smoohing o make ineffiieny an bes aoun fo he pesisene of high fequeny pie hanges. The bes aional explanaions of he volailiy in high os makes ae shoks o inees aes and unobseved inome shoks. * Glaese hanks he Taubman Cene fo Sae and Loal Govenmen a Havad Univesiy, and Gyouko hanks he Reseah Sponsos Pogam of he Zell/Luie Real Esae Cene a The Whaon Shool, Univesiy of Pennsylvania fo finanial suppo. We appeiae he ommens of semina paiipans a he Univesiy of Chiago, he NBER Summe Insiue, and he Fedeal Home Loan Mogage Copoaion on pevious vesions of he pape. Gaham Ellio and James Sok povided helpful guidane. Andy Mooe, Chales Nahanson, and Jon Seinnsen povided supeb eseah assisane.

2 I. Inoduion Housing onsiues nealy wo-hids of he ypial household s pofolio, and moe han $8 illion woh of eal esae is owned wihin he household seo. Despie he enomous size of his seo, eonomiss undesanding of many feaues of he housing make emains inomplee. Fo example, in he sample of 5 meopolian aeas fom 980 o 005 fo whih we have Offie of Fedeal Housing Enepise Ovesigh OFHEO onsan qualiy house pie seies, a $ inease in eal house pies in one yea is assoiaed wih a 7 en inease he nex yea. A $ inease in loal make pies ove he pas five yeas is assoiaed wih a 3 en deease ove he nex five yea peiod. This pediabiliy of pie hanges seems o pose a hallenge fo an effiien makes view Case and Shille, 989; Cule, Poeba, and Summes, 99. The lage amoun of ine-empoal volailiy in pies wihin makes is also puzzling. The sandad deviaion of hee-yea eal hanges in ou sample of meopolian aea aveage house pies is $6,354 in 000 dollas houghou he pape, whih is abou one-fifh of he median pie level. Ove one, hee, and five yea peiods, he sandad deviaion of house pie hanges is a leas hee imes he mean pie hange. Can his volailiy be he esul of eal shoks o housing make o mus i efle bubbles and animal spiis? The pofolio shae is fom Tay, Shneide, and Chan 999. The dolla value figue is fo he fouh quae of 005 and is fom Table B.00 Balane Shee of Households and Nonpofi Oganizaions whih may be downloaded a hp:// The Fedeal Reseve s daa inludes make value esimaes fo seond homes, vaan homes fo sale, and vaan land owned by he household seo. The debae ove whehe he een boom was a bubble is only he laes example. See MCahy and Peah 004, Himmelbeg, Maye and Sinai 005, and Smih and Smih 006 fo een analyses ha onlude hee is no lage-sale bubble in housing pies. Shille 005, 006 and Bake 006 ague o he onay ha he bubble is boh eal and vey lage.

3 Anohe moe suble puzzle is ha house pie appeiaion in he 990s was negaively oelaed wih ha in he 980s as shown in Figue, while housing uni gowh was posiively seially oelaed ove he same ime peiods see Figue. Basi demand-diven housing models pedi ha pies and quaniies should move symmeially. The mismah of quaniy and pie movemens seems o sugges ha models of housing pies need o moe fimly embed supply as well as demand. Many housing models also pu gea sok in maoeonomi vaiables suh as inees aes and naional inome, bu mos vaiaion in housing pie hanges is loal, no naional. Less han eigh peen of he vaiaion in pie levels and baely moe han one-quae of he vaiaion in pie hanges aoss iies an be aouned fo by naional yea-speifi fixed effes. The lage amoun of loal vaiaion and is elaionship wih maoeonomi vaiables is anohe hallenge fo a onsisen eonomi explanaion of housing make dynamis. In his pape, we pesen a dynami, aional expeaions model of house pie fomaion o see whehe suh a famewok an explain he salien momens of housing pie and quaniy hanges. The model follows he uban adiion of Alonso 96, Rosen 979 and Robak 98 in whih housing pies efle he willingness o pay fo one loaion vesus anohe. In his appoah, housing pies ae deemined endogenously by loal wages and ameniies, so ha loal heeogeneiy is naual. Ou model hen exends he Alonso-Rosen-Robak famewok by fousing on high fequeny pie dynamis and by inopoaing endogenous housing supply. In Seion II of his pape, we pesen he model and fou poposiions egading is impliaions. The model shows ha he pediabiliy of housing pie hanges is

4 ompaible wih a no-abiage aional expeaions equilibium. Slow onsuion esponses and mean eveing wage shoks imply ha pies will mean eve. And, posiive seial oelaion of labo demand shoks a high fequenies an geneae posiive seial oelaion of housing pies. The model an also explain he appaen puzzle of mean eveing pies and pesisen quaniy hanges shown in Figues and. Poposiion 4 shows ha long-em ends o iy poduiviy o loal ameniies will eae pesisene in populaion and housing supply hanges, bu will have a muh smalle impa on pies, sine hose ends ae aniipaed and inopoaed ino iniial pies. Pie hanges ae diven by unexpeed high fequeny shoks, whih mean eve, while quaniy hanges ae diven by aniipaed low fequeny ends ha pesis. The model also seves as he basis fo he alibaions disussed in Seions III and IV of he pape. Seion III pesens ou esimaes of he model s key paamees: he eal ae of inees, he degee o whih onsuion esponds o highe pies, and he vaiane and seial oelaion of loal demand shoks. We assume onsan inees aes fo mos of he pape, bu do un o ime-vaying inees aes in Seion V. We esimae onsuion os paamees using daa on onsuion and pie vaiane. The lieaue on housing demand povides ou esimaes of he heeogeneiy in pefeenes fo paiula loales. And, we use Bueau of Eonomi Analysis BEA inome daa o infe he ime seies popeies of loal inome shoks. In Seion IV, we ompae he momens of he eal daa wih he momens pedied by he model based on he paamee esimaes fom Seion III. We fis invesigae he seial oelaion popeies of pies and quaniies. The paamee values 3

5 desibed in Seion III pedi ha housing pies will mean eve ove five yea peiods a almos exaly he same ae ha we see in he daa. This mean evesion is he esul of new onsuion saisfying demand and he obseved mean evesion of eonomi shoks o loal poduiviy. We fi he modes mean evesion of onsuion quaniies less pefely, bu he paens in he eal daa ae quie ompaible wih easonable paamee values. Ove one yea peiods, we pedi song seial oelaion of new onsuion, bu in he daa seial oelaion of new pemis is even geae han he level ha ou model pedis. The model does no pedi he song seial oelaion of pie hanges a one and hee yea inevals. This seial oelaion ould be due o he aifiial smoohing of he undelying daa o less aional faos. Pesisene iself is no enough o ee a aional expeaions model, bu he mismah beween daa and model a annual fequenies indiaes ha Case and Shille s 989 onlusion egading ineffiieny ould be igh. Fuue wok needs o deal wih he daa smoohing poblem o see whehe he aual seial oelaion sill is fa oo high elaive o he model. Reasonable paamee values pedi vaianes of new onsuion and pie hanges ha ae quie lose o he vaianes seen in he median meopolian aea in ou sample. We do oveesimae he volailiy of pie hanges a annual fequenies, bu ha ould be he esul of daa smoohing. The model does no pedi oo muh vaiaion fo hee and five yea hanges, whee smoohing should be less of an issue. While he model an fi he median make, i anno explain he volailiy of eihe pies o onsuion in he naion s moe exeme makes. The model does no fi he pie volailiy in Califonia whih has huge pie hanges and i does no fi he 4

6 onsuion volailiy in sunbel iies suh as Alana and Houson. The high onsuion volailiy in he sunbel aeas is mos plausibly he esul of lumpiness in he onsuion poess and he possibiliy ha he sunbel aeas have muh lowe onsuion os paamees han we esimae. Howeve, hese explanaions anno help us explain he high pie volailiy aeas, and we y o undesand hem in he penulimae seion of he pape. We onside hee added soues of volailiy: ameniy fluuaion, unmeasued inome volailiy, and volaile inees aes. The one high fequeny ameniy vaiable ha we have ime aes shows lile abiliy o inease pedied demand and pie vaiabiliy. Using daa fom New Yok Ciy, we examine whehe he volailiy of inomes fo een home buyes is highe han he volailiy fo aveage inome, and find ha i is. The vaiane of inome in aeas wih big pie hange aeas is highe han he vaiane of inomes fo he aveage make. These faos may explain he high vaiaion of pies in he mos volaile makes on he eas oas, bu do lile o help us undesand Califonia ouside of he bay egion, whih has less inome volailiy. Volaile inees aes will no inease he volailiy of pies o onsuion in makes wih pies lose o onsuion oss o o he naional median pie in ou model, bu hey an inease he pedied vaiane fo plaes wih pemanenly high ameniies o poduiviy. Fo inees aes o geneae high levels of volailiy, shoks o inees aes mus be exemely high and aeas mus be innaely exemely aaive, bu hese ondiions may be ue fo Califonia ove he las wo deades. 5

7 II. A Dynami Model of Housing Pies Ou dynami model of housing pies is based on hee equilibium ondiions. Following Rosen 979 and Robak 98 we equie onsumes o be indiffeen aoss spae a all poins in ime, whih equies uiliy UW, A, R o be equal aoss spae, whee W efes o wages, A o ameniies, and R o he flow os of housing. Ou simplifying assumpion ha his spaial equilibium mus hold in all peiods is he housing equivalen of assuming no finanial ansaion oss as in Hansen and Jagannahan, 99. Ou seond equilibium ondiion is in he housing makes: we equie he expeed euns fom making a house is expeed pie o be equal o he os of onsuion. If he iy is no gowing, his equilibium ondiion need no hold as in Glaese and Gyouko, 005, bu we make he simplifying assumpion ha he iy is always adding new unis. Ou final equilibium ondiion onens wages whih mus equal he maginal podu of labo o fims in he iy. We implemen he spaial equilibium ondiion by assuming ha hee is a esevaion loale ha delives uiliy of U in eah peiod and ha he os of building a home hee always equals C, whih efles he physial oss of onsuion. Sine housing an be buil in he esevaion loale feely a os C, we assume ha he pie of a house hee always equals C. 3 The esevaion loale epesens he many meopolian aeas in he Ameian hineland wih seady gowh and whee pies say lose o he physial oss of onsuion Glaese, Gyouko and Saks, The annual os of living in he esevaion loale equals he diffeene 3 While i is possible ha pies will deviae aound his value beause of empoay ove- o undebuilding, we simplify and assume ha he pie of a house always equals C. 4 Van Neiuwebugh and Weill 006 pesen a simila model in hei exploaion of long un hanges in he disibuion of inome also sudied by Gyouko, Maye and Sinai, 006. Ou pape was podued 6

8 beween he pie of he house a ime and he disouned value of he house a ime, o C-C/ C/, whee is he assumed fixed ae of inees. 5 We absa fom axes, mainenane oss and allow ime-vaying inees aes only in Seion 5. 6 The spaial equilibium equies all iies a all imes o delive o he maginal esiden he same uiliy ha always is available in he esevaion loale. We fous on he dynamis in a single epesenaive iy whih is diffeen fom he esevaion iy. The uiliy flow fo peson i living in ha iy duing peiod is W i, A i,, o wages plus ameniies. We assume ha hee ae a fixed numbe of fims eah of whih has oupu ha is quadai in labo. This assumpion ensues ha he maginal podu a eah fim is linealy deeasing wih he numbe of wokes and ha wages in he iy ae linealy deeasing wih he numbe of wokes. These labo demand shedules geneaed by fim opimizaion undepin ou assumpion ha wages a he iy level inlude an exogenous omponen and is linealy deeasing in oal iy populaion. We assume ha he ime-speifi and individual-speifi effes ha make up he ne uiliy flow fom he iy ae sepaable so W i, A i, U an be wien as D θ i. The omposie vaiable D efles wages and ameniies, whih in un efle exogenous shoks and iy size. We le N denoe he housing sok in he iy and assume ha he iy s populaion and labo foe equal a onsan imes he amoun independenly of heis, and ou fous on high fequeny vaiaion in pies and quaniies is quie diffeen fom hei fous on hanges in he long un disibuion of housing pies. Moe geneally, he appoah aken hee diffes fom mos eseah ino housing pies, whih employs he use os appoah inodued by Hendesho and Slemod 983 and Poeba 984. Tha banh of he lieaue is oo voluminous o desibe in deail. The fis hee papes efeened in foonoe employ a use os famewok o examine he een housing boom. 5 This diffeene would also be he en ha a landlod eaning zeo pofis would hage a enan. 6 If mainenane oss ae independen of housing values and onsan ove spae, hey will no hange he analysis. If mainenane oss sale wih housing and if hee ae popey axes, hen he os of owning a house would be highe han he afe-ax inees ae. Fo his eason, we will assume a elaively high eal ae in ou simulaions. See below fo moe on ha. 7

9 of housing. 7 We fuhe assume ha D moves linealy wih iy populaion o allow fo he fa ha wages and ameniies may fall due o ongesion o ise beause of agglomeaion eonomies as iy size ineases. We assume ha θ i is a unifomly disibued ase fo living in his paiula loale, so ha he value of θ i fo he maginal esiden a ime denoed θ i * is also linealy deeasing in loale size. The exogenous omponens of iy ameniies and wages inlude a iy-speifi omponen denoed D, a iy-speifi ime end denoed q and a mean zeo sohasi omponen denoed x. Thus, he flow of uiliy fo he iy s maginal esiden a ime wih index i* elaive o he esevaion loale, D θ i *, an be wien D q x αn, whee α apues he assumpion ha wages, ameniies and he ase of he maginal esiden fo living in he loale an fall linealy wih iy size. We fuhe assume ha x follows an auo egessive moving aveage ARMA, poess so ha x x ε θε, whee 0 < <, and he ε shoks ae independenly and idenially disibued wih mean zeo. The expeed os of housing in he epesenaive loale equals H minus E H /, whee E. denoes he ime expeaion opeao. The diffeene beween he os of housing in he epesenaive iy and housing oss in he esevaion loale, C/, should be undesood as he os of eeiving he exa uiliy flow assoiaed wih loaing in he iy. If exa housing oss in he iy equals exa uiliy deliveed by he iy hen: E H C H D q x αn. 7 Glaese, Gyouko and Saks 006 povide evidene showing ha populaion is essenially popoional o he size of he housing sok. 8

10 Equaion epesens a dynami vesion of he Rosen-Robak spaial indiffeene equaion whee diffeenes in housing oss equal diffeenes in wages plus diffeenes in ameniies. We assume a ansvesaliy ondiion on housing pies suh ha H lim 0. 8 If housing supply was fixed, so NN as migh be he ase in a delining iy as analyzed in Glaese and Gyouko, 005 hen: D αn q q x θε H C. Housing pies ae a funion of exogenous populaion and exogenous shoks o wages and ameniies, and he deivaive of housing pies wih espe o a one dolla pemanen inease in wages will be /. Noe ha house pie hanges ae pediable in his famewok as long as hee ae pediable omponens o hanges in uban wages and ameniies. The ARMA, suue of he shoks makes i possible o have he posiive oelaion of hanges a high fequenies and he negaive oelaion a low fequenies ha we see in he daa. The iy an gow wih new onsuion so ha N equals N I, whee I is he amoun of onsuion in ime. 9 The physial, adminisaive and land oss of poduing a house ae C I N, whee > beause uen 0 housing poduion should have a bigge impa on uen onsuion oss han housing poduion many yeas ago. 0 Invesmen deisions fo ime ae made based on ime - infomaion, and hee is fee eny of isk neual buildes. Thus, if hee is any 8 This assumpion limis he possible ole of housing bubbles. While ou fous hee is on a puely aional model, we expe ha fuue wok will onside dopping his assumpion. 9 Fo simpliiy, we do no allow depeiaion whih may be easonable fo shoe em housing dynamis, bu would no be appopiae fo a vey long em analysis of iy populaion hanges. 0 We deviae fom he invesmen os assumpions of Topel and Rosen 988 by assuming ha oss ae ineasing wih he oal level of developmen and no wih hanges in he level of invesmen. 9

11 building, onsuion oss will equal he ime expeed housing pie as desibed in equaion 3: 3 E H C I N. 0 As menioned above, we assume ha demand fo he iy is suffiienly obus so ha hee is always a posiive quaniy of new onsuion and his equaion always holds. Equaions and 3 hen ogehe desibe housing supply and demand. These equaions give us he seady sae values of housing pies, invesmen and housing sok: q C D α C q 0 D q C q Hˆ 0 0 α α α α, Iˆ Iˆ q 0 α and 0 q α 0 D q D Nˆ 0 Iˆ. α If x0 fo all, and N ˆ N fo some iniial peiod, hen hese quaniies would fully desibe his epesenaive iy. Seula ends in housing pies an ome fom end in housing demand as long as > 0, o he end in onsuion oss as long as α > 0. If 0 so ha onsuion oss don inease wih oal iy size, hen ends in wages o ameniies will impa iy size bu no housing pies. If α 0 and iy size doesn deease wages o ameniies, hen ends in onsuion oss will impa iy size bu no pies. The model an be exended o allow fo he possibiliy ha, in some saes of he wold, new onsuion will be zeo. This adds muh ompliaion and only a modes amoun of insigh ino ou quesions. In his ase, he assumpion ha hee is always some onsuion equies ha q > 0. 0

12 Poposiion desibes housing pies and invesmen when hee ae shoks o demand and when ˆ N N. All poofs ae in he appendix. Poposiion : A ime, housing pies equal ˆ ˆ N N x H H α ε θ and invesmen equals ˆ ˆ N N x I I θε, whee and ae he wo oos of 0 y y α and 0 >. This poposiion desibes he movemen of housing pies and onsuion aound hei seady sae levels. A empoay shok,ε, will inease housing pies by θ and inease onsuion by θ. Highe values of i.e., moe pemanen shoks will make boh of hese effes songe. Highe values of mue he onsuion esponse o shoks and inease he pie esponse o a empoay shok by eduing he quaniy esponse. These ompaaive sais povide he inuiion ha plaes whih ae quaniy onsained should have less onsuion volailiy and moe pie volailiy. The nex poposiion povides impliaions abou expeed housing pie hanges. Poposiion : A ime, he expeed home pie hange beween ime and is ˆ ˆ ˆ N N H H α x E x, he expeed hange in he iy housing sok beween ime and is

13 ˆ I E x and expeed ime onsuion is I E ˆ x N N ˆ, N N ˆ. Poposiion delives he impliaion ha a aional expeaions model of housing pies is fully ompaible wih pediabiliy in housing pies. If uiliy flows in a iy ae high oday and expeed o be low in he fuue, hen housing pies will also be expeed o deline ove ime. Any pediabiliy of wages and onsuion means ha pediabiliy in housing pie hanges will esul in a aional expeaions model. The pediabiliy of onsuion and pies omes in pa fom he onvegene o seady sae values. If x ε 0 and iniial populaion is above is seady sae levels, hen pies and invesmen ae expeed onvege on hei seady sae levels fom above. If iniial populaion is below is seady sae level and x ε 0, hen pie and populaion is expeed o onvege on hei seady sae levels fom below. The ae of onvegene is deemined by and he aios and. Highe levels of hese α α aios will ause he ae of onvegene o slow by eduing he exen ha new onsuion will espond o hanges in demand. The impa of a shok, x, is exploed in he nex poposiion. Poposiion 3: If N Nˆ, x ε 0, θ > 0, 0, and ε > 0, hen invesmen and housing pies will iniially be highe han seady sae levels, bu hee * * exiss a value suh ha fo all >, ime expeed values of ime onsuion and housing pies will lie below seady sae levels. The siuaion is symmei whenε < 0.

14 Poposiion 3 highlighs ha his model no only delives mean evesion, bu oveshooing. Figue 3 shows he esponse of populaion, onsuion and pies elaive o hei seady sae levels in esponse o a one ime shok. Consuion and pies immediaely shoo up, bu boh sa o deline fom ha poin. A fis, populaion ises slowly ove ime, bu as he shok weas off, he heighened onsuion means ha he iy is oo lage elaive o is seady sae level. Evenually, boh onsuion and pies end up below hei seady sae levels beause hee is oo muh housing in he iy elaive o is wages and ameniies. Plaes wih posiive shoks will expeiene mean evesion, wih a quik boom in pies and onsuion, followed by a bus. Finally, we un o he puzzling empiial fa ha, aoss he 980s and 990s, hee was song mean evesion of pies and song posiive seial oelaion in populaion levels. We addess his by looking a he one peiod ovaiane of pie and populaion hanges. We fous on one-peiod fo simpliiy, bu hink of his poposiion as elaing o longe ime peiods. Sine mean evesion dominaes ove long ime peiods, we assumeθ 0 o avoid he effes of seial oelaion: Poposiion 4: If N 0 Nˆ 0, θ 0, x 0 ε 0, iies diffe only in hei demand ends q and hei shok ems ε 0, ε and ε, and he demand ends ae unoelaed wih he demand shoks, hen he oeffiien esimaed when egessing seond peiod populaion gowh on fis peiod populaion gowh will be posiive if and Va q only if α > while he oeffiien esimaed when Va ε egessing seond peiod pie gowh on fis peiod pie gowh will be negaive if and α Va q only if Ω >, whee Va ε α α Ω. 3

15 Poposiion 4 ells us ha posiive oelaion of quaniies and negaive oelaion of pies ae quie ompaible in he model. The posiive oelaion of quaniies is diven by he heeogeneous ends in demand aoss uban aeas. As long as he vaiane of hese ends is high enough elaive o he vaiane of empoay shoks, hen hee will be posiive seial oelaion in quaniies as in Figue. The mean evesion of pies is diven by he shoks, and as long as is suffiienly low, pies will mean eve. As disussed above, when is low, ends will have lile impa on seady sae pie gowh. The posiive ends show up mainly in he level of pies. Howeve, egadless of he value of, unexpeed shoks impa pies and, if hese shoks mean eve, hen so will pies. This suggess wo equiemens fo he obseved posiive oelaion of quaniies and negaive oelaion of pies: iy-speifi ends mus diffe signifianly and he impa of iy size on onsuion oss mus be small. The exensive heeogeneiy in iy-speifi ends is muh ommened on, wih he een papes by Gyouko, Maye, and Sinai 006 and Van Nieuwebugh and Weill 006 aemping o explain he phenomenon. The lieaue on housing invesmen suggess ha he impa of iy size on onsuion oss is small Topel and Rosen, 988; Gyouko and Saiz, 006. Thus, we shouldn be supised o see posiive seial oelaion in quaniy hanges and negaive seial oelaion in pie hanges. III. Key Paamee Values fo he Calibaion Exeises We now use he model as a alibaion ool o see wha momens of he daa, inluding is seial oelaion popeies and vaianes, an and anno be explained by 4

16 ou famewok. We fous on he movemens in pies and onsuion inensiy aound seady sae levels. The appendix onains he fomulae fo he pedied values of hese momens. 3 The model s pediions abou vaianes and seial oelaions depend on seven paamees: he eal inees ae, he degee o whih demand delines wih iy populaion α, he degee o whih onsuion esponds o highe oss and, he ime seies paen of loal eonomi shoks and θ, and he vaiaion of hose shoks σ ε. Table epos he value of hese paamees whih ae used in he alibaion exeise, wih he emainde of his seion disussing how we esimae o impue hem. The Real Inees Rae The fis ow of Table shows ha we use a eal inees ae of 4 peen in all alibaions. This value is highe han sandad esimaes of he eal ae beause i is also mean o efle ohe faes of he os of owning, suh as axes o mainenane expenses, ha migh sale wih housing. Expeimenaion shows ha he simulaion esuls ae obus o a wide ange of alenaive values of e.g., fom.5-5 peen. Supply Side Paamees: and The housing os paamees ae boh paiulaly impoan fo ou model and elaively undesudied by he lieaue. The paamee efles he exen ha onsuion oss, inluding land assembly, pemiing and physial onsuion oss, 3 We do no use he high fequeny oelaions of pies wih ohe vaiables o pin down paamee values. Changes in house pies and hanges in inome aompany eah ohe a longe hoizons e.g., ove he pas weny yeas, he oelaion of he wo hanges is ove 50 peen, bu he oelaion is muh weake a highe fequenies. Highe fequeny oelaions ae diffiul o inepe beause he eal wold infomaion suue may no mah ha pesumed in ou model. Fo example, if inome shoks ae known a peiod ealie, his will no mae muh fo pedied vaianes and seial oelaions, bu i will damaially ale he pedied elaionship beween inome and pie hanges. 5

17 ise wih he level of uen onsuion aiviy. The paamee measues he sensiiviy of oss o he level of oveall developmen, o make size. Topel and Rosen 988 use naional daa and esimae a supply elasiiy anging fom.4 and.. This supply elasiiy is he elaionship beween he logaihm of invesmen and he logaihm of pie, whih in ou model would equal H / I. Using he mean values of invesmen and housing pies aoss ou iies and an elasiiy of.8, his geneaes a ange of fom o 5. The median value is 8 whih seems oo high o us. The ange beween 5 h and 75 h peeniles of he disibuion is 5 o 8, whih povides us wih one ange of paamee esimaes. Alenaively, we an esimae fom he vaiane of pies and quaniies wihin he daa. While his violaes he ypial alibaion ule of using paamee esimaes fom ouside he daa o be explained, we hink ha his exeise is useful in geneaing a ange of possible onsuion os values. We esimae hem fo eah of ou 5 meopolian aeas and use his boad ange in ou simulaions. 4 Ou hope is ha by showing esuls fo a wide ange of esimaes, we an diffuse woies ha naually aise fom he fa ha ou esimaes wee made using he daa ha we ae ying o explain. We sa wih he basi supply-side equaion E H C I N and le H E H µ, whee µ is he 0 pediion eo. We fuhe assume ha he vaiane of µ equals 4 Physial onsuion oss vay he leas aoss U.S. makes, bu Gyouko and Saiz 006 epo a 0 peen gap aoss he inequaile ange of mao meopolian aeas. The diffeenes ae diven lagely by he degee of union peneaion in he loal onsuion ades and sele ohe loal faos. The naue of loal land use egulaion vaies muh moe damaially by make, wih lile binding onsain on new developmen in makes suh as Alana and Las Vegas, while he Boson and Bay Aea makes have vey singen and expensive egulaion ha makes i vey had o build even hough make pies of homes ae well above physial onsuion oss in hose plaes. [See Glaese and Gyouko 003, Glaese, Gyouko, and Saks 006, and Saks 006 fo sudies on he impas of diffeing land use egulaion.] 6

18 κ Va H C Iˆ N0 ˆ, whee he paamee κ is one minus he R 0 I fom he bes possible pediion of nex peiod s housing pie. To deemine his unexplained shae of he deviaion fom aual house pies, we begin by egessing house pies on yea and meopolian aea dummies. The R fom ha fixed effes speifiaion is When we add wo lags of house pies and housing pemis o he speifiaion, he R ineases o Thus, κ 0% o 0. ~ 0.07/0.7 based on hese values. We hen le ω and using he equaion Va H C Iˆ 0 N0 Iˆ Va µ 4, Va I Iˆ ω N N0 Iˆ i follows ha, 5 Va H C Iˆ N0 Iˆ κ. Va 0 I Iˆ ω N N0 Iˆ The numeao of his aio is he vaiane of he house pie pediion eo, weighed by he shae of unexplained vaiaion. The denominao onains wo omponens. The fis efles he vaiaion assoiaed wih yealy new onsuion deviaing fom is aveage level. The seond em in he denominao, whih is weighed by ω, apues he vaiaion assoiaed wih he make s housing sok being off is end amoun. To empiially use equaion 5, we mus impue he housing sok he N- em beause he ensus povides aual ouns of he sok only one eah deade. Fo eah meopolian aea, we know he housing sok a he beginning and end of eah deade and he pemis issued eah yea in beween. Ou esimae of he housing sok a Pemis i 0 i ime, is N N 0 N, whee N and N0 ae he 9 Pemis i 0 i 7

19 housing soks measued duing he wo loses ensuses. The hange in housing sok is poioned aoss yeas based on he obseved pemiing aiviy. To measue how many unis he make should have had eah yea he N 0 Iˆ em, we use he aual oun of he housing sok fom he deennial ensus in ou iniial yea of 980 and assume ha I-ha is he aveage hange in he aual housing sok beween 980 and 000 again using ensus daa o measue he sok. Sine oss do no appea o vay muh based on iy developmen, we onlude ha >, bu beyond ha, he lieaue yields lile o help us pin down he elaionship beween and. We onside a ange of values fo ω, inluding 0, 0.5, and The boom wo panels of Table epo he disibuion of esimaed values of and fo he hee diffeen values of omega. If ω0.5, hee is a wide ange of values fo fom.5 fo he 0 h peenile meopolian aea o 8. fo he 90 h peenile aea. The mean value of is 3.6 whih is wie he median make s value of 6.4, 5 An alenaive mehod of esimaing hese paamees suggess a value of 0.5 fo ω. Tha appoah o esimaing he onsuion os paamees follows Rosen and Topel 988 in inveing he onsuion os equaion o obain I / E - [H C / N -. In empiially implemening his equaion, we used oal housing pemis in peiod o poxy fo new onsuion in peiod, and aual house pies o measue expeed values. Obviously, he use of aual pies in lieu of expeed pies inodues some bias, bu i should be small sine he annual ime peiod ove whih pie is measued is elaively sho. We also impued he housing sok N eah yea as desibed above. A simple egession of eah make s esuling value on is value wih no ineep, as suggesed by ou assumed funional fom yielded a oeffiien of 0.5. The esimaed oeffiien is 0. if we allow fo an ineep. The simple oelaion beween and values esimaed his way is quie high a 0.9. Finally, i is noewohy ha he absolue level of hese values is highe han hose epoed in Table based on he appoah desibed in equaions 4 and 5. This was o be expeed given ha his alenaive saegy effeively assumes ha pie only efles demand, no supply, shoks. To he exen ha pies inopoae poduiviy-enhaning hanges, he elaionship beween new onsuion and values is magnified. Moe poblemai fo his alenaive appoah is he issue of he poenial endogeneiy of housing pies wih espe o new onsuion. We also esimaed a singe naionwide egession using he ineaion of iniial indusial haaeisis and naional eonomi suess of he indusies as insumens as in Baik, 989. When a linea speifiaion is esimaed, he oeffiiens ae quie impeise. When we follow Rosen and Topel 988 and use a log-log speifiaion, we peisely esimae an elasiiy of, whih implies a ange of esimaes of and simila o hose pesened in Table. 8

20 whih efles he skewness of he disibuion of oss. A handful of lage and expanding makes suh as Alana, Chaloe, Houson, and Dallas have values below one. 6 The op en peen of makes in ems of values ae all in Hawaii, along he oas of Califonia, o in he sububs of New Yok Ciy. These high values of appea o efle boh high labo oss and egulaions ha onsain onsuion. 7 The inequaile ange of uns fom 0.7 o 3.3. The median value is.6 Ineases in Populaion and he Maginal Valuaion of an Aea: α The value of α efles he impa ha an inease in he housing sok will have on he willingness o pay o live in a loale. If populaion was fixed, equaion ells us ha he deivaive of housing pies wih espe o he housing sok equals - α /, whih an be seen as he slope of he housing demand uve. Typially, housing demand elaionships ae esimaed as elasiiies. Consequenly, we mus ansfom esimaed demand elasiiies ino a levels esimae by muliplying by /. While many housing demand elasiiy esimaes ae aound one o slighly below-in absolue value, hee is a wide ange in he lieaue, so we expeimen wih a ange fom 0 o. We begin he ansfomaion fom an elasiiy o a level by muliplying by he aio of pie o populaion, whih podues a ange of esimaes fo α / of fom 0 o 3. Muliplying his span by / yields a ange fom 0 o 0.5. We will use a paamee esimae of 0. in ou simulaions whih implies ha fo evey 0,000 exa homes sold, he maginal puhase likes living in he aea $,000 less pe 6 The Alana aea has he lowes value a The values fo he meopolian aeas of Honolulu, Salinas, Sana Cuz, and Napa eah ae above 70. While we anno ell fo sue, hese magniudes pobably ae assoiaed wih egulaoy oss, as hey seem oo high o solely efle labo. 9

21 yea see ow 5 of Table. This esimae seems high o us, bu lowe esimaed values of α do no signifianly hange he simulaions. Time Seies Popeies and Vaiane of Shoks:, θ, and σ ε The model does no sepaaely addess wages and ameniies. Thee is lile evidene on high fequeny hanges in ameniies, exep fo ime aes whih we will disuss in Seion V. Consequenly, we assume hee ha he high fequeny movemen in demand is diven by hanges in labo demand, no hanges in he valuaion of ameniies. Moe speifially, obseved wages W ae pesumed o equal w γ N 0 w x γ N 0, whee w0 γn0 is a omponen of D, w is 0 N a omponen of q and γ is a omponen of α. Conolling fo a iy-speifi fixed effe and end will eliminae he em γ N 0 w, and he esidual omponen of wages w0 equals x γ N N0. 8 The mos diffiul pa of esimaing he x poess is ou aemp o onol he impa of populaion hanges, bu while ou poedue is debaable, i has lile impa on he esimaed popeies of x. The paamee γ epesens he impa ha an inease in iy size will have on wages, whih is popoional o he impa of labo supply on wage o he slope of he labo demand funion. Cusomaily, labo demand is esimaed as an elasiiy, Labo Foe Wage, and mos esimaes of his elasiiy ae Wage Labo Foe saisially indisinguishable fom zeo e.g., Cad and Buhe, 99. Boas 003 finds a highe esimae of -0.3, alhough his is a he naional level. We use his uppe- 8 The disinguished lieaue on egional shoks e.g. Blanhad and Kaz, 99 does no yield he paamee esimaes ha we need o alibae he model. 0

22 bound esimae, bu noe ha i has lile diffeenial effe on ou esuls ompaed o assuming an elasiiy of zeo. Jus as wih housing demand, we mus onve his elasiiy ino an esimae of γ. We use BEA daa on pesonal inome pe apia as ou measue of wages, and fo ou sample of meopolian aeas, he mean of his vaiable in 990 he middle of ou sample peiod was $6,965 in $,000. Mean employmen in 990 aoss hese meopolian aeas was 539,5, so ou aio of wage o he labo foe is abou 0.05 ~6,965/539,5. Based on hese numbes, an elasiiy of -0.3 suggess ha eah woke is assoiaed wih.5 ens less annual inome in he iy. In ou sample, hee ae on aveage.6 wokes pe home, so eah exa home is assoiaed wih.9 ens pe yea less annual inome, whih seves as ou esimae ofγ. The pe apia inome seies is onveed ino household inome by muliplying by.63 he aveage aio of people pe household in ou sample in 990. We adus his inome vaiable fo N using ou esimae of 0.09 fo γ and by using i N 9 Pemis 0 i Pemis i 0 i N N as above as ou esimae of oal housing sok beween ensus yeas. Wih his oeed inome seies, we an esimae he ime seies popeies of inome shoks a he loal level, by fiing an ARMA, o he wage seies ha is fis demeaned wih iy and yea fixed effes and hen oeed fo iy size hanges as

23 disussed above. As shown in Table, his esimaion poedue yields esimaes of 0.87, θ0.7, and σ ε $3,603, IV. Calibaing he Model and Mahing he Daa In his seion, we alibae he model using he paamees values disussed above. We hen ompae his alibaion o he momens of he eal daa. We fis disuss he ime seies oeffiiens of pies and onsuion, and hen disuss he volailiy of hese seies. Ou eal daa sample is a se of 5 meopolian aeas fo whih we have oninuously defined pie daa fom As disussed above, ou simulaions assume ha he eal inees ae equals 0.04, he vaiane of he loal eonomi shok σ ε equals $3,603,463, he paamees of he ARMA poess desibing ha shok ae 0.87 and 0.7 θ, and he valuaion of he meopolian aea by he maginal enan α is 0.. We le and equal he fifeen diffeen paiwise ombinaions assoiaed wih he hee diffeen values of omega and epo simulaion esuls fo he full se of hose values. Sho-Tem Momenum and Longe-Tem Mean Revesion in Pies, Rens and Pemis The op ow of Table povides evidene on momenum and mean evesion in OFHEO house pies wihin make ove ime. We use absolue pie hanges ahe han hanges in he logaihm of pies in ode o be ompaible wih he model, bu ou empiial esuls ae no sensiive o suh hanges in funional fom. Sine he OFHEO index only povides pie ineases elaive o a base yea, we onve his ino an implied 9 Lagely beause γ is so small houghou is elevan ange, his adusmen o wages does no have a maeial impa on ou esuls. If we use a value of 0 foγ, we esimae a value of 0.86, an esimae of θ 0.8, and an esimae of σ ε $3,408,50 In addiion, we aemped oin maximum likelihood esimaion of, θ, and σ ε fo given end effes and meopolian aea fixed effes, bu he pogam would no onvege beause he panel was oo sho elaive o he numbe of makes.

24 pie seies by using he median housing value in he meopolian aea in 980 as a base pie in he meopolian aea and hen saling ha value by he appeiaion in he OFHEO index eah yea. 0 The esuls ae esimaes fom a egession of he uen hange in pies on he lag hange in pies 6 P ie P ie γ β P ie P ie α, MSA Yea fo equal o one, hee and five yeas. Beause fixed effes esimaes suh as hese whih emove make-speifi aveages an be biased wih spuious mean evesion podued espeially when he numbe of ime peiods is elaively low, in he fis ow of Table, we epo Aellano-Bond esimaes whih use lagged values of he dependen vaiable pie hanges as insumens. Ou one yea esimae of pie hange seial oelaion is 0.7, so a $ inease in housing pies beween ime and is assoiaed wih a 7 en inease beween ime and. Ou esimae is lage han ha epoed by he pioneeing wok of Case and Shille 989. I is now well undesood ha smoohing of he undelying daa seies an bias one owads finding sho-un momenum. Case and Shille 989 wee able o addess his poblem by spliing hei sample, whih onsised of exensive mio daa on sales ansaions in fou makes Alana, Chiago, Dallas, and San Faniso. They epo oeffiiens anging fom , alhough hey use he logaihm, no he 0 This poedue essenially povides he eal pie fo a onsan qualiy house wih he qualiy being ha assoiaed wih he median house in 980. We have expeimened wih using values fom he 990 and 000 ensuses as he base. All he esuls epoed below ae obus o suh hanges. See Aellano and Bond 99 fo moe deail on his esimaion poedue. Moe speifially, we use he xabond Saa ommand wih yea and aea fixed effes. 3

25 level, of pies so he esuls ae no exaly ompaable. Beause we anno pefom any ompaable poedue wih he OFHEO daa, ou esimae is suely biased upwads. Ove hee yeas, hee is sill momenum. The esimae of 0.7 means ha a $ inease in housing pies beween ime and 3 is assoiaed wih a 7 en inease beween ime 3 and 6. Ove five yea peiods, we esimae a mean evesion oeffiien of -0.3, so a $ inease beween imes and 5 is assoiaed wih a 3 en deline beween ime 5 and 0. 3 These esimaes ae no an aifa of he Aellano- Bond poedue. The analogous odinay leas squaes esimaes ove, 3, and 5 yea hoizons ae 0.74, 0.8 and -0.39, espeively. 4 The mean evesion in pies ha we esimae ove five-yea hoizons is quie simila in magniude o ha obseved fo finanial asses by Fama and Fenh 988. Unfounaely, he sho ime peiod fo whih we have onsan qualiy daa a less han deadal fequenies makes i diffiul o know whehe his mean evesion is a pemanen feaue of uban life o whehe i epesens he impa of shoks ha ae speifi o he pos-980 ime peiod. Cule, Poeba and Summes 99 also find his The OFHEO index inludes daa on epea sales o efinanings of he same house. The lae ypially ely on an appaisal, no a make sale pie. Undoubedly, his esuls in smoohing of he seies and biases upwad ou esimae of sho-un momenum. Even he Case and Shille 989 esimaes, whih ely only on aual sales, ould be upwad biased. Woking wih a spli sample, bias an esul if, andomly, some faion of homes on whih a buye and selle agee on a pie have delayed losings ha move hei epoed sales daes ino he nex epoed peiod quae, yea, e.. Whaeve shok hee was in peiod ha influened he ageed upon pie, some of is measued impa will spill ove ino peiod. Obviously his is poenially moe of a poblem he shoe he measuemen peiod. 3 As noed in he Inoduion, deadal hanges also find signifian mean evesion aoss he 980s and 990s. 4 We also addessed onens abou spuious mean evesion by esimaing speifiaions wihou meopolian aea fixed effes. If we esimae he following equaion, P ie 5 P ie α γ Yea β P ie P ie5, he mean evesion oeffiien dops o -0. and beomes only maginally signifian. Howeve, as soon as we inlude peen of aduls wih ollege degees as a onol, he oeffiien beomes -0.8 wih a -saisi of hee. If we esimae he same hange egession using he logaihm of pies insead of he levels, he oeffiien is wih he ollege gaduae onol and has a -saisi of fou. 4

26 paen of sho un momenum and longe- un mean evesion fo housing and a numbe of ohe asse makes. Table 3 epos he ompaable esuls fo ou simulaions using he diffeen and values disussed above. All ohe paamee values ae fixed a he values lised in Table. The fis hee olumns show esuls fo annual seial oelaion in pies, he nex hee olumns pesen he analogous findings ove hee yea peiods, wih he final hee olumns being fo five yea peiods. Wihin eah ime hoizon, he fifeen ells oespond o he fifeen, pais epoed in Table. The fis hee olumns doumen he model s failue o mah he posiive seial oelaion obseved in he annual daa. In fa, ou paamee esimaes sugges a mild amoun of mean evesion even a suh a high fequeny. Similaly, he esuls fo hee yea hoizons epoed in he middle olumns of Table 3 find a mismah wih he daa. Assuming he middle ase fo omega ω0.5, olumn 4, we pedi mean evesion oeffiiens fom -0.8 o -0.8, no he posiive pesisene we see in he daa. Ou model does a muh bee ob of fiing he -0.3 mean evesion seen a five yea inevals olumns 6-9. A five yea hoizons, if and ae a hei medians fo he ase of ω0.5, we ome wihin en peen of mahing he daa see ow 3, olumn 8. And, if.7 and 0.7, he pediion lieally is -0.3 ow, olumn 8. Thus, he pediable mean evesion of pies a five yea inevals anno be seen as a hallenge fo a aional expeaions model of housing pie movemens. In he model, his mean evesion efles boh he endeny of shoks o mean eve and of new onsuion o ause fuue delines in pies. To deompose he impa of he wo foes, we also looked a he ases whee hee is no new onsuion 5

27 impa i.e., α0 and whee hee is no mean evesion in he x paamee. When mean evesion in wages is uned off i.e.,, ou simulaions pedi vey low levels of oveall mean evesion in house pies. Howeve, we pedi highe levels of mean evesion lose o hose found in he daa when hee is no effe allowed fom onsuion ineasing make size. Thus, ou analysis suggess ha he maoiy of mean evesion is oming fom he mean evesion of loal demand shoks. One way o hek whehe sho un momenum efles he dynamis of euphoia in an asse make is o see if he same phenomenon appeas in ens. In he seond ow of Table, we epo he esuls fom enal egessions of he fom: 7 Re n Re n γ β Re n Re n α. MSA Yea Renal daa on apamens is olleed by an indusy onsulan and daa povide, REIS In. Thei daa oves only a limied numbe of meopolian aeas 46 in ou sample, and in geneal, enal unis ae no ompaable o owne-oupied housing. 5 Ove one- and hee-yea hoizons, hee is song evidene of pesisene, wih he Aellano-Bond esimaes being 0.7 in boh ases. Ove five yea ime hoizons, we esimae a mean evesion paamee of The pesene of momenum and mean evesion in ens suggess ha hese feaues do no efle somehing unique o housing asse makes, bu ahe somehing abou he hanging demand fo iies. 6 Table 4 hen epos he pedied values of seial oelaion fom he simulaions of he model. A annual fequenies, we end o pedi vey modes pesisene, wih he 5 Renal unis ae ovewhelmingly in muli-uni buildings, while owne-oupied housing is ovewhelmingly single-family deahed housing. These diffeenes in housing ypes and he poblem of auaely measuing mainenane oss ae wo easons why i is exemely diffiul o ell whehe housing pies ae high o low elaive o ens. 6 The odinay leas squaes esimaes of hese oeffiiens ae 0.8, 0.08 and -0.5 fo one, hee and five yea hoizons, espeively. 6

28 esuls anging fom o 0.08 when ω0.5 olumn. These esimaes ae well below he 0.7 seen in he daa ove one yea hoizons. Ove hee yea hoizons, we onsisenly pedi mean evesion, while hee is sill a posiive oelaion of ens in he daa. Fo five yea inevals, we pedi ha en hanges should have a mean evesion oeffiien of abou if we use he median value of 6.4 and.6, espeively, fo and when ω0.5 ow 3, olumn 8. Slighly highe mean evesion is pedied if is lowe, bu ou esimaes sill ae only abou one-half of he obseved mean evesion in ha ase. We ae again unable o explain he song posiive seial oelaions a shoe ime hoizons. Sine hee ae many easons o be suspiious abou he popeies of he enal daa, espeially beause of aifiial smoohing, we do no aah muh impoane o he quaniaive mismah wih he daa hee. 7 Howeve, he sho un momenum and long un mean evesion of ens, whih ae pedied by he model, sugges ha hese feaues ould efle somehing ohe han iaionaliy in an asse make. To examine he dynamis of housing quaniy, we look a housing pemi daa fom he Census of Consuion. The final se of esuls epoed in Table use housing pemis esimaed in he following egession: Pemis α γ βpemis, MSA Yea whee Pemis efes o he numbe of pemis issued beween ime - and ime. The one-hee and five yea Aellano-Bond oeffiien esimaes ae 0.84, 0.43, and -0.07, 7 Fo example, smoohing is a geae poblem in he enal daa. The indusy onsulan ha povides he en daa does no suvey aual enes, bu he landlod ownes of apamen buildings. Undoubedly, aveages ae being epoed. 7

29 espeively. Thus, onsuion also displays high fequeny momenum, bu lile o no pesisene o mean evesion a longe hoizons. 8 The alibaion esuls fo his vaiable ae povided in Table 5. Fo he ase whee and ae he median values when ω0.5, he pedied oeffiiens ae 0.60, 0.9 and 0.06, fo one, hee, and five yea hoizons, espeively. These ae easonably lose o he aual paamees, and mino hanges in he values of one o boh of he supply side paamees enable us o fi he daa moe exaly. While he pediions abou he seial oelaion of onsuion ae no as auae as he pediions abou he mean evesion in pies, he momens of he eal daa anno be said o ee he model. Thus, he model does a easonable ob a fiing he ime seies popeies of new building and an exellen ob a fiing he long em mean evesion of ens. I does a poo ob of fiing he high fequeny posiive seial oelaion of pie hanges. This failue may be he esul of daa smoohing ausing us o empiially oveesimae momenum, o as Case and Shille 989 sugges, some so of iaionaliy in he housing make. House Pie Change and Consuion Vaianes Aoss Makes Table 6 epos he vaiane of pie hanges and of new onsuion in ou sample. 9 The volailiy of boh pies and onsuion vaies enomously aoss iies and is quie skewed, wih he mean vaiane muh highe han he median vaiane. Consequenly, ou appoah o doumening boh housing pie hange and onsuion vaiane is o fis un a pooled make egession sepaaely fo eah vaiable, of ouse 8 As is he ase wih he ohe daa, his paen is no an aifa of ou esimaion poedue. The analogous odinay leas squaes oeffiiens ae 0.8, 0.37, and 0.07, espeively. 9 Sine he en daa ae smoohed, we don pu muh weigh on he vaiane of ens and exlude hem fom his pa of he analysis. 8

30 onolling fo yea effes, and hen o ompue he vaiane of he esiduals fom his egession by meopolian aea. This vaiane gives us he volailiy of pies and onsuion, espeively, wihin a meopolian aea onolling fo naionwide effes. The op panel of Table 6 shows ha ha he vaiane of one yea pie hanges equals $4 million in he enh peenile meopolian aea and $09 million in he 90 h peenile make. The median make has a one yea pie hange vaiane of $34 million, whih is muh smalle ha he sample mean of $83 million. This skewness is diven pimaily by Califonia makes and Honolulu. The vaiane of one-yea pie hanges in Honolulu is $763 million, whih is he lages in ou sample. Five ohe makes San Jose, San Faniso, Sana Babaa, Sana Ana and Salinas--had vaianes ha wee en imes geae han he sample median. The seond and hid olumns of his able epo he disibuion of vaianes of hee and five yea pie hanges. The disibuion of longe hoizon pie hanges is again quie skewed, wih he mean pie hange subsanially exeeding he hange fo he median aea. The volailiy of pie hanges is vey high a longe hoizons. The vaiane in five-yea pie hanges is $65 million fo he median make, wih one quae of he meopolian aeas having vaianes of a leas $. billion. Table 7 epos pedied pie hange vaianes fom ou simulaions wih he esuls aayed in he same manne as in he seial oelaion ables above. A annual fequenies olumns -3, we pedi a ange of pie hange vaianes fom a low of $50 million o a high of $8 million. No supisingly, pie hange volailiy is lowe he smalle ae and makes in whih quaniy hanges a lo wih hanges in oss. Howeve, ou vaiane pediion fo he lowes, ombinaion sill is well above 9

31 he $34 million vaiane found in he median make. Daa smoohing would bias pie volailiy downwad ove sho ime peiods, and if so, we would expe his poblem o be less sevee fo longe ime peiods. Ou abiliy o mah he volailiy of pie hanges does inease wih he hoizon ove whih hose hanges ae measued. Fo example, he ange of pedied vaianes of 3-yea pie hanges aoss all 5, ombinaion uns fom $3-$488 million olumns 3-6, Table 7. This spans he inequaile ange of $4-$445 million found in he daa olumn, op panel of Table 6, bu we sill need o have a elaively low value fo.7 and a 0 o losely mah he median. This is no he ase fo he 5-yea pie hange vaiane pediions lised in he final hee olumns of Table 7. Ou ange of pediions uns fom $63-$78 million, allowing us o apue muh of he lowe half of he disibuion of aual pie hange vaiaion epoed in he hid olumn of Table 6 op panel. The median, pai of 6.4 and.6 when ω0.5 is assoiaed wih a pedied vaiane of $469 million, whih sill undepedis he sample median $65 million, bu highe values allow us o ome muh lose. Howeve, we ae sill unable o appoah mahing he vey high pie hange volailiy found in he op quae of makes, and he op en peen, espeially. Tha is an issue o whih we will un in he nex seion. In sum, he geneal paen of esuls in Table 7 shows an oveesimae of pie volailiy a high fequenies whih hen disappeas a lowe fequenies. This end is onsisen wih daa smoohing, bu i ould also efle a flaw in ou model. The boom panel of Table 6 epos he vaiane in unis pemied aoss ou 5 meopolian aea sample. As wih pie hanges, hee is subsanial heeogeneiy 30