Incorporating Financial Cycles in Output Gap Measures: Estimates for the Euro Area

Transcription

1 Incorporaing Financial Cycles in Oupu Gap Measures: Esimaes for he Euro Area Pau Rabanal Marzie Taheri-Sanjani January 15, 215 Absrac We sugges a new approach for analyzing he role of credi and house prices in esimaing he oupu gap. We presen a wo-counry DSGE model for he core and periphery of he euro area, wih nancial fricions a he household level. We use several macroeconomic variables, including house prices and household credi for each region, o esimae he model beween We nd ha, in he core, he measure of oupu gap is independen of nancial fricions because of he absence of a credi boom during he sample period. On he conrary, in he periphery, nancial fricions amplify economic ucuaions and he oupu gap. We also presen evidence of he rade-o s faced by he European Cenral Bank when rying o sabilize wo regions in a currency union wih unsynchronized economic cycles. Key words: Moneary Union, Oupu Gap, Financial Fricions, Bayesian Esimaion. JEL Codes: C51, E32, E52. The auhors would like o hank Helge Berger, Giovanni Dell Ariccia, Ivanna Vladkova Hollar, Luc Laeven, Erneso Ramirez Rigo, and Anonio Spilimbergo for useful commens. 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. Boh auhors are a liaed wih he Inernaional Moneary Fund, 7 19h. S. NW, Washingon, DC 2431, USA. addresses: prabanal@imf.org, maherisanjani@imf.org. 1

2 2 I. Inroducion The concep of he oupu gap, he difference beween acual and poenial GDP, is key in macroeconomic policy formulaion. In moneary policy, 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 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. Hence, i 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 prices (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 crisis showed i was no. Going forward, i is imporan o undersand when he financial cycle has beneficial or exuberan effecs on he business cycle, and a policy response is warraned. 1 The oucome of he GFC, and more generally he lieraure on credi booms and buss, provides a clear case for expanding he informaion se o measure poenial oupu and he oupu gap using financial daa. 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. 2 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 1 shows he bivariae relaionship beween excess credi and unemploymen in he core and periphery of he euro area using quarerly daa beween 26Q1 and 213Q4. 3 As Figure 1 shows, here is a srong negaive relaionship beween excess credi and he unemploymen rae in he periphery of he euro area, bu his relaionship was absen in he core. This differen response o he credi cycle will urn ou o be key in our oupu gap measures laer in he paper. 4 1 See Claessens, Kose and Terrones (29), and Chrisiano, Ilu, Moo and Rosagno (28). 2 See IMF (213). 3 The core consiss of France and Germany, while he periphery includes Greece, Ireland, Ialy, Porugal and Spain. 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. 4 See also he speech by Sein (214) on he imporance of financial volailiy in explaining he unemploymen cycle in he Unied Saes.

3 3 Figure 1: Credi and Unemploymen Rae, Core and Periphery Core Unemploymen Rae Excess Credi Periphery Unem mploymen Rae 6 Excess Credi Sources: Haver Analyics, ECB, IMF Saff calculaions. 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 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 flucaions. 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

4 4 he financial secor is inroduced. 5 In his paper, we follow he DSGE modeling approach o esimae he oupu gap in he euro area. Unlike previous papers, because he focus is o undersand he impac of he precrisis household credi and housing boom in he periphery counries of he euro area, we build a wo-counry model of a currency union ha incorporaes housing and financial fricions wih balance shee effecs a he household level (see Quin and Rabanal, 214). 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 counry level and in he housing marke) and housing demand shocks were he main source of he boom and bus cycle in he periphery of he euro area, while he cycle was less volaile in he core and was driven by 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. However, for he periphery, he use of financial daa gives a cycle ha 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 periphery for mos of he 2s, and abou -4 percen by end-213. 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. 6 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. II. The Model The model exends Quin and Rabanal (214) wih sicky wages and price markup shocks. The heoreical framework consiss of a wo-counry, wo-secor, wo-agen general equilibrium model of a single currency area. The wo counries, home and foreign, 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 counry, here are wo ypes of agens, savers (size λ in each counry) 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 5 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. 6 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.

5 5 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. 7 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 counry o he oher. Therefore, savings and (residenial) invesmen need no o be balanced a he counry level period by period, since excess credi demand in one region can be me by funding coming from elsewhere in he moneary union. In compensaion for his service, inernaional financial inermediaries charge a risk premium which depends on he ne foreign asse posiion of he counry. In wha follows, we only presen he home counry 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 foreign counry 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. 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. 8 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 ), 7 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. 8 A similar approach is aken by Suh (212) and Zhang (29).

6 6 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. 9 When graning credi, financial inermediaries do no know he hreshold ω which defines he cu-off value of hose households 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 B +1] = 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 9 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).

7 7 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 counry is: nλ (S B ) = n (1 λ) S B, (3) where B are claims on financial inermediaries in he foreign counry (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. Finally, we assume ha he deposi rae in he home counry equals he risk-free rae se by he cenral bank. In he foreign counry, 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 foreign counry R is deermined. A.2. Inernaional Inermediaries Inernaional financial inermediaries buy and sell bonds issued by domesic inermediaries in boh counries. For insance, if he home counry domesic inermediaries have an excess B of loanable funds, hey will sell hem o he inernaional inermediaries, who will lend an amoun B o foreign counry domesic inermediaries. Inernaional inermediaries apply he following formula o he spread hey charge beween bonds in he home counry (issued a an ineres

8 8 rae R ) and he foreign counry (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 counry (o be defined below). When home counry domesic inermediaries have an excess of funds ha hey wish o lend o he foreign counry domesic inermediaries, hen B >. Hence, he foreign counry inermediaries will pay a higher ineres rae R > R. The parameer κ B denoes he risk premium elasiciy and ϑ is a risk premium shock, which increases he wedge beween he domesic and he foreign deposi raes. Inernaional inermediaries are owned by savers in each counry, and opimaliy condiions will ensure ha he ne foreign asse posiion of boh counries is saionary. 1 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) 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 uiliy funcion is hi by wo preference shocks, affecing he marginal uiliy of eiher nondurable consumpion (ξ C ) or housing (ξ D ). 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. Moreover, non-durable consumpion is an index composed of home (C j H, ) and foreign (Cj F, ) 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 foreign goods. Following Iacoviello and 1 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).

9 9 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. 11 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 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 >. 12 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 counry, one 11 Noe ha when ι L = he aggregaor is linear in hours worked in each secor and here are no coss of swiching beween secors. 12 This cos funcion allows us o replicae hump-shaped responses of residenial invesmen o shocks, and reduce residenial invesmen volailiy.

10 1 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. 13 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 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: ( ) 1+ϕ E (β B ) L B,j γξ C log(c B,j ε B C 1) B + (1 γ)ξ D log(d B,j ) 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. 13 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.

11 11 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. C. Firms, Technology, and Sicky Prices In each counry, 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, and by f [n, 1] in he foreign counry). 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 counries and are bough by domesic final goods producers. In he final goods secor, non-durables are sold o domesic and foreign households. 14 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) 14 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.

12 12 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 counry (i.e. he CPI for he home counry) includes he price of domesically produced non-durables (P H ), and of impored nondurables (P F ): [ P C = τ ( ) P H 1 ιc + (1 τ) ( ) ] 1 P F 1 ιc 1 ι C. (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 counry- 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)

13 13 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 counry. In he 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, from he foreign counry): 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-counry inernaional financial inermediaries. This can also be viewed as he evoluion of ne foreign asses (NFA) of he home counry: nλb = nλr 1 B 1 + { [ [ (1 n) P H, λ CH, + (1 λ ) CH,] B npf, λcf, + (1 λ) CF,]} B, (24)

14 14 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 counry, 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) The euro area CPI (P EMU ) and real GDP (Y EMU ) are given by geomeric averages of he home and foreign counry variables, using he counry 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. 15 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 Appendix B deails he full se of normalized, linearized equilibrium condiions of he model. 16 The esimaion is done using Dynare The poserior disribuions are based on 25, draws of he Meropolis-Hasings algorihm.

15 15 A. Daa We disinguish beween a core (home counry) and a periphery (foreign counry) region of he euro area. Daa for he core is obained by aggregaing daa for France and Germany, whereas he periphery is represened by Greece, Ireland, Ialy, Porugal, and Spain. 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), 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, 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. 17 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. 18 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. 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. 19 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 counries, according o euro 17 See Appendix A for furher deails on he daa se. 18 hp:// coicop inw.4.u2w.en.hml 19 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.

16 16 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 periphery o core economies.6 1 τ Fracion of impored goods from core o periphery economies.9 α Size of non-durable secor in GDP.94 area daa such as Gerali e al. (21). We se he defaul rae on loans, F (.) o 2.5 percen. 2 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. 21 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 periphery o core economies. The analogous parameer for he periphery 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 non-durable secors is he same for he core and he periphery 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. 2 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 Developmen Indicaors daabase (hp://daa.worldbank.org/opic/financial-secor). 21 See Morgage Bankers Associaion (28).

17 17 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. 22 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 counry-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. 23 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 foreign nondurables, 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 foreign 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.63. The coefficiens on he Taylor rule sugges a moderae response o inflaion flucuaions in he euro area (coefficien of 1.34, below he prior mean), a moderae response o real GDP growh (poserior mean of.31) and a high degree of ineres rae ineria (.84). We op for a gamma prior for he risk premia elasiciy κ B beween counries wih a mean of.1. We find ha he risk premium elasiciy beween counries moves abou.6 basis poins wih a one 22 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 counry. 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 counry (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. 23 Gerali e al. (21) calibrae his fracion o be.8 for he euro area.

18 18 percen increase in he exernal deb-o-gdp raio. Nex, we commen on he coefficiens regarding nominal rigidiies in price and wage seing. 24 We op for Bea prior disribuions for all Calvo probabiliies wih a mean of.75 (average duraion of price and wage conracs of four quarers). We op for more informaive priors for he wage seing parameers han for he price seing parameers (prior sandard deviaion of.5 for wages and.15 for prices). We se he mean of he prior disribuions for all indexaion parameers o.33. This se of priors is consisen wih he survey evidence on price-seing presened in Fabiani e al. (26) and Knell (213). We find more price rigidiy in he nondurable secor, wih higher Calvo loeries han in he durable secor, and which are similar across counries. Prices are rese abou every 1 quarers in he non-durable secor and abou 2 quarers in he durable secor. Wage rigidiy is similar across counries and secors, which average wage duraions beween roughly 4 and 6 quarers. This resul could be due o he fac ha we are no using wage daa and hence poseriors are no oo differen from priors. We find ha boh price and wage indexaion is low in all prices and secors. Regarding he prior and poserior disribuions for he shock processes, we commen on wo main resuls. Firs, he common innovaions o non-durable echnology shocks and durable preference shocks are imporan. Second, he mean of he (log) risk shock is log(.1742) = We se a prior sandard deviaion for he innovaion o he housing risk shock of.25 (ha is, 25 percen), such ha, roughly, he wo-sandard deviaion prior inerval is beween and Given he properies of he log-normal disribuion, his means ha he defaul rae for morgages ranges beween.4 and 13.6 percen wih 95 percen probabiliy. This seems o be an accepable range for euro area member saes. 25 The esimaes for he variance of he qualiy shock in he periphery are smaller han he prior, while in he core here seems o be much less risk volailiy, as refleced by he poserior. D. Variance Decomposiion: The Role of Demand and Financial Shocks In Table 4 we provide he shock decomposiion of several variables of ineres a he poserior mode. 26 For each region, we decompose he conribuion of several ypes of shocks, aggregaed as in Figures 1 and 2, o he following variables: (derended) oupu, oupu gap, inflaion, credi and house prices. In addiion, we repor he shock decomposiion of he euro area oupu gap and CPI inflaion. The drivers of oupu and he oupu gap are differen in each region. In he core, nondurable 24 We do no use secoral wage daa ha would allow for a beer idenificaion of he parameers of he wage Phillips curves. We sill esimae hese parameers, raher han calibraing hem, o improve overall model fi. 25 See he World Developmen Indicaors daabase from he World Bank. 26 Poserior modes of he model parameers are numerically very close o he means we presened in Tables 2 and 3. They are available upon reques.

19 19 Table 2: Prior and Poserior Disribuions, Economic Parameers Prior Poserior Common Parameers Mean SD Mean 9% C.S. λ Fracion of savers Bea [.5,.64] ε Habi formaion savers Bea [.65,.78] ε B Habi formaion borrowers Bea [.52,.73] ϕ Labor disuiliy Gamma [.75,1.53] ι C Elasiciy of subs. beween goods Gamma [.86,2.17] ι L Labor reallocaion coss Gamma [.42,.83] ψ Invesmen adjusmen coss Gamma [1.31,2.55] γ π Taylor rule reacion o inflaion Normal [1.16,1.5] γ y Taylor rule reacion o real growh Gamma [.19,.41] γ r Ineres rae smoohing Bea [.81,.87] κ B Inernaional risk premium Gamma [.2,.9] Region-Specific Parameers θ C Calvo loery, price non-durables Bea [.82,.92] θc Calvo loery, price non-durables Bea [.89,.97] θ D Calvo loery, price durables Bea [.39,.61] θd Calvo loery, price durables Bea [.31,.54] φ C Indexaion, price non-durables Bea [.3,.28] φ C Indexaion, price non-durables Bea [.13,.47] φ D Indexaion, price durables Bea [.2,.25] φ D Indexaion, price durables Bea [.3,.36] θ W,C Calvo loery, wage non-durables Bea [.62,.77] θw,c Calvo loery, wage non-durables Bea [.79,.87] θ W,D Calvo loery, wage durables Bea [.71,.85] θw,d Calvo loery, wage durables Bea [.72,.82] φ W,C Indexaion, wage non-durables Bea [.6,.47] φ W,C Indexaion, wage non-durables Bea [.6,.51] φ W,D Indexaion, wage durables Bea [.6,.47] φ W,D Indexaion, wage durables Bea [.6,.48] Noe: Parameers wih an aserisk are he periphery s counerpar o he same parameer in he core. C.S. denoes confidence se.

20 2 Table 3: Prior and Poserior Disribuions, AR(1) Shock Processes Parameers Prior Poserior AR(1) coefficiens Mean S.D. Mean 9% C.S. ρ Z,C Technology, non-durables Bea [.67,.84] ρ Z,D Technology, durables Bea [.79,.94] ρ Z,C Technology, non-durables Bea [.68,.93] ρ Z,D Technology, durables Bea [.56,.87] ρ ξ,c Preference, non-durables Bea [.58,.83] ρ ξ,d Preference, durables Bea [.94,.98] ρ ξ,c Preference, non-durables Bea [.58,.89] ρ ξ,d Preference, durables Bea [.97,.99] ρ ω Risk shock, durables Bea [.61,.87] ρ ω Risk shock, durables Bea [.65,.82] ρ G Demand shock Bea [.71,.88] ρ G Demand shock Bea [.38,.6] ρ ϑ Risk premium, core-periphery Bea [.82,.92] Sandard Deviaion Shocks σ A Technology, EMU-wide Gamma [.49,.81] σ C,Z Technology, non-durables Gamma [.62,1.32] σ C,Z Technology, non-durables Gamma [.43,1.9] σc,z COM Technology, non-durables, common Gamma [.5,1.2] σ D,Z Technology, durables Gamma [.78,1.41] σ D,Z Technology, durables Gamma [.56,1.16] σ C,ξ Preference, non-durables Gamma [1.55,2.58] σ C,ξ Preference., non-durables Gamma [.27,1.23] σ D,ξ Preference, durables Gamma [2.99,6.19] σ D,ξ Preference, durables Gamma [2.54,4.93] σd,ξ COM Preference, durables, common Gamma [.48,2.52] σ µ C Mark-up, non-durable prices Gamma [.17,.29] σ µ C Mark-up, non-durable prices Gamma [.24,.36] σ G Demand Gamma [1.21,1.72] σ G Demand Gamma [.79,1.17] σ m Moneary Gamma [.1,.14] σ ϑ Risk premium Gamma [.15,.35] σ uω Risk shock Gamma [9.74,15.88] σ u ω Risk shock Gamma [27.13, 39.42] Noe: Parameers wih an aserisk are he periphery s counerpar o he same parameer in he core. C.S. denoes confidence se.

21 21 (consumpion) preference shocks and aggregae demand (fiscal and exernal) shocks drive he behavior of oupu (38 and 24 percen). However, since echnology shocks move poenial oupu, hey end up being an imporan driver of he oupu gap (5 percen), ogeher wih aggregae demand shocks (25 percen). Moneary shocks explain 9 percen of he flucuaions of boh oupu and he gap, while he conribuion of oher shocks is small. In he periphery, financial, housing demand and echnology are he main drivers of derended oupu (29, 16, and 34 percen). However, once he effec of hese shocks on poenial is accouned for, he financial shocks are he one ha explain oupu gap flucuaions in he periphery (65 percen). The drivers of poenial oupu, CPI inflaion, house prices and credi are similar in boh regions. As expeced, echnology shocks are he shocks ha move poenial oupu he mos, explaining abou 76 percen of is flucuaions a he core and 66 percen in he periphery. Ineresingly, in he periphery, he effecs of housing demand and risk shocks also affec poenial: hese shocks are fundamenal and hus incorporaed in he measure of poenial. Markup and echnology shocks roughly explain 3 percen of CPI inflaion in each region. Moneary policy shocks have a sronger impac in he core (18 percen) while financial shocks have a sronger impac in he periphery (2 percen). In boh regions, credi and house prices are mosly explained by housing preference shocks, specially in he periphery where hey accoun for abou 9 percen of he volailiy of boh variables. A he EMU level, boh he oupu gap and CPI inflaion are driven by a combinaion of several shocks.