Capitalization of Federal Taxes, the Relative Price of Housing, and Urban Form: Density and Sorting Effects. Richard Voith and Joseph Gyourko

Transcription

1 Capitaization of Fedea Taxe, te Reative Pie of Houing, and Uban Fom: Denity and Soting Effet by Riad Voit and Joep Gyouko Latet Daft: Ma 12, 2001 (Reviion) Ze/Luie Rea Etate Cente Woking Pape #366 Riad Voit: Reea Depatment, Fedea Reeve Bank of Piadepia Joep Gyouko: Rea Etate and Finane Depatment, Te Waton Soo, Univeity of Pennyvania Jan Buekne, Ed Gaee, Pete Linneman, and two efeee povided epfu omment on peviou veion of ti pape. Natuay, we ae eponibe fo a emaining eo. Te view expeed in ti pape ae oey toe of te auto and do not neeaiy epeent te view of te Fedea Reeve Bank of Piadepia o te Fedea Reeve Sytem.

2 Abtat We invetigate te impat of te tax teatment of owne-oupied ouing on uban fom in an eonomy in wi ig and ow inome oueod ooe among ity and ububan ommunitie. Beaue ouing tax poiie diffeentiay affet te eative, afte-tax pie of ouing fo ig and ow inome oueod, and beaue te extent of apitaization of ouing tax poiie an diffe ao ity and ububan ommunitie, ou anayi find tat ouing tax poiie an affet not ony te denity of te metopoitan aea, but ao an infuene wee i and poo oueod ooe to ive. Te impat of ouing tax poiie diffe depending upon te extent to wi te ubidy i apitaized into ity and pie and wete a and ue ontaint u a ububan age ot zoning exit to make pooe oueod e mobie. If te i and poo bot ae fuy mobie, ineaing a ubidy to ome owneip tat i poitivey oeated wit te inome of te owne ead to te deentaization of bot i and poo; te geate te extent of apitaization, te age te deentaization impat. In te peene of binding age ot zoning in te ubub, te i ave a geate inentive to deentaize wie te poo ae ontained to te ity. Tu, it i ony wen te mobiity of te poo i etited tat ouing tax poiy of te type we ave in te U.S. oud ave eped exaebate te intene eidentia oting by inome tat we ee in many pat of te ounty. Finay, it i notewoty tat ou anayi of ommunity oie i not diven by diffeent pefeene fo ity o ubub tat may be aoiated wit te inome eatiity of ouing demand. Rate, ou onuion aie fom ange in eative afte-tax ouing pie faed by poo and i oueod. Detemining te empiia eevane of pie veu pefeene in ti matte oud be an ugent tak fo futue eea. 2

3 1. INTRODUCTION Ti pape anayze ow uent ouing tax poiy, wi povide benefit to ome owne tat ineae wit inome, an infuene uban fom. Mi (1987) and ote ave own tat te favoabe tax tatu of owne-oupied ouing a euted in moe ouing invetment tan otewie woud ave oued. We woud expet tat beaue and i an input to ouing, ti ineaed ouing invetment woud ao eut in owe popuation denitie. Wit te exeption of Bakey and Foain (1983), oweve, anaye of te patten of metopoitan deveopment geneay ave not eiouy onideed te impat of te tax teatment of ouing. 1 In ti pape, we fou on te diffeentia impat tat te tax teatment of ouing an ave on te onumption of and and on te oation oie of ig veu ow inome oueod. Tee ae two eaon wy te tax teatment of ouing an affet patten of metopoitan deveopment beyond impy eduing denity. Fit, uent ouing tax poiy a geate diet effet on te afte-tax eative pie of ouing fo ig inome oueod, teeby poviding inentive wit epet to ouing and oation oie tat diffe fom toe fo ow inome oueod. Seond, diffeing uppy ondition ao ommunitie ae ikey to yied diffeent apitaization of ouing-eated tax inentive tat ao an infuene afte-tax eative pie ao oation. Fo exampe, tee oud be a diffeent uppy epone, and ene diffeent apitaization, in ommunitie wit imited undeveoped and veu ommunitie on te uban finge tat ave pentifu uppie of open and. In addition, te uppy of ouing 1 Fo exampe, in tei widey ited eview of te aue of ububanization, Miezkowki and Mi (1993) onide te impat of tanpotation poiie and te ike, but not ouingeated tax expenditue. 1

4 avaiabe to ig inome oueod wi ao depend on te ouing deiion of ow inome eident, o tat te extent to wi ouing tax benefit ae apitaized into te maket pie of ouing itef wi depend on te ditibution of ig and ow inome oueod ao ommunitie. Tee two featue ae inopoated in a mode tat i ued to anayze te impat of ouing eated-tax inentive on te ouing onumption and ommunity oie of ig and ow inome oueod wo od idioynati pefeene fo itie (bounded, uppyontained ommunitie) and ubub (unbounded, uppy-unontained ommunitie). A key featue of ou anayi of ommunity oie i tat oueod oie ae not diven by diffeent pefeene between ig and ow inome oueod, but by te effet of poiy on afte-tax ouing pie. Te impat of te tax teatment of ouing i examined unde two egime: one wit no and-maket ontaint and one wit a binding, age ot zoning equiement in te ubub tat etit te mobiity of te poo. Wen no binding zoning ue exit o tat i and poo oueod ae equay mobie witin te metopoitan aea, oweing te eative pie of ouing fo ig inome oueod unambiguouy eate an inentive fo bot ow inome and ig inome eident to eave te ity. Te magnitude of te inentive to deentaize i poitivey eated to te extent of te apitaization of te ubidy. Beaue te fato detemining te extent of apitaization ae ikey to diffe ao metopoitan aea, te deentaization impat ae ikey to diffe a we. In te peene of a binding, ububan zoning ontaint tat imit te abiity of te poo to puae a ot in te ubub, tax poiy tat ubidize te i ineae te degee of patia oting by inome in te metopoitan aea. Moe peifiay, if age ot zoning in te ubub 2

5 onfine pooe oueod to te enta ity, ten a popotiona ubidy tat edue te eative pie of ouing fo ig inome oueod wi eut in geate deentaization of te i and a geate epaation of ig veu ow inome oueod tan otewie woud ou. Tu, it i ony in te peene of ome fato u a a binding age ot-type zoning ontaint tat etit te mobiity of te poo tat a popotiona ubidy to owne an geneate eidentia oting by inome of te type we ee in te United State. 2 Te patia eevane of tee teoetia onuion deive patiay fom tei impiation tat poiy infuening te patia patten of eative and pie, not jut pefeene fo owe denity ifetye ombined wit iing inome and bette tanpotation ytem, may ave eped ape uban fom in te U.S. 3 In addition, ou finding ave potentiay impotant impiation fo te emeging debate uounding Smat Gowt initiative. If enated, ome of toe initiative eay wi affet te eative pie of and ao ommunitie witin individua metopoitan aea. And, ou eut indiate tat te patia patten of deveopment and te degee of eidentia oting by inome an be infuened by poiy affeting eative and pie ao pae. 2 Coneptuay, poiy need not be te ony fato tat oud onfine te poo to te enta ity. If te poo ytematiay ad a pefeene fo ity ife, te ame outome woud eut. Howeve, we peifiay do not want pefeene paying u a oe in ou mode o tat we an fou on eative pie effet. And, we tink zoning poiy i a potentiay eevant way in wi te mobiity of te poo migt be etited. 3 Te inentive identified ee ao may be eated to ommunitie deiion to enat zoning etition. Voit (2000) ow tat ommunity beavio ao may be infuened by ouing tax poiy. He demontate tat, unde pauibe ondition, ouing ubidie ike toe in te US may enouage ig inome ommunitie to enat exuionay zoning. 3

6 2. THE MAGNITUDE AND DISTRIBUTION OF THE TAX SUBSIDY TO OWNER- OCCUPIED HOUSING It i we known tat owne-oupied ouing i favoed by te uent tax ytem beaue it oupant an dedut etain expene witout aving to deae any inome on te aet. Speifiay, motgage inteet and oa popety taxe ae dedutibe fom taxabe inome fo toe wo itemize, wie no owne oupant a to inude te enta vaue of te ome a pat of taxabe inome. A tandad ue ot equation tat take into aount tee featue i expeed in equation (1) (1) R H = (1-τ ded )αi + (1-τ ded )τ p + (1-τ int )(1-α) + M + δ - Π H. Te eft-and ide vaiabe, R H, i te impiit ent pe doa of ouing vaue te owne pay eef. In equiibium, it mut equa te ot of owne oupany pe doa of ouing vaue. Tee ot inude: (a) te afte-tax ot of motgage inteet, (1-τ ded )αi, wee α i te oan-tovaue atio on te oue, i i te motgage inteet ate, and τ ded i te owne-oupie magina tax ate wi equa e magina ate (denoted τ int ) if e itemize and equa zeo otewie; (b) te afte-tax ot of popety tax payment, (1-τ ded )τ p, wit τ p te effetive popety tax ate; () te afte-tax oppotunity ot of inveting equity in te oue ate tan in ome ote invetment at ate of etun, ; ti i given by (1-τ int )(1-α) and i a ot to a owne, wete tey itemize o not 4 ; (d) annua maintenane ot pe unit of ouing wi ae given by M; (e) te ot of tue eonomi depeiation pe unit of oue wi i aumed to ou at ate δ; and 4 Ti notation aume te oppotunity ot of inveting equity in te ome i foegoing taxabe etun. 4

7 (f) any annua appeiation in te oue vaue, Π H, wi edue te ay ot. 5 Te ubidy pe doa of owne-oupied ouing an be etimated by ompaing ti ue ot of owne oupany unde te uent ode to tat unde a ypotetia ode tat doe not favo owne-oupied ouing. One eaonabe atenative i a tax ode tat teat te ome owne ike a andod o tat owne-oupied ouing i not teated diffeenty fom enta ouing (o fom mot ote aet fo tat matte). Sine te ome owne effetivey ent te oue to eef, neuta tax teatment equie taxing te impiit enta inome on one ome. Howeve, if teated ike a andod, owne oupie ao woud be abe to dedut maintenane and depeiation expene in addition to te motgage inteet and oa popety tax ot peenty aowed. Making tee ange (and auming aua taxation of apita gain fo aity of expoition) yied te foow new equiibium ent, R H, pe doa of ouing vaue (2) R H = (1-τ)αi + (1-τ)τ p + (1-τ)(1-α) + τ R H + (1-τ)M + (1-τ)δ - (1-τ)Π H. wee τr H i te tax due on imputed ent and a ote tem ae a defined above. Te diffeene in ue ot unde te two tax egime, R H - R H, epeent te ubidy to owne oupany pe doa of ouing vaue unde te uent ode and i aptued beow in equation (3) (3) R H -R H = τ ded αi + τ ded (τ p ) + τ int (1-α). Ti equation meaue te ange in ue ot, o impiit ent fo owne-oupie, tat woud eut if te uent tax ytem wee modified o tat one doa of invetment in owne-oupied 5 Ti peifiation teat apita gain on ouing a untaxed and eaized evey yea. Given tat tee now i a $250,000 apita gain exuion ($500,000 fo maied oupe fiing jointy) tat an be appied evey ote yea, ti i ikey to be te ae. 5

8 ouing wa not favoed ove ote aet. 6 Tu, te tax ubidy to owne-oupied ouing an be deompoed into tee fato: (a) te tax vaue of ome motgage inteet dedution (τ ded *α*i); (b) te tax vaue of oa popety tax dedution (τ ded *τ p ); and () te tax tat woud ave been paid on te equity inveted in te ome ad it been inveted eewee (τ int *(1-α)*). 7 Gyouko and Sinai (2001) etimate ea omponent of equation (3), and onude tat te tota vaue of te tax ubidy in 1989 wa ove $160 biion. Tey ao ow tat te ubidy i igy kewed aong inome ine wit uppe inome owne eeiving a dipopotionate ae of te tota ubidy. Tat te net impat of te tax teatment of ouing i to povide geate benefit fo oueod wit geate inome and weat i not upiing and aod wit ote eea in ti aea. Fo exampe, Auten and Reovky (1998) ave etimated tat te tax expenditue aoiated wit motgage inteet and oa popety tax dedution aone amount to $72.1 biion in fia yea Le tan one quate of a fie and e tan 40 peent of a ome owne ave uffiient inome, oue vaue, and eveage to waant itemizing in ieu of taking te tandad dedution. 8 Tee i no doubt tat non-itemize tend to ave owe 6 Ti aateization ignoe eond-ode affet aoiated wit ange in oue vaue tat may eut fom a ange in ouing tax poiy. Ti i done fo impiity ony, o tat te undepinning of wat eate te ubidy an be eadiy identified. Capitaization and it impiation wi ave pominent oe in te mode peented beow. 7 We do not intend to impy tat te motgage inteet o oa popety tax dedution temeve eate ubidie to owne oupie. Te ubidy aie fom te non-taxation of imputed ent in onjuntion wit toe dedution. Howeve, matematiay te ubidy an be epeented by te tee tem in equation (3). 8 Te Statiti of Inome Buetin (Intena Revenue Sevie, Waington D.C.:Fa 1995) epot tat 23.2 peent of a fie ued te motgage inteet dedution. Atoug te IRS doe not tabuate data epaatey fo owne and ente, if we aume tat 65 peent of a fie ae ome owne, ten te fat tat 23.2 peent of a fie ue te dedution ugget tat ougy 36 peent of a owne ue te tandad dedution. 6

9 inome. 9 In addition, even toug a ome owne pofit fom te non-taxation of imputed ent, ti apet of te ouing ubidy ao i diffeentiay vaued by ig and ow inome oueod. Beaue ig inome oueod fae ige magina tax ate, te non-taxation of imputed ent effetivey owe te afte-tax pie of ouing moe fo ig inome oueod tan fo ow inome oueod. 10 In um, te tax benefit to owne-oupied ouing eay ae kewed towad ige inome oueod tat tend to be in moe vauabe ome. Te emainde of te pape examine ow ti an affet te denity and eidentia make-up of a metopoitan aea. 3. A MODEL OF THE IMPACTS OF RELATIVE HOUSE PRICE CHANGES IN A METROPOLITAN AREA WITH BOUNDED AND UNBOUNDED COMMUNITIES Te tutue of ou mode i aateized by te foowing featue: (a) a metopoitan aea in wi tee i a ity wit a fixed bounday and a ububan ommunity tat away an expand on te magin; (b) two type of woke, ig and ow inome; () a ouing ubidy wi ony ig inome oueod eeive; and (d) a ytem of pefeene in wi oueod of a given type ave identia pefeene ove ouing evie and non-ouing evie, but 9 Ceetti and Rupet (1996) epot tat ove 70 peent of te tax expenditue aoiated wit te motgage inteet dedution aue to oueod wit annua eaning in exe of $75, Gyouko and Sinai (2001) and Auten and Reovky (1998) etimate ti omponent of te tax ubidy to ome owneip to be about $100 biion on an annua bai. In addition, Poteba (1991) etimate tat tax ode-eated benefit to owne-oupied ouing owe ig tax baket owne ue ot by a mu a 15 peent. 7

10 an diffe in tem of an idioynati pefeene fo ity veu ububan oation. 3.1 Caateization of te Metopoitan Aea Tee i a inge metopoitan aea oniting of two juidition indexed by j = (,), wit denoting te enta ity and denoting te ububan juidition. Te enta ity bounday i exogenouy given and annot be anged o tat te enta ity and aea, L&, i fixed. We efe to te enta ity a being a bounded ommunity wit it and in pefety ineati uppy. In ontat, unimpoved and in te ububan egion, L, i aumed to be pefety eatiay uppied. Hene, te ubub ae te unbounded ommunity. 11 Beaue tee i a potentiay infinite uppy of and to te ububan ommunity, it pie,, i fixed at te vaue of it atenative ue agiutue. City and pie,, adjut to aoate te ae eoue, ity and. 12 In addition, two type of woke indexed by i=(,), wit denoting ig inome and denoting ow inome, ive in te metopoitan aea. Ea goup i fixed in ize, N i, wit ig inome woke eaning wage w and ow inome woke eaning wage w. 13 Te ditibution of tee two goup ao te metopoitan aea depend on ytemati and idioynati pefeene, equiibium pie, and ouing ubidie.3.2 Caateization of te Houing 11 Wie te enta ity away i te bounded ommunity and te ubub te unbounded ommunity in ou exion, te eut deived beow geneay appy to ommunitie wit ow veu ig uppy eatiitie. 12 We wi to abtat fom inome effet in ode to fou quaey on eative pie ange. Hene, we effetivey aume tat and ent ae ditibuted unifomy ao oueod. 13 Te metopoitan aea i aumed to be an integated abo maket and a oation ae equay aeibe to empoyment o tat tee ae no ommuting-eated ent o wage gadient. In addition, fixing te popuation ize effetivey aow u to abtat fom te deiion of fim and fom te oe of non-eidentia and. 8

11 Subidy Te vaiou tax ode-eated benefit to owne oupany deibed above an owe te afte-tax pie of owne-oupied ouing. We peify tem a a ubidy, τ i, defined a te fation of te pie of ouing evie paid by te govenment. Fo impiity, we aume tat te tax ode-eated benefit ae attative ony to ig inome woke. 14 Fo ow inome oueod, τ =0, o tat te afte-tax pie of ouing evie ( j a) equa te obeved maket pie of toe evie j. Beaue te afte-tax pie equa te maket pie fo ow inome oueod, we dop te upeipt on afte-tax ent fo te emainde of te diuion. Fo ig inome oueod, te afte-tax pie of ouing evie i given by equation (1) and (2), ja = (1- τ ) j wee 0 < τ < 1, j =,. (4), (5) Note tat te afte-tax pie of ouing fo ig inome individua depend not ony on te diet effet of τ, but ao on te effet of τ on equiibium pie. At one exteme, τ oud be pefety apitaized into maket pie u tat afte-tax pie wee unanged by te ubidy; at te ote exteme, tee oud be no apitaization and j woud be unaffeted by τ wie ja woud fa by te fu amount of τ.3.3 Pefeene Individua onume a maket good, X (woe pie i te numeaie), and ouing evie, H j. An individua onume, k, maximize utiity by ooing eidentia oation and optima quantitie of X and H j given j, τ i, and w i, oueod inome. Moe fomay, 14 Ti i an obviou impifiation beaue a owne oupie, inuding toe wo do not itemize, benefit fom te non-taxation of imputed ent. Te bai eut od if a ontinuou ubidy meaue i ued, a ong a te tax benefit ae poitivey oeated wit inome. Howeve, ou impifiation make te ageba mu e umbeome. 9

12 Max U ik ( X, H j ) Subjet to: X + (1-τ i ) j H j = w i. (6) Individua of a given type ae aumed to ave identia pefeene ove X, and H j, but tey diffe in tei pefeene fo ity o ububan oation. Ti idioynati oation pefeene efet eteogeneou tate egading te deiabiity of fae to fae inteation and pubi pae in itie veu te avaiabiity of open pae and pivay in ububan ommunitie. 15 Te utiity funtion i defined u tat te indiet utiity funtion, V ik, take te foowing fom Hig inome: V k = V( ja, w ) + ε k j Low inome: V k = V( j, w j) + ε jk, (7) ik wee V(.) i te ytemati omponent of utiity and ε j i te inement to indiet utiity aoiated wit te oie of oation j. We fute define ε ik ik ik = ε - ε to be te eative idioynati pefeene fo oation and. 3.4 Loation Coie Beaue a onume ave identia tate exept fo idioynati pefeene fo ity o ububan iving, te magina onume i defined (epaatey fo i and poo individua) by tat ε k, ε i*, atifying ε i* = V i - V i. Moe fomay, fo ea woke type te magina onume i defined u tat ε * = V( a, w ) - V( a, w ) (8) ε * = V(, w ) - V(, w ). (9) 15 Tee tate diffeentia may efet bai diffeene ao onume, o tey may epeent diffeene in tate ove te ife-ye of te onume. Tat aid, ou mode abtat fom ife-ye onideation in ommunity oie. 10

13 Sine $, ε i* # 0 o no oueod woud ooe to ive in te ity. 16 By peifying a ditibution, Ψ i, fo ε ik, te numbe of i o poo oueod ooing ity eidene, N i, an be detemined a a funtion of eative ent in te ity and ubub. 17 Tu, te numbe of i and poo oueod ooing to ive in te ity ae given by: i N = Ψ i (ε i* ), fo i =,. (10), (11) Note tat if indiffeene equie a vey negative ε i*, few peope wi ooe a ity eidene. Eentiay, ity ent ae eativey ig if ε i* i tongy negative. Howeve, a ε i* ineae towad zeo, te numbe of peope ooing ity eidene ineae. Finay, beaue te numbe of ig and ow ki individua i fixed, i N = N i i - N, i =,. (12), (13) 3.5 Houing Demand Given an indiet utiity funtion, Roy identity povide te demand fo ouing by ea oueod. Conditiona on te oie of juidition, individua ouing demand i a funtion of ja and w fo ig-ki oueod, and j and w fo ow-ki oueod a own in equation (14)-(17). 16 Beaue ububan ent i fixed at te vaue of it atenative ue, ity ent ae away geate tan o equa to ububan ent. A pointed out by an anonymou efeee, ti impiity peume tat ity and oud be tuned bak into fam and. Tu, te ytemati omponent of utiity in te ity i away e tan o equa to te ytemati omponent of ububan utiity. Stated diffeenty, oueod ooing to ive in te ity mut ave an idioynati pefeene fo te ity, and ene ε i* # Note tat ineaing weat i peumed not to ange one intini pefeene fo a ity veu ububan oation. Tu, wen ubidie ineae, tey do not favo ity o ubub. Simiay, w i doe not affet te popuation ditibution beaue wage fo individua of a given type witin te inge metopoitan aea abo maket ae aumed to be te ame in bot juidition. 11

14 H j = H ( ja, w ), fo j=,; (14), (15) H j = H ( j, w ), fo j=, (16), (17) 3.6 Aggegate Demand and Suppy of Land Land onumption i aumed to be popotiona to te demand fo ouing evie. Auming puey fo onveniene tat te popotionaity fato equa one, and onumption, wi annot exeed L& in te ity, i given by L& = H N + H N. (18) Sububan and, wi i not exogenouy given, i defined by L = H N + H N. (19) Wie te aumption of popotionaity i a uefu one beaue it impifie te ageba in te ompaative tati anayi beow by doing away wit te need to expiity mode te podution of ouing wit apita and and, it obviouy i not eaiti. Hene, it potentia impat on te eut need to be examined up font. Ceay, if and pie wee to ineae, apita oud be ubtituted fo and in te podution of ouing evie. Tat i, moe peope oud be aommodated in te iing and pie aea by ineaing te ue of apita (i.e., by buiding up). By auming popotionaity, we abtat fom ti magin fo ubtitution. Howeve, a ou key ompaative tati eut od a ong a tee ae diminiing etun to uing apita in te podution of ouing. Beaue and i a fixed fato in te ity, te unit ot of ouing wi ie wit an ineaing numbe of oueod in te ity, even a apita i ubtituted fo and. Rent in te ity ti adjut to aoate te ae eoue. 18 Ti igigt tat te bounded- 18 Ti doe impy tat, wen popuation fa in te ity, te emaining ity eident onume moe ity ouing evie. Impiity, we ae auming tat te ouing tok adjut 12

15 unbounded ditintion between ommunitie in te metopoitan aea i mu moe impotant to te mode tan i ou impified ouing uppy ide. 4. COMPARATIVE STATICS 4.1 Cae 1: No Lot-Size Containt Te fit ae onideed i one in wi no and-ue ontaint of any type ae peent. Wit w i exogenouy fixed, equation (4), (5), (8)-(19) fom a ytem of fouteen equation (ix of wi ae identitie) in fouteen vaiabe, a, a, ε *, ε *, N, N, N, N, H, H, H, H, and L. Note tat doe not adjut in ti ae beaue agiutua and i pefety eatiay uppied. To examine te effet of anging a tax ubidy to owne-oupied ouing tat i poitivey oeated wit inome on te oation oie and ouing onumption of ig- and ow-inome woke, we totay diffeentiate tee equation and ove fo d /, dn /, dn /, dh /, dh /, dh /, and dl /. (Tota diffeentia ae own a equation A1-A14 in te appendix.) Rent Fit, onide te effet of a ange in ubidy on te pie of ouing evie in te ity, wi i given by: d { H ψ * ( V V ) + NH } ε a a a = H ψ V ( 1 τ) + N H ( 1 τ) + H ψ V + N H ε * * a a ε > 0 (20) in tem of ize of ouing to mat demand. Ti ao i uneaiti in te ot un, a ouing tat doe not mat onume demand often i eft vaant. It i notewoty tat ti ot of fixity of ity ouing tok ony einfoe te eut beow aoiated wit oting by inome. 13

16 In te denominato, te fit and tid tem ae negative beaue te demand fo ouing by ea inome type fa a pie ineae (i.e., MH /M <0 and MH /M a <0) and beaue te numbe of peope ooing ity eidene ineae wit ε * (i.e., MΨ /Mε >0). Te eond and fout tem ae ao negative beaue utiity deeae a afte-tax ent ineae (i.e., MV /M a <0 and MV /M <0). Tu, te denominato eay i negative. Signing te numeato equie a bit moe anayi. Te eond tem of te numeato i away negative beaue demand uve ope down. Howeve, te ign of te fit tem depend on te ign of te quantity ( V V ). a a Invoking Eue teoem fo funtion tat ae omogeneou of degee zeo (wi i te ae fo te indiet utiity funtion), it i taigtfowad to ow tat ti tem equa zeo. 19 Tu, te numeato and denominato of equation (20) bot ae negative and te deivative i unambiguouy poitive. Ti eut i not upiing eonomiay ine an ineae in ouing ubidie ineae te ovea demand fo ouing. Ti, in tun, ineae ity pie beaue ouing in ti pat of te metopoitan aea i ineatiay uppied. Te impotant apet of equation (20) i tat it iutate te extent to wi tax ubidie fo ouing ae apitaized into maket pie. A u, tee ae two apet of te equation tat waant fute diuion. Te fit i tat te degee of apitaization wi be owe wen tee ae age numbe of ow inome oueod iving in te ity. Capitaization ao wi be owe 19 Utiizing te fat tat te indiet utiity funtion ae omogenou of degee zeo, Eue Teoem ten impie tat V + V w V V w a a w a a w =0. Subtituting in fo a = (1-τ) and a = (1-τ) a fom equation (4)-(5) and eaanging yied te quantity ( V V )=0. a a 14

17 if tee oueod ity ouing onumption i igy enitive to pie. To ee ti moe eay, note tat te at two tem in te denominato epeent te epone of ow inome oueod to ange in pie, and te age tee tem ae, te e apitaization of ubidie into maket pie. Te eonomi intuition fo ti i tat ow inome eident ae te uppie of and to te ig inome oueod eeiving te ubidie. And, te moe eati tat uppy, te owe te apitaization of te ubidie to te i owne. A eond featue to be noted i tat ouing ubidie ae neve ompetey apitaized into maket pie even if tee ae no ow inome oueod in te enta ity in wi and uppy i fixed. Inompete apitaization aie fom te fat tat ig inome oueod an opt fo a ububan eidene wee ubidie away owe afte-tax maket pie (beaue ouing tee i in pefety eati uppy). Ti an be een moe fomay by noting tat ompete apitaization woud eave afte-tax pie unanged o tat d a / = (1-τ)d / - = 0, o d / = /(1-τ). Manipuation of (20) evea tat d / < /(1-τ) even wen tee ae no ow inome oueod in te ity. 20 Tee finding wit epet to apitaization wi be impotant fo ou anayi beow of te impat of ouing ubidie on te ommunity oie of ig and ow inome oueod Numbe of Houeod Cooing City Reidene Ineae in ubidie away edue te numbe of ow inome oueod ooing to ive in te ity a i evident by 20 Note tat if tee ae no ow inome oueod in te ity, te at two tem in te denominato of (20) dop out. Te emaining expeion an be manipuated to yied d H V ψ * ε a =. Note tat te eond tem of ti equation i ( 1 τ) ( 1 τ)( H ψ V + N H ) poitive o tat d ε * a a <. Tu, te ubidy i not fuy apitaized. ( 1 τ) 15

18 dn V d = ψ < ε * 0. (21) A ubidie ie, ent in te ity ineae, o fewe ow inome oueod, wo pay te fu maket pie, ooe to ive in te ity. Te i ao deentaize a indiated by te ompaative tati eut in equation (22): dn d = ψ * ( V ( 1 τ) + ( V V ε a a a )) (22) A quik inpetion of eevant tem ow te inequaity i unambiguouy negative. Tat i, te deivative wit epet to te umuative ditibution funtion i poitive by definition, utiity i deeaing in ity ent (i.e., MV /M a <0), d />0 fom equation (20), and te quantity ( V V )=0 fom above. a a Te extent to wi te ubidy aue bot ig and ow inome oueod to move depend uiay on te degee of apitaization, a ee ontant. If te ubidy i igy apitaized, it a geate deentaization effet, uggeting tat te impat oud diffe ao metopoitan aea. Buiding upon te diuion in te peviou etion, toe aea wit enta itie popuated by a age numbe of ow inome oueod we tend to ave ee apitaization, teeby eduing te inentive fo deentaization epeiay if te ow inome oueod ouing onumption and ommunity oie ae igy pie eati. On te ote and, enta itie ontaining pimaiy ig inome oueod wi tend towad geate 16

19 apitaization, and ene te ubidy wi povide a geate inentive fo deentaization. 21 In um, a popotiona ubidy to owne oupie tat ineae wit inome fote deentaization of bot oueod type if ie and pooe owne ae fuy mobie. Unde tee ondition, ouing tax poiy i not a andidate to expain te intene degee of eidentia oting by inome tat we ee in many metopoitan aea ao te United State Houeod Land Conumption Houeod and onumption depend on te afte-tax ent fo ig inome oueod and maket ent fo ow inome oueod. Fo ig inome oueod, te effet of ubidie on ity and onumption i given by dh H d a = 0. (23) a A diued in etion 4.1.1, te ubidy annot be fuy apitaized, o ubidie mut owe afte-tax ent in te ity fo ig inome oueod. Tu, ouing onumption by ig inome oueod ie wit an ineae in ubidy. In te ubub, beaue and i eatiay uppied, tee i no apitaization and, a i evident fom equation (A4) in te appendix, d a / = - < 0. Tu, dh H d a = > 0. (24) Ineaed ubidie owe afte-tax ububan pie and ineae ububan and onumption by 21 Capitaization i not te ony fato detemining te extent of deentaization. Ti ao depend impotanty on te ditibution of idioynati pefeene. Tey ep detemine ow eponive a oueod ommunity oie i to pie. 17

20 ig inome oueod. Sine ow inome oueod do not eeive any ubidy and maket ent in te ity ineae wit ubidie, ineaed ubidie mut owe ow inome oueod and onumption in te ity a own in equation (25) dh H d = < 0 (25) Finay, beaue ubidie do not affet ububan maket ent, dh / = Aggegate Land Conumption Aggegate and onumption in te ity i fixed at L&, and teefoe i unaffeted by ubidie. 22 Te effet of ubidie on te amount of ububan and onumed i given by ubidie on te amount of ububan and onumed i given by: dl H dn N dh H dn = + + (26) Sububan and onumption ie unambiguouy beaue bot te i and poo ae inented to move to te ubub in te fae of an ineaed ubidy Summay Wit no ontaint in te and maket, intoduing a ubidy to owneip tat i poitivey oeated wit inome a te foowing impat. Fit, it unambiguouy ineae 22 We aume tat tee away ae enoug oueod wo wi to ive in te ity at ent equa to tei atenative ue ( ) o tat a avaiabe ity and i oupied. 18

21 maket ent in te ity. Seond, ow inome oueod tat do not benefit fom te ouing ubidy pogam and teefoe onfont ige maket ent in te ity ave an inentive to deentaize to te ubub. Te fat tat ow inome oueod in te ity fae ige pie o move to te ubub impie tat te ubidy owe te aveage wefae of ow inome oueod. Moe peifiay, te wefae of ow inome oueod aeady iving in te ubub i unaffeted ine tey onfont no ange in pie. Howeve, ow inome oueod moving to te ubub eeive owe utiity in te ubub tan tei utiity woud ave been in te ity pio to te ubidy ineae. Tid, ig inome oueod ao ave an inentive to ububanize on te magin, o tat te tax poiy doe not neeaiy ead to ineaed eidentia oting by inome wen bot i and poo owne ae fuy mobie. Fout, aggegate and onumption in te ubub ineae unambiguouy. On a pe oueod bai, an ineae in te ubidy eay ead a i oueod to onume moe and in te ity and te ubub. Fo te typia ow inome oueod, and onumption eay fa in te ity and i unanged in te ubub. Finay, it i notewoty tat te impat deibed by ti mode ae ymmeti. If ow inome oueod eeived te ubidy ate tan ig inome oueod, ow inome oueod oie woud be affeted in te ame way tat ig inome oueod woud be if tey eeived te ubidy. Tat i, if a peia tax edit wa intituted tat wa avaiabe ony to ow inome oueod, we woud expet to ee motivation to ububanize anaogou to toe deibed above (wit te inome abe anged). Tu, in ou mode it i te effet of te ubidy on te eative pie of ouing tat dive beavio, not te inome of te owne pe e. 19

22 4.2 Cae 2: Lot-Size Containt Te eond ae intodue a ommon ububan and-ue etition in te fom of a minimum ot-ize equiement fo eidentia deveopment. To ep impify te anayi, it i aumed tat ot-ize ontaint exit u tat no ow inome peope ooe to ive in te ubub, but te ontaint ae not binding fo ig inome woke. 23 In ote wod, ig inome woke ean uffiienty ig wage tat tey away ooe ot at eat a age a te ontaint weneve tey ooe a ububan ite. Low inome woke, on te ote and, ave uffiienty ow wage tat tey neve ooe to puae a ot a age a te minimum in te ubub. 24 Te new ompaative tati eut fo ity ent i given in equation (27): d H ψ * ( V V ) + NH ε a a a = H ψ V ( 1 τ) + N H ( 1 τ) + N H ε * a a > 0 (27) Equation (27) i te ame a (20) exept tat it doe not inude te tem epeenting ow inome oueod ommunity oie epone to a ange in ity pie. Atoug it i not poibe to diety ompae te magnitude of te ent impat unde te two ae beaue tey epeent 23 Te mode woud geneate te ame quaitative eut wit a weake aumption. Te ony equiement i tat zoning peude ome ow-ki woke fom ooing a ububan oation. 24 Tee impifying aumption impy te foowing modifiation to te ompaative tati anayzed in Cae 1. Equation (A6) i no onge eevant, ine ow inome woke neve ooe to ive in te ubub, and equation (A7) and (A8) impify to HdN + NdH = NdH and dl = H dn + N dh, epetivey. 20

23 diffeent equiibia, one i tempted to ague tat te impat on ent i geate in te ontained ae beaue ow inome oueod annot move away fom te ity and, ene, ave ony one magin on wi to adjut tei onumption of ity and. Ti woud impy tat and woud be e eatiay uppied to ig inome oueod wo eeived te ineaed ubidy, and ene a geate ae of te ubidy woud be apitaized. Ti i not te ompete toy, oweve, beaue tee ao may be moe ow inome oueod in te ity. Conequenty, te aggegate epone due to oueod oweing ouing demand in epone to ineaing maket pie oud exeed te aggegate epone in te unontained ae in wi ow inome oueod an adjut bot by moving and by eduing ouing onumption. Tat aid, given an exiting et of and ue etition and a oeponding ditibution of ow inome oueod, ineaing ubidie woud eut in geate apitaization of te ubidy tan woud ou onditiona on te ame ditibution of ow inome oueod woe futue mobiity wa unontained. Subidy ange geneay take pae in te ontext of and ue poiie tat ae ong-tanding, ate tan in te ontext of ifting fom ontained to unontained egime. Teefoe, empiiay we woud expet to ee geate apitaization of ubidy ange in aea in wi and ue poiie etit te mobiity of ow inome oueod. Fute foowing te ogi outined in te peviou etion, ouing ubidie to ige inome peope ae moe ikey to fote te epaation of te i into ububan neigboood and poo in ity neigboood wen a and ue ontaint u a binding age ot zoning exit. 5. DISCUSSION AND CONCLUSION Ou anayi a own tat a pubi poiy ubidizing ome owneip diffeentiay 21

24 aong inome ine an affet te denity of te metopoitan aea, a we a infuene wee i and poo oueod ooe to ive. We ave own tat tee impat an depend impotanty on te extent of apitaization and on wete binding and ue ontaint exit tat etit te mobiity of te poo. If i and poo oueod ae fuy mobie, ineaing te ubidy ead to deentaization of te poo and te i; te geate te apitaization of te ubidy in te ity, te geate te inentive fo deentaization. In ti ae, ouing tax poiy i unabe to aount fo te intene eidentia oting by inome tat we ee in mot metopoitan aea in te United State. Te impiation fo eidentia oting, oweve, ae diffeent wen a ontaint u a age ot ububan zoning exit. Te i ti ave an inentive to deentaize on te magin. And, wit te poo tuk in te ity due to te age ot zoning imitation, eidentia oting by inome i ikey to be geate beaue of te ubidy poiy a ong a tee i ome eatiity to te demand uve fo eidentia and. Detemining te empiia eevane of ti ae oud be an impotant iue fo futue eea, a it ugget tat poiy, not jut pefeene fo e denity, oud ave payed a oe in aping Ameia uban fom. Pinning down te infuene tat pie and pefeene ave ad not ony woud be inteeting in it own igt, but etainy woud ep infom te uent debate uounding uban paw and it ot and benefit. Caefu meauement of te ubidie temeve, aong wit etimate of key demand and uppy edue paamete ae needed to detemine if poiy oud ave infuened ou uban fom in a meaningfu way. Anote uefu extenion of te mode woud be to inopoate oa amenitie tat ae at eat patiay detemined by te makeup of te oa popuation. Endogenou oa amenitie oud affet 22

25 pie in a way tat enouage even moe oting by inome tan in ou eond mode. Howeve, we eave tat wok fo te futue. 23

26 Refeene 1. Gead Auten and Andew Reovky. Te New Exuion fo Capita Gain on Pinipa Reidene, U.S. Teauy Depatment, mimeo (Deembe 1998). 2. Dixie Bakey and Jame R. Foain, Infation, Tax Advantage to Homeowneip and te Loationa Coie of Houeod, Regiona Siene and Uban Eonomi, Vo. 13 (1983), pp Stepen Ceetti and Pete Rubet, Motgage Inteet Dedutibiity and Houing Pie, Eonomi Comentay, Fedea Reeve Bank of Ceveand, Joep Gyouko and Todd Sinai, Te Spatia Ditibution of Houing-Reated Tax Benefit in te United State, NBER Woking Pape #xxxx, Ma Pete Miezkowki and Edwin Mi, Te Caue of Metopoitan Sububanization, Jouna of Eonomi Pepetive, Vo. 7, no. 3 (Summe 1993): Edwin Mi, Dividing Up te Invetment Pie: Have We Oveinveted in Houing? Buine Review, Fedea Reeve Bank of Piadepia, Ma-Api, Jame Poteba, Houe Pie Dynami: Te Roe of Tax Poiy and Demogapy, Booking Pape on Eonomi Ativity, 1991, 2, Riad Voit, Zoning and te Tax Teatment of Houing, Booking-Waton Pape on Uban Affai, (2000) Te Booking Intitution. 24

27 Appendix Te tota diffeentia ued in te ompaative tati anayi ae * dε = v d v d a a a a (A1) * dε = v d (A2) d = ( 1 τ) d a (A3) d a = (A4) dn dn =ψ dε * ε * =ψ dε * ε * (A5) (A6) dh = H d a a (A7) dh = H d (A8) dh = H d a a (A9) dh = H d = 0 HdN + NdH = HdN NdH dl = H dn + N dh + H dn + N dh (A10) (A11) (A12) dn = dn (A13) dn = dn (A14) 25