The Drivers of Housing Cycles in Spain

Transcription

1 WP/9/23 The Drivers of Housing Cycles in Spain Oriol Aspachs-Bracons and Pau Rabanal

2 29 Inernaional Moneary Fund WP/9/23 IMF Working Paper Research Deparmen The Drivers of Housing Cycles in Spain 1 Prepared by Oriol Aspachs-Bracons and Pau Rabanal Auhorized for disribuion by Gian Maria Milesi-Ferrei Sepember 29 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. Since Spain joined he EMU, wo main imporan facors behind he housing boom appear o be he decrease of nominal ineres raes and demographic facors. In his paper we esimae a New Keynesian model of a currency area, using daa for Spain and he res of he EMU o sudy he imporance of hose facors. We also examine he role of differen rigidiies and find ha labor marke fricions are crucial o explain main feaures of he daa. On he oher hand, financial fricions ha impose a collaeral consrain on borrowing do no appear o be relevan. JEL Classificaion Numbers: E44, E52, F41 Keywords: Housing, Moneary Policy, Financial Consrains Auhor s Address: oaspachs@lacaixa.es; prabanal@imf.org 1 Paper prepared for he Banco de España Conference on "Esimaion and Empirical Validaion of Srucural Dynamic Sochasic Models for he Spanish Economy," Madrid, March 13, 29. We are hankful o Michel Juillard for help wih DYNARE programming. Oriol Aspachs-Bracons is an economis in he Research Deparmen a Caixa d'esalvis i Pensions de Barcelona, Avinguda Diagonal , 828 Barcelona. Pau Rabanal is an economis in he IMF Research Deparmen. This paper should no be repored as reflecing he views of Caixa d'esalvis i Pensions de Barcelona ("la Caixa") or he Inernaional Moneary Fund or is Execuive Board. Any errors and omissions are our own.

3 3 Conens Page I. Inroducion...5 II. III. IV. The Model...1 A. Households...1 B. Producers...13 B.1 Final Goods Producers...14 B.2 Inermediae Goods Producers...15 C. Closing he Model...16 C.1 Marke Clearing Condiions...16 C.2 Moneary Policy Rule...17 Bayesian Esimaion...18 A. Daa...18 B. Priors and Poseriors...19 C. Implicaions of he Model: Poserior Second Momens and Impulse Responses...25 C.1 Second Momens...25 C.2 Model Simulaion...26 C.3 Impulse Responses...28 Robusness: The Role of Financial Fricions and Labor Marke Rigidiies...32 V. Conclusions...34 References...37 Figures 1. Residenial Invesmen (y-o-y real growh rae) House Price Indices (y-o-y percen growh rae) Monh T-Bill Raes in Spain and in he EMU Number of Households and Populaion. Annual Growh Raes Priors (black solid line) and Poseriors (red dashed line) Priors (black solid line) and Poseriors (red dashed line) Model Simulaion wih Smoohed Shocks. Percen Conribuion of Each Shock o Overall Volailiy Poserior Impulse Responses (mean and 95% C.I.) o a Technology Shock in he Housing Secor Poserior Impulse Responses (mean and 95% C.I.) o a Preference Shock in he Housing Secor...3

4 4 1. Poserior Impulse Responses (mean and 95% C.I.) o a Moneary Policy Shock in he Euro Area...31 Tables 1. Calibraed parameers...2 2a. Prior and Poserior Disribuions...2 2b. Prior and Poserior Disribuions a. Second Momens in Spain b. Second Momens in he res of EMU Variance Decomposiion (in percen) Model Comparison...34

5 5 I. Inroducion The origins of he curren global crisis are muliple and complex bu, undoubedly, he housing secor has played a cenral role in is amplificaion and propagaion. Indeed, a recen paper by Leamer (27) pus he housing secor a he cener sage of mos U.S. economic downurns. Reinhar and Rogoff (29) have sudied hisorical banking crises episodes and have showed heir srong link, among oher variables, o housing prices. Aspachs-Bracons (29) has also sudied he correlaion of housing prices wih main macroeconomic variables in an inernaional conex, and finds a significan relaionship beween economic downurns and housing price declines in a sample of 18 indusrialized counries. Following a cumulaive decline of housing prices of 23 percen in a five-year period, real GDP declines 1.5 percen in he following year, and he unemploymen rae roughly doubles in 3 years. The imporance of he housing secor comes from he cenral role i plays in he households process o accumulae nonfinancial asses. Also, housing wealh can be used as a way o finance nondurable consumpion. The housing spillovers o he res of he economy have been sudied by esimaing he marginal propensiy o consume ou of housing wealh, eiher using reduced form regressions or srucural models. 1 Therefore, undersanding he causes and consequences of he housing cycle, and is implicaions for he broader economy and he appropiae policy response have become key in recen years, and he focus of aenion of cenral banks and inernaional insiuions (IMF, 28). Given he widely recognized imporance of his secor, i is no suprising ha he mos recen generaion of dynamic sochasic general equilibrium (DSGE) models have been exended o incorporae a housing secor and all he economic effecs associaed o i. In a highly influenial paper, Iacoviello (25) exends an oherwise sandard DSGE model o allow for durable (housing) consumpion. In such a model housing plays a double role. Firs, i allows households o use heir housing sock as a saving vehicle, in addiion o providing insananeous uiliy. Second, if a fracion of individuals face borrowing consrains, bu financial markes allow hem o borrow agains heir housing wealh, hen moneary policy can have a sronger propagaion mechanism. An expansionary moneary policy shock will lead o higher nondurable and durable consumpion because of lower ineres raes. Increased housing prices will increase he wealh of hose who are long on housing, ypically mos households in he economy, boosing nondurable consumpion even furher. 2 Monacelli (28) has sressed he role of his ype of credi fricions o help explain several feaures of he daa, mos imporanly he comovemen beween residenial invesmen and privae consumpion o a moneary policy shock. Despie he srong 1 An excellen survey ha summarizes sudies for he Unied Saes can be found in CBO (27). For he spanish case, see Bover (27). 2 Kiyoaki and Moore (1997) and Bernanke, Gerler and Gilchris (1999) iniiaed he large lieraure emphasizing he role credi consrains play in he ransmission mechanism of shocks. Aoki e al. (24) formalize hese ideas by building a model where housing plays a criical financial acceleraor role for consumers in he UK.

6 6 propagaion mechanism of moneary policy embedded in his ype of models, oher ypes of shocks are sill needed o fi he daa. For insance, Iacoviello and Neri (28) esimae a DSGE model for he Unied Saes using Bayesian mehods, and hey find ha preference (demand) and echnology (supply) facors explain half of he variaion in he housing secor, while moneary facors explain 2 percen. A similar resul is obained in Darracq-Parries and Noarpiero (28) esimaing a wo-counry model for he Unied Saes and he European Moneary Union (EMU). The presen paper srongly borrows from hese las wo references, and esimaes a DSGE model wih Bayesian mehods using Spanish and EMU daa, o shed ligh on he causes of he recen behavior of housing prices during he EMU period. As shown in Figures 1 and 2, housing prices soared in boh economies during more han a decade, wih double-digi increases (a an annualized rae) for he Spanish economy during mos of he 2s. The housing boom is also obvious from he real residenial invesmen numbers, wih again several periods of double-digi growh raes. A poenially imporan channel ha is relaed o he effecs of moneary policy is he reducion of ineres rae spreads beween Spain and is EMU parners during he mid 199s. As agens assigned a large probabiliy o he euro being creaed in 1999, and Spain belonging o he moneary union from he very beginning, ineres raes rapidly converged o he european average (Figure 3) as he currency risk premium disappeared. The spread in he 3-monh T-bill raes narrowed from more han 3 basis poins in early 1996 o basically zero a he end of Since hen, he spread has remained a insignifican levels. 3 Finally, demographic pressures have been very imporan in Spain (Figure 4). Populaion growh has been much higher han he res of counries of he EMU mosly due o immigraion. In a addiion, he baby boom generaion, which is younger in Spain, reached he age of hiry during his period. Oher demographic facors (increased divorce raes and single-paren families) have increased he number of households even more han he populaion growh raes, adding addiional pressure o housing demand. To capure his effec, in he model, increased demand pressures due o populaion growh are capured wih a housing demand shock. To undersand he role of declining ineres raes, demographic pressures, as well as oher facors in explaning he evidence we have jus discussed, in his paper we build and esimae a wo-counry, wo-secor model of a currency union, wih durable and nondurable goods. Our model can be seen as a wo-counry exension of Monacelli (28), from which we borrow he key ingrediens. 4 The use of a wo counry seup allows us o provide a more realisic framework o sudy moneary policy in Spain since he launch of he euro. Our baseline specificaion does no include borrowing consrains, since we found his version of he model o fi he daa beer, unlike Iacoviello and Neri (28) for he case of he Unied Saes. The model is esimaed using sandard Bayesian 3 Using oher raes, such as 2 year governmen bonds, or inerbank raes, delivers a very similar picure. We presen he 3-monh T-bill rae because we will be using his series when we esimae he model. 4 Darracq-Paries and Noarpiero (28) have esimaed a wo-counry model using US and EMU daa. Rubio (28) has also buil a wo-counry model wih housing in a currency union.

7 7 Figure 1: Residenial Invesmen (y-o-y real growh rae) Q Q Q1 2 Q1 22 Q1 24 Q1 26 Q Spain EMU Figure 2: House Price Indices (y-o-y percen growh rae) Q Q Q1 2 Q1 22 Q1 24 Q1 26 Q Spain EMU

8 8 Figure 3: 3-Monh T-Bill Raes in Spain and in he EMU Q Q Q Q1 21 Q1 23 Q1 25 Q1 27 Spain EMU Figure 4: Number of Households and Populaion in Spain. Annual Growh Raes. 4.% 3.5% 3.% 2.5% 2.% 1.5% 1.%.5%.%.5% 1.% Household unis Populaion

9 9 mehods, following he approach used by Smes and Wouers (23) and Rabanal and Rubio-Ramírez (28) in models of he euro area, and by Rabanal (29) in a wo-counry model of Spain inside he euro area. Oher DSGE models of he Spanish economy esimaed wih Bayesian mehods include Burriel e al. (28), and Andrés e al. (28). Turning o a preview of he resuls, we find ha he prices of durable goods are more flexible han he prices of non-durable goods. This fac was firs poined ou by Bils and Klenow (24) and posed a challenge o he capabiliy of he New Keynesian model o replicae he comovemen beween durables and nondurables consumpion afer a moneary policy shock. The poserior esimaes also reveal ha cosly labor reallocaion plays an imporan role in explaining he ransmission of shocks in he Spanish economy: he higher poserior esimae suggess ha labor marke reallocaion is more cosly in Europe han in he US. Finally, we observe ha he relaive magniude of he sandard deviaion of he shocks is similar across secors wihin a counry. However, all sandard deviaions of he shocks are higher for Spain. This suggess ha he sources of variaion of he housing secor are similar beween he wo economies, bu he larger size of he shocks in Spain lead o a higher housing boom. The model provides a good fi o mos second momens of ineres in he daa, and hence allows us o decompose he sources of variaion of he observable variables hrough he lens of he model. Overall, domesic echnology shocks are he main source of variaion of real residenial invesmen and real consumpion of non-durable goods, boh in Spain and he EMU. For housing prices and he HICP, domesic preference shocks generae he bulk of he variaion. Quie surprisingly, moneary shocks (boh in he aggregae of he EMU as well as he declining risk premia in Spain) play a minor role explaining he housing price boom, agains he view ha he susained low levels of real ineres raes was behind i. On he oher hand, moneary shocks explain an imporan fracion (abou 2 percen) of he volailiy of nondurable consumpion boh in Spain and in he res of he EMU. We also find ha boh he durable secor echnology shock and he housing preference shock have a posiive and persisen impac on residenial invesmen, bu have negligible spillover effecs o he res of he economy. Finally, o es for he imporance ha financial imperfecions migh play in amplifying housing secor cycles we exend he model o allow for a fracion of individuals ha face borrowing consrains as in Iacoviello and Neri (28) and Monacelli (28). Using sandard ools in he Bayesian model comparison lieraure (see Fernández-Villaverde and Rubio-Ramírez, 24), we conclude ha he inroducion of borrowing consrains does no lead o an improvemen of model fi o he daa. On he oher hand, we confirm he calibraion resuls found in Aspachs-Bracons and Rabanal (28), who show ha he inroducion of cosly labor reallocaion across secors induces a posiive comovemen of privae consumpion and residenial invesmen even when differences in he degree of nominal rigidiies across secors induce large relaive price shifs. The res of he paper is organized as follows. In secion 2, we presen he model. In secion 3, we discuss he Bayesian esimaion and is implicaions. In secion 4, we presen some

10 1 robusness checks. We leave secion 5 for concluding remarks. II. 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 final 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. In order o be able o esimae he model and avoid singulariy problems in he likelihood funcion, he model conains eleven shocks. These shocks can be divided ino demand (preference), supply (echnology) shocks, and moneary shocks. For each secor, a demand shock leads oupu and prices o move in he same direcion, while a supply shock will lead oupu and prices o move in opposie direcions. Hence, we richly specify he shock srucure o allow he model o be able o explain all possible paerns in he daa, a he aggregae, secor-specific, and counry-specific levels. 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 where C j denoes consumpion of non-durable goods, D j denoes consumpion of durable goods and L i is he labor disuiliy index. The uiliy funcion denoes exernal habi formaion, as in Smes and Wouers (23) and Iacoviello and Neri (28). 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: #) (1) C j = 1 C C j C 1 C H; H 1 C + (1 ) 1 C C j C 1 C F; C C 1 ; where C > (2) 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, and is he fracion of domesically produced non-durables a home. D is a housing preference shock, ha ries

11 11 o capure exogenous changes in he demand for housing, as he demographic changes ha we presened in Figure 4. H is a home-consumpion preference shock. Boh preference shocks follow AR(1) processes in logs. Finally, following Iacoviello and Neri (28), 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) where L i;j denoes hours worked by household j in each secor i = C; D, and 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. The budge consrain of he home agen, in nominal erms, is given by: P C C j + P D I D;j + B j R ~ 1 B j 1 + W C L C;j + W D L D;j + j (4) where P C and P D are he price indices of durable and non-durable goods, o be defined below, W i is he nominal wage in each secor i = C; D, and B j denoes unconingen nominal asses ha are raded among households across he moneary union, and ha pays (or coss) a gross nominal ineres rae R ~ > 1: j denoes nominal profis, because firms are ulimaely owned by households. 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 (:), ha is a convex funcion (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 several shocks. We assume ha households in he home counry have o pay a premium above he union-wide riskless nominal ineres rae if he counry s deb level as percen of GDP increases. This assumpion is needed o obain a well-defined seady sae for he aggregae level of deb as percen of nominal GDP. 5 The relevan ineres rae for he home households and he union-wide ineres are relaed as follows: 5 See Schmi-Grohé and Uribe (23).

12 12 B ~R = R # exp P Y B P Y 1 (6) where P is he aggregae price level, o be defined below, and Y is real GDP, also o be defined 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 effec as given when choosing beween consuming durables, non-durables, and saving. # is a risk premium shock ha affecs he domesic ineres rae bu no he union-wide nominal ineres rae. Noe ha he risk premium is declining in he ne foreign asse posiion of he counry as percen of GDP, B P Y. We can separae he household s decision as 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 in home and foreign produced goods, aking ino accoun ha, 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 will be 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 firs order condiions o he household problem are given by: 6 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 1 I D I D (9) Absen adjusmen coss o residenial invesmen, hese hree equaions can be reduced o he following condiion: 6 Since all households behave he same way, we drop he j subscrips in wha follows.

13 13 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 The labor supply condiions o boh secors are given by: "C L L L L C L = C "C 1 L (1 ) L L D L = C "C 1 L W C P C W D P C (1) (11) (12) The allocaion of nondurable consumpion expendiures beween home and foreign-produced goods is: PH; C C (13) C H; = H P C C F; = (1 ) The price index for non-durables is (he CPI): PF; P C C C : (14) P C 1 C = H (P H; ) 1 C + (1 ) (P F; ) 1 C (15) 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 differen parameer values. Tha is, is he weigh of non-durables in he uiliy funcion, and he fracion of domesically produced non-durables. B. 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 final goods producers in each secor. There is a coninuum of final goods producers in he wo secors ha operae under perfec compeiion and flexible prices. Producers of he final durable good sell is produc o domesic households only in each counry. Producers of he final non-durable good sell heir produc o domesic and

14 14 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 (P C ) because of he presence of impored non-durable goods, whose price is P F;. B.1 Final Goods Producers In he durable secor, final goods producers purchase inermediae goods 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 (16) Profi maximizaion delivers he following demand for individual inermediae non-durable goods: Y D (h) = P D where he price level is given by imposing he zero-profi condiion. P D (h) D Y D ; (17) P D 1 n Z n P D (h) D D dh : In he non-durable goods secor, expressions are similar bu wih an appropiae 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 ; (18) individual inermediae non-durable goods demand is: where he price level is: Y C (h) = PH; (h) P H; C Y C ; (19) P H; 1 n Z n 1 [P H; (h)] 1 1 C C dh :

15 15 B.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 final 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) receive a signal o rese heir price opimally. In addiion, a fracion i index heir price o las period s secorial inflaion rae whenever hey are no allowed o rese heir price. Inermediae goods in boh counries are produced wih labor: Y i (h) = A A H;i L i (h); for all h 2 [; n], and i = C; D: (2) Y i (f) = A A F;i L i (f); for all f 2 [n; 1], and i = C; D: (21) Noe ha in each counry and secor, he producion funcion is hi by counry and secor specific echnology shocks, each of which follows an AR(1) in logs. In addiion, here is a non-saionary EMU wide echnology shock wih he following process: log(a ) = log(a 1 ) + " a This shock gives growh o he model and delivers a model-consisen way of derending he daa (by aking firs differences). Also, as long as he sandard deviaion of " a is posiive, here will be some correlaion of echnology shocks across counries and secors, as in mos of he Inernaional Real Business Cycle lieraure (see, for insance, Backus, Kehoe and Kydland, 1992). In he remaining par of his subsecion, we work ou he condiions for he home counry firms pricing decisions. In each secor, cos minimizaion implies ha he real marginal cos of producion is: MC i = W i =P i ; i = C; D: A A H;i Noe ha even hough labor is he only producion inpu, labor coss may differ across secors because of imperfec labor subsiuabiliy, which can lead o differen real wages. Also, real uni labor coss can differ because of he secor-specific echnology shocks. This effec induces an addiional channel of heerogeneous inflaion responses across secors, even when he parameers governing nominal rigidiies are similar across secors. 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 >= >;

16 16 subjec o fuure demand 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 >= >; (22) 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 : (23) 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 appropiae change of noaion. C. Closing he Model C.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; (24) while residenial invesmen is used o increase he domesic housing sock: Y D = ni D (25) Hence, oal oupu is,

17 17 Y = Y D + Y C For he foreign counry, he analogous condiions are: Y C = nc F; + (1 n) C F; (26) Y D = (1 n)i D (27) Y = Y D + Y C 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 (28) L D;j dj (29) Marke clearing in he inernaional bonds marke is: nb + (1 n)b = (3) Finally, he evoluion of aggregae ne foreign asses is: nb = n R ~ 1 B 1 + (1 n) P H; CH; np F; C F; (31) C.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 inflaion and also exhibis ineres rae ineria: R = R P EMU =P EMU 1 EMU 1 R R R 1 exp(" m ) (32) " m is he moneary policy shock and 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

18 18 III. Bayesian Esimaion We esimae he model of he previous secion using sandard Bayesian mehods, following he approach used by Smes and Wouers (23) and Rabanal and Rubio-Ramírez (28) in models of he euro area, and by Rabanal (29) in a wo-counry model of Spain inside he euro area. The Bayesian esimaion approach has been presened in deail in hese and oher papers (see, for insance, An and Schorfheide, 27) so we do no discuss i here. 7 Hence, in his secion we describe he daase ha we use, he prior and poserior disribuions of he models parameers, as well as poserior second momens and impulse responses from he esimaed model. A. Daa We use en macroeconomic series o esimae he model: real privae household consumpion, real residenial invesmen, he Harmonized Index of Consumer Prices (HICP), housing prices, and he 3-monh T-bill rae for boh Spain and he res of he EMU. We obain he firs hree series for each counry from Eurosa. For housing prices in Spain, we use he free marke housing price index published by he Spanish Minisry of Housing (Miniserio de Vivienda). For he euro area as a whole, we use he residenial propery price index published by he European Cenral Bank. For hese four series, we obain res of he euro area aggregaes by subsracing from he euro area aggregae is Spanish counerpar series using Spain s weigh in he EMU HICP. Also, since he series of housing prices of he euro area is half-yearly, we conver i o quarerly frequency by using linear inerpolaion. We seasonally adjus he daa when i has no been done so by he original source. Finally, we use he hree monh T-bill rae for Spain and an aggregae of he euro area including he larges economies. We have discussed he behavior of hese series in he inroducion. Our sample period goes from 1995:4 o 28:2. There are several reasons ha lead us o his choice. The firs one is daa availabiliy: Eurosa provides harmonized naional accouns and consumer price indices for all he member counries of he EMU only since The ECB index of housing prices sars in he second half of Second, we are using a model of a currency union and hence we should be including only daa from 1999 onwards. Since his is a shor sample period, we decided o include he period oo, making he assumpion ha agens anicipaed ha he EMU would be formed in 1999, and ha Spain would be a par of i. A similar approach is conduced by Rabanal (29). When esimaing he model, we use quarerly growh raes of all price and quaniy variables, and we divide he ineres raes by 4 o obain a quarerly equivalen. We 7 Basically, we use sandard mehods o obain a linear approximaion and solve for he law of moion of he model, evaluae he likelihood funcion, and draw from he poserior disribuion. The resuls we presen in his secion are based on 2, draws of he Meropolis-Hasings algorihm.

19 19 demean all daa. 8 B. Priors and Poseriors In Table 1 we presen he parameers ha are calibraed before esimaing he model. In he seady sae, we assume zero inflaion, ha he rade balance is 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 assume ha he degree of monopolisic compeiion in boh ypes of goods is he same ( C = D = ), and hence he raio of all prices is one in he seady sae. Noe ha he economic size of he nondurable secor () and he weigh of he nondurable consumpion in he uiliy funcion () canno be solved separaely. The opimal seady-sae raio of durable o non-durable consumpion is: C(1 ") D = [1 (1 )] (1 ) (33) In a sandard model wih wo non-durable goods (! 1) and no habi formaion in nondurable consumpion (" = ), he opimal seady sae raio of he wo ypes of goods would be equal o he raio of relaive weighs in he uiliy funcion. The fracion of spending allocaed o non-durable consumpion over oal spending () is equal o: C C + D = Given values for,,, and "; we can solve for he value of by puing ogeher he previous ingrediens, which leads o he following expression for : 1 = (1 ") 1 [1 (1 )] : We se he size of he home economy o n = :1 and 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. 8 We have also esimaed he same model by derending he quaniy series wih a linear rend. The resuls ha we obained are very similar o he ones ha we presen by firs-differencing he (log) of he real variables, and hey are available upon reques.

20 2 Table 1. Calibraed parameers Discoun facor.99 Depreciaion rae.25 =( 1) Price Markup 1% n Size of Spain.1 Size of Non-Durable Secor.9 Fracion of impored goods from EMU.15 Fracion of impored goods from Spain.15 In Table 2a we presen priors and poseriors of he parameers of he model. Firs of all, we would like o remark ha we use he same values of he parameers for boh counries, including he AR(1) coefficiens of he shocks. We proceed his way because we do no have a long ime series (jus 5 observaions), and hence i is useful o resric he number of parameers o esimae. Second, and mos imporanly, we have esimaed versions of he model where he coefficiens of he Phillips Curves (he Calvo loery and he backward looking indexaion parameer) and/or he AR(1) coefficiens of he shock were differen across counries. In all cases, we found ha he numerical differences of parameer esimaes across counries were small. We chose he specificaion ha we presen in Table 2a because he marginal likelihood of he models wih differen parameers across counries decreased. 9 The only parameers ha are allowed o be differen across counries are he sandard deviaions of he shocks. Table 2a. Prior and Poserior Disribuions Parameers Priors Poseriors Mean Sd.Dev. Mean 95% C.I. C Calvo loery, non-durables Bea [.77,.97] D Calvo loery, durables Bea [.26,.44] C Indexaion, non-durables Bea [.23,.82] D Indexaion, durables Bea [.5,.93] " Habi formaion Bea [.29,49] Labor disuiliy Gamma [.21,1.49] C Elasiciy of subs. beween goods Gamma [3.7,5.63] L Cosly labor reallocaion Gamma [.77,1.74] Risk premium elasiciy Gamma [.1,.3] Invesmen adjusmen coss Gamma [.18,.45] Taylor rule reacion o inflaion Normal [1.,1.48] R Ineres rae smoohing Bea [.72,.83]] 9 These resuls are available upon reques. As explained by Fernández-Villaverde and Rubio-Ramírez (24), he marginal likelihood ells he researcher how she would updae her priors on which model is closer o he rue one afer observing he daa. Hence, he marginal likelihood is key for model comparison exercises. We should remind he reader ha he marginal likelihood averages all possible values of he likelihood of he model across he parameer space using he priors as weighs. Hence, i ends o penalize overparamerizaion of a model if he exra parameer does no help in model fi.

21 21 We now commen on he mos imporan prior and poserior disribuions of he parameers. The probabiliies of he Calvo loeries are Bea disribuions, in order o keep hem bounded beween zero and one. The priors imply an average duraion of opimal price changes of 3 quarers, as is sandard in he lieraure for aggregae prices. Also, we do no force prices in he durable secor o be more flexible han hose in he nodurable secor, so we se he same prior means for he Calvo loeries of boh ypes of goods. However, he poserior esimaes indicae ha he prices of durable goods are more flexible, a resul ha was firs poined ou by Bils and Klenow (24). The proporion of firms in he non-durable secor ha canno reopimize prices in a given period is esimaed a :87, which delivers a mean poserior average duraion beween opimal price changes of abou 6 quarers. The proporion of firms in he durable secor ha canno reopimize is much lower, :34, which would imply an average duraion of abou 1:5 quarers beween opimal price changes. The prior mean for he parameers capuring he indexaion o las period s inflaion rae is also se symmerically for boh ypes of goods. The poserior esimaes confirm ha he proporion of firms ha index heir price o las period s inflaion rae when hey are no allowed o reopimize is similar across secors: :52 for he non-durable secor and :71 for he durable secor. Regarding he parameer ha capures he habi formaion, we se a prior mean similar o sandard parameer esimaes in he lieraure (see Smes and Wouers, 23). The poserior mean confirm ha he habis in non-durable consumpion are an imporan elemen o capure he persisence of his variable. The prior mean for he elasiciy of subsiuion beween home and foreign goods is se a 1 wih a large sandard deviaion o accoun for uncerainy abou is rue value. The poserior esimae urns ou o be much larger han he esimaes usually obained using DSGE models, which are ypically well below 1 (see, for insance Lubik and Shorfheide (25) and Rabanal and Tuesa (26)). In his case, we obain a poserior mean of 4:37 and he 95 percen poserior confidence inerval rules ou a value of 1. This suggess ha home and foreign oupu are quie responsive o movemens in he erms of rade. These resuls would be more similar o wha is obained in he rade lieraure using produc or firm level daa, as found for insance in Imbs and Mejean (28). Cosly labor reallocaion also seems o play an imporan role. The prior mean is also se o 1, which is he value esimaed for he US in Iacoviello and Neri (28). The higher poserior esimae suggess ha labor marke reallocaion is even more cosly in Europe han in he US. Finally, he poserior mean for he parameer capuring invesmen adjusmen coss is much lower han he prior. We seleced a prior mean of 2 because in calibraed exercises his value allows o obain a persisen response of residenial invesmen o moneary policy shocks. However, he lower esimaed value of :31 would sugges ha such srong propagaion mechanism is no needed when oher shocks are allowed o explain residenial invesmen. Finally, we obain a risk-premium elasiciy o he level of ne foreign asses of :2, which is higher han he prior mean bu in line wih he evidence repored in Lane and Milesi-Ferrei (21) for a group of OECD counries. The coefficiens of he Taylor rule are quie similar o he priors and o wha has been obained in previous sudies of he euro area. In Figures 5 and 6, we plo he priors and poseriors of he parameers we have jus

22 22 Figure 5: Priors (black solid line) and Poseriors (red line). 1 θ c 1 θ d 5 φ c φ d 1 ε 3 η ι C 3 ι L 1 κ discussed. In mos cases, he priors and poseriors are quie differen, suggesing ha hose parameers are idenified and ha he likelihood funcion conains revelan informaion abou he model s parameers. The only excepions are he backward indexaion parameer in he durable secor inflaion process ( D ) and he labor disuiliy parameer (), for which he prior and poserior are quie similar.

23 23 Table 2b. Prior and Poserior Disribuions Parameers Priors Poseriors AR(1) Coefficiens Mean Sd.Dev. Mean 95% C.I. A;C Technology shock, durable Bea [.91,.99] A;D Technology shock, non-durable Bea [.76,.91] ;H Preference shock, home goods Bea [.84,.98] ;D Preference shock, durable goods Bea [.96,.99] # Risk premium Bea [.78,.91] Sandard Deviaion Shocks m Moneary Gamma [.7,.12] # Risk Premium Gamma [.6,.9] A Common echnology Gamma [.47,.74] A;C Technology nondurable home Gamma [.85,1.67] A;C Technology nondurable foreign Gamma [.54,1.17] ;H Preference nondurable home Gamma [.34,.53] ;F Preference nondurable foreign Gamma [.17,.27] A;D Technology durable home Gamma [1.63,2.29] A;D Technology durable foreign Gamma [1.7,1.52] ;D Preference durable home Gamma [2.67,4.34] ;D Preference durable foreign Gamma [1.66,2.77] In Table 2b we presen he prior and poserior esimaes of he AR(1) coefficiens and he sandard deviaions of he shocks. We se he prior means of he AR(1) coefficiens o :7 for all shocks and we assume a Bea disribuion o keep hem bounded beween zero and one. The poserior esimaes show ha he persisence of echnology shocks in he durable secor is :94, while he esimaed poserior mean of echnology shocks in he non-durable secor is :83. The persisence of he preference shocks in he durable secor is he highes, :97, while ha of home-produced radable goods is :9. Finally, he persisence of he premium shock falls in beween, wih a poserior mean of :85. Figure 6 also plos he prior and poserior disribuions, which in all cases are quie differen, suggesing ha he parameers are well idenified. Following he resuls obained in he lieraure, we se he prior mean of he sandard deviaion of moneary and risk premium shocks o be lower han for echnology shocks. We do he opposie for preference shocks, bu we se he sandard deviaion high enough so as o accommodae a wide range of parameer values. The poserior esimaes confirm he low sandard deviaion of moneary and risk premium shocks, and among hese wo, he risk premium shocks are smaller han he moneary policy shocks. The sandard deviaion of he preference and echnology shocks in he durable secor are higher han hose in he nondurable secor.

24 24 Figure 6: Priors (black solid line) and Poseriors (red line). 1 ψ 1 γ π 15 γ r ρ A,C 1 ρ A,D 1 ρ ϑ ρ ξ,c ρ ξ,d

25 25 C. Implicaions of he Model: Poserior Second Momens and Impulse Responses C.1 Second Momens Since i is difficul o draw conclusions by looking a he esimaed processes for he shocks, in Tables 3a and 3b we presen he poserior mean of seleced second momens, as well as a 95 percen poserior confidence band, for he en observable variables. To have an assessmen of he fi of he model, we compare hem wih he acual second momens in he daa. Wih regards o Spain, he model generaes a sandard deviaion of residenial invesmen which is higher han he sandard deviaion of non-durable consumpion, as we observe in he daa. The model also capures he higher volailiy of housing prices wih respec o he prices of non-durable goods, proxied by HICP inflaion. The higher volailiy of housing prices and quaniies wih respec o nondurable consumpion is explained by higher volailiy of he shocks in he durable secor, as well as a lower degree of nominal rigidiy in ha secor. The sandard deviaion of non-durables consumpion implied by he model is higher han he one we observe in he daa, bu for he res of he variables he fi is quie good: he acual sandard deviaion of each series is included in he 95 percen poserior confidence inerval implied by he model. The auocorrelaions generaed by he model are also quie similar o he ones we observe in he daa, specially for he firs lags. Table 3a. Second Momens in Spain Sd. Dev. Auocorrelaion (lag) c Daa Model :72 :4 :17 :7 :4 [:64;:8] [:27;:5] [:7;:27] [:;:14] [ :2;:9] y d Daa :2 [ :3;:6] Model 3:33 :12 :1 :8 :5 [2:88;3:69] [:2;:28] [ :15; :3] [ :12; :5] [ :7; :3] p C Daa :3 [ :5; :2] Model :47 :24 :23 :21 :19 [:36;:55] [:;:56] [ :1;:5] [ :1;:47] [ :2;:44] p D Daa :18 [:2;:38] Model 1:75 :33 :5 :7 :2 [1:58;1:94] [:2;:43] [ :11;:] [ :12; :2] [ :8;:3] ~r Daa Model :32 [:23;:4] :87 [:81;:94] :76 [:65;:88] :67 [:53;:82] :61 [:43;:76] : [ :3;:3] :54 [:36;:72]

26 26 Table 3b. Second Momens in he res of EMU Sd. Dev. Auocorrelaion (lag) c Daa Model :59 :38 :14 :4 : [:5;:66] [:26;:48] [:23;:5] [ :2;:11] [ :4;:4] y d Daa :2 [ :4;:1] Model 2:35 :8 :9 :7 :4 [2:;2:66] [:19; :2] [ :14; :4] [ :1; :4] [ :6; :2] p C Daa :3 [ :5; :2] Model :35 :38 :35 :32 :3 [:23;:46] [ :2;:73] [:7;:1] [:65;:1] [:1;:61] p D Daa :28 [:2;:57] Model 1:18 :33 :3 :5 :1 [1:2;1:3] [:23;:45] [ :1;:3] [ :13;:1] [ :7;:6] r Daa Model :31 [:18;:41] :89 [:81;:96] :8 [:65;:93] :72 [:52;:88] :66 [:44;:85] :2 [ :2;:6] :61 [:38;:81] A similar conclusion is reached for he second momens generaed for he variables of he EMU. As was he case wih he Spanish daa, he model is able o explain he high volailiy of residenial invesmen and housing prices, bu i oversaes he volailiy of consumpion growh of non-durable goods. A he same ime, he model does a good job in explaining he auocorrelaion of housing prices and he 3 monh T-bill rae, bu i does a worse job in geing he auocorrelaions of CPI inflaion, and of consumpion and residenial invesmen righ. Given ha he model is able o replicae he second momens of he daa fairly well, we now urn o decompose he sources of variaion of he observable variables. The resuls are presened in Table 4. Overall, domesic echnology shocks are he main source of variaion of real residenial invesmen and real consumpion of non-durable goods, boh in Spain and he EMU. The opposie picure emerges for housing prices and he HICP. For hose variables domesic preference shocks generae he bulk of he variaion, while domesic echnology shocks play a secondary role. These resuls are very similar o wha Iacoviello and Neri (28) find for he US, and Darracq-Parries and Noarpiero (28) for he EMU. Regarding moneary shocks and risk premium shocks, ogeher hey accoun for almos one fourh of he variabiliy of real consumpion in Spain, bu have a negligible effec in explaining he volailiy of residenial invesmen. Quie surprisingly, moneary shocks play a minor role explaining he housing price boom, agains he widespread view ha he susained low levels of real ineres raes was behind i (Brunnenmeier and Julliard, 29). Finally, only 2 percen of he variaion of he 3-monh T-bill rae in Spain is explained by he risk premium shock, while 7 percen is explained by facors coming from he res of he EMU. This resul is somewha expeced given ha since 1999 he risk premia have been negligible, and hence he 3-monh T-bill rae in Spain moves closely wih is EMU counerpar.

27 27 " A " A;C Table 4: Variance Decomposiion (in percen) Technology Preference Moneary " A;D " A;C " A;D " ;D " ;H " ;D " ;F " m " # c i D p C p D ~r c i D p C p D r The qualiaive resuls for he EMU are quie similar, bu here are some quaniaive differences. In he res of he EMU, he innovaion o he common echnology shock explains more han 4 percen of he volailiy of consumpion growh and 2 of he volailiy of residenial invesmen growh. Similar o he Spanish case, however, echnology shocks in each secor explain a large fracion of he volailiy of real quaniies, while preference shocks explain an imporan par of price inflaion in each secor. Finally, moneary policy shocks also affec he behavior of consumpion, explaining more han 2 percen of is volailiy, bu have a very small influence in he volailiy of residenial invesmen. To conclude his subsecion, i is imporan o remark ha here are no many spillovers of shocks across counries. In paricular, he effecs of Spanish shocks on he res of EMU variables are basically zero in mos cases. From he EMU side, he only shock ha affecs Spanish variables is he echnology shock in he foreign nondurable secor, which explains abou 2 percen of he volailiy of inflaion in Spain. C.2 Model Simulaion A differen way of looking a wha shocks are behind he flucuaions in he daa is o simulae he model wih he shocks obained using he Kalman smooher (Hamilon, 1994). The procedure works as follows: given a se of parameer esimaes and he law of moion of he model, we use he observed daa o obain a series of shocks ha, given he model, explain he daa. In Figure 7 we presen he decomposiion of residenial invesmen in Spain and housing prices in Spain. 1 Since he model has 11 shocks, in order o make he figure readable we presen he percen conribuion of each domesic shock (preference and echnology, durable and nondurable), he aggregae echnology shock, he 1 We only presen his figure o focus he discussion on he housing secor in Spain. All he oher decomposiions are available upon reques.

28 28 Figure 7: Model Simulaion wih Smoohed Shocks. Percen Conribuion of Each Shock o Overall Volailiy Res. Invesmen Spain 1% 8% 6% 4% 2% % 2% 4% 6% 8% 1% 1996Q1 1998Q1 2Q1 22Q1 24Q1 26Q1 28Q1 Housing Prices Spain 1% 8% 6% 4% 2% % 2% 4% 6% 8% 1% 1996Q1 1998Q1 2Q1 22Q1 24Q1 26Q1 28Q1 Prefh Prefd Tech Techc Techd Mon/Pre Res moneary and risk premium shock, and he res of he shocks in he model, o overall flucuaions. As we can see in boh panels, he red color and he yellow color dominae: hese are he preference and he echnology shock in he housing (durable) secor. On he oher hand he imporance of moneary facors is in general no imporan. In he period of longes expansion of he housing price boom (22-26), he preference shock explains a very imporan fracion of he flucuaion, as well as in he subsequen deceleraion. Also, moneary facors have had some conribuion in he volailiy of housing prices beween 24 and 26, when he European Cenral Bank ended he susained period of low ineres raes a 2 percen. Quie surprisingly, he decline of he risk premia in he begining of our sample period does no appear o have conribued significanly o he housing price flucuaion in ha period. C.3 Impulse Responses In order o beer undersand he propagaion mechanisms implied by he model, in his subsecion we commen on he effecs of echnology and preference shocks in he housing secor in Spain, and o moneary shocks. In order o focus he discussion on he housing

29 29 secor in Spain, we do no presen he responses o nondurable secor shocks and he response of EMU variables, which are available upon reques. As we have jus discussed in he previous subsecion, he spillover effecs across counries are quie small, and he qualiaive effecs of he EMU shocks on EMU variables are very similar. In Figure 8 we presen he response o a housing secor echnology shock. As expeced, his shock increases residenial invesmen bu decreases housing prices, by reducing he relevan real marginal cos in he durable secor. The response of residenial invesmen displays a hump-shaped response, while he response of housing prices is more shor-lived, wih he decline in durable inflaion only lasing one period. The spillover effecs o he nondurable secor are small and nonsignifican a he 95 percen poserior confidence level. Figure 9 presens he response o a preference shock in he housing secor. This shock leads o a posiive comovemen beween housing prices and residenial invesmen, which is shor lived in erms of he reacion of durables price inflaion. The spillover effecs o he res of he economy are small, and nonsignifican. Figure 8: Poserior Impulse Responses (mean and 95% C.I.) o a Technology Shock in he Housing Secor..6 C 4 I D x 1 3 DPC.5 DPD

30 3 Figure 9: Poserior Impulse Responses (mean and 95% C.I.) o a Preference Shock in he Housing Secor..15 C 3 I D x 1 3 DPC 1.5 DPD

31 31 Figure 1: Poserior Impulse Responses (mean and 95% C.I.) o a Moneary Policy Shock in he Euro Area..6 C.6 I D DPC.6 DPD