Financial Factors: Implications for Output Gaps

Transcription

1 WP/15/153 Financial Facors: Implicaions for Oupu Gaps by Pau Rabanal and Marzie Taheri Sanjani IMF Working Papers describe research in progress by he auhor(s) and are published o elici commens and o encourage debae. The views expressed in IMF Working Papers are hose of he auhor(s) and do no necessarily represen he views of he IMF, is Execuive Board, or IMF managemen.

2 215 Inernaional Moneary Fund WP/15/153 IMF Working Paper European Deparmen and Research Deparmen Financial Facors: Implicaions for Oupu Gaps Prepared by Pau Rabanal and Marzie Taheri Sanjani 1 Auhorized for disribuion by Helge Berger and Giovanni dell Ariccia July 215 IMF Working Papers describe research in progress by he auhor(s) and are published o elici commens and o encourage debae. The views expressed in IMF Working Papers are hose of he auhor(s) and do no necessarily represen he views of he IMF, is Execuive Board, or IMF managemen. Absrac We sugges a new approach for analyzing he role of financial variables and shocks in compuing he oupu gap. We esimae a wo-region DSGE model for he euro area, wih financial fricions a he household level, beween Afer joining he moneary union, a decline in some counries borrowing coss conribued o a credi, housing and real boom and bus cycle. We show ha financial fricions amplified economic flucuaions and he measure of he oupu gap in hose counries. On he conrary, in counries such as France and Germany, financial fricions played a minor role in oupu gap measures. We also presen evidence of he rade-offs faced by he European Cenral Bank when rying o sabilize wo regions in a currency union wih unsynchronized economic cycles. Keywords: Moneary Union, Oupu Gap, Financial Fricions, and Bayesian Esimaion. JEL Codes: C51, E32, E52. Auhor s Address: prabanal@imf.org; maherisanjani@imf.org 1 The auhors would like o hank Tamim Bayoumi, Helge Berger, Olivier Blanchard, Giovanni Dell Ariccia, Giang Ho, Ivanna Vladkova Hollar, Olivier Jeanne, Peer Karadi, Nir Klein, Luc Laeven, Alber Marce, Reza Moghadam, Erneso Ramirez Rigo, Jorge Roldós, Anonio Spilimbergo, Lars Svensson and Jerome Vandenbussche for useful commens and discussions.

3 Conens I. Inroducion 5 II. The Model 9 A. Credi Markes A.1. Domesic Inermediaries A.2. Inernaional Inermediaries B. Households B.1. Savers B.2. Labor Unions and Wage Seing B.3. Borrowers C. Firms, Technology, and Sicky Prices C.1. Final Goods Producers C.2. Inermediae Goods Producers D. Closing he Model D.1. Marke Clearing Condiions D.2. Moneary Policy and Ineres Raes III.Parameer Esimaes 19 A. Daa B. Calibraed Parameers C. Prior and Poserior Disribuions D. Variance Decomposiion: The Role of Demand and Financial Shocks IV.Decomposing he Business Cycle in he Euro Area 27 A. HBS Counries B. Core C. The Role of Financial Fricions V. Does One Moneary Policy Fi All? 35 VI.Impulse Response Analysis 37 VII.Conclusions 41 A Appendix: Daa and Sources 46 B Appendix: Linearized Condiions 47 Lis of Tables 1 Calibraed Parameers Prior and Poserior Disribuions, Economic Parameers Prior and Poserior Disribuions, AR(1) Shock Processes Variance Decomposiion

4 4 Lis of Figures 1 Ten Year Governmen Bond Raes in Seleced Euro Area Counries Excess Credi and Unemploymen Raes Shock Decomposiion, Oupu and Oupu Gaps Shock Decomposiion, Credi and House Prices Oupu Gaps and Financial Wedges Naural Raes of Ineres and Deviaions from Taylor Rule IRF - Financial Shocks IRF -Housing Demand Shocks IRF -Moneary Policy Shocks

5 5 I. Inroducion The concep of he oupu gap, he difference beween acual and poenial GDP, is key in macroeconomic policy formulaion. Cenral banks need an assessmen of he oupu gap o undersand if fuure inflaionary pressures are building up. In addiion, he cenral bank may also have an explici objecive of sabilizing he oupu gap. The ask of esimaing oupu gaps is complicaed by he fac ha we do no observe poenial oupu. Therefore, assumpions are needed o consruc a measure of poenial oupu, and an ex-pos assessmen of he accuracy of he esimaes is no possible. A simple and popular way o obain a measure of poenial oupu and he oupu gap is he Hodrick and Presco (1997, HP) filer, which fis a smooh rend o a ime series. In he HP filer, poenial oupu is a weighed average of pas and fuure values of acual oupu. Since his is he only informaion ha is required, he HP filer canno explain wha is driving poenial oupu and he oupu gap. Therefore, he use of mulivariae filers provides he nex sep o incorporae addiional informaion. As an example, Benes e al. (21) presen a mulivariae filer ha makes use of addiional variables (such as inflaion and unemploymen) and economic relaionships (such as a Phillips Curve and Okun s Law) o esimae poenial oupu. However, he recen Global Financial Crisis (GFC) has shown ha large flucuaions in asse markes (including housing and credi), if lef unaddressed, can lead o large boom and bus real GDP cycles, wih imporan welfare consequences. Before he GFC, hese imbalances did no necessarily show up as inflaionary pressures in he consumer price index (CPI), which suggesed ha he surge in asse prices (in paricular, housing), credi and GDP could be susainable. The severe credi and housing buss ha followed in many indusrialized counries afer 27 sugges acual GDP growh significanly oupaced poenial during he boom years. One such example is he case of some counries of he Economic and Moneary Union (EMU), ha winessed a srong reducion in borrowing coss during he firs years of he euro, and a sharp increase in he afermah of he GFC. Greece, Ireland, Ialy, Porugal, and Spain s borrowing coss (measured as he 1-year rae on governmen bonds) displayed a similar behavior beween 1995 and 214, a leas qualiaively (Figure 1). Before he creaion of he euro, hese counries faced higher borrowing coss han France and Germany, bu hese ineres rae differenials disappeared afer hese counries joined he currency union. Lower raes during ha period conribued o a surge in residenial invesmen, credi and house prices inflaion in some of hese counries (in paricular in Greece, Ireland and Spain), bu no widespread CPI inflaion. Conrary o France and Germany, hese counries faced higher borrowing coss afer he GFC, and in paricular during he period, hereby worsening he recession. In his paper, we sudy he role of financial facors, including he decline in risk premia and acceleraor effecs, in explaning macroeconomic flucuaions and he assessmen of he oupu gap in he euro area. We conduc he sudy for wo main regions of he euro area. Throughou he paper, we refer o he aggregae of France and Germany as he core of he euro area, and o he aggregae of he remaining counries in Figure 1 as he euro area counries wih high borrowing spreads or HBS counries. While here are similariies in his second group, such as he behavior of borrowing coss, i is imporan o sress ha here are also differences.

6 6 Ireland s borrowing coss were no as high as he oher counries before he creaion of he euro, ye i wen hrough a housing and credi boom and bus cycle as much as Spain did. Porugal had a credi boom, bu growh was never as high as Greece, Ireland and Spain during he 2s. Ialy s credi growh and real house price appreciaion was milder, and real GDP growh was lower during he early 2s han he res of he HBS counries. 1 Figure 1: Ten Year Governmen Bond Raes in Seleced Euro Area Counries FRANCE GERMANY GREECE IRELAND ITALY PORTUGAL SPAIN Noe: Horizonal axis shows he year, and he verical axis presens ineres raes in percen. The oucome of he GFC, and more generally he lieraure ha documens he comovemen beween credi, house prices and real aciviy, provides a clear case for expanding he informaion se o measure poenial oupu and he oupu gap using financial daa. 2 In addiion, in recen years, inflaion appears o have been less responsive o changes in economic slack, hereby reducing is informaional conen o esimae he oupu gap, a phenomenon known as he flaening of he Phillips Curve. 3 However, here appears o be a consisen negaive correlaion beween counries experiencing a credi boom and he unemploymen rae, which can be empirically used. Figure 2 shows he bivariae relaionship beween excess credi and unemploymen in he wo regions of he euro area using quarerly daa beween 26Q1 and 213Q4. 4 As Figure 2 shows, here is a srong negaive relaionship beween excess credi and 1 Ideally, we would wan o use a muli-counry model of he EMU for each counry member, bu his would be compuaionally burdensome. Therefore, we group counries according o he behavior of borrowing coss as shown in Figure 1. 2 See Claessens, Kose and Terrones (29), and Chrisiano, Ilu, Moo and Rosagno (28). 3 See IMF (213). 4 The unemploymen rae is a weighed average using he European Cenral Bank (ECB) weighs o compue he Harmonized Index of Consumer Prices (HICP). Excess credi is he deviaion beween seasonally adjused loans o nonfinancial corporaions and is 4-year moving average.

7 7 he unemploymen rae only in he euro area HBS counries, bu his relaionship was absen in he core. This differen response o he flucuaions in credi will urn ou o be key in our oupu gap measures laer in he paper. 5 Using a model wih financial fricions and housing, his paper ries o idenify he drivers of he oupu gap more accuraely, including he role of ineres rae spreads flucuaions in a currency union. Figure 2: Excess Credi and Unemploymen Raes 2 Core Unemploymen Rae 6 Excess Credi HBS Unemploymen Rae 6 4 Excess Credi Noe: Horizonal axis shows excess credi in percenage deviaion from rend and verical axis presens unemploymen raes in percen. Several alernaive mehods have been proposed o deal wih he measuremen of poenial oupu wih financial variables. One mehod consiss in incorporaing financial variables in a mulivariae filer environmen (see Borio e al. 214, Berger e al., 215). In his approach, he coefficiens are reduced-form and have lile guidance from heory. Therefore, i does no allow for an undersanding of he channels hrough which financial variables affec he real economy. Hence, a more srucural approach specifies and esimaes a Dynamic Sochasic 5 See also he speech by Sein (214) on he imporance of financial volailiy in explaining he unemploymen cycle in he Unied Saes.

8 8 General Equilibrium (DSGE) model wih financial fricions. Chrisiano, Moo, and Rosagno (214) esimae he financial acceleraor model of Bernanke, Gerler and Gilchris (1999) and show he imporance of financial fricions and financial shocks in explaining macroeconomic flucuaions. Furlaneo, Gelain and Taheri Sanjani (214) use a similar framework o derive a measure of poenial oupu, undersood as he counerfacual level of oupu when nominal rigidiies (sicky prices and wages) and inefficien shocks (price and wage mark-up shocks) are removed from he model. They confirm he imporan amplificaion role of financial fricions, he key role of financial shocks o explain flucuaions, and wha is more imporan, ha he implicaions for he behavior of he oupu gap of he Unied Saes are radically differen once he financial secor is inroduced. 6 In his paper, we follow he DSGE modeling approach o esimae he oupu gap in he euro area, using a wo-region model of a currency union ha incorporaes housing and financial fricions wih balance shee effecs a he household level (see Quin and Rabanal, 214). 7 Once he model is esimaed wih hireen macroeconomic ime series and Bayesian mehods, we perform a variance decomposiion exercise o undersand he sources of he boom-and-bus cycle in he euro area during he las fifeen years. Risk premium shocks (boh a he region level and in he housing marke) and housing demand shocks were he main source of he boom and bus cycle in some of he HBS counries of he euro area. Moreover, he inroducion of financial fricions maers: he model gives a larger cycle when hese feaures are aken ino accoun, and he aggregae oupu gap measure for he HBS group appears more consisen wih he narraive evidence. For insance, he HP filer gives a negaive oupu gap during he mid-2s and a close-o-zero oupu gap by end-213. On he conrary, he DSGE model implies ha he oupu gap was posiive in he HBS counries for mos of he 2s, and abou -4 percen by end According o our esimaes, he cycle was less volaile in he core and was driven by non-financial facors: echnology and aggregae demand shocks. The measure of oupu gap consisen wih he model is very similar o he one consruced by he HP filer for he core of he euro area, because of he absence of a credi boom. We also show he rade-offs ha he European Cenral Bank (ECB) faced when rying o conduc a single moneary policy wih wo regions facing differen business cycles. The res of he paper is organized as follows. Secion 2 presens he model, while Secion 3 presens he economeric mehodology and parameer esimaes. Secion 4 discusses he model-consisen measures of poenial oupu and he oupu gap and he drivers in each region. Secion 5 presens impulse response funcions o seleced shocks in he model, while Secion 6 sudies he moneary policy rade-offs faced by he ECB. Secion 7 concludes. 6 Galí, Smes and Wouers (212) show ha he measure of oupu gap also depends on inroducing labor marke rigidiies and unemploymen as an observable variable in a DSGE model. 7 The model has several nominal and real fricions o fi he daa, and a closed-form expression for he oupu gap canno be derived. See Cúrdia and Woodford (29) for a model wih financial fricions a he household level, where a erm involving credi fricions affecs he Phillips curve and oupu gap expressions. 8 In a companion paper, Berger e al. (215) compare oupu gaps using mulivariae filers similar o Borio e al. (214) and a DSGE model like he one presened in his paper.

9 9 II. The Model The model is an exension of Quin and Rabanal (214), wih sicky wages and price markup shocks. We use a wo-region model of a common currency area where savings and invesmen can differ, and where a region can obain credi financing from he oher. 9 We ignore developmens coming from ouside he euro area and do no include a res-of-he-world block. There is no evidence suggesing ha exernal (ouside of he EMU) shocks riggered he housing and credi boom and bus cycle in some counries of he euro area, and adding anoher region would complicae he analysis and he esimaion. The heoreical framework consiss of a wo-region, wo-secor, wo-agen general equilibrium model of a single currency area. The wo regions are of size n and 1 n. There are wo ypes of goods, durables and non-durables, ha are produced under monopolisic compeiion and nominal rigidiies. While non-durables are raded across counries, durable goods are non-radable. In each region, here are wo ypes of agens, savers (size λ in each region) and borrowers (1 λ), who differ in heir discoun facor and habi formaion parameer. Boh agens consume non-durable goods and purchase durable goods o increase heir housing sock. Borrowers are more impaien han savers and have a preference for early consumpion, which creaes he condiion for credi o occur in equilibrium. In addiion, borrowers are hi by an idiosyncraic qualiy or valuaion shock o heir housing sock, which affecs he value of collaeral ha hey can use o borrow agains. 1 Hence, we adap he mechanism of Bernanke, Gerler and Gilchris (1999), henceforh BGG, o he household side and o residenial invesmen: shocks o he valuaion of housing affec he balance shee of borrowers, which in urn affec he defaul rae on morgages and he lending-deposi spread. There are wo ypes of financial inermediaries. Domesic financial inermediaries ake deposis from savers, gran loans o borrowers, and issue bonds. Inernaional financial inermediaries rade hese bonds across counries o channel funds from one region o he oher. In compensaion for his service, inernaional financial inermediaries charge a risk premium which depends on he ne foreign asse posiion of he region. Therefore, savings and (residenial) invesmen need no o be balanced a he region level period by period, since excess credi demand in one region can be me by funding coming from elsewhere in he moneary union. In wha follows, we only presen he home region block of he model, by describing he domesic and inernaional credi markes, households, and firms. Moneary policy is conduced by a cenral bank ha arges he union-wide CPI inflaion rae, and also reacs o flucuaions in he union-wide real GDP growh. The res of he euro area region block is characerized by a similar srucure regarding credi markes, households and firms. Unless specified, all shocks follow zero-mean AR(1) processes in logs. 9 This is an advanage over models where he euro area is reaed as a single counry, such as he Smes and Wouers (23) model, ha canno explain inra-union imbalances. 1 We could also assume ha savers are hi by a housing qualiy shock. Since hey do no borrow and use heir housing sock as collaeral, his qualiy shock would no have any macroeconomic impac.

10 1 A. Credi Markes We adap he BGG financial acceleraor idea o he housing marke, by inroducing defaul risk in he morgage marke, and a lending-deposi spread ha depends on housing marke condiions. There are wo main differences wih respec o he BGG mechanism. Firs, here are no agency problems or asymmeric informaion in he model, and borrowers will only defaul if hey find hemselves underwaer: ha is, when he value of heir ousanding deb is higher han he value of he house hey own. Second, unlike he BGG seup, we assume ha he one-period lending rae is pre-deermined and does no depend on he sae of he economy, which seems o be a more realisic assumpion. 11 A.1. Domesic Inermediaries Domesic financial inermediaries collec deposis from savers S, for which hey pay a deposi rae R, and exend loans o borrowers S B for which hey charge he lending rae R L. Credi graned o borrowers is backed by he value of he housing sock ha hey own (P D D B ), where P D is he nominal house price and D B is he housing sock owned by borrowers. We inroduce risk in he credi and housing markes by assuming ha each borrower (indexed by j) is subjec o an idiosyncraic qualiy shock o he value of her housing sock, ω j, ha is log-normally disribued wih CDF F (ω). We choose he mean and sandard deviaion so ha Eω = 1 and, hence, here is idiosyncraic risk bu no aggregae risk in he housing marke. This assumpion implies ha log(ω j ) N( σ2 ω,, 2 σ2 ω,), wih σ ω, being he sandard deviaion characerizing he qualiy shock. This sandard deviaion is ime-varying, and follows an AR(1) process in logs: log(σ ω, ) = (1 ρ σω ) log( σ ω ) + ρ σω log(σ ω, 1 ) + u ω, wih u ω, N(, σ uω ). The qualiy shock ω j can lead o morgage defauls and affecs he spread beween lending and deposi raes. The realizaion of he shock is known a he end of he period. High realizaions of ω j 1 allow households o repay heir loans in full, and hence hey repay he full amoun of heir ousanding loan R 1S L 1. B Realizaions of ω j 1 ha are low enough make households defaul on heir loans in period. Afer he household defauls on her loan, he bank calls a deb-collecion agency ha forces he household o repay he value of he housing sock afer he shock has realized, ω 1P j D D B. Afer paying his amoun, he household keeps her house. These deb-collecion agencies charge banks a fracion µ of he value of he house. The profis of hese agencies are ransferred o savers, who own hem. The value of he idiosyncraic shock is common knowledge, so households will only defaul when hey are underwaer. 12 When graning credi, financial inermediaries do no know he cu-off value of hose house- 11 A similar approach is aken by Suh (212) and Zhang (29). 12 Under his assumpion, no fracion of he housing sock is desroyed during he foreclosure process. If, as in BGG, a fracion of he collaeral was los during foreclosure, risk shocks migh have unrealisic expansionary effecs on housing and residenial invesmen. See Forlai and Lamberini (21).

11 11 holds ha defaul and hose who do no. The ex-ane hreshold value expeced by banks is hus given by: [ ω a E P D +1 D+1] B = R L S B. (1) Inermediaries behave in a risk-neural way and require he expeced reurn from graning one euro of credi o be equal o he funding rae of banks, which equals he deposi rae (R ): ω a R = E {(1 µ) ωdf (ω, σ ω, ) P D +1D B +1 S B + [1 F ( ω a, σ ω, )] R L { = E (1 µ)g ( ω a, σ ω, ) P +1D D +1 B + [1 F ( ω a S B, σ ω, )] R L } }, (2) wih [1 F ( ω a, σ ω, )] = df (ω; σ ω a ω, )dω being he expeced probabiliy ha he shock exceeds he ex-ane hreshold ω a and G ( ω a, σ ω, ) = ω a ωdf (ω; σ ω, ) being he expeced value of he shock condiional on he shock being less han ω a. The paricipaion consrain (2) ensures ha he opporuniy coss R are equal o he expeced reurns, which are given by he expeced foreclosure selemen as percen of ousanding credi (he firs erm of he righ hand side of equaion 2) and he expeced repaymen of households wih higher housing values (he second erm). Due o he fees paid o deb-collecion agencies o make defauling households pay heir debs, financial inermediaries only receive a fracion (1 µ) of he morgage selemen. The aggregae balance shee of domesic financial inermediaries in he home region is: nλ (S B ) = n (1 λ) S B, (3) where B are claims on financial inermediaries in he res of he euro area region (as explained below). Combined wih he paricipaion consrain equaion (2), we obain he following relaionship: R L 1 = E R + [1 F ( ω a, σ ω, )]. (4) (1 µ)g( ω a,σω,) ω a According o equaion (4), for a given demand of credi [ from borrowers, observed values of risk σ ω,, and expeced values of he housing sock E P D +1 D+1] B, inermediaries passively se he lending rae R L and he expeced (ex-ane) hreshold ω a so ha equaion (1) and he paricipaion consrain (2) are fulfilled. Unlike he original BGG se-up, he one-period lending rae R L is deermined a ime, and does no depend on he sae of he economy a + 1. This means ha he paricipaion consrain of financial inermediaries delivers ex-ane zero profis. However, i is possible ha, ex-pos, hey make profis or losses. We assume ha savers collec profis or recapialize financial inermediaries as needed. As discussed in Quin and Rabanal (214), he paricipaion consrain delivers a posiive relaionship beween LTV raios (S B /P+1D D +1) B and he spread beween he funding and he lending rae, due o he probabiliy of defaul.

12 12 Finally, we assume ha he deposi rae in he home region equals he risk-free rae se by he cenral bank. In he res of he euro area, domesic financial inermediaries behave he same way. In heir case, hey face a deposi rae R and a lending rae R L, and he spread is deermined in an analogous way o equaion (2). We explain below how he deposi rae in he res of he euro area R is deermined. A.2. Inernaional Inermediaries Inernaional financial inermediaries buy and sell bonds issued by domesic inermediaries in boh regions. For insance, if he home domesic inermediaries have an excess B of loanable funds, hey will sell hem o he inernaional inermediaries, who will lend an amoun B o he res of he euro area domesic inermediaries. Inernaional inermediaries apply he following formula o he spread hey charge beween bonds in he home (issued a an ineres rae R ) and in he res of he euro area regions (issued a R ): R = R + { ϑ exp [ κ B ( B P C Y C )] } 1. (5) The spread depends on he raio of real ne foreign asses B /P C o seady sae non-durable GDP (Y C ) in he home region (o be defined below). When home domesic inermediaries have an excess of funds ha hey wish o lend o he res of he euro area domesic inermediaries, hen B >. Hence, he res of he euro area inermediaries will pay a higher ineres rae R > R. The parameer κ B denoes he risk premium elasiciy and ϑ is a region-wide risk premium shock, which increases he wedge beween he home and he res of he euro area deposi raes. Inernaional inermediaries are owned by savers in each region, and opimaliy condiions will ensure ha he ne foreign asse posiion of boh counries is saionary. 13 They always make posiive profis (R R ) B, which are equally spli beween savers of boh counries. B. Households B.1. Savers Savers indexed by j [, λ] maximize he following uiliy funcion: { E β [γξ C log(c j εc 1 ) + (1 γ)ξ D log(d j ) = ( L j ) 1+ϕ 1 + ϕ ]}, (6) 13 Hence, he assumpion ha inernaional inermediaries rade unconingen bonds amouns o he same case as allowing savers o rade hese bonds. Under marke incompleeness, a risk premium funcion of he ype assumed in equaion (5) is required for he exisence of a well-defined seady sae and saionariy of he ne foreign asse posiion. See Schmi-Grohé and Uribe (23).

13 13 where C j, D j, and L j represen he consumpion of he flow of non-durable goods, he sock of durable goods (housing) and he labor disuiliy of agen j. Following Smes and Wouers (23) as well as Iacoviello and Neri (21) we assume exernal habi persisence in non-durable consumpion, wih ε measuring he influence of pas aggregae non-durable consumpion C 1. The parameer β sands for he discoun facor of savers, γ measures he share of non-durable consumpion in he uiliy funcion, and ϕ denoes he inverse elasiciy of labor supply. The uiliy funcion is hi by wo preference shocks, affecing he marginal uiliy of eiher non-durable consumpion (ξ C ) or housing (ξ D ). As we show in Secion IV, he housing demand shock is key o explain he housing and credi boom and bus cycle in some counries of he euro area. This shock can be seen as a shor-cu for unmodeled facors affecing he demand of housing, such as populaion growh and speculaive demand for housing. 14 However, we are no able o ake a sand on which facor is he mos imporan one. (C j F, Non-durable consumpion is an index composed of home (C j H, ) and res of he euro area ) produced goods: C j = [ τ 1 ι C ( ) C j ι C 1 1 ι C H, + (1 τ) ι C ( C j F, ) ι C 1 ι C ] ιc ι C 1, (7) wih τ [, 1] denoing he fracion of domesically produced non-durables a home and ι C governing he subsiuabiliy beween domesic and res of he euro area consumpion goods. Following Iacoviello and Neri (21), we inroduce imperfec subsiuabiliy of labor supply beween he durable and non-durable secor o explain comovemen a he secor level: L j = [ ( α ι L L C,j ) 1+ιL + (1 α) ι L ( L D,j ) 1+ιL ] 1 1+ι L. (8) The labor disuiliy index consiss of hours worked in he non-durable secor L C,j and durable secor L D,j, wih α denoing he share of employmen in he non-durable secor. Reallocaing labor across secors is cosly, and is governed by he parameer ι L. 15 The budge consrain of savers in nominal erms reads: P C C j + P D I j + S j R 1 S j 1 + W C L C,j + W D L D,j + Π j, (9) where P C and P D are he price indices of non-durable and durable goods, respecively, which are defined below. W C and W D are nominal wage indices paid in boh secors, as explained below. Savers allocae heir expendiures beween non-durable consumpion C j and residenial invesmen I j. They have access o deposis in he domesic financial sysem S j, ha pay 14 Adam, Kuang, and Marce (211) show ha deparing from raional expecaions and inroducing learning mechanisms is imporan o explain large boom and bus cycles in housing. However, i is no sraighforward o inroduce learning in a large scale model as ours, and perform Bayesian esimaion. Therefore, he housing demand shock can also be seen as a shor-cu for deparures from raional expecaions. 15 Noe ha when ι L = he aggregaor is linear in hours worked in each secor and here are no coss of swiching beween secors.

14 14 he deposi ineres rae R. In addiion, savers also receive profis Π j from inermediae goods producers in he durable and he non-durable secor, from domesic and inernaional financial inermediaries, and from deb-collecion agencies ha charge fees o domesic financial inermediaries o make defauling households pay heir debs. Purchases of durable goods, or residenial invesmen I j are used o increase he housing sock D j wih a lag, according o he following law of moion: [ ( )] D j = (1 δ)d j Ϝ I j 1 I j 2 I j 1 (1) where δ denoes he depreciaion rae of he housing sock and Ϝ ( ) an adjusmen cos funcion. Following Chrisiano, Eichenbaum, and Evans (25), Ϝ ( ) is a convex funcion, which in seady sae mees he following crieria: Ϝ = Ϝ = and Ϝ >. 16 B.2. Labor Unions and Wage Seing Nominal wages are assumed o be sicky as in Smes and Wouers (23) and Iacoviello and Neri (21). Households provide heir homogenous labor services o labor unions, which differeniae hese services, negoiae wages, and sell hem o labor packers aferwards. These perfecly compeiive wholesale labor packers reassemble hese services ino homogenous labor composies and offer hem o inermediae goods producers. There exis wo unions in each region, one for each secor, which se nominal wages for he respecive secor subjeced o a Calvo scheme. The probabiliies of being able o readjus wages in a given period for he non-durable and durable secor are given by 1 θ C,W and 1 θ D,W, respecively. In addiion, remaining wages which are no readjused are parially indexed o pas CPI inflaion (wih he fracions ϕ C,W and ϕ D,W, respecively). We assume ha wages are he same in he non-durable and durable secor, regardless of he ype of households. Unions are run by savers while borrowers are merely members. Thus, unions maximize he uiliy of savers (6) subjec o heir budge consrain (9) and o he demand schedule of labor packers. 17 B.3. Borrowers Borrowers differ from savers along hree main dimensions. Firs, heir preferences are differen. Their discoun facor of borrowers is smaller (β B < β), and we allow for differen habi formaion coefficiens ε B. Second, borrowers do no earn profis from inermediae goods producers, financial inermediaries, or deb-collecion agencies. Finally, as discussed above, borrowers are 16 This cos funcion allows us o replicae hump-shaped responses of residenial invesmen o shocks, and reduce residenial invesmen volailiy. 17 Borrowers ake wages as given and supply labor o boh secors by equaing heir marginal rae of subsiuion o ha of savers. We assume ha he wage mark-up is high enough and shocks are small enough such ha boh ypes of workers will always wan o supply labor a he prevailing wage.

15 15 subjec o a qualiy shock o he value of heir housing sock ω j. Since borrowers are more impaien, in equilibrium, savers are willing o accumulae asses as deposis, and borrowers are willing o pledge heir housing wealh as collaeral o gain access o loans. Analogously o savers, he uiliy funcion for each borrower j [λ, 1] reads: E (β B ) γξ C = log(c B,j ε B C 1) B + (1 γ)ξ D log(d B,j ) ( L B,j 1 + ϕ ) 1+ϕ, (11) where all variables and parameers wih he superscrip B denoe ha hey are specific o borrowers. The indices of consumpion and hours worked, and he law of moion of he housing sock have he same funcional form as in he case of savers (equaions 7, 8, and 1). The budge consrain for borrowers differs among hose who defaul and hose who repay heir loans in full. Hence, aggregaing borrowers budge consrains and dropping he j superscrips, we obain he following: P C C B + P D [ I B + G ( ω p 1, σ ω, 1 ) D B ] + [ 1 F ( ω p 1, σ ω, 1 )] R L 1 S B 1 (12) S B + W C L C,B + W D L D,B. Borrowers consume non-durables C B, inves in he housing sock I B, and supply labor o boh secors (L C,B and L D,B ). Savers and borrowers are paid he same wages W C and W D in boh secors. Borrowers ake wages (which are bargained by unions owned by savers) as given, and equae hem o heir marginal rae of subsiuion beween consumpion and hours in each secor. Borrowers obain loans S B from financial inermediaries a a lending rae R L. Afer aggregae and idiosyncraic shocks hi he economy, borrowers will defaul if he realizaion of he idiosyncraic shock falls below he ex-pos hreshold: ω p 1 = RL 1S 1 B. (13) P D D B Since invesmen increases he housing sock wih a lag (equaion 1), D B is a pre-deermined variable. The lending rae is also pre-deermined and no a funcion of he sae of he economy. So i is possible ha ω a and ω p differ. Noe, however, ha when he loan is signed, ω a = E ω p. The erm [ 1 F ( ω )] 1, p σ ω, 1 = ω df (ω; σ p ω, 1 )dω defines he fracion of loans which are 1 repaid by he borrowers, because hey were hi by a realizaion of he shock above he hreshold ω 1. p Similarly, P D G ( ω ) 1, p σ ω, 1 D B = P D ω p 1 ωdf (ω; σ ω, 1 )D B is he value of he housing sock on which borrowers have defauled on and which is paid o banks afer a deb-collecion agency inervenes.

16 16 C. Firms, Technology, and Sicky Prices Homogeneous final non-durable and durable goods are produced using a coninuum of inermediae goods in each secor (indexed by h [, n] in he home region, and by f [n, 1] in he res of he euro area region). Inermediae goods in each secor are imperfec subsiues of each oher, and here is monopolisic compeiion as well as Calvo (1983)-syle saggered price seing. Inermediae goods are no raded across regions and are bough by domesic final goods producers. In he final goods secor, non-durables are sold o domesic and res of he euro area households. 18 Durable goods are solely sold o domesic households, who use hem o increase he housing sock. Boh final goods secors are perfecly compeiive, operaing under flexible prices. C.1. Final Goods Producers Final goods producers in boh secors aggregae he inermediae goods hey purchase according o he following producion funcion: Y k [ ( ) 1 1 σ k n n ] σ k σ k 1 σ k 1 Y k σ (h) k dh, for k = C, D, (14) where Y k represens he final goods produced from inermediae goods Y k (h), while σ k denoes he price elasiciy of inermediae goods, which is ime-varying because here are iid price markup shocks. Final goods producers purchase non-durable inermediae goods a a price of P H (h) and durable inermediae goods a a price P D (h). Profi maximizaion leads o he following demand funcion for individual inermediae goods: Y C (h) = ( P H P H (h) ) σc Y H, and Y D (h) = Price levels for domesically produced non-durables P H hrough he usual zero-profi condiion: ( P D P D (h) ) σd Y D. (15) and durable final goods P D are obained P H { 1 n n [ P H (h) ] } 1 1 σ 1 σ C C dh, and P D { 1 n n [ P D (h) ] } 1 1 σ 1 σ D D dh. (16) The price level for non-durables consumed in he home region (i.e. he CPI for he home region) includes he price of domesically produced non-durables (P H ), and of impored non-durables (P F ): [ P C = τ ( ) P H 1 ιc + (1 τ) ( ) ] 1 P F 1 ιc 1 ι C. (17) 18 Thus, for non-durable consumpion we need o disinguish beween he price level of domesically produced non-durable goods P H,, of non-durable goods produced abroad P F,, and he consumer price index P C, which will be a weighed combinaion of hese wo price levels.

17 17 C.2. Inermediae Goods Producers Inermediae goods are produced under monopolisic compeiion wih producers facing Calvosyle saggered price seing, which implies ha in each period only a fracion 1 θ C (1 θ D ) of inermediae goods producers in he non-durable (durable) secor receive a signal o re-opimize heir price. For he remaining fracion θ C (θ D ) we assume ha heir prices are parially indexed o lagged secor-specific inflaion (wih a coefficien φ C, φ D in each secor). In boh secors, inermediae goods are produced solely wih labor: Y C (h) = A Z C L C (h), Y D (h) = A Z D L D (h) for all h [, n] (18) The producion funcions include region- and secor-specific saionary echnology shocks Z C and Z D, each of which follows a zero mean AR(1)-process in logs. In addiion, we inroduce a non-saionary union-wide echnology shock, which follows a uni roo process: log (A ) = log (A 1 ) + ε A. This shock inroduces non-saionariy o he model and consiues a model-consisen way of derending he daa by aking logs and firs differences o he real variables ha inheri he random-walk behavior. In addiion, i adds some correlaion of echnology shocks across secors and counries, which is helpful from he empirical poin of view because i allows o explain comovemen of main real variables. Since labor is he only producion inpu, cos minimizaion implies ha real marginal coss in boh secors are given by: MC C /P H, = W C A Z C, MC D = W D A Z D /P D. (19) Inermediae goods producers solve a sandard Calvo model profi maximizaion problem wih indexaion. As shown in he appendix, inflaion dynamics in each secor depend on one expeced lead and one lag of inflaion, and he secor-specific real marginal cos. We assume he here are price mark-ups in he non-durable price level (CPI), such ha µ C = σ C = µ σ C 1 C exp(ε µc ), where he innovaion (price mark-up shock) is iid. This shock is inended o pick up high frequency movemens in he consumer price level in boh counries, due o unmodelled volaile facors such as energy and food prices. D. Closing he Model D.1. Marke Clearing Condiions For inermediae goods, supply equals demand. We wrie he marke clearing condiions in erms of aggregae quaniies and, hus, muliply per-capia quaniies by populaion size of each region. In he home non-durable secor, producion is equal o domesic demand by savers C H, and borrowers CH, B and expors (consising of demand by savers C H, and borrowers CB H,

18 18 from he res of he euro area region): ny C = n [ ] [ λc H, + (1 λ) CH, B + (1 n) λ CH, + (1 λ ) CH,] B. (2) Durable goods are only consumed by domesic households and producion in his secor is equal o residenial invesmen for savers and borrowers: ny D = n [ λi + (1 λ) I B ]. (21) In he labor marke, oal hours worked has o be equal o he aggregae supply of labor in each secor by boh savers and borrowers: n L k (h)dh = λ n L k,j dj + (1 λ) n L k,b,j dj, for k = C, D. (22) Credi marke clearing implies ha for domesic credi and inernaional bond markes, he balance shees of financial inermediaries are saisfied. Besides equaion (3), his requires: nλb + (1 n)λ B =. (23) Finally, aggregaing he resource consrains of borrowers and savers, and he marke clearing condiions for goods and financial inermediaries, we obain he law of moion of bonds issued by he home inernaional financial inermediaries. This can also be viewed as he evoluion of ne foreign asses (NFA) of he home region: nλb = nλr 1 B 1 + { [ [ (1 n) P H, λ CH, + (1 λ ) CH,] B npf, λcf, + (1 λ) CF,]} B, (24) which is deermined by he aggregae sock of las period s NFA imes he ineres rae, plus ne expors. D.2. Moneary Policy and Ineres Raes Moneary policy is conduced a he currency union level by he cenral bank wih an ineres rae rule ha arges deviaions of he union-wide CPI inflaion and real oupu growh from heir seady-sae values. The cenral bank ses he deposi rae in he home region, and he oher raes are deermined as described in he model. Le Π EMU be he seady sae level of union-wide CPI inflaion, R he seady sae level of he ineres rae and ε m an iid moneary policy shock, he ineres rae rule is given by: [ R = R ( P EMU /P EMU 1 Π EMU ) γπ ( Y EMU ] ) 1 γr /Y 1 EMU γy R γ R 1 exp(ε m ). (25)

19 19 The euro area CPI (P EMU ) and real GDP (Y EMU ) are given by geomeric averages of he home and res of he euro area region variables, using he region size as a weigh: P EMU = ( P C ) n ( ) P C 1 n, and Y EMU = (Y ) n ( ) Y 1 n. where he naional real GDPs are expressed in erms of non-durables: Y = Y C + Y D P D P C, and Y = Y C + Y D P D P C. III. Parameer Esimaes We apply sandard Bayesian mehods o esimae he parameers of he model (see An and Schorfheide, 27). Firs, he equilibrium condiions of he model are normalized such ha all real variables become saionary. This is achieved by dividing real variables in boh counries by he level of non-saionary echnology, A. Second, he dynamics of he model are obained by aking a log-linear approximaion of equilibrium condiions around he seady sae wih zero inflaion and ne foreign asse posiions. 19 Third, he soluion of he model is expressed in sae-space form and he likelihood funcion of he model is compued using a Kalman filer recursion. Then, we combine he prior disribuion over he model s parameers wih he likelihood funcion and apply he Meropolis-Hasings algorihm o obain he poserior disribuion o he model s parameers. 2 A. Daa Daa for he core (home) region is obained by aggregaing daa for France and Germany, whereas he HBS (res of euro area) region, as discussed in Secion 1, includes Greece, Ireland, Ialy, Porugal, and Spain. We follow his classificaion because he HBC counries experienced a similar shock afer enering he EMU (he large decline in risk premia and ineres raes), and exhibied a somewha similar behavior in borrowing spreads in he run-up and afer he GFC. However, his is no a homogeneous group and each counry is differen in some aspecs. Ireland experienced a smaller decline of borrowing coss when joining he euro, ye i wen hrough a housing and credi boom and bus cycle as much as Spain did. Porugal had a credi boom, bu growh was never as high as Greece, Ireland and Spain. Ialy s credi boom was milder han he res, and i displayed lower growh han he res during he 2s. Greece s problems sared wih he fiscal secor, raher han wih a housing bus. We use quarerly daa ranging from 2q1-213q4 and hireen macroeconomic ime series. Hence, unlike oher esimaed DSGE models of he euro area, such as Smes and Wouers (23), 19 Appendix B deails he full se of normalized, linearized equilibrium condiions of he model. 2 The esimaion is done using Dynare The poserior disribuions are based on 25, draws of he Meropolis-Hasings algorihm.

20 2 we do no mix he sample periods before and afer he creaion of he euro. For boh regions we use six observables: real privae consumpion spending, real residenial invesmen, real gross domesic produc (GDP), he harmonized index of consumer prices (HICP), housing prices, and ousanding deb for households. We also include he 3-monh Euribor rae, which we use as counerpar of he deposi rae in he core. 21 The daa is aggregaed aking he economic size of he counries ino accoun, using he household expendiure weighs used by he Harmonised Index of Consumer Prices (HICP) for euro area counries. 22 We use quarerly growh raes of all price and quaniy (seasonally adjused) daa and we divide he ineres raes by 4 o obain a quarerly and logged equivalen variable o he model. We demean all series. 23 The measure of GDP in he model and in he daa is differen. In paricular, he measure of GDP in he model only includes non-durable consumpion and residenial invesmen. Hence, he model leaves ou business invesmen, governmen spending and ne expors wih hird counries. As a resul, we include an aggregae demand shock ha collecs all hese componens. In log-linear form his can be wrien as: gdp = (1 ḡ)y + ḡ(g ) where ḡ is he seady sae raio of exogenous demand o GDP, and g is an exogenous AR(1) process. 24 B. Calibraed Parameers Some parameers are calibraed because he se of observable variables ha we use does no provide informaion o esimae hem (Table 1). We assume ha he discoun facors are he same in boh counries for each ype of agen (β = β and β B = β B ). We se he discoun facor of savers o β =.99. The seady sae LTV raio, which also deermines he cu-off poin for defauling on a loan, is se o ω =.7 and equally across regions, according o euro area daa such as Gerali e al. (21). We se he defaul rae on loans, F (.) o 2.5 percen See Appendix A for furher deails on he daa se. 22 hp:// coicop inw.4.u2w.en.hml 23 We ried o o include spreads beween lending and deposi raes in boh regions as an observable variable, bu we did no ge sensible resuls. The daa available from he ECB confirms ha in a credi bus, quaniies adjus insead of prices, and hence conain more informaion abou credi condiions. In addiion, he ECB s acions afer he crisis (including he Long Term Refinancing Operaions) have helped reduce lending-deposi spreads in he counries ha iniially faced high borrowing coss during , and have hus reduced he informaion conen of he spreads. 24 We include business invesmen in his definiion, bu his variable affecs labor produciviy hrough capial deepening. Hence, when we decompose he conribuion of individual shocks on he observable variables and he oupu gap in Secion 4, we deduc he share of business invesmen ((Business Invesmen)/(Business Invesmen + Governmen Spending + Ne Expors )) from he aggregae demand shock and include i in he echnology shock. To do his ransformaion, we use annual daa on ne expors, governmen expendiure and business invesmen from he OECD daabase. We aggregae he daa using he same weighs and mehodology ha we described earlier in his secion. 25 I is difficul o find non-perfoming loans for household morgages only. Therefore, we use non-performing loans as percen of oal loans for he euro area beween aken from he World Bank World Develop-

21 21 Table 1: Calibraed Parameers β Discoun facor savers.99 ω Loan-o-value raio.7 F Defaul rae on loans.25 σ ω Seady sae risk.1742 µ Proporion of housing value paid o deb-collecion agency.2 β B Discoun facor borrowers.985 δ Depreciaion rae.125 σ Elasiciy of subsiuion beween inermediae goods 1 σ L Elasiciy of subsiuion beween labor ypes 1 n Size core economies.6 ḡ Fracion of exogenous demand in GDP.3 1 τ Fracion of impored goods from HBS o core economies.6 1 τ Fracion of impored goods from core o HBS economies.9 α Size of non-durable secor in GDP.94 As a resul, he seady sae value of he risk shock is σ ω = We se he deb-collecion agency fee o µ =.2, which is a value higher han ha calibraed by Forlai and Lamberini (21), bu lower han he recovery raes for loans esimaed for he Unied Saes. 26 Using hese values, he zero-profi condiion for financial inermediaries, and he consumpion Euler equaion for borrowers, we obain a discoun facor of borrowers of β B =.985. The depreciaion rae is assumed o be 5 percen (annual) and equal across counries (δ = δ =.125). The degree of monopolisic compeiion in he goods markes σ and in he labor markes (σ L ) is he same across secors and counries, implying mark-ups of 1 percen. We se he size of he core counries in he euro area o n =.6, based on GDP daa. We se he seady-sae raio of exogenous demand o GDP (ḡ = ḡ ) o.3. The bilaeral rade parameer 1 τ is calibraed based on he weighed average of oal impors o privae consumpion from HBS o core economies. The analogous parameer for he HBS counries 1 τ is calculaed in a similar way, bu is rounded o ensure ha he rade balance and he ne foreign asse posiion are zero in he seady sae. Finally, we assume ha he size of he durable and nondurable secors is he same for he core and he HBS counries of he euro area (α = α ). The assumpions of symmery and balanced rade make i easier o compue a seady sae where all relaive prices in all secors are equal o one, and where all per capia quaniies are he same. men Indicaors daabase (hp://daa.worldbank.org/opic/financial-secor). 26 See Morgage Bankers Associaion (28).

22 22 C. Prior and Poserior Disribuions In Table 2 we presen he prior disribuions, he poserior mean and 9 percen credible se of he economic esimaed parameers. 27 In Table 3, we presen he esimaed parameers of he shock processes. Given he shor sample, in addiion o calibraing some parameers, we resric ohers o be he same across counries. More specifically, we allow he parameers relaed o nominal rigidiies and shocks o differ across secors and counries, in order o permi quaniaively differen ransmission channels of moneary policy. However, he parameers relaing o preferences, adjusmen coss, and he fracion of savers are assumed o be he same in boh counries. As in Quin and Rabanal (214), we assume ha he housing demand shock and he TFP shock in non-durables has a common componen across counries. For insance, he housing demand shock follows: where he region-specific (ε ξ,d log(ξ D ) = ρ ξ,d log(ξ D 1) + ε ξ,d log(ξ D ) = ρ ξ,d log(ξ 1) D + ε ξ,d + ε ξ,d,com and ε ξ,d + ε ξ,d,com (26) ) as well as common (ε ξ,d,com ) innovaions are Normal iid wih mean zero. This helps explain he cross correlaion of prices and quaniies across counries. Firs, we commen on he parameers ha relae o preferences of borrowers and savers. We op for a prior disribuion cenered a.5 for he fracion of savers in he economy. We se a highly informaive prior by seing a small sandard deviaion of.5. The poserior mean suggess a somewha higher fracion (.57) o fi he macro daa. 28 We make a simplifying assumpion ha he number of savers in each region (λ) is he same in boh regions. 29 Ineresingly, we find ha he habi formaion coefficien is roughly he same (.71 for borrowers and.63 for savers). We cener he priors relaed o he elasiciy of subsiuion beween home and res of he euro area non-durables, he elasiciy of labor supply and he coefficien measuring cosly labor reallocaion o parameers available in he lieraure (Smes and Wouers, 23; Iacoviello and Neri, 21; and Adolfson e al., 27). We find an elasiciy of subsiuion beween home and res of he euro area goods close o he prior (a poserior mean of 1.5, jus like he prior mean). Regarding he coefficiens ha deermine labor supply, we find ha he poserior mean of he labor disuiliy coefficien ϕ is 1.14 and he degree of cosly labor reallocaion is abou For each sep of he Meropolis-Hasings algorihm, given a draw of he parameers ha we wish o esimae, we mus solve for he seady sae levels of consumpion of durables and non-durables, hours worked in each secor by each ype of agen, and for each region. Then, hese seady sae values are needed o obain he log-linear dynamics o he sysem. Also, for every draw, we solve for he weigh of non-durables in he uiliy funcion in each region (γ and γ ), which is no a free parameer bu raher a funcion of α, δ, λ, β, β B, ε, ε B, and ϕ. 28 Gerali e al. (21) calibrae his fracion o be.8 for he euro area. 29 Ideally, we would wan o esimae a differen λ, for each region. This heerogeneiy complicaes compuing he seady sae of he model for each ieraion of he Meropolis-Hasings algorihm, and criically slows down he esimaion process.