The Effects of Housing Prices and Monetary Policy in a Currency Union

Transcription

1 WP/11/6 The Effecs of Housing Prices and Moneary Policy in a Currency Union Oriol Aspachs-Bracons and Pau Rabanal

2 211 Inernaional Moneary Fund WP/11/6 IMF Working Paper Research Deparmen The Effecs of Housing Prices and Moneary Policy in a Currency Union 1 Prepared by Oriol Aspachs-Bracons and Pau Rabanal Auhorized for disribuion by Gian Maria Milesi-Ferrei January 211 Absrac This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. The recen boom-and-bus cycle in housing prices has refreshed he debae on he drivers of housing cycles as well as he appropriae policy response. We analyze he case of Spain, where housing prices have soared since i joined he EMU. We presen evidence based on a VAR model, and we calibrae a New Keynesian model of a currency area wih durable goods o explain i. We find ha labor marke rigidiies provide sronger amplificaion effecs o all ype of shocks han financial fricions do. Finally, we show ha when he cenral bank reacs o house prices, he non-durable secor suffers an imporan conracion. As a resul, he boom-and-bus cycle would no have been avoided if Spain had remained ouside he EMU during he period. JEL Classificaion Numbers: E44; E52, F41. Keywords: Housing, Moneary Policy, Financial Consrains. Auhor s Address: oaspachs@lacaixa.es; prabanal@imf.org 1 This paper is forhcoming in he Inernaional Journal of Cenral Banking. We hank Jordi Galí, Rober King (our discussan) and wo anonymous referees for useful commens. This paper should no be repored as reflecing he views of Caixa d Esalvis i Pensions de Barcelona ( la Caixa ) or of he Inernaional Moneary Fund. Any errors and omissions are our own. Oriol Aspachs-Bracons is an economis a Caixa d Esalvis i Pensions de Barcelona. Pau Rabanal is an economis a he Inernaional Moneary Fund s Research Deparmen.

3 2 Conens Page I. Inroducion...4 II. The VAR Response o Housing Demand and Ineres Rae Shocks...6 A. Daa...7 B. Resuls...8 C. Variance Decomposiion...9 D. Hisorical Decomposiion...9 E. Robusness...9 III. The Model...1 A. Households...1 B. Wage Seing...14 C. Producers...15 C.1 Final goods producers...15 C.2 Inermediae goods producers...16 D. Closing he Model...18 D.1 Marke clearing condiions...18 D.2 Moneary policy rule...19 IV. Calibraion...19 A. Impulse Response Funcions...21 A.1 Moneary policy shock...21 A.2 Housing preference shock...22 V. Robusness Checks...23 A. The Role of Labor Marke Fricions...23 B. The Effecs of Financial Fricions...24 VI. The Effecs of Belonging o he EMU...26 A. Impulse Response from The Model...27 B. Counerfacual Simulaion of The Model...28 VII. Concluding Remarks...29 References...31 Appendix: Linear Approximaion...34 Tex Table 1. Calibraed Parameers of he Model Variance Decomposiion VAR...39 Figures 1. Nominal house prices and ineres raes Residenial invesmen and ineres raes...4

4 3 3. Morgage credi and he curren accoun Demographic paerns Impulse response from VAR, moneary policy shock Impulse response from VAR, housing demand shock Hisorical decomposiion from he VAR Impulse response o moneary policy shock Impulse response o a housing preference shock Impulse response o a moneary shock. The role of labor marke fricions Impulse response o a housing preference shock. The role of labor marke fricions Impulse response o a moneary shock. The role of financial fricions Impulse response o a housing preference shock. The role of financial fricions Impulse response o housing preference shock Counerfacual simulaion of he model...52

5 4 I. Inroducion The recen boom and bus cycle in housing prices in many advanced economies has refreshed he debae on he drivers of housing cycles and he role of he housing secor in amplifying economic volailiy, as well as he appropriae response of he moneary auhoriies. The case of Spain is of special ineres since is recen economic expansion has been characerized by susained growh of residenial invesmen, privae consumpion, credi and housing prices for more han a decade. Moreover, during his period nominal and real ineres raes fell o excepionally low levels during he convergence period in order o ener he european Economic and Moneary Union (EMU). As a resul, a large curren accoun de ci emerged, reaching almos 1 percen of GDP a he peak of he cycle in 27. In addiion o growing exernal imbalances, a special source of concern for he Spanish economy was he loss of moneary policy auonomy afer enering he EMU. In counries wih heir own naional currency and moneary policy, such as he US, he UK, Ausralia and New Zealand, he cenral bank can increase ineres raes o slow down he growh rae of housing prices (alhough in pracice hey were no successful in doing so in he mos recen cycle), and also respond o a housing price collapse. 1 However, Spain belongs o he EMU, and he European Cenral Bank ses raes according o he in aion rae of he Harmonized Index of Consumer Prices (HICP) of he Euro area as a whole. This means ha moneary policy canno be he rs line of defense in response o negaive secor- and counry-speci c shocks. The recen evoluion of he Spanish economy since 1996, including he housing marke boom-bus cycle, is shown in Figures 1 hrough 4. Spain su ered from wo developmens going o he EMU: a loss of moneary auonomy and a large decline in ineres raes. The period of convergence o and adopion of he euro ( ) was also characerized by increased residenial invesmen and house price growh raes. The demand for housing was furher increased by he high levels of immigraion and he baby boom generaion (which peaked in he early 197s in Spain) urning ino adulhood, fuelling residenial invesmen and even furher increasing house prices. This increase in housing prices raised wealh and borrowing capaciy of house owners who, in principle, could use hese mechanisms o nance oher consumpion. 2 The growing curren accoun de ci is he oher indicaor of he magniude of he consumpion and borrowing boom, and he large 1 Mishkin (27) suggesed ha in response o a 2 percen housing price drop in he Unied Saes, he Federal Reserve should cu ineres raes beween 75 and 175 basis poins, depending on he assumpions abou he ransmission mechanism. 2 However, we should noe ha esimaes of he marginal propensiy o consume ou of housing wealh in Spain are lower han in oher counries. Bover (25) obains esimaes of abou :1-:2.

6 5 savings-invesmen imbalance was nanced from abroad. Since lae-27, he boom cycle has urned ino a bus. Hence, in his paper we sudy he response of a small economy in a currency union (such as he Spanish one) o ucuaions in housing prices and residenial invesmen. Firs, we presen VAR evidence ha shows he response of privae consumpion, residenial invesmen, aggregae GDP, and real house prices o an ineres rae shock and o a housing demand shock. We show ha a decrease of ineres raes and a posiive housing demand shock lead o a rise in boh nal consumpion and residenial invesmen, a nding labelled as comovemen in he lieraure when sudying US daa. We raionalize our ndings by building a wo-counry, wo-secor model of a currency union in he spiri of Benigno (24) and Rabanal (29). The model includes durable and non-durable goods. Holding durables (i.e. housing) no only provides uiliy o he consumer bu is also a vehicle for savings. In addiion, he inernaional dimension of he model implies ha he savings and invesmen balance need no hold period per period a he counry level. This will allow us o explain how increased credi demand in one counry of a currency union can be me hrough funds coming elsewhere in he union. We calibrae he model, and examine he reacion of domesic variables and he nominal ineres rae o a moneary policy shock and a demand/preference shock in he durable secor. Overall, he demand shock and he ineres rae shock produce e ecs on he main aggregaes of he economy similar o he ones observed in he VAR. Then, we conduc a robusness exercise o undersand how imporan are labor marke and credi marke rigidiies in undersanding he ransmission of housing demand and moneary shocks in he economy. As opposed o he exising lieraure ha sresses he role of nancial fricions and borrowing consrains o explain comovemen, we nd ha he e ec of labor marke rigidiies has imporan implicaions for he persisen response of variables o shocks, and o explain he comovemen beween consumpion and residenial invesmen. Financial fricions amplify he moneary and preference shocks, bu heir quaniaive e ecs are raher small when compared wih a model wih homogeneous agens and no credi consrains (bu wih labor marke fricions). This does no mean credi consrains are no imporan. Bu hey need o be modelled in a di eren way han has been included in he lieraure. One avenue o sudy would be o allow agens o borrow agains heir labor income, in addiion o housing collaeral. In he las secion of he paper we sudy he policy opions for a small open economy such as he Spanish one, ha faces large secor-speci c shocks. In addiion o our benchmark currency union model, we consider wo addiional cases. In he rs one, we assume ha Spain follows a Taylor rule which is similar o he one

7 6 followed by he res of he EMU. In he second case, we examine wha would have happened if he Spanish auhoriies, ouside he euro, had ried o "lean agains he wind" and included house price in aion in heir reacion funcion. We nd ha if Spain had followed an in aion argeing regime wih a pure oaing exchange rae, he moneary policy reacion o a domesic demand shock would no have been very di eren han ha of belonging o a currency union. If we allow he cenral bank o reac o house prices, he iniial boom in housing in aion and residenial invesmen can be reduced. However, o achieve sabiliy in he housing marke using he nominal ineres rae as a policy ool leads o an imporan and persisen conracion in he non-durable secor. Hence, even if he Spanish auhoriies had kep moneary policy managemen, i is no clear ha hey would have chosen o "lean agains he wind". I is imporan o noe ha his paper sudies he period, and he exercise only focuses on he possible coss of no being able o address demand-speci c shocks in one secor or counry using moneary policy. We show ha hese coss are small. Our model does no evaluae oher imporan coss of no belonging o he EMU such as hose associaed wih exchange rae volailiy (e.g. higher domesic ineres raes and lower inernaional rade) which could a ec growh. The res of he paper is organized as follows. In secion II, we presen some VAR-based evidence. In secion III, we presen he model, and in secion IV we discuss a lengh he quaniaive implicaions of he model. The robusness checks are presened in secion V and in secion VI we analyze he e ecs of belonging o he EMU. We leave secion VII for concluding remarks. II. The VAR Response o Housing Demand and Ineres Rae Shocks In his secion, we presen evidence on he response of main macroeconomic variables o housing demand and ineres rae shocks wih he help of a Vecor Auoregressive (VAR) model. Several papers in he lieraure have sudied he response of durable and non-durable consumpion o a moneary policy shock using a VAR and he recursive ideni caion scheme of Chrisiano, Eichenbaum, and Evans (1999, 25). This approach consiss of idenifying he e ec of he moneary policy shock by using he Cholesky decomposiion of he variance-covariance marix of he reduced form residuals of he VAR. Papers following his approach include Erceg and Levin (26) and Monacelli (29). In addiion, we seek o idenify a housing demand shock from he VAR. We do so by assuming ha he housing demand shock a ecs he real price of housing wihin a period, bu i does no a ec is quaniy: in he shor run he supply of housing is xed, and demand shocks mus be absorbed via price movemens. In pracice, his

8 7 shock leads o an increase of residenial invesmen and prices, hereby con rming our labeling. In he las par of he secion, we discuss several robusness resuls ha include: inroducing euro area variables ino he sysem, exending he sample period, and using sign resricions o idenify he housing demand shock. We esimae he following VAR using k variables: LX Y = C + A j Y j=1 j + Bu where Y is a kx1 vecor of observable variables, C is a kx1 vecor of consans, A j are kxk marices ha collec he e ec of endogenous variables a lag j on curren variables, L is he lag lengh in he VAR, B is a kxk lower riangular marix wih diagonal erms equal o uniy, and u is a kx1 vecor of zero-mean, serially uncorrelaed shocks wih diagonal variance-covariance marix. The vecor of endogenous variables is divided as follows: Y = Y 1 R Y 2, where Y 1 is a group of macroeconomic variables predeermined when moneary policy decisions are aken, R is a relevan ineres rae, and Y 2 conains he variables a eced conemporaneously by moneary policy decisions. As is cusomary in he lieraure, o idenify he ineres rae shock we place he nominal ineres rae afer he macroeconomic variables. On he oher hand we assume ha house prices can respond o changes in moneary policy wihin a period: as an asse price, housing prices are likely o respond conemporaneously o changes in he nominal ineres rae, so we include hem in Y 2. Hence, we idenify he housing demand shock as he shock ha a ecs housing prices wihin a period, afer aking ino accoun he e ec ha changes in he ineres rae have on housing prices. 3 A. Daa The vecor of observable variables is divided he following way. In Y 1 we include: (i) real household consumpion of nal goods in Spain, (ii) real residenial invesmen in Spain, and (iii) real GDP in Spain. We use as a relevan ineres rae (R ) he reference inerbank rae. Finally, we include in Y 2 real house prices in Spain. All variables are inroduced in he VAR in levels afer aking naural logarihms, excep for he nominal ineres rae ha we inroduce direcly in levels. Privae consumpion, residenial invesmen and GDP come from Spanish naional 3 We have also esimaed a VAR wih he ordering Y = Y 1 Y 2 R and he resuls are very similar o he ones we presen.

9 8 accouns daa and are de aed by he Spanish GDP de aor. Nominal housing prices come from he OECD and are de aed by he HICP in Spain. In sudies involving US daa he Federal Funds rae is ypically he variable used as an indicaor of he sance of moneary policy, following he sudy of Bernanke and Blinder (1992). Spain relinquished is moneary policy auonomy when i joined he EMU January 1s, 1999, and hence a domesic reference rae is no longer available. We choose he 3-monh inerbank rae as he reference ineres rae. From 1999 we use he 3-monh Euribor rae, and before he EMU period we use he 3-monh MIBOR rae (he Madrid Inerbank rae). Noe ha because of his reason, we call our shock an ineres rae shock raher han a moneary policy shock in he VAR. The relevan inerbank ineres rae for morgages in Spain is he 12-monh rae. In pracice, using he 3-monh or he 12-monh rae delivers he same resuls, since he reference rae se by he European Cenral Bank, he 3-monh inerbank rae and he 12-monh inerbank rae move very closely ogeher. We esimae he VAR from 1997:1 o 28:4 a a quarerly frequency, wih 2 lags. While he euro was launched in 1999, moneary policy in Spain followed is european counerpars closely in , and his allows us o include 8 more observaions in he sysem. B. Resuls In Figures 5 and 6 we presen he impulse responses of he ve variables o an increase in ineres raes and a housing demand shock. We presen he mean and 85 percen con dence bands. 4 In order o beer inerpre he VAR evidence, we presen impulse-responses o a 25 basis poins ineres rae shock and o a housing demand shock ha increases residenial invesmen by 1 percen in he second period (by consrucion, he housing demand shock only a ecs prices in he iniial period). An ineres rae shock of 25 basis poins is followed by furher increases in he ineres rae, which leads o a decline of real consumpion of.6 percen afer 12 quarers and a decline of 2 percen of residenial invesmen afer 7 quarers. This higher responsiveness of durable consumpion and residenial invesmen has been found in oher papers such as Erceg and Levin (26) and Monacelli (29). The increase in ineres raes also leads o a decline of real house prices of 2 percen afer 7 quarers. On he oher hand, he housing demand shock leads o an increase of real house prices of 8 percen and an increase of residenial invesmen of 1 percen afer one period. There are signi can spillovers o he res of he economy and boh privae consumpion and real GDP increase by more han 1 percen afer 1 quarers. These are he feaures ha our model will reproduce, in paricular he comovemen 4 Given he shor sample, i is di cul o obain signi cance a he convenional 95 percen inerval.

10 9 in he response of boh privae consumpion and residenial invesmen o shocks. C. Variance Decomposiion The resuls of he variance decomposiion are presened in Table 2. Since we aemp o idenify he e ecs of ineres rae and housing demand shocks, we presen he fracion of he variance decomposiion for hese wo shocks only, and assign he remaining share o he aggregae of he oher unspeci ed hree shocks in he VAR sysem. Housing demand shocks explain a small fracion of he variance decomposiion of privae consumpion and real GDP a shor horizons, bu a longer horizons (saring a 1 quarers) heir conribuion rises o abou 25 percen. Housing demand shocks explain a similar fracion of he variance decomposiion of invesmen a boh shor and long horizons. Ineres rae shocks explain an imporan par of he variance decomposiion of real variables a long horizons, beween 1 and 2 percen depending on he variable. Finally, boh ineres raes and house price variance decomposiions are driven by heir own shock a shor horizons, bu by he "oher shocks" in he model (6 percen of he share) a longer horizons. D. Hisorical Decomposiion Figure 7 presens he conribuion of each shock in explaining he deviaion of he acual daa from he balanced growh pah of he sysem in he absence of shocks. I becomes eviden ha mos ucuaions are driven by he shocks ha we do no aemp o idenify in he VAR, bu boh moneary policy and housing demand shocks also played an imporan role. I is ineresing o noe ha conracionary moneary policy shocks and negaive housing demand shocks help explain he slowdown in A he same ime, boh shocks, and in paricular housing demand shocks, had a very srong e ec in he mos recen boom since 24, fueling house prices, residenial invesmen, privae consumpion, and real GDP. E. Robusness We have conduced several robusness exercises wih our VAR-based evidence, which are no presened here o save space, bu are available upon reques. In he rs exension, we include he Harmonized Index of Consumer Prices (HICP) in aion and real GDP growh in he euro area o conrol for he endogenous response of ineres raes. In his case, we nd ha he qualiaive resuls do no

11 1 change. This suggess ha, from he Spanish perspecive, changes in ineres raes can be seen as purely exogenous shocks. Second, we have also experimened by using he sample period All he resuls are very similar o he ones presened here, excep in he response of real house prices o a moneary policy shock, which is small and nonsigni can. Finally, we have used sign resricions as in Uhlig (25) and Cardarelli e al. (29) o idenify he e ecs of housing demand, housing supply and moneary policy shocks, and found ha he main message of Figures 5 and 6 does no change. III. The Model The heoreical framework consiss of a general equilibrium wo counry, wo secor model in a single currency area. The counries are of size n and 1 n, and each of hem produces wo ypes of goods, durables and non-durables, under monopolisic compeiion and nominal rigidiies. Only he non-durable goods are radable. Producers of he nal durable good sell is produc o domesic households only in each counry, which allows hem o increase heir housing sock. For his reason, we use he erms durable good producion and residenial invesmen inerchangeably hroughou he paper. Since our VAR analysis has only focused on he e ecs of moneary and demand shocks on he housing secor and he spillover e ecs o he macroeconomy, he model will only include hese shocks, so we leave aside echnology shocks in he curren analysis. In wha follows, we presen he home counry block of he model. The analogous foreign counry variables will be denoed by an aserisk. A. Households Each household j in he home counry maximizes he following uiliy funcion: ( X 1 E " log(c j "C 1 ) + (1 ) D log(d j ) = L j #) (1) where C j denoes consumpion of non-durable goods, D j denoes consumpion of durable goods and L j is he labor disuiliy index. D is a housing preference shock, which follows an AR(1) process in logs.

12 11 The uiliy funcion denoes exernal habi formaion, as in Smes and Wouers (23) and Iacoviello and Neri (21). is he discoun facor and is he inverse elasiciy of labor supply. The parameer " denoes he imporance of he habi sock, which is las period s aggregae consumpion (C 1 ). In addiion, consumpion of non-durables is an index composed of home and foreign consumpion goods: C j = 1 C C j C 1 1 C H; + (1 ) C C j C 1 C F; C C 1 ; where C > (2) and where C j H; and Cj F; are, respecively, consumpion of he home non-durable goods and consumpion of foreign non-durable goods by he home agen. is he fracion of domesically produced non-durables a home. Finally, following Iacoviello and Neri (21), we assume ha here is imperfec subsiuabiliy of labor supply across secors, such ha he labor disuiliy index can be wrien as: L j = L L C;j 1+L + (1 ) L L D;j 1+L 1 1+ L ; where L > (3) and where L i;j denoes hours worked by household j in each secor i = C; D: is he economic size of each secor. This imperfec subsiuabiliy implies ha here is a cosly labor reallocaion across secors following a shock. Noe ha when L = he aggregaor is linear in hours worked in each secor, so here are no coss of swiching from working in one secor o he oher. 5 The budge consrain of he home agen, in nominal erms, is given by: P C C j +P D I D;j +P A A j +B j R ~ 1 B j 1 + W C L C;j X C + W D X D L D;j +(R A +P A )A j 1 + j (4) where P C and P D are he price indices of durable and non-durable goods, o be de ned below, W i is he nominal wage in each secor i = C; D, and B j denoes non-coningen nominal asses ha are raded among households across he moneary union, and ha pays (or coss) a gross nominal ineres rae R ~ > 1: Following Iacoviello and Neri (21), X j denoes he mark up (due o monopolisic compeiion in he labor marke) beween he wage paid by inermediae rms and he wage ha households receive (he deails of he nominal rigidiies in he labor marke are discussed below). j denoes nominal pro s, because rms are 5 Labor marke rigidiies could be a proxy for oher real rigidiies, such as produc marke enry, ha he model does no include.

13 12 ulimaely owned by households. A denoes he level of land owned by households, which is purchased a a price P A and which is rened o durable inermediae goods producers a a renal rae of R A. denoes residenial invesmen o increase he housing sock. We assume ha he law of moion of he housing sock evolves as follows: I D;j D j = (1 )D j 1 + " 1 S ID;j I D;j 1!# I D;j (5) where denoes he rae of depreciaion of he housing sock and, following Chrisiano, Eichenbaum, and Evans (25), we inroduce an adjusmen cos funcion, S (:), which is convex (i.e. S () > ). Furhermore, in he seady sae S = S= and S > : The aim of inroducing his cos is o allow for he possibiliy ha he model can generae hump-shaped responses of residenial invesmen o shocks. We assume ha households in he home counry have o pay a premium above he union-wide riskless nominal ineres rae as he counry s deb level as a percenage of GDP increases. This assumpion is needed o obain a well-de ned seady sae for he aggregae level of deb. 6 The relevan ineres rae for he home-counry households and he union-wide ineres are relaed as follows: B ~R = R exp P Y B P Y 1 (6) where P is he aggregae price level, o be de ned below, and Y is real GDP, also o be de ned below. R is he riskless ineres rae and is he risk premium elasiciy. This risk premium depends on aggregae variables, such ha each household akes his e ec as given when choosing beween consuming durables, non-durables, and saving. Noe ha he risk premium is declining in he ne foreign asse posiion of he counry as a percenage of GDP, B P Y. We can separae he household s decision in a wo sage process. Firs, households choose he amoun of labor o supply o each secor, and he consumpion of durables and non-durables. Second, hey allocae how much o spend on home and foreign produced goods, aking ino accoun ha, 6 See Schmi-Grohé and Uribe (23).

14 13 P C C = P H; C H; + P F; C F; where P H; denoes he price of home non-durable consumpion goods and P F; he price of foreign non-durable consumpion goods. The variables corresponding o he foreign counry are denoed wih an aserisk, bu he prices of foreign non-durable consumpion goods do no carry i because hey are also se in euros, and here is no price discriminaion across counries. The rs order condiions o he household problem are given by: 7 U C = P C (7) U D = (1 )E +1 (8) I P D D = 1 S I D 1 " I S D I D I +E I D 1 I D +1 S D +1 I D 2 # +1 : (9) 1 I D I D Absen adjusmen coss o residenial invesmen, hese hree equaions can be reduced o he following condiion: P D P C = 1 D (C "C 1 ) D + (1 )E C "C 1 P D C +1 "C +1 P C +1 : Noe ha if he durable good was in fac non-durable (i.e. = 1), his condiion simply saes ha he marginal uiliies of consumpion should equal relaive prices. Since he durable good has a residual value he following period, his induces he exra-erm of holding an addiional uni of he durable good. A sandard Euler equaion for he consumpion of non-durable goods is: 1 = R ~ P C E P+1 C C "C 1 C +1 "C : (1) 7 Since all households behave he same way, we drop he j subscrips in wha follows.

15 14 A similar Euler equaion for land is as follows: ~R = E R A +1 + P A P A +1 (11) such ha households are indi eren beween invesing in land and riskless bonds. The allocaion of nondurable consumpion expendiures beween home and foreign-produced goods is: C PH; C H; = C (12) C F; = (1 ) P C PF; P C C C : (13) The price index for non-durables is (he CPI): P C 1 C = (P H; ) 1 C + (1 ) (P F; ) 1 C : (14) The uiliy maximizaion problem of foreign counry households is quie similar. We assume ha he funcional forms for preferences are he same across counries, bu allow for di eren parameer values. Tha is, is he weigh of non-durables in he uiliy funcion, and he fracion of domesically produced non-durables. B. Wage Seing Nominal wage sickiness is inroduced as in Smes and Wouers (27) and Iacoviello and Neri (21), so we omi mos funcional forms here and refer he ineresed reader o hose papers. Households supply homogeneous labor services o unions. These unions di ereniae hese labor services and se wages subjec o a Calvo (1983)-ype resricion, where he probabiliies in each secor of no being able o readjus wages in a given period are C;W and D;W. They o er hese labor services o wholesale labor packers, who reassemble hese services ino homogeneous labor composies, which are in urn hired by inermediae rms from hese packers. Under Calvo wage seing and wih parial indexaion o pas non-durable (CPI) in aion (wih coe ciens ' C;W and ' D;W ), he wage-seing equaions can be loglinearized ino he following wage Phillips curves, where lower case variables denoe percen deviaions from seady-sae values:

16 15! C! C 1 + p C ' C;W p C 1 = E! C +1! C + p C +1 ' C;W p C + C;W c "c 1 + [(' ) + ] l C + (' )(1 )l D! C 1 " (15) where C;W = (1 C;W )(1 C;W ) C;W, and! D! D 1 + p C ' D;W p C 1 = E! D +1! D + p C +1 ' D;W p C + D;W c "c 1 + [(' )(1 ) + ] l D + (' )l C! D 1 " (16) where D;W = (1 D;W )(1 D;W ) D;W. C. Producers There is a coninuum of inermediae goods producers, indexed by h 2 [; n] in he home counry, and by f 2 [n; 1] in he foreign counry, ha are imperfec subsiues of each oher, and ha supply nal goods producers in each secor. There is a coninuum of nal goods producers in he wo secors ha operae under perfec compeiion and exible prices. Producers of he nal durable good sell heir producs o domesic households only in each counry. Producers of he nal non-durable good sell heir producs o domesic and foreign households. Hence, i is imporan o disinguish he price level of domesic non-durable consumpion goods, P H;, which does no coincide wih he price level of non-durables or CPI (P C ) because of he presence of impored non-durable goods, whose price is P F;. C.1 Final Goods Producers In he durable secor, nal goods producers purchase inermediae goods producers and aggregae hem according o he following producion funcion: Y D " 1 Z 1 n D Y D (h) D 1 D n dh # D D 1 (17) Pro maximizaion delivers he following demand for individual, inermediae

17 16 non-durable goods: Y D (h) = P D P D (h) D Y D ; (18) where he price level is given by imposing he zero-pro condiion, P D 1 n Z n P D (h) D D dh : In he non-durable goods secor, expressions are similar bu wih an appropriae change of noaion since he price level of domesic non-durables and of a baske of durables is no he same. The aggregae producion funcion is: Y C " 1 1 C n Z n Y C (h) C 1 C dh # C C 1 ; (19) individual inermediae non-durable goods demand is: where he price level is: Y C (h) = P H P H (h) C Y C ; (2) P H 1 n Z n P H (h) C C dh : C.2 Inermediae Goods Producers There is a coninuum of inermediae goods producers, indexed by h 2 [; n] in he home counry, and by f 2 [n; 1] in he foreign counry, ha are imperfec subsiues of each oher, and ha supply nal goods producers in each secor. Inermediae goods producers face a Calvo-ype resricion when seing heir price. In each period, a fracion 1 i in each secor (i = C; D) receives a signal o rese prices opimally. In addiion, a fracion i (i = C; D) index heir price o las period s secorial in aion rae whenever unable o reopimize.

18 17 Inermediae nondurable goods in boh counries are produced wih labor: Y C (h) = L C (h); for all h 2 [; n]; (21) Y C (f) = L C (f); for all f 2 [n; 1]: Inermediae goods in he durable secor are produced combining land and labor wih he following Cobb-Douglas producion funcion: Y D (h) = (A 1 ) 1 D L D (h) D ; for all h 2 [; n]; (22) Y D (f) = (A 1 ) 1 D L D (f) D ; for all f 2 [n; 1]; where D denoes he labor share in he housing secor. In he remaining par of his subsecion, we work ou he condiions for he home counry rms pricing decisions. In he nondurable secor, cos minimizaion implies ha he real marginal cos of producion equals he real wage: MC C = W C : (23) P C In he durable secor, afer imposing ha he supply of land is xed (A = A), he marginal cos is given by: MC D = 1 W D D P C L D 1 D A (1 D ) ; (24) where we have subsiued for he opimal expression of he renal rae of land: 8 1 R A = D D W D L D A : Firms in he durable secor face he following maximizaion problem: 82 X 1 >< Max P D (h)e k 6 D ;+k 4 >: k= P D (h) P D D +k 1 P D 1 P D +k MC D +k Y D +k (h) 9 >= >; subjec o fuure demand 8 We choose he level of A, such ha he level of real wages is he same across secors in he seady-sae.

19 18 Y D +k (h) = " P D (h) P D P+k D +k 1 P D 1 D # D Y D +k; where ;+k = k +k is he sochasic discoun facor, and is he marginal uiliy of non-durable consumpion. The opimal choice is given by: ^P D P D = D ( D 1) E 8 >< >: 1X k k D +k k= 1X k k D +k k= ky s=1 ( D +s 1) D ky s=1 D +s ( D +s 1) D D +s! D MC D +k Y D! 1 D Y D +k +k 9 >= >; (25) Given he assumpions abou Calvo pricing, he evoluion of he price level is: h i P D = D P D 1 D D 1 D 1 1 D 1 D 1 + (1 D ) ^P D : (26) Firms in he non-durable secor face a similar maximizaion problem, and hence he opimal price and he evoluion of he price level have similar expressions, wih he appropriae change of noaion. D. Closing he Model D.1 Marke Clearing Condiions In each inermediae good, supply equals demand. We wrie he marke clearing condiions in erms of aggregae quaniies. Hence, we muliply per-capia quaniies by populaion size of each counry. Toal producion in he non-durable secor is equal o oal domesic consumpion and expors: Y C = nc H; + (1 n) C H; (27) while residenial invesmen is used o increase he domesic housing sock: Y D = n [D (1 )D 1 ] : (28)

20 19 Toal hours worked equals labor supply in each secor: Z n Z n L C (h)dh = L D (h)dh = Z n Z n L C;j dj (29) L D;j dj: (3) Marke clearing in he inernaional bonds marke is: nb + (1 n)b = : (31) Finally, he evoluion of aggregae ne foreign asses is: nb = n ~ R 1 B 1 + (1 n) P H; C H; np F; C F; : (32) D.2 Moneary Policy Rule In order o close he model, we need o specify a rule for moneary policy, which is conduced by he European Cenral Bank wih an ineres rae rule ha arges CPI in aion and also exhibis ineres rae ineria: R = R P EMU =P EMU 1 EMU 1 R R R 1 exp(" m ): (33) where he euro area CPI is given by a geomeric average of he home and foreign counry CPIs, using he counry size as a weigh: P EMU = P C n P C 1 n : IV. Calibraion In he seady sae, we assume zero in aion, a rade balance of zero, and ha he ne inernaional posiion of boh economies is zero. Therefore, we only need o solve for he per-capia values of he home counry, which are he same as hose in he foreign counry. We also assume ha he degree of monopolisic compeiion in boh ypes of goods is he same ( C = D = ), and hence he raio of prices is one. Now, we solve for he levels of consumpion of durables, non-durables, hours, and he economic size of each secor. The opimal seady-sae raio of durable o non-durable consumpion is: C D = [1 (1 )] 1 = : (34)

21 2 The fracion of spending allocaed o non-durable consumpion over oal spending () is equal o: C C + D = : Noe ha and canno be calibraed independenly. Given values for,,, we can solve for he value of in he uiliy funcion. To ensure ha he level of real wages in boh secors is he same (despie di eren labor shares), we need o calibrae A = 1 1 L D 1 D D. As a resul, from he labor supply condiions by households, (1 )L C = L D ; (35) which means ha agens spend a fracion of ime working in he non-durable secor, and a fracion 1 in he durable secor. Table 1 summarizes he values of he exogenous and endogenous parameers of he model. We se as he home counry Spain, and he foreign counry he res of he EMU. Hence, we se he size of he home economy o n = :1. We se he size of he consrucion secor a 1 = :1, boh in Spain and in he EMU, which is roughly he average size for he value added of he consrucion secor in he las decade. We calibrae he bilaeral rade parameer () based on oal impors from he EMU o Spain over oal spending, and calibrae is analogous parameer in he EMU ( ) in a similar way. For he parameer capuring he deb elasiciy o he domesic ineres rae, he echnology, preference and nominal rigidiies parameers, we use he esimaed values in a companion paper of ours. 9 In ha paper, we imposed he same parameer values across counries (excep he bilaeral impors raio), so we follow his sraegy here. Therefore, he value for is xed o :2, which capures he idea ha ineres raes spreads beween Spain and he EMU have been negligible during his period. In Aspachs-Bracons and Rabanal (21), he poserior mean esimae for he labor marke rigidiies, L ; is 1:2, a value which is very similar o he one esimaed by Iacoviello and Neri (21) using US daa. We also calibrae he degree of habi formaion ", he elasiciy of labor supply, he elasiciy of subsiuion beween home and foreign goods C, and he invesmen adjusmen cos parameer, from our companion paper. Having calibraed he real side of he economy, we now proceed o discuss he 9 In Aspachs-Bracons and Rabanal (21), we use sandard Bayesian mehods o esimae a DSGE model similar o he one presened here for Spain and he res of he EMU using daa beween 1995 and 28.

22 21 calibraion of he degree of nominal rigidiy in each secor and counry. In he lieraure, here is a long sanding debae on he degree of nominal rigidiies beween housing and he oher secors of he economy, and how his migh a ec he ransmission mechanism of moneary policy. For insance, Carlsrom and Fuers (27) use he evidence on frequency of price adjusmens in he durable and non-durable secors of Bils and Klenow (24) o argue ha prices in he housing secor are more exible han in he consumpion goods secor. Using his calibraion is problemaic because, in he model, a moneary conracion leads o an expansion of residenial invesmen ha is a odds wih he daa. This resul arises because he di ering degree of nominal rigidiy across secors causes a srong movemen of relaive prices. We also use he values esimaed in Aspachs-Bracons and Rabanal (21) o calibrae he nominal rigidiies. Hence, we se prices o be more sicky in he non-durable secor, C = :87, han in durable goods, D = :34. Nominal rigidiies parameers are assumed o be he same beween Spain and he res of he EMU. 1 We assume ha he Calvo loeries for wage seing imply average duraions of wage conracs of one year ( C;W = D;W = :75) and we also assume full indexaion o las period s in aion, given he way wage conracs are se in Spain. 11 Finally, we also calibrae he parameers of he Taylor rule according o he esimaes in our companion paper. A. Impulse Response Funcions In his secion, we discuss he main feaures of he model by presening he impulse response funcions of a moneary policy shock and a housing preference shock. We obain he model s dynamics by aking a log-linear approximaion around he seady sae. In Appendix A we deail he full se of linear equaions of he model. A.1 Moneary Policy Shock Figure 8 presens he impulse response funcions of he main variables in Spain o an expansionary moneary policy shock in he euro area. We choose he size of he shock " m in he Taylor rule expression (33) o simulae an increase of 25 basis poins 1 Assuming ha durable prices are exible does no change he qualiaive resuls of our analysis. Aspachs-Bracons and Rabanal (21) use informaion conained in survey evidence for he euro area in, as explained in Fabiani e al. (26), as priors. 11 Smes and Wouers (23) obain a poserior mean of :66 for backward looking wage indexaion in he euro area. Using his paramer value insead of full indexaion does no change he resuls.

23 22 on impac in he nominal ineres rae. Following he shock, consumpion of boh good ypes declines. Similar o wha we obained in he VAR, he e ec is quaniaively sronger in he durable secor, alhough we have rouble maching he long lags in he ransmission mechanism presen in he daa. Noe ha we obain a srong comovemen beween boh secors even hough he degrees of nominal rigidiy in price seing are di eren across secors. Why is his he case? Afer a moneary policy ighening, and in response o lower demand, durable good producers can decrease prices faser han he non-durable producers and, hence, he relaive price beween durables and non-durables decreases (jus as in he VAR-based evidence). Wage sickiness limis he degree o which real uni labor coss di er across secors and, hence, he movemen in relaive prices is lower even under asymmeric nominal rigidiies in price seing. 12 In addiion, cosly labor reallocaion limis he degree o which secorial oupu can di er due o di eren labor inpus. Hence, as we discuss in he following secion, labor marke and wage rigidiies are key o explaining he daa. A.2 Housing Preference Shock Nex, we examine he e ecs of a housing preference shock in Figure 9. In heir sudy of he US economy, Iacoviello and Neri (21) conclude ha hese ype of shocks explain a signi can fracion of he volailiy of house prices and residenial invesmen. Darracq-Parriès and Noarpiero (29) reach a similar conclusion when looking a euro area daa, and Aspachs-Bracons and Rabanal (21) nd a similar resul when using daa for Spain and he euro area. In he conex of our model, one could see hese demand pressures as semming from populaion changes: increased immigraion, he baby boom generaion ha in Spain peaked in he 197s, and changes in social aiudes ha reduce he number of persons per households and increase he number of household unis. The housing demand shock is normalized such ha residenial invesmen increases abou 1 percen above is long-run value, and he shock has an AR(1) coe cien of.9. The preference shock in he durables secor also leads o an increase in he relaive price of durables. 13 Given he small size of he Spanish economy wih respec o he Euro area, ineres raes barely reac o developmens in he Spanish economy, allowing i o experience a long-lived expansion in his secor. Noe also ha non-durable oupu slighly increases wih he housing demand shock, which 12 Di Ceccio (29) nds a similar resul in a wo-secor RBC model. 13 Noe ha since he model soluion is linear, he e ecs of he shock are proporional o he size of he shock. In a non-linear world, a shock ha increases residenial invesmen by 1 percen could have proporionally larger e ecs han a shock ha increases invesmen by, le s say, 1 percen.

24 23 coincides wih he VAR evidence presened above. However, as in Iacoviello and Neri (21), he posiive response of non-durable consumpion is quaniaively small. In he following subsecion, we seek o undersand which mechanism in he model generaes he comovemen beween he wo secors. V. Robusness Checks As argued by Calsrom and Fuers (27) and Monacelli (29), if prices are exible in one secor bu sicky in he oher, hen a moneary policy conracion will imply ha oupu falls in he sicky price secor bu will increase in he exible price secor, conradicing VAR evidence using US daa. These papers sugges ha inroducing credi consrains and/or labor marke rigidiies migh help solve he comovemen problem even under heerogeneous degrees of nominal rigidiy. Hence, in his secion we sudy how he impac of moneary and demand shocks changes for di eren degrees of labor marke rigidiies and nancial fricions in he conex of our model. The key o explaining he VAR evidence is he lack of exibiliy in he labor marke. This is crucial when here are secor-speci c shocks. A. The Role of Labor Marke Fricions In Figures 1 and 11 we plo how he e ec of boh shocks changes as we remove wage sickiness and indexaion in boh secors (by seing C;W = D;W = C;W = D;W = ), and he degree of labor marke reallocaion (by seing L = ). When we removed a rigidiy we do so for boh counries. The rs resul o noe is ha we do no nd lack of comovemen under a moneary policy shock. Even when boh ypes of rigidiies are eliminaed, i.e. wages are allowed o be fully exible and he work force can be reallocaed insananeously across secors, non-durable oupu and durable oupu decrease afer a moneary policy ighening. Sicky wages are key o explaining he fac ha residenial invesmen reacs more srongly han non-durable consumpion o a moneary policy shock. When here are no labor marke rigidiies, real house prices experience a larger decline, and his ends o push demand for housing upwards because: a) housing becomes cheaper and b) i is expeced o appreciae from a low level. By limiing he variabiliy in real uni labor coss across secors and hence he relaive price di erenial, wage sickiness helps in lowering he response of residenial invesmen and helps explain is higher sensiiviy o ineres rae changes. Bu i does no a ec he comovemen properies of he model. Given ha he shock symmerically a ecs boh secors, he inroducion of labor marke reallocaion rigidiies does no a ec he resuls in an imporan way.

25 24 On he oher hand, since he housing preference shock is asymmeric by naure, he model needs he labor marke reallocaion rigidiies o explain he VAR evidence. In Figure 11, we sill calibrae he shock o deliver a 1 percen increase of residenial invesmen under he benchmark calibraion. We keep he same size of he shock as we change feaures of he model. When he workforce is allowed o be reallocaed insananeously afer he shock, non-durable oupu decreases while durable oupu increases by a larger amoun, making i impossible o explain comovemen. Wage sickiness helps in increasing he persisen response of he endogenous variables o he shocks, bu does no a ec he comovemen properies of he model under housing demand shocks. Therefore, he conclusion o his subsecion is ha cosly labor reallocaion helps explain he comovemen beween consumpion and residenial invesmen, while wage rigidiies increase he response and persisence o shocks. Hence, boh rigidiies are needed. B. The E ecs of Financial Fricions An imporan reason for concern for policy makers is he acceleraor e ec associaed wih ucuaions in housing prices. The nominal (and real) growh of he housing secor increases he amoun of collaeral available, allowing households o borrow more (or o save less in oher insrumens) and hence simulaes consumpion. There is a well esablished lieraure ha highlighs he role of collaeral as a key elemen in he ampli caion in he ransmission mechanism of shocks hrough business invesmen (see Kiyoaki and Moore, 1997; and Bernanke, Gerler and Gilchris, 1999). More recenly, a new srand of he lieraure has focused on he role of residenial invesmen in he ransmission mechanism (see Aoki e al., 24; Iacoviello, 25; Iacoviello and Neri, 21; and Monacelli, 29). We herefore proceed wih our analysis by sudying how he impac of each shock changes when he fracion of credi-consrained agens increase, and/or heir borrowing capaciy changes. To evaluae he imporance of nancial fricions we analyze how he impac of a moneary policy and housing preference shocks varies as he fracion of agens wih limied borrowing capaciy increases, and heir pledging capaciy changes. We exend he model of secion 3 by assuming ha a fracion 1 of agens face credi consrains. In paricular, we assume ha hese agens, which are ypically labelled as borrowers in he lieraure (see Monacelli, 29), are more impaien han he regular agens, whose mass is, and ha now we label as savers. We denoe all variables for borrowers wih a superscrip B.

26 25 E 8 >< >: 1X = B; log(c B;j "C B 1) + (1 ) D log(d B;j ) L B;j 1 + ' 1+' 39 >= 7 5 >; where all he indices of consumpion and hours worked, and he law of moion of he housing sock are he same as for he case of savers. Noe ha borrowers are more impaien and discoun he fuure a a lower rae: B <. Their budge consrain in nominal erms is given by: P C C B;j + P D I B;j + R ~ 1 S B;j 1 S B;j + W C L B;C;j X C + W D L B;D;j X D : (36) While borrowers can inves in housing, hey do no own land as savers do. Also, borrowers do no have access o inernaional capial markes, and hence hey obain credi from savers, who can rade in inernaional bonds subjec o an ineres rae di erenial, jus as in Secion 3. Borrowers face a collaeral consrain ha is ied o he curren value of durable goods (i. e. he housing sock hey own): S B;j (1 )D B;j P D : (37) One can inerpre he fracion as a down-paymen rae, and hence (1 ) is he loan-o-value (LTV) raio. When house prices increase, borrowers are able o borrow more in order o nance addiional durable and non-durable consumpion. 14 We presen he impac e ec of moneary and housing demand shocks as a funcion of and in Figures 12 and 13. All oher parameer values are se o hose in Table 1. We sudy an economy where = :5 and ha includes wo levels of indebedness of borrowers: a low level ( = :5, corresponding o an LTV raio of 5 percen) and a high level ( = :1, which implies an LTV of 9 percen). We obain similar resuls o hose repored in he exising lieraure: he responses of boh non-durables and durables consumpion are larger when nancial fricions are igher. By nancial fricions being igher we mean ha eiher here is a larger fracion of credi consrained agens (lower ) in he economy and/or heir borrowing capaciy is more resriced (higher ). Afer a moneary policy shock, he response of non-durable consumpion does no appear o be sensiive o di eren levels of nancial fricions. The e ecs on residenial invesmen are more imporan, especially o di eren speci caions of he LTV, 1. The igher he credi condiions (lower LTV), he larger is he response of durable oupu o a moneary conracion. The conclusions are similar when we analyze he housing preference shock. The response of consumpion is 14 In an appendix available upon reques we deail he full se of log-linearized equaions.

27 26 barely a eced by he presence of nancial fricions, especially when agens can borrow agains i, bu he numerical di erences are very small when comparing he response of non-durable consumpion o residenial invesmen. The ighness of credi condiions implici in he LTV raio a ecs he response of durable oupu, while he fracion of consrained agens in he economy does no appear o play a major role in amplifying he shock. Overall, even if nancial fricions seem o amplify he moneary and preference shocks, heir quaniaive e ecs are raher small when compared wih a model wih homogeneous agens and no credi consrains (bu wih labor marke fricions). In Aspachs-Bracons and Rabanal (21) we esimaed ha he fracion of nancially consrains individuals in he Spanish economy was low and i did no improve model. In he same spiri, Darracq-Parriès and Noarpiero (29) have di culy idenifying he fracion of credi-consrained individuals in a DSGE model of he euro area, and show ha his exension does no improve model. This does no mean credi consrains are no presen in he Spanish or EMU daa. Bu hey need o be modelled in a di eren way han has been included in he lieraure since Iacoviello (25). One avenue o sudy would be o allow agens o borrow agains heir labor income, in addiion o housing collaeral. VI. The E ecs of Belonging o he EMU The ools available o Spanish policymakers o reac o shocks were reduced subsanially when Spain joined he EMU. To analyze he consequences of having abandoned moneary policy independence, we exend he model of Secion 3 by assuming ha boh counries can run heir own moneary policy wih di eren naional currencies as unis of accoun. 15 We herefore inroduce Taylor rules for boh counries (Spain, and an EMU wihou Spain) and an uncovered ineres rae pariy condiion, and we assume producer currency pricing for impors and expors of non-durable goods, as in Lubik and Schorfheide (26). The goal is o sudy he reacion of a small open economy in a wo counry model when faced wih housing demand shocks. I is imporan o noe ha his paper sudies he period, and he exercise only focuses on he possible coss of no being able o address demand-speci c shocks in one secor or counry using moneary policy. Our model does no evaluae oher imporan coss of no belonging o he EMU such as hose associaed wih exchange rae volailiy (e.g. higher domesic ineres raes and lower inernaional rade) which could a ec growh. 15 Of course, he model absracs from oher poenial bene s of joining a moneary union, like he disappearance of exchange rae risk and he lowering of risk premia.