Temi di Discussione. Taxation and housing markets with search frictions. (Working Papers) March by Danilo Liberati and Michele Loberto.

Transcription

1 Temi di Discussione (Working Papers) Taxaion and housing markes wih search fricions by Danilo Liberai and Michele Lobero March 2017 Number 1105

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3 Temi di discussione (Working papers) Taxaion and housing markes wih search fricions by Danilo Liberai and Michele Lobero Number March 2017

4 The purpose of he Temi di discussione series is o promoe he circulaion of working papers prepared wihin he Bank of Ialy or presened in Bank seminars by ouside economiss wih he aim of simulaing commens and suggesions. The views expressed in he aricles are hose of he auhors and do no involve he responsibiliy of he Bank. Ediorial Board: Ines Buono, Marco Casiraghi, Valenina Aprigliano, Nicola Branzoli, Francesco Caprioli, Emanuele Ciani, Vincenzo Cuciniello, Davide Delle Monache, Giuseppe Ilardi, Andrea Linarello, Juho Taneli Makinen, Valerio Nispi Landi, Lucia Paola Maria Rizzica, Massimiliano Sacchini. Ediorial Assisans: Robero Marano, Nicolea Olivani. ISSN (prin) ISSN (online) Prined by he Prining and Publishing Division of he Bank of Ialy

5 TAXATION AND HOUSING MARKETS WITH SEARCH FRICTIONS by Danilo Liberai* and Michele Lobero* Absrac Housing axaion is an imporan policy insrumen ha shapes households choices abou homeownership and rening as well as he evoluion of he housing marke. We sudy he effecs of housing axaion in a model wih search and maching fricions in he propery marke and a compeiive renal marke. We show a new ransmission channel for a housing ax reform ha works hrough a shifing effec from landlords o enans. We calibrae he model in order o esimae he long-run effecs of a recen housing marke axaion reform and he exen of propery ax capializaion on house prices. We show ha propery axaion on owner-occupied dwellings has a negaive effec on propery and renal prices, whereas axes on second homes have opposie qualiaive effecs. The simulaneous increase in boh hese insrumens may miigae he dynamics of prices and rens as well as he change in he raio beween he share of owners and reners, leading o a parial capializaion axaion on prices. JEL Classificaion: R21, R31, E62. Keywords: housing marke, maching, propery axaion. Conens 1. Inroducion Relaed lieraure The model economy Household urnover and maching Households value funcions and ransacion prices Simulaion resuls Calibraion Effecs of propery axaion Effecs of 2011 housing axaion reform in Ialy Discussion Conclusions References Appendix A Appendix B * Bank of Ialy, Direcorae General for Economics, Saisics and Research.

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7 1 Inroducion 1 In he housing marke rade is no insananeous, despie here are simulaneously many buyers and sellers. Poenial buyers need a subsanial period of ime in order o nd and buy a home hey like, while sellers have o wai several monhs before hey are able o sell heir home. Houses are heerogeneous goods, somewha unique, and hey are raded in a marke characerized by large uncerainy regarding rading opporuniies. Consequenly, as he assumpion of insananeous and cosless coordinaion of rade is no suiable, he Walrasian paradigm seems inadequae o describe his marke and a growing lieraure is resoring o search and maching models. Buyers and sellers should search for each oher unil hey nd a rading opporuniy ha saisfy boh paries. Search heory is no only more appropriae from a heoreical poin of view bu, as shown by many auhors, i allows o raionalize several sylized facs of he housing markes: he observed naural vacancy rae (Wheaon, 1990), price momenum (Head e al., 2014) and seasonaliy of house prices (Ngai and Tenreyro, 2014), he correlaion of prices wih sales and ime on marke (Diaz and Jerez, 2013). Search and maching models have been also used o analyze he eecs of policy ools, such as ransacions axes (Lundborg and Skedinger, 1999). In his paper we propose an applicaion of search and maching models o he analysis of he longrun eecs of propery axaion on he srucure of he housing marke. We also consider he eecs of a renal income axaion's variaion o landlords. We sar from he seminal model by Wheaon (1990) and we explicily include an acive renal marke wih endogenous demand and supply in order o consider he household enure choice. As discussed by Poerba (1984), his decision crucially depends on he user cos of owner-occupaion which is relaed o depreciaion, ax and mainenance coss. In an asse-pricing perspecive, in equilibrium he price of a house is equal o he presen discouned value of is fuure service sream, represened by is real renal service value minus he user cos of owning a home: his highlighs he link beween propery axes and house prices. There is a large consensus abou ax capializaion ino prices. Neverheless, he empirical lieraure fail o agree on he exen of his eec (Palmon and Smih, 1998). 2 Bai e al. (2014) nd oally opposie eecs of propery axaion on home prices in dieren ciies, depending on insiuional deails of he axaion framework oher han ax raes. We believe ha a major issue ha hinders a sound assessmen of housing propery axaion is relaed o he possible presence of a preferenial reamen 1 We wish o hank Giorgio Albareo, Elisa Guglielminei, Giovanna Messina, Libero Monefore, Alfonso Rosolia, Giordano Zevi, Robera Zizza and Francesco Zollino for heir insighful commens and suggesions. The views expressed in his paper are hose of he auhors and do no reec he views of Bank of Ialy. Any residual errors are ours alone. 2 Empirical papers face endogeneiy issues well recognized in he lieraure and, in addiion, he diculy o conrol for all he componens of housing services and user cos. 5

8 for owner-occupied dwellings in place in many counries (i.e. hrough lower ax raes). Anoher issue is ha propery axaion reforms could be associaed wih a more general review of he housing axaion framework. Indeed, his is he case of Ialy. Here, ax raes on owner-occupied dwellings are lower han no owner-occupied dwellings. Furhermore, in he period he reform of propery axes was almos simulaneous o he one on landlords renal income axaion. The almos conemporaneous change of dieren insrumens and he ineria of house prices make he idenicaion of he eecs of he dieren policy ools very challenging, especially if, in principle, hey can have opposie eecs. We will ry o overcome his issue by calibraing our model o reproduce some sylized facs relaed o he Ialian housing marke in he period Therefore, we esimae he exen of ax capializaion on prices and he eecs of each policy ool on he long-run equilibrium levels of he main variables. In our model here is a coninuum of families. Each of hem should live in a house, which can be owned or rened, and derives uiliy from he ype of enure and idiosyncraic preferences. There are wo markes for dwellings. The rs one is a decenralized propery marke subjec o maching fricions as in Wheaon (1990), where boh buyers and sellers search for a counerpar and he ransacion price is bilaerally deermined by Nash bargaining. The second one is a fricionless renal marke, where hose who do no own a house mee landlords and sipulae one period conracs a a endogenous marke price. Since he presence of he renal marke is crucial for our research quesion, we explicily model demand and supply: households who own wo dwellings mus choose beween rening or searching for buyers, while only a fracion of all enans are searching o buy (because of a search cos). This means ha we allow for an endogenous paricipaion from boh he demand and he supply side, a he cos o giving up some degree of racabiliy of he model. According o our calibraion, he inroducion of an acive renal marke provides new insighs compared o a sandard search model. On he one hand, an increase of propery axes on owneroccupied houses have a negaive eec on housing demand and prices, as sandard in he lieraure. On he oher hand, he opposie eec resuls from an increase of propery axes on second homes: landlords who own wo houses shif par of he ax burden on enans. Since enans have o pay a higher ren, i is more convenien o become homeowner. Consequenly, demand for owner-occupied housing rises, puing an upward pressure on prices. In he long run he sysem adjuss o he permanen ax variaion and in he new seady sae he fracion of homeowners increases, as well as house prices and rens. Given ha our model allows for an acive renal marke, we can also consider he eecs of a reducion of he renal income axaion on landlords: he shifing eec works also in his scenario. As a maer of fac, here are more incenives for owners of a second home o ren his dwelling. As he oer increases, renal prices decrease, inducing households o ren insead o buy. By a mechanism 6

9 similar o he one described above, boh house prices and homeownership decrease. Of course, we are aware ha oher feaures can be included. Neverheless, we believe hey do no qualiaively change our resuls.assuming perfec capial markes can be handled by observing he posiive relaionship beween he house prices dynamics and he amoun of resources used a downpaymen. Relaxing he assumpion of xed housing sock does no change our insighs because he low elasiciy of housing supply wih respec o he home prices. Finally, our model is robus o he inclusion of vacan houses: we are able o show ha if a vacan house have no ow uiliy, he implicaions in his new economy are he same of he benchmark seup. We employ our model for an evaluaion of he axaion reforms adoped in Ialy in recen years. Regarding propery axaion, he scal legislaion in Ialy allows for dieren ax raes among owneroccupied houses and oher dwellings, encouraging homeownership. Beween 2008 and 2011 owneroccupied houses were compleely exemped from propery axes (and before 2008 hey received a preferenial reamen), bu in 2012 axaion was resored. A he same ime he ax burden on second homes was raised furher. We nd ha in he long run he propery ax reform approved a he end of 2011 would make house prices decreasing by 1.3 percen and rens increasing by 6.0 percen in real erms. 3 Moreover, i should increase homeownership by 1.2 percenage poins. Moreover, in 2011 a reform of renal income axaion for landlords reduced heir average ax burden. Through he simulaneous consideraion of renal and propery reforms we nd ha in he long run also rens go down (by 15.3 percen in real erms). 4 As here are some shorcus in our analysis ha make us believe ha he resuls for renal income axaion could be jus an upper bound, we consider his applicaion useful o remark ha addiional changes in he housing axaion a large modify he assessmen of he eecs of propery axaion. We use our model o esimae he exen o which propery axes are capialized on housing prices. We nd ha propery axes are parially capialized, alhough our esimaes imply a signican degree of capializaion, in line wih hose by Palmon and Smih (1998) for U.S. Dierenly from he previous lieraure, we are able o show ha parial capializaion emerges because of he simulaneous working of he wo mechanism described above. While he impac on prices of an increase of axaion on owner-occupied dwellings is signicanly negaive, he same percenage poin increase of ax raes on 3 We wan o sress ha our exercise has nohing o say abou he shor-run evoluion of he housing marke. Therefore, we canno exclude ha in shor-run he eecs of propery axaion could have been dieren. 4 Previously, rens added o oher incomes deermining he oal axable income of landlords and, herefore, renal income axes were progressive. Landlords can now choose he new alernaive regime: renal income axes are proporional and hey do no cumulae o oher incomes, implying a lower ax burden especially for medium-high income landlords (Chiri e al., 2013). 7

10 second homes leads o a sligh rise of house prices, ha reduces he exen of ax capializaion. The paper is srucured as follows. The nex secion reviews he heoreical and empirical lieraure on housing marke and axaion while secion 2 describes he model. Secion 3 describes he calibraion sraegy and show he resuls of our policy experimens. Finally, secion 4 concludes. 1.1 Relaed lieraure A large volume of empirical lieraure saring wih Oaes (1969) has analyzed if increasing propery axes aec negaively house prices and o which exen. Thi is consisen wih he fricionless assepricing model of he owner-occupied housing marke proposed by Poerba (1984): buyers should equae he price of a house wih he presen discouned value of is fuure service sream, represened by is real renal service value minus he user cos, including propery axes. As discussed by Palmon and Smih (1998) his lieraure fails o reach a consensus regarding he exen of such capializaion, also due o several issues involved in his exercise: rsly, here can be reverse causaliy (from prices o ax raes) when a xed amoun of ax revenue is argeed, as higher house values allow o impose lower ax raes; secondly, when propery axes are used o nance local public services, higher ax rae could be associaed wih higher prices because of he beer qualiy of public goods. Recenly, Bai e al. (2014) nd oally opposie eecs of propery axaion on home prices in dieren Chinese ciies, depending on axaion specics oher han ax raes. The asse pricing approach o house price deerminaion does no consider he ineracion beween ax policies and oher marke imperfecions, such as informaional fricions ha hinder rade coordinaion in he housing marke. Saring from his consideraion, bu also hanks o he abiliy o reproduce some sylized fac of he real esae marke, he search and maching approach has received growing aenion in recen years. The seminal conribuion in his lieraure was provided by Wheaon (1990). In his model households buy and sell dwellings in a decenralized housing marke subjec o search fricions. Each family derives a ow uiliy from living in a house i likes. Due o an idiosyncraic preference shock a household becomes uncomforable wih is home and sars looking for a new one, incurring in a cosly search eor. Once a new dwelling is found, he household move in he new locaion and pu he previous home on sale. In his framework marke prices are deermined on a bilaeral basis by Nash bargaining. Han and Srange (2015) provide a review of he growing lieraure originaed from his conribuion. 5 Wih respec o hese conribuions, we exend he basic framework 5 Ngai and Sheedy (2015) analyze he case in which he decision of moving house is endogenous and show how i is sensiive o macroeconomic and policy variables such as ineres raes and axes. Moen e al. (2015) show how he ransacion sequence decision of moving homeowners (buy rs or sell rs) is inerdependen on housing marke condiions and his can give rise o muliple equilibria and cycles. Lundborg and Skedinger (1999) show how ransacion 8

11 of Wheaon (1990) including a fully specied renal marke wih endogenous ren prices and explicily modeling he enure choice. Also oher papers in his lieraure feaure a renal marke, bu dierenly from us i is generally modeled as a reservaion sae for unmached buyers (Diaz and Jerez, 2013) or such ha here is no rade-o for owners beween rening or searching for buyers (Moen e al., 2015). Sommer e al. (2013) presen a dynamic general equilibrium model wih markes for homeownership and renal properies o sudy he eecs of ineres raes, loan-o-values and income disribuion on equilibrium house prices and rens, bu assume credi fricions raher han search fricions in he housing marke. The mos relaed conribuions o our work in his lieraure are Gervais (2002) and Sommer and Sullivan (2014). Boh papers consider he eecs of preferenial ax reamen of homeownership in US in a sochasic life cycle economy populaed by heerogeneous individuals who can eiher own or ren a house. In Gervais (2002) repealing he morgage ineres deducion leads o a decline in homeownership, because i increases he cos of ownership bu does no reduce downpaymen requiremens (because house prices are kep xed). In Sommer and Sullivan (2014), where boh house prices and rens are allowed o adjus, a reducion in he ax deducions available o homeowners leads o a decline in house prices because of he higher user cos. This allows low wealh households o become homeowners because of he lower downpaymen required. Moreover, as rens remain roughly consan while house prices decline, he posiive eec on homeownership reinforces, because i becomes cheaper relaive o rening. The main dierence beween our resuls and hose of Sommer and Sullivan (2014) are relaed o he impac of propery axaion on renal prices. Indeed, we nd ha renal prices should increase, in line wih he empirical ndings of Tsoodle and Turner (2008). 2 The model economy Time is discree, sars a = 0, and coninues forever. The economy is populaed by a coninuum of long-lived households wih measure 1. They have linear preferences over consumpion and receive each period a consan endowmen w of goods, equal across all of hem. The discoun facor of fuure uiliy is β < 1. Each family lives in a house, which can be owned or rened. Living in he house provides a consan ow uiliy, ha depends on he ype of enure and preferences: if he household owns he house and she likes i, hen she enjoys a uiliy u m, oherwise he uiliy ow is u u < u m (meaning also he case in which she lives in a rened dwelling). We dene a household ha likes he house where she lives as mached. A he same ime, he owners incur in each period a cos of mainenance and hey should pay a real esae propery ax. axes reduce search eor and maching raes in he Wheaon (1990) model, because lower he privae gains of a search. 9

12 Each family owns zero, one or wo dwellings. Non-owners live in a rened house, while hose who own wo houses live in he one hey prefer and pu he oher for sale or for renal. No household has he incenive o keep a vacan dwelling, because he ownership of a second house does no provide any uiliy per se. 6 Moreover, we assume perfec capial markes and, herefore, households do no own houses as a mean of saving. 7 As sandard in he lieraure, we also impose ha families canno live in a dwelling hey have pu on sale. There are wo markes for dwellings. The rs is a decenralized housing marke subjec o maching fricions as in Wheaon (1990) where boh buyers and sellers search for a counerpar. In his marke a buyer mees a seller wih a probabiliy sricly less han one. When here is a mach, he ransacion price, P, is bilaerally deermined hrough generalized Nash bargaining. As all families need a house o live, non-owners mus nd a dwelling in he renal marke. Since he choice of he house o buy is deniively much more dicul and challenging han he choice of he house o ren, we assume ha he laer marke is fricionless and cenralized: reners sipulae one-period conracs wih landlords in exchange for he paymen of an endogenously deermined marke price R. This assumpion allows us o keep he model more racable. Finally, here is no consrucion secor and he sock of houses is xed, equal o H > Household urnover and maching Since we wan o explicily model he equilibrium on he renal marke, he number of saes each family can visi during her lifeime is greaer han in he sandard search lieraure. 8 In paricular, we wan o consider he problem of boh households ha volunarily live in a rened dwelling and hose who insead are acively searching in order o buy. Moreover, households ha own more han one dwelling should choose if hey wan o pu heir second house for sale or for ren. Therefore, a ime households can say in eigh dieren saes H kxy, depending on hree dieren dimensions: (i) he number of houses hey own, k {0, 1, 2}; (ii) if hey enjoy uiliy u m or u u, x {m, u}; (iii) if hey paricipae ino he sales, he renal marke or neiher of he wo, y {h, r, o}. From now on we dene N kxy as he fracion of families in sae H kxy. Table 1 and Figure 1 summarize household ypes and ransiions from one sae o he ohers. We sar he descripion of he model from ype H 1mo, i.e. families who own only one house, perfecly 6 We will show in secion 3.4 an exension of he model where a vacan house gives o he owner a per period uiliy ow. In his case in equilibrium a posiive fracion of households keep heir second house vacan. 7 Since we assume linear preferences, households are indieren abou he iming of heir consumpion. 8 In sandard models as in Wheaon (1990) households can visi only hree saes: (i) hose who own one house and hey are comforable wih i; (ii) hose who own one house bu hey are searching for a new one; (iii) hose who own wo dwellings and are searching in he sales marke as sellers. 10

13 Figure 1: Transiions among saes N 0uh p d N 1mo p s N 2mh δ α σ N 0ur 1 ν N 1uo ν N 2mr p s p d N 1ur N 1uh mached and wih no paricipaion in he renal and propery markes, meaning ha hey receive a ow uiliy u m. However, hey are subjec o idiosyncraic preference shocks and wih probabiliy α hey have o change heir house. This can reec he fac ha hey have o move in a dieren place for work reasons or oher changes in heir saus (i.e. in he household size) or income gains/losses ha make hem uncomforable wih heir curren dwelling. 9 Those families who receive he shock, dened as H 1uo, remain in heir house, bu hey become unmached and receive uiliy u u. In he nex period we assume ha a fracion ν of hem choose o ener he housing marke as buyers looking for a new house (H 1uh ) whereas he remaining fracion, 1 ν, eners as sellers in he housing marke and move in a rened house (H 1ur ). 10 You can hink a his ype as hose who have o move o a dieren own and have no possibiliy o search for a new house while hey live in he old one; in his case, i would be beer o move in a rened dwelling and o ake ime before o sar searching. Moreover, as can be seen from Figure 1, if ν = 1 in seady sae here will be no reners and, herefore, no renal marke: in his case our model collapses o Wheaon (1990). 11 Following Figure 1, H 1ur households ha a ime sell heir house a +1 become volunary reners (H 0ur ). Those are families ha do no own dwellings and do no search for a new house (H 0ur ). Each period some of hem sar o acively search for a new house. Families ha do no own any house bu are acively searching are dened as H 0uh. Households H 1uh ha nd a counerpary in he housing marke in he nex period move in he new house and ren he old one, becoming landlords (H 2mr ). Finally, in he nex periods some of hem can decide o pu heir second house for sale. 12 In he following equaions we describe how he mass 9 In doing his assumpion we follow he lieraure. In Wheaon (1990) his is raionalized assuming ha here are only wo dieren ypes of dwellings, herefore only hose wih own one dwelling can be mismached. 10 By he assumpion we have made a beginning, sellers canno live in he dwelling hey have pu for sale, herefore if hey do no own any oher house hey should ren. 11 See he Appendix A Dierenly from us, Moen e al. (2015) assume ha a house pu for sale can be rened, allowing he owner o ge some ren while is searching for a buyer. As shown by Krainer (2001), he wo opposie assumpions can lead o dieren 11

14 of dieren ypes evolve dynamically: N+1 0ur N 0ur = p s N 1ur δ N 0ur (1) N+1 0uh N 0uh = p d N 0uh + δ N 0ur (2) N+1 1mo N 1mo = p d N 0uh + p s N 2mh αn 1mo (3) N+1 1uo N 1uo = αn 1mo νn 1uo (1 ν)n 1uo (4) N+1 1ur N 1ur = (1 ν)n 1uo p s N 1ur (5) N+1 1uh N 1uh = νn 1uo p d N 1uh (6) N+1 2mr N 2mr = p d N 1uh σ N 2mr (7) N+1 2mh N 2mh = σ N 2mr p s N 2mh (8) The ransiion probabiliies α and ν are exogenous and ime-invarian because hey reec preference shocks. All he oher ransiion probabiliies are endogenous. Buyers and sellers nd a counerpary in he housing marke wih probabiliies p d and p s, deermined by a maching echnology described below. In each period here is a fracion δ of H 0ur households ha sar searching for a dwelling. We assume, as will be shown laer, ha reners should pay each period a search cos in he housing marke and δ is pinned down by a free enry condiion. Somehing similar happens for families ha own wo houses. We will assume ha hose households are indieren among rening or selling heir second house and we le σ o be pinned down by a free enry condiion. N 1ur We dene he mass of buyers in he housing marke as D h N 0uh + N 2mh +N 1uh, while he sellers are S h. The number of ransacions beween buyers and sellers is given by a sandard maching echnology M ( D h, S h ). We assume i is coninuous, non-negaive, increasing in boh argumens and concave, wih M ( 0, S h ) ( = M D h, 0 ) = 0 for all ( D h, S h ). We also assume ha M displays consan reurns o scale. Consequenly, he probabiliy o nd a counerpar for buyers and sellers are p d = M ( D h, S h ) p s = M ( D h, S h ) D h Since here is no endogenous search eor, arrival probabiliies are equal for all buyers (sellers) and do no depend on heir ypes. I is also useful o dene he ighness of housing marke as θ Dh. Given S h he assumpion of consan reurns o scale, we can rewrie he maching funcion as S h M (θ, 1) and p s = θ p d. In our empirical exercise we will assume ha M is a Cobb-Douglas funcion resuls abou marke behavior. S h ( ) ( ) η ( ) 1 η M D h, S h = A D h S h 12

15 Table 1: Household Typologies Household Saes H 0ur H 0uh H 1mo H 1uo H 1uh H 1ur H 2mr H 2mh Households who do no own dwellings, live in a rened houses and are no searching in he housing marke Households who do no own dwellings, live in a rened houses and are searching in he housing marke Households who own he dwelling where hey live and hey like i Households who own he dwelling where hey live bu hey dislike i Households who own he dwelling where hey live, hey dislike heir house and hey are searching in he housing marke in order o buy a second house Households who own one dwelling, bu hey live in a rened house and hey are searching in he housing marke o sell heir house Households who own wo dwellings, hey live in he house hey like and ren he oher house Households who own wo dwellings, hey live in he house hey like and are searching in he housing marke o sell he oher house Renal conracs for ime are signed a he beginning of he period in a cenralized and fricionless marke. Therefore, he marke clearing condiion implies ha in each period he mass of landlords mus be equal o he mass of families who need a rened dwelling: N 2mr = N 0ur + N 0uh + N 1ur (9) In addiion o he equilibrium condiion on he renal marke, he equaion sysem (1)-(8) is closed by he wo following condiions: 1 = N 0ur H = N 1mo + N 0uh + N 1uo + N 1mo + N 1ur + N 1uo + N 1uh + N 1ur + 2N 2mr + N 1uh + N 2mr + N 2mh (10) + 2N 2mh (11) Equaions (10) and (11) imply ha he measure of households and he sock of houses are xed. 2.2 Households value funcions and ransacion prices The curren value for households of being in a paricular sae a he beginning of ime is given by he ow uiliy from housing and consumpion and heir expeced discouned uiliy. The componens of ow uiliy are heerogeneous among households ypes, apar from he endowmen w, due o dierences 13

16 in housing uiliy bu also because of he coss associaed wih he ownership of a house. Owners should pay axes on real esae propery, τ 1 P or τ 2 P, and mainenance coss m, while reners only pay he ren R. We allow for a dieren propery ax raes on dwellings, depending on wheher hey are occupied by he owner (τ 1 ) or no (τ 2 ). The ax base is he average value of housing barp, dened below. The value funcions of households who do no own any house are given by: V 0ur V 0uh [ = u u + w R + β max = u u + w R κ + β V 0uh { p d ] +1, V+1 0ur [ V 1mo +1 E (P i = 0) ] + ( ) 1 p d } V+1 0uh Households H 0ur and H 0uh have he same ow uiliy, apar from he disuiliy cos o search in he housing marke, κ. This cos, ha can be inerpreed as he opporuniy cos of he ime spen o nd a morgage, avoids all reners o ener he housing marke. Sellers do no incur any search cos. Since reners decide endogenously o sar searching, here should be a free-enry condiion V 0ur all. 13 = V 0uh Since in he housing marke here are wo dieren ypologies of buyers and sellers and prices are deermined by Nash bargaining, he eecive price ha buyers should pay is no ex ane known because i depends also on he ype of seller hey mee. Ex ane he price ha H 1uh households expec o pay is E (P i = 0), ha we dene below. Households ha own only he house where hey live have o pay each period a real esae propery ax τ 1 P and a mainenance cos m. Families perfecly mached ge uiliy u m while hose ha dislike heir house enjoy u u. The fuure expeced uiliy of households H 1mo reec he possibiliy ha hey receive an idiosyncraic preference shock and in he nex period hey are no comforable anymore wih heir house. (12) (13) for V 1mo = u m + w τ 1 P m + β [ (1 α)v+1 1mo + αv+1 1uo ] (14) Mismached households wih only one house have dieren value funcions, depending on he fac hey wan o buy a new dwelling or o pu for sale he old one in order o move in a rened house. V 1uo [ ] = u u + w τ 1 P m + β (1 ν)v+1 1ur + νv+1 1uh (15) The following wo equaions are he value funcions for ypes H 1ur and H 1uh : V 1ur V 1uh = u u + w R τ 2 P m + β { p s [ V 0ur +1 + E (P j = 0) ] + (1 p s ) V+1 1ur } { = u u + w τ 1 P m κ + β p d [ V 2mr +1 E (P i = 1) ] ( ) } + 1 p d V+1 1uh (16) (17) 13 Le's suppose, in fac, ha V 0ur housing demand increases lowering p d unil V 0ur < V 0uh : in his case more reners would sar looking for a house and herefore = V 0uh is resored. 14

17 I should be noed ha H 1ur households pay a ren R and axes τ 2 P, because hey do no occupy heir house. In erms of expeced uiliy hey dier from H 1uh because hey have he perspecive o become volunary reners, while he seconds will become landlords. Moreover, H 1uh are subjec o a search cos κ < κ, meaning ha for hose who are already homeowners is easier o buy a house. Finally, he value funcions of agens ha own wo houses are he following: V 2mr V 2mh [ ] = u m + w + R (1 τ i ) τ 1 P (1 d)τ 2 P 2m + β max V+1 2mh, V+1 2mr { = u m + w τ 1 P τ 2 P 2m + β p s [ V 1mo +1 + E (P j = 1) ] } + (1 p s ) V+1 2mh (18) (19) Boh ypes of households enjoy housing uiliy u m, pay mainenance coss on boh houses and he same axes on he rs house. However, landlords pay renal income axes R τ i, bu receive a discoun on propery axes for he second house hey ren. Since σ is endogenously deermined, we impose he free enry condiion on he housing marke V 2mr = V 2mh indieren beween rening heir house or rying o sell i. for all. This means ha households are Since in he sales marke here are wo ypes of buyers and wo of sellers, each wih a dieren value funcion, ransacion prices will be heerogeneous, independenly of he fac ha here are no qualiy dierences among dwellings. This is because prices are deermined by Nash bargaining and he dieren households have also dieren reservaion uiliies. We dene he eecive ransacion price as P i,j, where i, j = 0, 1. The index i idenies he ypology of buyers, while j he sellers: 0 if buyers = N 0uh 0 if sellers = N 1ur i = j = 1 if buyers = N 1uh 1 if sellers = N 2mh Assuming buyers have bargaining power χ (0, 1), ransacion prices are dened as follows: [ ( ) P 00 = β (1 χ) V+1 1mo V+1 0uh + χ ( V+1 1ur V+1 0ur ) ] (20) [ ( ) ( )] P 01 = β (1 χ) V+1 1mo V+1 0uh + χ V+1 2mh V+1 1mo (21) [ ( ) P 10 = β (1 χ) V+1 2mr V+1 1uh + χ ( V+1 1ur V+1 0ur ) ] (22) [ ( ) ( )] P 11 = β (1 χ) V+1 2mr V+1 1uh + χ V+1 2mh V+1 1mo (23) and, herefore, he expeced prices in value funcions (13), (16), (17) and (19) are equal o: E (P i = 0) = N 1ur S h P 00 E (P i = 1) = N 1ur S h P 10 E (P j = 0) = N 0uh D h P 00 E (P j = 1) = N 0uh D h P 01 + N 2mh S h P 01 (24) + N 2mh S h P 11 (25) + N 1uh D h P 10 (26) + N 1uh D h P 11 (27) 15

18 Finally, he average house value, used as ax base for propey axes, is a weighed average of prices deermined in he various ransacions: ( N 0uh P = D h ( N 1uh D h p d N 1ur ) S h p s P 00 p d N 1ur ) S h p s P 10 + The equilibrium of he model is dened below: ( N 0uh + D h ( N 1uh D h p d N 2mh ) S h p s P 01 + p d N 2mh ) S h P 11 p s P 11 (28) Deniion 1 (Equilibrium) A search equilibrium is a lis of value funcions, (V 0ur V 1uo, V 1uh, V 1ur, V 2mr, V 2mh ), measures of households, (N 0ur, N 0uh, N 1mo, N 1uo, N 1uh, V 0uh, V 1mo,, N 1ur, N 2mr, N 2mh ), prices, (R, P 00, P 01, P 10, P 11 ) and probabiliies, (δ, σ, p d, p s ), such ha, given all he parameers, V 0ur = V 0uh, V 2mr = V 2mh and equaions (1)-(27) are saised. 3 Simulaion resuls 3.1 Calibraion The seady sae of he model is a funcion of 16 parameers. Among hem 9 are direcly calibraed, while he remaining seven are esimaed in order o mach a same number of arges of he Ialian housing marke during he period a quarerly frequencies. The choice of his period is relaed o he availabiliy of daa on he microsrucure of he housing marke: he Ialian housing marke was aeced by a severe recession. When looking o he resuls of our simulaions his should be kep in mind. Our benchmark paramerizaion is summarized in Table 2. The household income is normalized o 1. We se he discoun facor β = (1 + r) 0.25 such as he real ineres rae r is equal o 3.5 percen. The mainenance cos m is calibraed equal o , as he average raio of mainenance expendiure over household disposable income in he period (based of Naional Accouns). Sanchez and Andrews (2011) show ha in Ialy he percenage of households ha changed residence wihin he wo-years period was equal 9.2 percen (based on EU-Silc 2007 daa). According o his evidence we se he quarerly probabiliy for homeowners o become mismached, α, equal o 1.15 percen. 14 Using Isa daa abou populaion movemens across municipaliies over he same woyears period, we assume ha only hose households ha move across dieren regions are unmached homeowners ha sar searching o sell heir home and become enans. Then, we implicily assume ha agens H 1ur have a greaer informaion problems abou he housing marke of he new region: 14 Indeed, we are also implicily assuming ha no household moved more han once in he wo-year period and ha he disribuion of movemens was uniform across dieren quarers. 16

19 hey prefer ren a new home in he new locaion and pu on sale he dwelling of he old region. As in he average of he annual share of households who moved across dieren regions can be esimaed o be equal o 0.56 percen, while according o Eu-Silc hose who changed residence were abou 4.6 percen, we se he probabiliy 1 ν o 0.56/4.6 = 0.12 (herefore ν = 0.88). The esimaed elasiciy of he house sales wih respec o ow of buyers, η, is equal o We compued he number of ransacions per households using daa on sales provided by OMI-Agenzia delle Enrae whereas he number of households is provided by Isa. The ow of buyers is measured as he percenage of households who declare he inenion o purchase a home in he nex 12 monhs in he consumers' survey by Isa. 16 The axaion seup is se in order o replicae he Ialian ax sysem in As will be explained laer, in Ialy he ax base for propery axes is no he marke value of dwellings, bu he impued value recorded in he cadasral regisry. In his paper we always se he propery ax raes in eecive erms, as hey were compued on marke values of dwellings. The propery ax rae on he owner-occupied dwellings, τ 1, was se o zero, as beween 2008 and 2011 owners were exemped from propery axes. Insead, he propery ax rae on he second houses, τ 2, was equal o 0.19 percen. 17 We allow for a discoun in favor of landlords relaed o he axaion on he second house, d = 4.4 percen, 18 and we ake ino accoun he income axaion by seing τ i = 30.5 percen. 19 The remaining parameer are se in order o mach several empirical arges relaed o he Ialian housing marke. Acually, we compue hem and he main seady sae values hrough a Newon- Raphson algorihm. Using he average ime on he marke (T OM) from he Ialian Housing Marke Survey (equal o 2.3 quarers) we derive ha he probabiliy o sell in a quarer is p s = Our arge for housing marke ighness is θ = 1.40, compued by using he raio beween housing demand (D h ) and housing supply (S h ). The demand is approximaed by he ow of buyers used in he compuaion of η. On he oher hand, he supply S h is esimaed as he raio of normalized ransacions over he probabiliy o sell, p s, derived above. We will consider as a arge also he shares of households ha owns only one house (N 1mo +N 1uo +N 1uh = 57.3 percen) and he one of enans (N 0ur +N 1ur +N 0uh = 20.8 percen) obained by he SHIW (Survey on Household Income and Wealh conduced by Bank 15 Given he srucural naure of η we esimae i over a period as long as possible (2004Q1-2012Q4). 16 We consider as poenial buyers hose who declare ha will buy a home for sure and hose who answer hey will probably buy. 17 According o Banca d'ialia (2013a), in 2011 he average ax rae was equal o 0.65 percen of he cadasral value (increased by 5 percen). As we esimae ha marke values were abou 3.4 imes greaer han he ax base (see secion 3.3), he eecive ax rae as a percenage of marke values was equal o 0.19 percen. 18 Tax discoun is compued on he basis of he ax raes se by he Ialian region capials in 2011 and in We found ha afer he reform his parameer remained unchanged. 19 The esimae for τ i was compued on he basis of daa colleced by Lungarella (2011). 17

20 of Ialy). Hereafer, we refer o homeowners as hose who own only one house, keeping apar hose who own also a second home. 20 We derive from he same daasource he price-o-income (number of quarers of average household income ha would be required o purchase he households' dwelling) and he ren-o-income raios (equal o 26 and 0.23 respecively). The scaling parameer of he maching funcion (A) is se o ge he number of house sales per family which is equal o per quarer. 3.2 Eecs of propery axaion In order o highligh he channels by which our model works, we now consider separaely an increase of axaion on owner-occupied dwellings and on second homes. We show hey have qualiaively opposie eecs. Then, keeping hese experimens in mind we sudy he issue of propery ax capializaion on house prices. Figure 2 describes he eecs on house prices and ren of propery axes for dieren combinaion of ax raes ( τ 1, τ 2). Taxaion on owner-occupied dwellings: an increase of he propery ax on owner-occupied houses (Policy B) induces a decrease of he coninuaion uiliy for homeowners, because he user cos of housing rises. Landlords are iniially less aeced, because he ax rae on he rened dwelling remains unchanged. As here is more convenience for enans o manain heir curren enure, housing demand goes down. The propery marke ighness drops, as he he probabiliy o sell and he number of house sales (Figure 3); a he opposie, p d increases. Since houses become more illiquid heir prices decrease and, since in equilibrium N 2mr and N 2mh households have he same coninuaion uiliy, also rens mus decrease, making reners beer o. Indeed, in he new seady sae he fracion of enans on oal households increases and homeownership correspondingly reduces (Figure 4). This resuls is a he opposie of Sommer and Sullivan (2014), where homeownership goes up. In heir heerogenous agens model an increase of propery axes on owner-occupied dwellings leads o a decrease of house prices while rens are almos unaeced. Therefore, he fracion of low income households ha can aord o buy a dwelling rises and he share of homeowners goes up. Taxaion on second homes: a change o τ 2 aecs only he owners of wo houses (Policy C). In his case, landlords shif par of he greaer ax burden on reners hrough an increase of renal prices. Therefore, as τ 1 was lef unchanged, enans nd more convenien o become homeowners, driving up housing demand in he propery marke. Consisen wih he congesion eec due o he rise of he housing demand, sellers have a greaer probabiliy o sell heir house whereas buyers have a lower probabiliy o buy a home. Marke ighness increase and also he number of ransacions goes up 20 This separaion is done only o make simpler he calibraion exercise, while i should be clear ha also hose who own a second home are usually included among he homeowners. 18

21 Table 2: Calibraed Parameers a quarerly frequency of he Benchmark Economy: (a) Assumpion and normalizaion, (b) Calibraed o mach he Ialian housing marke arge, (c) Ialian housing marke arges. Descripion Parameer Value Type Discoun facor β a Household income w a Mainenance coss m a Probabiliy o become mismached α a Probabiliy o sar searching for a second home ν 0.88 a Tax rae on owner-occupied dwellings τ a Tax rae on second homes τ a Landlords propery ax discoun rae d a Renal income ax rae τ i a Elasiciy of he maching funcion η b Scalar parameer of maching funcion A b Enry cos for owners κ h b Enry cos for reners κ r b Owners' uiliy u m b Reners' uiliy u u b Buyers' bargaining power χ b Sales per family M c Housing marke ighness θ c Price-o-income raio Ren-o-income raio P w c R w c Share of owners living in or searching for a comforable house N 1mo + N 1uo + N 1uh c Share of reners N 0ur + N 1ur + N 0uh c Time on he Marke T OM c 19

22 Table 3: Resuls of policy experimens. Variables Baseline Policy A Policy B Policy C θ p d p s Homeowners % Reners % Owners of wo houses % %R %P % House sales Ren-o-price raio % Policy A: addiional 0.1% propery axes on all dwellings. Policy B: addiional 0.1% propery axes on owner-occupied dwellings. Policy C: addiional 0.1% propery axes on second homes. (Figure 5). This induces an increase in house prices, bu much lower han he one in rens, because landlords have o resore he proabiliy (ne of propery axes) of heir second home. Indeed, he fracion of reners goes down and he share of homeowners goes up. This mechanism is a novely in he lieraure because we explicily model he renal marke. In order o be more clear on his regard, we presen in Fig. A.1 he resuls of hese policy experimens in he basic model of housing search proposed by Wheaon (1990). In his model here is no renal marke and each household owns is home. This implies ha axaion on owner-occupied dwellings amouns o a change in he numeraire, lefing unchanged he relaive price of housing. An increase of τ 2, insead, drives house prices down, because here is no way o shif he ax burden and he increase in axaion is borne by households who own wo dwellings; as heir coninuaion uiliy decreases, households ha are going o buy a second dwelling discoun he lower fuure uiliy and house prices goes down. House price capializaion: according o a sandard asse pricing equaion as in Poerba (1984) and absracing from all he componens of he user cos oher han propery axes, housing values can be wrien as follows P = T =1 1 (1 + r) 1 (S πt ) where S is he renal sream of housing services and T are propery ax paymens. If here is only parial capializaion we should observe π < 1. The debae in he lieraure have been focusing on he 20

23 Figure 2: Eecs of housing propery axes on house prices and rens (a) House prices (b) Rens value aken by π. Assuming innie house life and holding xed household characerisics, he eec on prices can be rewrien as a funcion of eecive ax rae τ: log(p ) = π τ r Using his simple formula and assuming π = 1 we provide a benchmark for house price variaion agains which we will compare he resuls coming from our model. According o (29) and assuming a real ineres equal o 3.5 percen, if here is full capializaion an increase of he eecive ax rae by 0.1 percen would lead o a price reducion of 2.9 percen. Then, we use he model presened in he previous secion o evaluae he exen of ax capializaion in Ialy. Since we allow for dieren eecive ax raes among owner-occupied dwellings (τ 1 ) and oher houses (τ 2 ), we increase boh raes permanenly by 0.1 percen. As can be seen in he second column of Table 3 (Policy A), increasing he eecive ax rae by 0.1 percen leads o a reducion of house price by 1.8 percen. Therefore, our model suppor he view ha propery axes are only parially capialized in house prices. In paricular, we nd ha π is equal o 0.6, in line wih he esimaes of Palmon and Smih (1998). In addiion o he eecs on house prices, we also consider he impacs on oher imporan variables. Firs of all, he eec on marke rens is posiive (1.2 percen). This is in line wih he resuls of Tsoodle and Turner (2008), according o which in US an increase in he propery ax rae has a signican posiive eec on residenial rens. More ineresingly, in our experimen he shares of homeowners and reners remain unchanged, challenging he common view ha an increase of propery axes should discourage homeownership Our seup resuls obviously depend on he implemened calibraion. Hence, e.g., if we modify our parameerizaion (29) 21

24 Figure 3: Eecs of housing propery axes on housing marke ighness and probabiliy o sell (a) Housing marke ighness (b) Probabiliy o sell a house 3.3 Eecs of 2011 housing axaion reform in Ialy In his secion we will quanify he eecs of he Ialian housing ax reforms achieved in Firsly, we will consider he eecs of he propery ax reform aken alone; secondly, hose coming from he change of renal income axaion for landlords. Finally, we will show he resuls coming from he simulaneous inroducion of boh reforms. Propery axes in Ialy are no compued on housing marke values. The ax base is derived by he values recorded in he cadasral regisry, ha are no consisen wih marke prices because hey are no periodically updaed. Moreover, he ax regime is characerized by a preferenial reamen for owner-occupied dwellings ha consiss especially in lower ax raes for homeowners: beween 2008 and 2011 owner-occupied dwellings were even exemped. A he end of 2011 a broad reform of real esae propery axaion ook place. There are wo main feaures of he reform ha we will consider in our analysis. 22 Firsly, he ax base is sill represened by he cadasral values, bu for scal purposes hey are augmened by 60 percen. This increase of he ax base by sixy percen was aimed o reduce he huge gap beween marke values and hose recorded in he land regisry record. Neverheless, according o Agenzia delle Enrae (2012), he ax base remains in average abou 2.3 imes lower han he marke value. Secondly, all propery ax raes were subsanially increased. Propery axes were imposed also on owner-occupied dwellings, ha were o mach a share of reners equal o 33.3 per cen (similar o he U.K. renal marke) he parial ax capializaion is conrmed bu i is slighly more complee (π = 0.65). 22 A comprehensive descripion of he recen housing axaions reforms goes beyond he scope of his paper and can be found in Messina and Savegnago (2014). 22

25 Figure 4: Eecs of housing propery axes on homeowners and reners' shares (a) Share of homeowners (b) Share of reners exemped since For hose class of dwellings an average eecive ax rae of percen of house marke values was se. The average ax rae on second homes was increased from 0.19 o 0.42 percen of marke values. 23 In order o be coheren wih he Ialian housing axaion sysem when we se dieren ax raes we will mainain he same ax base i.e, he seady sae average house price used o compue he new amoun of axes. As can be expeced from he previous secion, he whole eec of he 2011 reform is he ne resul of he compensaion among he opposie eecs implied by an increase in τ 1 ans τ 2. According o our model in he long-run equilibrium house prices should decrease by only 1.3 percen (see policy D in Table 4), because he negaive eec of an increase of user cos for homeowners dominaes he indirec eec coming from he increase of τ 2. Equilibrium renal prices should insead increase by 6.0 percen, because landlords shif par of he increased ax burden o reners in order o ose he iniial negaive eec on rening proabiliy. This is more clear looking o he ren-o-price raio, ha in he new seady sae increases o 3.8 percen. Moreover, as homeownership becomes relaive more convenien han renal, housing demand rises and so also marke ighness. As a resul he fracion of homeowners increase by more han one percenage poin, o 58.5 percen. In equilibrium also house sales increase (by 2 percen) As wih he reform he ax base was increased by sixy percen, in order o compare he eecive ax raes afer he reform wih hose prevailing before, we compue all of hem in erms of percenage of marke values. Moreover, considering he eecive ax raes we include he lump sum deducion for owner-occupied dwellings, bu we absrac from is disribuional eecs (see Messina and Savegnago, 2014). The average ax raes were compued in Banca d'ialia (2013b). 24 Despie our model encompasses many realisic feaures of he housing markes, here are of course some simplicaions made in order o keep he model racable. In secion 3.4 we will discuss he bias deriving from he assumpion of perfec 23

26 Figure 5: Eecs of housing propery axes on ransacions and ren-o-price raio (a) Transacions (b) Ren-o-price raio Indeed, a key message of our experimen is ha he overall eec of he propery axaion reform on he housing marke is quie limied in he long run. However, we believe i is really challenging o es his resul using sandard economeric analysis, because of he almos conemporaneous change of renal income axaion for landlords as well as he ineria of house prices. Before 2011 rens on leased houses were subjec o progressive renal income axaion, as hey were added o oher incomes deermining he oal income of landlords. According o he new axaion regime inroduced in 2011 (named "cedolare secca"), landlords had he opporuniy o choose beween he previous progressive framework and he new proporional ax rae. In 2012, his rae was se o 21 percen for marke conracs and he ax base was he nominal value of he renal conrac. 25 This guaranees a lower ax burden for almos all he landlords. We simulae he renal income axaion reform as a permanen reducion of τ i from he baseline value of 30.5 percen o 21 percen (Policy E). Furhermore, i should be considered we are assuming ha he reducion of he renal ax rae is relaed o all conracs while in he realiy he new ax regime is an alernaive wih respec o he old one. According o Chiri e al. (2013), before he reform he eecive marginal ax rae was equal o percen for landlords wih a oal income in he range housands euro, while i was equal o percen over 28 housands euro. Indeed, his capial markes and he absence of a consrucion secor. We will consider also he case in which second homes are no rened or pu for sale. The laer is paricularly relevan for Ialy, where abou 16 percen of he housing sock is kep as vacan or for holidays (Chiri e al., 2013). 25 In his work we concenrae on marke renal conracs (hose where rens are freely deermined by landlords and reners). According o Chiri e al. (2013), in Ialy abou 20 percen of renal conracs are no individually negoiaed ("canone concordao"): rens are predeermined and generally lower han hose prevailing on he marke. 24

27 Figure 6: Eecs of renal income axes on house prices and rens Price variaion 0 2 Rens variaion τ i τ i (a) House prices (b) Rens suppors our assumpion. As for propery axes on second homes he ransmission channel is he shifing of ax burden from landlords o enans. Since for he iniial level of R a fall of renal income axes increase he ne reurn of landlords, perfec compeiion and free-enry on he renal marke push rens down, making homeownership relaively less convenien. Housing demand decreases, prices go down and he fracion of reners increases. We nd ha he 9.5 percenage poins decrease of renal income axaion leads o a reducion of house prices by 8.3 percen in he seady sae equilibrium. The decline is sronger for renal prices (-19.9 percen), while he share of enans increases by slighly less han 2 percenage poins. 26 The reducion of prices and rens are explained by he fac ha he eecive reurn of renal invesmen for landlords keeps in accoun also renal income axaion; consequenly adjusmens of he ren-o-price raio are needed o resore he ne reurn of landlords. The resuls shown in Table 3 mus be considered as a lower bound, because of our modeling assumpions: in paricular, we do no conrol for ax evasion. 27 According o he model, as a resul of he join consideraion of he ax propery on all owners and 26 See also he Appendix B Wih respec o he new regime we should keep in mind wo issues: (i) companies have no possibiliy o choose i; (ii) he eecs can be less imporan as he renal marke is seriously aeced by ax evasion. The laer is paricular relevan, as one of he main goal for he reform was o reduce ax evasion and o induce landlords o pay axes. Our model is no able o provide conrol for his issue, as here is no endogeonus choice for landlords o pay axes or no. However, we believe ha his will reduce drasically he negaive variaion on rens, because for landlords ha before did no pay any axes he new regime would imply an increase of axaion (if hey decide o leave he underground economy). Indeed, we simulaed an increase of renal income axaion for all landlords from 0 o 21 percen and we go as a resul ha house prices would increase by abou 10 percen and rens by 24 percen. 25

28 he reducion of τ i (Policy F) house prices and rens go down by 10.3 and 15.3 percen respecively. The fracion of enans increases o 21.8 percen, while house sales drops by 3.6 percen. Table 4: Resuls of policy experimens. Variables Baseline Policy D Policy E Policy F θ p d p s Homeowners % Reners % Owners of wo houses % %R %P % House sales Ren-o-price raio % Policy D: 0.098% (from zero) propery ax rae on owner-occupied dwellings, 0.42% (from 0.19%) on second homes. Policy E: 21% (from 30.5%) renal income ax rae. Policy F: policy D plus policy E. 3.4 Discussion Despie our model encompasses many realisic feaures of he housing markes, here are of course some simplicaions made in order o keep he model racable. In his secion we will discuss some cavea ha we consider paricularly relevan. The role of credi markes: as sandard in he housing search lieraure we assume perfec capial markes. However, here is an imporan srand of heoreical lieraure ha explicily sress he imporance of credi fricions in he morgage marke. The key fricion in his lieraure is observable when households buy a dwelling and hey need o have a sucien wealh o be used as downpaymen. Indeed, credi fricions preven households from borrowing he full value of he house (loan-o-value lower han 100 percen). In a heerogeneous agens framework á la Aiyagari, only a fracion of he households can aord housing propery, in paricular hose who have been able o accumulae enough wealh in he pas. Considering his addiional channel in our framework is hardly feasible because of he compuaion diculies involved. However, here is a recen paper ha made a similar analysis for he U.S. housing marke. Sommer and Sullivan (2014) consider he eecs of a disposal of he propery ax deducions on owner-occupied dwellings, aking ino accoun explicily he individuals 26

29 enure choice. An increase in he ax propery o homeowners leads o a decline in house prices because he user cos rises, bu reduced house prices allow low wealh households o become homeowners because he downpaymen falls. This counerbalances he iniial decline. In equilibrium rens remain roughly consan even as house prices decline, so his relaive price shif encourages a shif from rening o owning. The role consrucion secor: The second issue is relaed o he housing sock, ha we assume xed. In he long run i is plausible ha i will evenually adjus in response o house prices changes. A higher level of house prices would lead o an increase of he housing sock, because of he increased reurn of housing invesmen for consrucion rms. The opposie evenually is no rue when house prices lower, because as Glaeser and Gyourko (2005) show, posiive and negaive demand shocks have asymmeric eecs. Houses are durable goods ha do no disappear quickly when demand falls. Ignoring housing supply does no aec qualiaively our resuls relaed o propery axaion, due o he low sensiiviy of he housing supply wih respec o a reducion of home prices. The role of vacan houses: The hird cavea is ha in our model all second houses are eiher rened or pu for sale; none of hem are kep vacan or for holidays by heir owners. I could be argued ha afer an increase of propery axes on second houses he owners can decide o ren he house or pu i for sale, herefore increasing supply and adding downward pressure on prices and rens. This issue is Figure 7: Transiions among saes N 0uh p d N 1mo p s N 2mh δ α σ N 0ur 1 ν N 1uo ν N 2mr p s γ N 1ur N 1uh p d N 2mo paricularly imporan in Ialy, where abou 16 percen of he housing sock is kep as vacan or for holidays (Chiri e al., 2013). The absence of houses kep as vacan is no an assumpion bu a resul of he model, because owners derive no uiliy from a vacan second house. Wha we will do here, insead, is o assume ha a vacan house gives he owners a ow uiliy ũ. 28 For he sake of racabiliy and 28 You can hink a his uiliy in dieren ways: i can be he uiliy from having a house for he holidays or a place were o hos friends or relaives, bu i could also represen he opporuniy cos o argue wih your parens because he house was heir gif. 27

30 o have some heerogeneiy among households, we assume ha ũ is equal for everyone, bu a each period households have o pay an idiosyncraic disuiliy cos c o keep he house vacan. This cos is independenly and randomly disribued among households according o a cumulaive disribuion F (c) on he coninuous suppor [0, c]. 29 Households discover a ime he cos c hey should pay a + 1 o keep he house vacan, apar from he rs period in which hey sar owning he house. We will assume ha H 1uh agens ha successfully buy a second house in he rs period keep hem vacan; we will call his ype of households H 2mo. Once hese households discover heir disuiliy cos c, hey decide o keep he household as vacan or o ren i (Figure 7). 30 Since we have he new sae H 2mo a new ransiion equaion has o be inroduced and (7) mus be accordingly modied: N+1 2mo N 2mo = p d N 1uh γ N 2mo (30) N+1 2mr N 2mr = γ N 2mo σ N 2mr (31) where γ is he endogenous fracion of households ha become landlords in he nex period. 31 enry in he renal marke implies ha here exiss some hreshold level c = V 2mo V 2mr such ha families wih c c will keep he house vacan, while he ohers will ren i. The coninuaion uiliy of H 2mo households in seady sae is V 2mo = u m + ũ + w τ 1 P τ 2 P 2m + β {(1 γ) [ V 2mo where he fracion H 2mo enering he renal marke is given by c 0 ] } c F (c df (c) + γv 2mr ) Free (32) γ = 1 F (c ) (33) Household wih a disuiliy cos greaer han c will be beer o enering he renal marke. Using (32), (18) and he free enry condiion c = V 2mo V 2mr we derive he hreshold a he seady sae as he soluion o: c (1 βγ)c + β c df (c) = ũ h R(1 τ i ) τ 2 d P (34) 0 29 An equivalen way o formalize households heerogeneiy is o assume ha each of hem has an i.i.d. idiosyncraic uiliy ũ i, ha is exraced in each period from some random disribuion. However, his formalizaion is less racable from a compuaional poin of view. 30 This assumpion is innocuous, since we know ha in equilibrium he coninuaion uiliy of a landlord is he same of a seller. Moreover, if we would le ype H 1ur households o keep vacan hey have lef, he resuls would almos similar. 31 An addiional dierence wih he baseline model is abou he relaion among he oal sock of housing and he housing supply. While in he baseline model can be shown ha in he seady sae S h = H 1, now he relaion becomes S h + N 2mo = H 1. 28

31 For a given R, here exiss only one value of c for which (34) holds. 32 Since boh H 2mo and landlords are subjec o he same mainenance coss and axes, he hreshold disuiliy cos for keeping a house vacan is a funcion of he uiliy ũ, he opporuniy cos of rening R(1 τ i ) and he ax discoun τ 2 d P. I is clear from (33) and (34) ha he direc eec of an increase of propery axes on second houses is relaed o he presence of ax discouns on rened houses. When d = 0 he fracion of H 2mo households ha wan o become landlords increase only if R increases (because c decreases). 33 As a consequence, he inroducion of H 2mo households should a mos lessen he magniude of our previous simulaions, bu should no change he qualiaive eecs. Then, we perform wo exercises in order o give some insighs on he quaniaive eecs compared wih hose of he previous secion. 34 We modied he baseline model assuming ha before he policy inervenion he fracion of H 2mo households on oal populaion was abou 2 and 5 percen and we calibraed again he model, following he procedure described in As expeced, we nd ha he ne eec of he propery ax increase is similar o he main experimens in boh our exercises. 36 Figures B.2 and B.3 provides a broad picure of wha happens and how resuls depends on he iniial level of N 2mo. 4 Conclusions We propose a framework for evaluaing he long-run eecs of housing axaion on house prices, rens and household enure choice. Our main conribuion is he inroducion of an acive renal marke in a sandard search model of he housing marke. In his way we can deepen he analysis of housing 32 For a given R he righ hand side of (34) is a consan. The lef hand side is insead an increasing funcion of c : dlhs dc = 1 βγ (c ) > 0 For c = 0 he LHS is null, while for c = c i is equal o c E (c). Therefore, if ũ h R(1 τ i ) τ 2 d P is in he inerval beween 0 and c E (c) here exiss a single soluion for (34). 33 Indeed, looking o he ax raes se by he ialian capial regions we found ha following he propery axaion reform of 2011 ax discouns on rened houses remained almos unchanged. For his reason we believe ha his channel did no work in ha case. 34 A sound calibraion proves o be dicul. A rs issue is relaed o he resricion ha each household can a mos own wo dwellings, ha hampers he abiliy o mach he empirical disribuion of he sock of dwellings across households. A second issue is ha no informaion can be rerieved on he shape of he disribuion F (c). 35 For simpliciy we assume ha he disuiliy cos is disribued according o a uniform disribuion. In his case we have wo new parameers, ũ and c, ha we pin down using as arge he assumed value for N 2mo and he share of reners in he populaion. When N 2mo = 0.02 we have ũ = 0.72 and c = 1.43, while for N 2mo = 0.05 we ge ũ = 0.76 and c = However, i is ineresing o noe ha he eecs on he share of homeowners are generally sronger when we ake ino accoun vacan homes. If propery axaion makes homeownership more aracive han rening, in equilibrium he sock of vacan homes goes down and i is absorbed by demand for homeownership. 29

32 propery axaion, in which he household enure choice has a crucial role. In paricular, he join consideraion of boh housing and renal markes highlighs a new channel: landlords shif par of he ax burden on reners, aecing he economy's evoluion of prices and quaniies. A permanen increase of ax raes on owner-occupied dwellings causes a decrease of he share of homeowners and of he housing and renal prices, as expeced. The opposie eecs derive from an increase of ax raes on second homes; landlords shif par of he ax burden on enans. As he laer have o pay a higher ren, i is more convenien o become homeowner. Consequenly, demand for owner-occupied housing rises, puing an upward pressure on prices. In he long run he sysem adjuss o he permanen ax variaion and in he new seady sae he fracion of homeowners increases, as well as house prices and rens. We can provide answers o old quesions, such as he exen of propery axes capializaion on house prices. We nd ha he pass hrough of ax raes on house prices is only parial, bu he magniude is subsanial (sixy percen), conrming he resuls found in previous conribuions. We also evaluae housing axaion reforms occurred in Ialy. In 2012 propery axaion increased subsanially for boh owner-occupied dwellings and second homes; according o our model, as a ne resul house prices should decrease in real erms by 1.3 percen, while rens should increase by 6.0 percen. Based on our model' simulaion, he share of homeowners rises (by 1.2 percenage poins). Moreover, in 2011 a reform of renal income axaion for landlords reduced heir average ax burden. In our heoreical framework, hrough he simulaneous consideraion of renal and propery reforms we nd ha in he long run also rens go down (by 15.3 percen in real erms). Of course, given ha we solve for he seady-sae of he model, i is no possible o run plausible policy implicaions, as we are silen abou he shor-run dynamics of he sysem associaed o policy changes. Anoher insigh of he model is ha he same policy arge (i.e. promoing homeownership) can be achieved hrough dieren insrumens or combinaions of hem. Indeed, while i is obvious ha a reducion of axaion on owner-occupied dwellings has he direc eec o promoe homeownership, i is no equally obvious ha he same resul is reachable by increasing axes on second homes. Moreover, he same qualiaive eecs of propery axaion on second homes can be reached by varying he renal income ax rae for landlords. Of course, such modelling comes wih poenial caveas and semplicaions in order o keep he model more racable. Neverheless, we believe ha including some of hem does no qualiaively change our resuls. Firsly, we absrac from credi fricions (downpaymen). However, Sommer and Sullivan (2014) did an analysis similar o ours for he U.S. housing marke and hey found ha an increase in he ax propery o homeowners leads o a decline in house prices because he user cos rises, 30

33 bu reduced house prices allow low wealh households o become homeowners because he downpaymen falls. This counerbalances he iniial decline. In equilibrium rens remain roughly consan even as house prices decline, so his relaive price shif encourages a shif from rening o owning, as in our model. The second issue is relaed o he housing sock, ha we assume xed. In he long run i is plausible ha i will evenually adjus in response o house prices changes and he quaniaive eec depends on he elasiciy of housing supply wih respec o he home prices. However, according o Nobili and Zollino (2016) and Lobero and Zollino (2016) his elasiciy in Ialy is relaively low. Moreover, i is plausible ha a lower level of house prices has no eec on he housing sock, because as argued by Glaeser and Gyourko (2005) houses are durable goods ha do no disappear quickly when demand falls. Therefore, we believe ha ignoring housing supply does no aec qualiaively our resuls relaed o propery axaion. The hird cavea is ha in our model all second houses are eiher rened or pu for sale; none of hem are kep vacan or for holidays by heir owners. I could be argued ha afer an increase of propery axes on secondary dwellings he owners can decide o ren he house or pu i for sale, herefore increasing supply and adding downward pressure on prices and rens. In secion 3.4 we allow vacan dwellings o provide a xed ow uiliy, bu we show ha his exension does no qualiaively change our resuls. 37 Our analysis can be exended in wo direcions. As so far we have considered only he eecs on he seady sae equilibrium of he housing marke, a naural evoluion is o analyze he full evoluion pah oward he new equilibrium. This exension is ricky, as he evaluaion of he shor run dynamics canno avoid he modeling of saggered renal conracs and he consideraion ha dieren eecs can emerge depending on he macroeconomic condiions (boom/recession). A second exension will be o analyze he eecs of variaions on samp and duies axes, as search models are he naural environmen of his policy. 37 The inuiion goes as follows. The marginal households is indieren beewen rening ou is secondary dwelling or keeping i as vacan. As an increase of propery axaion on secondary houses aecs all dwellings, he previous marginal household decides o ren ou only if renal prices increases. Then, he qualiaive eec is he same. 31

34 References Agenzia delle Enrae. Gli immobili in Ialia C. Bai, Q. Li, and M. Ouyang. Propery axes and home prices: A ale of wo ciies. Journal of Economerics, 180(1):1 15, Banca d'ialia. Relazione annuale. 2013a. Banca d'ialia. Audizione nell'ambio dell'indagine conosciiva sulla assazione degli immobili. June 2013b. S. Chiri, F. Borselli, A. Buoncompagni, and S. Manesra. Tassazione delle abiazioni e mercao degli af- i. In B. d'ialia, edior, Le endenze del mercao immobiliare: l'ialia e il confrono inernazionale. Banca d'ialia, Rome, A. Diaz and B. Jerez. House prices, sales, and ime on he marke: a search-heoreic framework. Inernaional Economic Review, 54(3):837872, M. Gervais. Housing axaion and capial accumulaion. Journal of Moneary Economics, 49(7): , Ocober E. L. Glaeser and J. Gyourko. Urban Decline and Durable Housing. Journal of Poliical Economy, 113 (2):345375, April L. Han and W. C. Srange. Chaper 13 - he microsrucure of housing markes: Search, bargaining, and brokerage. In J. V. H. Gilles Duranon and W. C. Srange, ediors, Handbook of Regional and Urban Economics, volume 5 of Handbook of Regional and Urban Economics, pages Elsevier, A. Head, H. Lloyd-Ellis, and H. Sun. Search, Liquidiy, and he Dynamics of House Prices and Consrucion. American Economic Review, 104(4): , April J. Krainer. A Theory of Liquidiy in Residenial Real Esae Markes. Journal of Urban Economics, 49(1):3253, January M. Lobero and F. Zollino. Housing and credi markes in Ialy in imes of crisis. Temi di discussione (Economic working papers) 1087, Bank of Ialy, Economic Research and Inernaional Relaions Area, Oc

35 P. Lundborg and P. Skedinger. Transacion Taxes in a Search Model of he Housing Marke. Journal of Urban Economics, 45(2):385399, March R. Lungarella. Una valuazione degli eei della cedolare secca sul mercao dell'edilizia residenziale in ao. mimeo, G. Messina and M. Savegnago. Beyond he acronyms: local propery axaion in Ialy. Quesioni di Economia e Finanza (Occasional Papers) 250, Bank of Ialy, Economic Research and Inernaional Relaions Area, Nov E. R. Moen, P. T. Nenov, and F. Sniekers. Buying Firs or Selling Firs in Housing Markes. mimeo, L. R. Ngai and K. D. Sheedy. Moving House. CEPR Discussion Papers 10346, C.E.P.R. Discussion Papers, Jan L. R. Ngai and S. Tenreyro. Ho and Cold Seasons in he Housing Marke. American Economic Review, 104(12): , December A. Nobili and F. Zollino. A srucural model for he housing and credi marke in Ialy. Journal of Housing Economics, forhcoming, W. E. Oaes. The eecs of propery axes and local public spending on propery values: An empirical sudy of ax capializaion and he iebou hypohesis. The Journal of Poliical Economy, pages , O. Palmon and B. A. Smih. New evidence on propery ax capializaion. Journal of Poliical Economy, 106(5): , J. M. Poerba. Tax subsidies o owner-occupied housing: An asse-marke approach. The Quarerly Journal of Economics, 99(4):729752, A. C. Sanchez and D. Andrews. Residenial mobiliy and public policy in oecd counries. OECD Journal: Economic Sudies, 7(1):122, K. Sommer and P. Sullivan. Implicaions of us ax policy for house prices, rens, and homeownership. mimeo, K. Sommer, P. Sullivan, and R. Verbrugge. The equilibrium eec of fundamenals on house prices and rens. Journal of Moneary Economics, 60(7): ,

36 L. J. Tsoodle and T. M. Turner. Propery Taxes and Residenial Rens. Real Esae Economics, 36(1): 6380, W. C. Wheaon. Vacancy, Search, and Prices in a Housing Marke Maching Model. Journal of Poliical Economy, 98(6):127092, December

37 A Appendix A A.1 Seady sae equaions Transiion equaions: p s N 1ur = δn 0ur p d N 0uh = δn 0ur p d N 0uh = p s N 2mh αn 1mo αn 1mo = νn 1uo (1 ν)n 1uo p s N 1ur = (1 ν)n 1uo νn 1uo = p d N 1uh p d N 1uh = σn 2mr σn 2mr = p s N 2mh Value funcions: V 0ur = uu + w R 1 β V 0uh = uu + w R κ + βp d [ V 1mo E (P i = 0) ] 1 β (1 p d ) V 1mo = um + w τ 1 m + βαv 1uo 1 β(1 α) [(1 ν)v 1ur + νv 1uh] V 1uo = u u + w τ 1 m k + β V 1ur = uu + w R τ 2 m + βp s [ V 0ur + E (P j = 0) ] 1 β (1 p s ) V 1uh = uu + w τ 1 + βp d [ V 2mr E (P i = 1) ] 1 β (1 p d ) V 2mr = um + w + R(1 τ i ) τ 1 τ 2 (1 d) 2m 1 β V 2mh = um + w τ 1 τ 2 2m + βp s [ V 1mo + E (P j = 1) ] 1 β (1 p s ) 35

38 Prices: [ P 00 = β (1 χ) (V 1mo V 0uh) + χ ( V 1ur V 0ur)] [ ( P 01 = β (1 χ) V 1mo V 0uh) + χ (V 2mh V 1mo)] [ (V 2mr V 1uh) + χ ( V 1ur V 0ur)] P 10 = β P 11 = β (1 χ) [ (1 χ) ( V 2mr V 1uh) + χ E (P i = 0) = N 1ur S h E (P i = 1) = N 1ur S h E (P j = 0) = N 0uh D h E (P j = 1) = N 0uh D h (V 2mh V 1mo)] P 00 + N 2mh S h P 01 P 10 + N 2mh S h P 11 P 00 + N 1uh D h P 10 P 01 + N 1uh D h P 11 A.2 Wheaon's model In Wheaon (1990) here is no renal marke. All households are homeowners and hey can be in one of hree occupancy saes. There is a measure N 1mo of households living in a house hey like; N 2mh are he mached households ha own also a second dwelling; N 1uh are mismached households (living in a house hey do no like). N 1mo households become mismached wih probabiliy α. There is a decenralized housing marke where N 1uh households nd a counerpary N 2mh and house prices are deermined by Nash bargaining wih equal bargaining power among buyers and sellers; N 1uh households ha successfully rade become N 2mh, while he N 2mh households become N 1mo. The oal number of households is 1 and he sock of houses is xed and equal o H. The number of vacancies is V = H 1. The Wheaon's model is dened on coninuous ime and he ransiions among saes are described by he following dierenial equaions: ( N 1uh = N 1uh (2α + m) + α 1 N 2mh) (A.1) ( N 2mh = mn 1uh 1 N 2mh ) V (A.2) N 1mo = N 1uh N 2mh (A.3) where m is he arrival rae for N 1uh households of a counerpary in he housing marke. Wheaon (1990) assumes ha m is a funcion of cosly search eor and he fracion of vacan unis: ( m E, V ) ( ; m 0, V ) = 0, H H m E > 0, 2 m E 2 < 0, m V/H 0 (A.4) 36

39 and he cos of eor is dened as c(e); c(0) = 0, c E > 0, 2 c E 2 > 0 (A.5) The presen discouned value of being in each of he hree occupancy saes, modied in order o consider propery axes, is dened by he following equaions: rv 1mo = u m τ 1 α(v 1mo V 1uh ) rv 2mh = u m τ 1 τ 2 + q(v 1mo V 2mh + P ) rv 1uh = u u τ 1 c(e) + α(v 1mo V 1uh ) + m(e)(v 2mh V 1uh P ) (A.6) (A.7) (A.8) where r is he discoun rae and q = m(e) N 1uh V is he arrival rae of a counerpary in he housing marke for N 2mh households. Housing prices are deermined by Nash barganining: P = V 2mh V 1uh + V 2mh V 1mo 2 (A.9) Since households selec he level of search eor E so as o maximize he value of being mismached, in equilibrium search mus be conduced unil he marginal gain from he las uni of search eor equals he cos of ha eor. Therefore, he nal equaion ha close he model is C(E) E = m(e) E ( ) V 2mh V 1uh P (A.10) Figure A.1: Eecs of housing propery axes on house prices in Wheaon's model 37