Monetary and Macroprudential Policy in an Estimated DSGE Model of the Euro Area

Transcription

1 Moneary and Macroprudenial Policy in an Esimaed DSGE Model of he Euro Area Dominic Quin y Pau Rabanal z February 1, 213 Absrac In his paper, we sudy he opimal mix of moneary and macroprudenial policies in an esimaed wo-counry model of he euro area. The model includes real, nominal and nancial fricions, and hence boh moneary and macroprudenial policies can play a role. We nd ha he inroducion of a macroprudenial rule would help in reducing macroeconomic volailiy, improve welfare, and parially subsiue for he lack of naional moneary policies. Macroprudenial policies always increase he welfare of savers, bu heir e ecs on borrowers depend on he shock ha his he economy. In paricular, macroprudenial policies may enail welfare coss for borrowers under echnology shocks, by increasing he counercyclical behavior of lending spreads. Key words: Moneary Policy, EMU, Basel III, Financial Fricions. JEL Codes: C51, E44, E52. We hank Helge Berger, Larry Chrisiano, Ivo Krznar, Jesper Lindé, Jorge Roldós and Thierry Tressel for useful commens and discussions. This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. y Conac deails: Free Universiy Berlin, Bolzmannsr. 2, Berlin, Germany, dominic.quin@fu-berlin.de z Conac deails: Inernaional Moneary Fund, 7 19h Sree, N.W., Washingon, D.C. 2431, prabanal@imf.org 1

2 1 Inroducion The recen nancial crisis, ha sared in he summer of 27, lead o he wors recession since World War II. Excessive leverage has complicaed he recovery and he reurn o pre-crisis growh raes in several advanced counries. Before he crisis, a combinaion of loose moneary and regulaory policies encouraged excessive credi growh and a housing boom in many counries. This urned ou o be a problem when he world economy slowed down: as Claessens e al. (28), Crowe e al. (211) and IMF (212) show, he combinaion of credi and housing boom episodes ampli es he business cycle and in paricular, he bus side of he cycle, measured as he ampliude and duraion of recessions. There is wide recogniion ha he bes way o avoid a large recession in he fuure is precisely o reduce he volailiy of credi cycles and heir e ecs on he broader macroeconomy. However, he search for he appropriae oolki o deal wih nancial and housing cycles is sill in is infancy. There is high uncerainy on which measures can be more e ecive a delivering resuls. Convenional moneary policy is oo blun of an insrumen o address imbalances wihin he nancial secor or overheaing in one secor of he economy (such as housing). There is a need o furher srenghen oher insrumens of economic policy in dealing wih secor-speci c ucuaions. 1 In paricular, a key quesion o be addressed is wha should be he role of macroprudenial regulaion. Should i be used as a counercyclical policy ool, leaning agains he wind of large credi and asse and house price ucuaions, or should i ake a more passive role and jus aim a increasing he bu ers of he banking sysem (provisions and capial requiremens), hereby minimizing nancial secor risk, as currenly envisioned in Basel III? Early conribuions o his debae include several quaniaive sudies conduced by he BIS on he coss and bene s of adoping he new regulaory sandards of Basel III (see Angelini e al., 211a; and MAG, 21a and 21b), and in oher policy insiuions (see Bean e al., 21; Roger and Vlcek, 211; and Angelini e al., 211b). This paper conribues o his debae by sudying he opimal policy mix needed wihin a currency union, where counry- and secor-speci c boom and bus cycles canno be direcly addressed wih moneary policy. Speci cally, we focus on he European Economic and Moneary Union (EMU), whose cenral bank has mandae of price sabiliy a he union-wide level. We provide a quaniaive sudy 1 See Blanchard e al. (21). 2

3 on how moneary and macroprudenial measures could inerac in he euro area, and pay special aenion o coordinaion issues beween he European Cenral Bank (ECB), naional supervision auhoriies and he newly creaed European Sysemic Risk Board (ESRB) ha will be responsible of macroprudenial oversigh a he euro area level. The recen developmens in Souhern Europe share many characerisics wih oher crises. Real exchange rae appreciaion (which in he EMU ook he form of persisence in aion di erenials), large capial in ows mirrored by large curren accoun de cis, and above-poenial GDP growh fuelled by cheap credi and asse price bubbles are he radiional sympoms of ensuing nancial, banking and balance of paymens crises in many emerging and developed economies. 2 The sory of he euro-zone deb crisis is now well know, and in addiion o all hese over-heaing sympoms, many Souhern European economies faced prolonged negaive real ineres raes, which magni ed he business cycle. When he crisis hi, all problems came a once: a sudden sop of capial ows, concerns abou deb susainabiliy, low or negaive real GDP growh, and credi spreads ha helped amplify he business cycle. The four Souhern European economies (and also Ireland) could no use moneary policy o cool down heir economies and nancial sysems, address asse and house price bubbles and abnormal credi growh. Therefore, he use of oher policy insrumens in a currency union can poenially help in sabilizing he business and nancial cycle. Recenly, several auhors have suggesed ha he use of macroprudenial ools could improve welfare by providing insrumens ha arge large ucuaions in credi markes. In an inernaional real business cycle model wih nancial fricions, Gruss and Sgherri (29) sudy he role of loan-o-value (LTV) limis in reducing credi cycle volailiy in a small open economy, while Lamberini e al. (211) also look a he role of using LTV raios and heir e ec on welfare. Bianchi and Mendoza (211) sudy he role of macroprudenial axes o avoid he exernaliies associaed o overborrowing. Borio and Shim (28) poin ou he prerequisie of a sound nancial sysem for an e ecive moneary policy and, hus, he need o srenghen he ineracion of prudenial and moneary policy. IMF (29) suggess ha macroeconomic volailiy can be reduced if moneary policy does no only reac o signs of an overheaing nancial secor bu if i is also com- 2 See Kaminsky and Reinhar (1999) and IMF (29). 3

4 bined wih macroprudenial ools reacing o hese developmens. 3 Angelini e al. (211b) sudy he ineracion beween opimal moneary and macroprudenial policies in a se-up where he cenral bank deermines he nominal ineres rae and he supervisory auhoriy can choose counercyclical capial requiremens and LTV raios. Unsal (211) sudies he role of macroprudenial policy when a small open economy receives large capial in ows. 4 In his paper we sudy he role of moneary and macroprudenial policies in sabilizing he business cycle in he euro area. The model includes: (i) wo counries (a core and a periphery) who share he same currency and moneary policy; (ii) wo secors (non-durables and durables, which can be hough of as housing); and (iii) wo ypes of agens (savers and borrowers) such ha here is a credi marke in each counry and across counries in he moneary union. The model also includes a nancial acceleraor mechanism on he household side, such ha changes in he balance shee of borrowers due o house price ucuaions a ec he spread beween lending and deposi raes. In addiion, risk shocks a ec condiions in he credi markes and in he broader macroeconomy. The model is esimaed using Bayesian mehods and includes several nominal and real rigidiies o he daa. Having obained esimaes for he parameers of he model and for he exogenous shock processes, we proceed o sudy di eren policy regimes. In all cases, we assume ha he opimal policy aims a maximizing he welfare of all households in he EMU, by maximizing heir uiliy funcion aking ino accoun he populaion weighs of each ype of household in each counry. Firs, we derive he opimal moneary policy when he ECB opimizes over he coe ciens of he Taylor rule ha reacs o EMU-wide consumer price index (CPI) in aion and oupu growh. We nd ha he opimal Taylor rule reacs srongly o deviaions of CPI in aion and oupu growh from heir seady-sae values, as is ypical in he lieraure. Nex, we exend he moneary policy rule o reac o eiher credi aggregaes or house prices. We nd ha he exended Taylor rule improves welfare wih respec o he original one, bu he welfare improvemens are smaller han from moving from he esimaed o he opimized rule, wih borrowers being worse o. 3 Bank of England (29) liss several reasons, why he shor-erm ineres rae may be ill-suied and should be suppored by oher measures o comba nancial imbalances. 4 Beau, Clerc and Mojon (212) sudy he role of macro-prudenial policies in an esimaed DSGE model of he euro area bu do no disinguish beween di eren counries. Brzoza-Brzezina e al. (212) disinguish beween a core and a periphery in a model wih opimal moneary and macroprudenial policies in he euro area, bu do no esimae he model. In boh cases, he credi fricion consiss in a borrowing consrain a la Iacoviello (25). 4

5 Nex, we inroduce a macroprudenial insrumen ha in uences credi marke condiions by a ecing he fracion of liabiliies (deposis and loans) ha banks can lend. This insrumen can be hough of as addiional capial requiremens, liquidiy raios, reserve requiremens or loan-loss provisions ha reduce he amoun of loanable funds by nancial inermediaries and increase credi spreads. We nd ha he welfare gains of inroducing macroprudenial policies are comparable o hose of moving from an esimaed o an opimal rule, bu ha here are winners and losers of including macroprudenial measures. This is a common heme for mos opimizaion resuls: we nd ha while savers bene from he ECB or a macroprudenial auhoriy reacing o nancial variables, borrowers do no. As we discuss in Secion 4, under housing demand or risk shocks, opimal moneary and macroprudenial policies improve everyone s welfare by reducing he volailiy of real variables by reducing acceleraor e ecs riggered by hese shocks. However, when echnology shocks hi he economy, macroprudenial policies increase he counercyclical behavior of he spreads, hereby magnifying ucuaions for borrowers and reducing heir welfare. Therefore, idenifying he source of he credi and house price boom is crucial. Finally, we nd ha when macroprudenial policies are lef o naional regulaors insead of being conduced a he EMU-level, he opimal response of he macroprudenial insrumen is very similar. I is imporan o noe from he sar ha while he model includes nancial fricions on he household side, nancial inermediaries are very simple eniies ha ake deposis, engage in bond rading across counries and give morgage loans. Because of his simpliciy, he model does no allow us o measure oher poenially large bene s from improving banking regulaion a he macro and he micro level such as reducing he frequency and cos of nancial and banking crisis. The res of he paper is organized as follows: Secion 2 presens he model, and Secion 3 discusses he daa and he economeric mehodology o esimae he parameers of he model. In Secion 4, we discuss he di eren exercises of opimal moneary and macroprudenial policies, while we leave Secion 5 for concluding remarks. 2 The Model 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, 5

6 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 and used o increase he housing sock. In each counry, here are wo ypes of agens, savers and borrowers, who di er in heir discoun facors and habi formaion parameers. Boh agens consume non-durable goods and purchase durable goods o increase heir housing sock. Borrowers are more impaien han savers and have preference for early consumpion, which creaes he condiion for credi o occur in equilibrium. In addiion, borrowers are hi by an idiosyncraic qualiy shock o heir housing sock, which a ecs he value of collaeral ha hey can use o borrow agains. 5 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 a ec he balance shee of borrowers, which in urn a ec he defaul rae on morgages and he lending-deposi spread. Domesic nancial inermediaries ake deposis from savers, give loans o borrowers, and issue bonds ha are raded across counries by inernaional inermediaries. 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. Inernaional nancial inermediaries channel funds from one counry o he oher, and also charge a risk premium which depends on he ne foreign asse posiion of he counry. In wha follows, we presen he home counry block of he model, by describing he domesic and inernaional credi markes, households, and rms. Moneary policy is conduced by a cenral bank ha arges he union-wide CPI in aion rae, and also reacs o ucuaions in he union-wide real GDP growh. The foreign counry block has a similar srucure for credi markes, households and rms, and o save space is no presened. Unless speci ed, all shocks follow zero-mean AR(1) processes in logs. 5 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 does no have any macroeconomic impac. 6

7 2.1 Credi Markes We adap he Bernanke, Gerler and Gilchris (1999) nancial 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 di erences 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 nd 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 predeermined and does no depend on he sae of he economy, which seems o be a more realisic assumpion Domesic Inermediaries Domesic nancial inermediaries collec deposis from savers (S ), for which hey pay a deposi rae ha equals he risk-free rae of he cenral bank (R ), and exend loans o borrowers (S B ) for which hey charge he lending rae (R L ) in he home counry. Credi given o borrowers is backed by he value of he housing sock ha hey own. 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 heir housing sock,! j, ha is log-normally disribued wih CDF F (!) and parameers!; and!;, and wih E! = 1. Hence, here is idiosyncraic risk bu no aggregae risk in he housing marke. This assumpion implies ha log(! j ) N( 2!; ; 2 2!;). We assume ha he variance of he qualiy shock is imevarying, and follows an AR(1) process in logs: log(!; ) = (1! ) log(! ) +! log(!; 1 ) + u!; and u!; N(; u! ). The presence of his qualiy shock leads o morgage defauls and a ecs he spread beween lending and deposi raes. The realizaion of he shock is known a he end of he period. High realizaions of! j 1 allow households o repay heir loans in full, and hence hey repay he full amoun of he ousanding loan (R L 1S B 1) back. Realizaions of! j 1 ha are low enough force he household o defaul on is loans 6 A similar approach is aken by Suh (212). 7

8 in period, and i can only repay he value of is housing sock afer he shock has realized,! j 1P D D B;j. The value of he idiosyncraic shock is common knowledge, so households will only defaul when hey are underwaer. Afer defauling, banks pay a fracion of he value of he house o real esae agens ha pu he house back ino he marke and resell i. The pro s of hese real esae agens are ransferred o savers, who own hem. 7 When graning credi, nancial inermediaries do no know he hreshold! which de nes he cu-o value of hose households ha defaul and hose who do no. The ex-ane hreshold value expeced by banks is hus given by:! a E P D +1 D B +1 = R L S B : (1) Inermediaries 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 ): Z! a R = (1 ) = (1 )G (! a ;!; ) E!dF (!;!; ) E P D +1 D+1 B S B P D +1 D+1 B S B + [1 F (! a ;!; )] R L + [1 F (! a ;!; )] R L ; (2) The paricipaion consrain 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 rs erm in he righ hand side of 2) and he expeced repaymen of households wih higher housing values (he second erm). Due o he fees paid o real esae agens o pu he house back in he marke, nancial inermediaries only receive a fracion (1 ) of he morgage selemen. When we examine macroprudenial policies in Secion 4.2, we assume ha hey work by a ecing he supply and demand of credi by borrowers, and hence a ec he lendingdeposi spread implied by equaion (2). We assume ha, for a given demand of credi from borrowers, observed values of risk (!; ) and expeced values of he housing sock, inermediaries passively se he lending rae R L and he expeced (ex-ane) hreshold! a so ha (1) and he paricipaion consrain (2) are ful lled. Unlike he original BGG se-up, he oneperiod lending rae R L is deermined a ime, and does no depend on he sae 7 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 would have unrealisic expansionary e ecs on housing. 8

9 of he economy a + 1. This means ha he paricipaion consrain delivers exane zero pro s. However, i is possible ha, ex-pos, nancial inermediaries can make pro s or losses. We assume ha savers collec pro s or recapialize nancial inermediaries as needed. I is very imporan o noe ha he paricipaion consrain delivers a posiive relaionship beween LTV raios and he spread beween he funding and he lending rae, due o he probabiliy of defaul. To see he inuiion more clearly, we se = 1 (so, in case of defaul, he nancial inermediary recovers nohing from he defauled loan). The paricipaion consrain becomes: R L R = 1 [1 F (! a ;!; )] : Hence, he higher is he LTV raio, he higher is he hreshold! a ha leads o defaul. This shrinks he area of no-defaul [1 F (! a ;!; )], and herefore increases he spread beween R L and R. Similarly, an increase in!; increases he spread beween he lending and he deposi raes. When!; rises, i leads o a meanpreserving spread for he disribuion of! j : he ails of he disribuion become faer bu he mean is unchanged. As a resul, because lower realizaions of! j are more likely, more borrowers will defaul on heir loans. Clearly, in an economy where aggregae LTV raios are high, and he range of possible realizaions is large, higher raes of defauls are more likely. When he nancial inermediary is able o recover a fracion (1 value, he paricipaion consrain can be wrien as: R L R = (1 )G(! a ;!;)! a 1 + [1 F (! a ;!; )] ) of he collaeral (3) I can be shown (using he properies of he lognormal disribuion when E! = 1) ha he denominaor in he spread equaion is always declining in! a ; and hence he spread is always an increasing funcion of he LTV. Evidence for he euro area suggess ha morgage spreads are an increasing funcion of he LTV raio, as discussed in Sorensen and Lichenberger (27) and ECB (29). 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 nancial inermediaries behave he same way. In heir case, hey face a deposi rae R and a lending rae 9

10 R L, and he spread is deermined in an analogous way o equaion (2). We explain how he deposi rae in he foreign counry R is deermined Inernaional Inermediaries Inernaional nancial 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 (ineres rae R ) and he foreign counry (R ): R = R + # exp B B P C Y C 1 : (4) The spread depends on he raio of real ne foreign asses o seady-sae non-durable GDP in he home counry (o be de ned 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, which is also he deposi rae in he foreign counry. In ha case, inernaional nancial inermediaries make a pro equal o (R R )B. Conversely, if he foreign counry becomes a ne credior, hen is deposi rae becomes smaller han in he home counry. In ha case, pro s also equal (R R )B which is a posiive quaniy because boh (R R ) < and B <. These pro s of inernaional inermediaries are spli equally across savers of boh counries. The parameer B denoes he risk premium elasiciy and # is a risk premium shock, which increases he wedge beween he domesic and he foreign ineres deposi raes. This funcional form is also chosen for modeling convenience: 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. 8 8 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 (4) is required for he exisence of a well-de ned seady-sae and saionariy of he ne foreign asse posiion. See Schmi-Grohé and Uribe (23). 1

11 2.2 Households In each counry a fracion of agens are savers, while he res 1 are borrowers Savers Savers indexed by j 2 [; ] in he home counry maximize he following uiliy funcion: ( X 1 E " C log(c j "C 1 ) + (1 ) D log(d j ) = L j 1+' 1 + ' #) ; (5) where C j, D j, and L j represen he consumpion of he ow of non-durable goods, he sock of durable goods (i.e. housing) and he index of labor disuiliy of agen j. Following Smes and Wouers (23) and Iacoviello and Neri (21) we assume exernal habi persisence in non-durable consumpion, wih " measuring he in uence of pas aggregae non-durable consumpion C 1. The uiliy funcion is hi by wo preference shocks, each one a ecing he marginal uiliy of non-durable consumpion ( C ) and housing ( D ). The parameer sands for he discoun facor of savers, measures he share of non-durable consumpion in he uiliy funcion, and ' is he inverse elasiciy of labor supply. Furhermore, non-durable consumpion is an index composed of home (C j H; ) and foreign (Cj F; ) non-durable consumpion goods: C j = 1 C C j C 1 1 C H; + (1 ) C C j C 1 C F; C C 1 ; (6) wih 2 [; 1] denoing he fracion of domesically produced non-durables a home and C governing he subsiuabiliy beween domesic and foreign goods. In order o be able o explain comovemen a he secor level, i is useful o inroduce, as in Iacoviello and Neri (21), imperfec subsiuabiliy of labor supply beween he durable and non-durable secors: L j = L L C;j 1+L + (1 ) L L D;j 1+L 1 1+ L : (7) The labor disuiliy index consiss of hours worked in he non-durable secor L C;j and 11

12 durable secor L D;j, wih denoing he share of employmen in he non-durable secor. Reallocaing labor across secors is cosly, and is governed by parameer L. 9 Wages are exible and se o equal he marginal rae of subsiuion beween consumpion and labor in each secor. The budge consrain 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 + j ; (8) where P C and P D are he price indices of non-durable and durable goods, respecively, which are de ned below. Nominal wages paid in he wo secors are denoed by W C and W D. Savers have access o deposis in he domesic nancial sysem (S j ), ha pay he deposi ineres rae (R ). In addiion, savers also receive pro s ( j ) from inermediae goods producers in he durable and he non-durable secors, from domesic and inernaional nancial inermediaries, and from housing agens ha charge fees o domesic nancial inermediaries o pu repossessed houses back in he marke. Purchases of durable goods, or residenial invesmen (I j ) are used o increase he housing sock D j, according o he following law of moion: D j = (1 )D j 1 + " 1 z Ij I j 1!# I j (9) where denoes he depreciaion rae and z () an adjusmen cos funcion. Following Chrisiano, Eichenbaum, and Evans (25), z () is a convex funcion, which in seady sae mees he following crieria: z = z = and z > Borrowers Borrowers di er from savers along hree main dimensions. Firs, heir preferences are di eren. The discoun facor of borrowers is smaller han he facor of savers ( B < ), and we allow for di eren habi formaion coe ciens (" B ). Second, borrowers do no earn pro s from owning inermediae goods producers and nan- 9 Noe ha when L = he aggregaor is linear in hours worked in each secor and here are no coss of swiching beween secors. 1 This cos funcion can help he model o replicae hump-shaped responses of residenial invesmen o shocks, and reduce residenial invesmen volailiy. 12

13 cial inermediaries. For his reason, 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. Finally, as discussed above, borrowers are subjec o an qualiy shock o he value of heir housing sock,! j, ha is log-normally disribued wih E! = 1. Their uiliy funcion for each borrower j 2 [; 1] reads: E 8 >< >: 1X = B; C log(c B;j " B C B 1) + (1 ) D log(d B;j ) L B;j 1 + ' 1+' 39 >= 7 5 >; ; where all variables and parameers wih he superscrip B denoe ha hey are speci c 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. The budge consrain for borrowers di ers beween hose who defaul and hose who repay heir loans in full. Hence, aggregaing borrower s budge consrains and dropping he j superscrips, we obain he following: P C C B + P D S B + W C L C;B (1) I B + G! p 1;!; 1 D B + 1 F! p 1;!; 1 R L 1 S B (11) 1 + W D L D;B : Borrowers consume non-durables and inves in he housing sock, and supply labor o boh secors. Savers and borrowers are paid he same wages W C and W D in boh secors. Tha is, hiring rms are no able o discriminae ypes of labor depending on wheher a household is a saver or a borrower. Borrowers obain loans S B from nancial 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:! p 1 = RL 1S B 1 : (12) P D D B Because he lending rae is predeermined and is no a funcion of he sae of he economy, i is possible ha! a and! p di er. Noe, however, ha when he loan is signed,! a = E! p. The erm 1 F! p R 1 1;!; 1 = df (!;! p!; 1 )d! de nes 1 he fracion of loans which are repaid by he borrowers, because hey were hi by 13

14 a realizaion of he shock above he hreshold! p 1. Similarly, G! p 1;!; 1 = R! p 1!dF (!;!; 1 )d! is he value of he housing sock on which borrowers have defauled on and which is pu back ino he marke by real esae agens. 2.3 Firms, Technology, and Nominal Rigidiies In each counry, homogeneous nal non-durable and durable goods are produced using a coninuum of inermediae goods in each secor (indexed by h 2 [; n] in he home, and by f 2 [n; 1] in he foreign counry). Inermediae goods in each secor are imperfec subsiues of each oher, and here is monopolisic compeiion and saggered price seing a la Calvo (1983). Inermediae goods are no raded across counries and are bough by domesic nal good producers. In he nal good secor, non-durables are sold o domesic and foreign households. 11 Durable goods are solely sold o domesic households, who use hem o increase he housing sock. Boh nal goods secors are perfecly compeiive, operaing under exible prices Final Good Producers Final good producers in boh secors aggregae he inermediae goods hey purchase according o he following producion funcion: Y k " 1 Z 1 n k Y k (h) k 1 k n dh # k k 1 ; for k = C; D (13) where C ( D ) represens he price elasiciy of non-durable (durable) inermediae goods. Pro maximizaion leads o he following demand funcion for individual inermediae goods: Y C (h) = P H P H (h) C Y H ; and Y D (h) = P D P D (h) D Y D (14) Price levels for domesically produced non-durables (P H ) and durable nal goods 11 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 combinaion of hese wo price levels. 14

15 (P D ) are obained hrough he usual zero-pro condiion: P H 1 n Z n P H (h) C C dh ; and P D 1 n Z n P D (h) D D dh : 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 non-durables (P F ): h P C = P H 1 C i 1 + (1 ) P F 1 C 1 C : (15) Inermediae Good Producers Inermediae goods are produced under monopolisic compeiion wih producers facing saggered price seing in he spiri of Calvo (1983), which implies ha in each period only a fracion 1 C (1 D ) of inermediae good producers in he non-durable (durable) secor receive a signal o re-opimize heir price. For he remaining fracion C ( D ) we assume ha heir prices are parially indexed o lagged secor-speci c in aion (wih a coe cien C; D in each secor). In boh secors, inermediae goods are produced solely wih labor: Y C (h) = Z Z C L C (h); Y D (h) = Z Z D L D (h) for all h 2 [; n] (16) The producion funcions include counry- and secor-speci c 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 (Z ) = log (Z 1 ) + " Z : This shock inroduces non-saionariy o he model and gives a model-consisen way of derending he daa by aking logs and rs di erences 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 15

16 coss in boh secors are given by: MC C =P H; = W C Z Z C ; MC D = W D Z Z D =P D : (17) Inermediae goods producers in he durable secor face he following maximizaion problem: 82 X 1 >< Max P D (h)e s 6 D ;+s 4 >: s= P D (h) P D D +s 1 P D 1 P D +s MC D +s Y D +s (h) 9 >= >; subjec o fuure demand Y D +s (h) = " P D (h) P D P+s D +s 1 P D 1 D # D Y D +s; where ;+k = k +k is he sochasic discoun facor, wih being he marginal uiliy of non-durable consumpion by savers (since hey are he owner of hese rms). The evoluion of he durable secor price level is given by: P D = cp D D 1 D + (1 D )[P D 1 1(P D 1=P D 2) 1 D D ] 1 D : (18) where P c D is he opimal price of durables chosen a ime. Producers in he nondurable secor face a similar maximizaion problem wih he appropriae change of noaion, which delivers a Phillips curve for domesically produced non-durables P H. 2.4 Closing he Model 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 16

17 demand by savers CH; and borrowers CB H; from he foreign counry): ny C = n C H; + (1 ) CH; B + (1 n) CH; + (1 ) CH; B : (19) 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 I + (1 ) I B : (2) In he labor marke oal hours worked has o be equal o he aggregae supply of labor in each secor: Z n L k (h)dh = Z n L k;j dj + (1 ) Z n L k;b;j dj; for k = C; D: (21) Credi marke clearing implies ha for domesic credi and inernaional bond markes, he balance shees of nancial inermediaries are sais ed: n(s + B )= = n (1 ) S B ; (22) nb + (1 n) B = : The macro-prudenial insrumen,, is assumed o be consan and equal o one in he esimaion exercise. When we discuss opimal macroprudenial policies, we allow o be se counercyclically in order o maximize household s welfare. Finally, aggregaing he resource consrains of borrowers and savers, and he marke clearing condiions for goods and nancial inermediaries, we obain he law of moion of bonds issued by he home-counry inernaional nancial inermediaries. This can also be viewed as he evoluion of ne foreign asses (NFA) of he home counry: nb = nr 1 B 1 + (1 n) P H; CH; + (1 ) CH; B np F; CF; + (1 ) C B F; ; which is deermined by he aggregae sock of las period s NFA imes he ineres rae, plus ne expors. (23) 17

18 2.4.2 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 union-wide CPI in aion and real oupu growh. We assume ha he cenral bank ses he deposi rae in he home-counry. Le EMU be he seady sae level of union-wide CPI in aion, R he seady sae level of he ineres rae and " m given by: R = R P EMU =P EMU 1 EMU an iid moneary policy shock, he ineres rae rule is Y EMU 1 =Y EMU y 1 R R R 1 exp(" m ): (24) The euro area CPI P EMU is given by a geomeric average of he home and foreign counry CPIs, using he counry size as a weigh: P EMU = P C n P C 1 n : Real GDP in he euro area is given by: Y EMU = (Y ) n Y 1 n ; where he naional GDPs are expressed in erms of non-durables, using he employmen weighs o aggregae boh secors: Y = Y C Y D P D P C 1 ; and Y = Y C Y D P D P C 1 : 3 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, Z. Second, he dynamics of he model are obained by aking a log-linear approximaion of equilibrium condiions around he seady sae wih zero in aion and ne foreign asse posiions. 12 Third, he soluion of he model is expressed in sae-space form 12 Appendix A deails he full se of normalized, linearized equilibrium condiions of he model. 18

19 and using a Kalman ler recursion he likelihood funcion of he model is compued. 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 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 Ireland, Ialy, Greece, Porugal, and Spain. We use quarerly daa ranging from 1995q411q4. 14 For boh regions we use ve 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. 15 The daa is aggregaed aking he economic size of he counries ino accoun (measured by GDP). All daa is seasonally adjused in case his has no been done by he original source. We use quarerly growh raes of all price and quaniy daa and we divide he ineres raes by 4 o obain a quarerly equivalen. All daa is nally demeaned. 3.2 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 ( = and B = B ) We se he discoun facor of savers o = :99. The seady sae LTV raio, which also deermines he cu-o poin for defauling on a loan, is se o! = :7 and equally across counries, according o euro area daa such as Gerali e al. (21). We se he defaul rae on loans, F (:) o 2:5 percen. 16 As a resul, he seady-sae 13 The esimaion is done using Dynare The poserior disribuions are based on 25, draws of he Meropolis-Hasings algorihm. 14 Due o he raher shor hisory of he EMU we include he years alhough during his ime span European counries were sill responsible for heir own moneary policy, bu were conducing i in a coordinaed way. 15 See Appendix B for furher deails on he daa se. 16 I is di cul o nd non-perfoming loans for household morgages only. Therefore, we use nonperforming loans as percen of oal loans for he euro area beween 211, from he World Bank World Developmen Indicaors daabase (hp://daa.worldbank.org/opic/ nancial-secor). 19

20 value of he risk shock is! = :1742: We se he housing agen fee o = :2, which is a value higher han ha calibraed by Forlai and Lamberini (21), bu lower han recovery raes for loans esimaed for he Unied Saes. 17 Using hese values, he zero-pro condiion for nancial inermediaries, and he consumpion Euler equaion for borrowers, we calibrae he discoun facor of borrowers o B = :985. The depreciaion rae is assumed o be 1 percen annually and equal across counries ( = = :25). The degree of monopolisic compeiion in he goods markes 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. The bilaeral rade parameer 1 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 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 abou he same for he core and he periphery of he euro area ( = ). The assumpion of symmery makes i easier o compue a seadysae where all relaive prices in all secors equal o one, and where all per capia quaniies are he same. Table 1: Calibraed Parameers Discoun facor savers.99! Loan-o-Value raio.7 F Defaul rae on loans.25! Seady-sae risk.1742 Proporion of housing value paid o real esae agens.2 B Discoun facor borrowers.985 Depreciaion rae.25 Elasiciy of subsiuion beween inermediae goods 1 n Size core economies.6 1 Fracion of impored goods from periphery o core economies.6 1 Fracion of impored goods from core o periphery economies.9 Size of non-durable secor in GDP See Morgage Bankers Associaion (21). 2

21 3.3 Prior and Poserior Disribuions In Table 2 we presen he prior disribuions and he poserior mean and 9 percen credible se of he esimaed parameers. 18 We face he problem of a shor sample, so, in addiion o calibraing some parameers, we resric ohers o be he same across counries. More speci cally, we only le he parameers relaed o nominal rigidiies across secors and counries o di er across counries, o allow for quaniaively di eren ransmission channels of moneary policy. On he oher hand, he parameers relaing o preferences, adjusmen coss, and fracion of savers are assumed o be he same in boh counries. Also, in order o reduce he number of parameers o be esimaed, we assume ha he AR(1) coe ciens of he shocks are he same across counries. In order o capure di eren volailiies in he daa, we le he sandard deviaion of he shocks di er across counries. Also, in order o beer capure he correlaion of key macro variables across counries, 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-speci c (" ;D ) and common (" ;D;COM ) innovaions are Normal iid, and wih zero mean. log( D ) = ;D log( D 1) + " ;D log( D ) = ;D log( D 1) + " ;D ; " ;D + " ;D;COM (25) + " ;D;COM Firs, we commen on he parameers ha relae o preferences of borrowers and savers. in he economy. We op for a prior disribuion cenered a :5 for he fracion of savers We se a highly informaive prior by seing a small sandard deviaion of :1. The poserior mean suggess a larger fracion (:7) o he macro daa. 19 Ineresingly, we nd ha he habi formaion coe cien for borrowers is smaller han ha of savers even hough we se he same prior for boh coe ciens. These esimaes sugges ha above and beyond he e ec of he nancial acceleraor, consumpion of savers is less volaile han consumpion of borrowers, who will reac more o changes in heir relevan (lending) ineres raes. We cener he priors 18 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 nondurables, 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 ( and ), which is no a free parameer bu raher a funcion of ; ; ;, B ; "; " B ; and '. 19 Gerali e al. (21) calibrae his fracion o be :8 for he euro area. 21

22 relaed o he elasiciy of subsiuion beween home and foreign non-durables, he elasiciy of labor supply and he coe cien measuring cosly labor reallocaion o parameers available in he lieraure (Smes and Wouers, 23; Iacoviello and Neri, 21; and Adolfson e al., 27). We nd a large elasiciy of subsiuion beween home and foreign goods (he poserior mean of 1:94 is much higher han he prior mean of 1:5). Regarding he coe ciens ha deermine labor supply, we nd ha he poserior mean of he labor disuiliy coe cien ' and he degree of cosly labor reallocaion is abou one half, which is similar o Iacoviello and Neri (21). Table 2: Prior and Poserior Disribuions Prior Poserior Parameers Mean SD Mean 9% C.S. Fracion of savers Bea [.6,.81] " Habi formaion Bea [.63,.79] " B Habi formaion borrowers Bea [.22,.61] ' Labor disuiliy Gamma [.36,.82] C Elasiciy of subs. beween goods Gamma [1.6,2.73] L Labor reallocaion cos Gamma [.37,.81] Invesmen adjusmen coss Gamma [1.11,2.47] Taylor rule reacion o in aion Normal [1.41,1.71] y Taylor rule reacion o real growh Gamma [.13,.29] r Ineres rae smoohing Bea [.76,.83] B Inernaional risk premium Gamma [.2,.7] C Calvo loery, non-durables Bea [.5,.67] C Calvo loery, non-durables Bea [.64,.77] D Calvo loery, durables Bea [.51,.7] D Calvo loery, durables Bea [.52,.67] C Indexaion, non-durables Bea [.3,.32] C Indexaion, non-durables Bea [.2,.26] D Indexaion, durables Bea [.3,.39] D Indexaion, durables Bea [.16,.64] The coe ciens on he Taylor rule sugges a srong response o in aion ucuaions in he euro area (coe cien of 1:56, close o he prior mean), a moderae response o real GDP growh (poserior mean of :21) and a high degree of ineres rae ineria (:79). We op for a gamma priors for he risk premia elasiciy ( B ) beween counries wih a mean of :1. We nd ha he risk premium elasiciy beween counries moves abou :45 basis poins. Nex, we commen on he coe ciens regarding nominal rigidiies. We op for Bea prior disribuions for Calvo probabiliies wih a mean of :75 (average duraion of price conracs of hree quarers) and sandard deviaion of :15. We se he 22

23 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). The poserior means for he Calvo loeries are lower han he prior means, and in all cases prices are rese roughly every hree quarers. Overall, hese probabiliies are lower han oher sudies of he euro area like Smes and Wouers (23). We also nd ha price indexaion is low in all prices and secors. One possible explanaion is ha we are using a shorer and more recen daa se where in aion raes are less sicky han in he 197s and 198s. In Table 3 we presen he prior and poserior disribuions for he shock processes. While i is di cul o exrac oo much informaion from jus discussing he shock processes, he poserior means for he AR(1) coe ciens sugges highly correlaed shocks, in paricular for boh echnology shocks and for he preference shock o durables. Table 3 also shows ha for boh echnology and preference shocks, he sandard deviaions end o be larger for shocks a ecing durables, which re ec ha housing variables (prices and quaniies) are more volaile han consumpion and he CPI. The common innovaion o non-durable echnology shocks and durable preference shocks is imporan, and as we discuss in he nex subsecion i is key o obain cross-counry correlaions of some key macro variables. The scaling of he housing risk shocks deserve some explanaion. As we showed in Table 1, he mean of he (log) risk shock is log(:1742) = 1:74. Therefore, 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 inerval is beween and.25. Given he properies of he log-normal disribuion discussed above, 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 in he euro area. 2 The esimaes for he qualiy shock in he periphery are similar o he prior, while in he core here seems o be much less risk volailiy, and he poserior of he sandard deviaion of he innovaion o risk is abou a half of he prior mean. 3.4 Model Fi and Variance Decomposiion In order o beer undersand he model, we presen he sandard deviaion and rs ve auocorrelaions of he observable variables, and heir counerpar in he 2 See he World Developmen Indicaors daabase from he World Bank. 23

24 Table 3: Prior and Poserior Disribuions, Shock Processes Parameers Prior Poserior AR(1) coe ciens Mean S.D. Mean 9% C.S. Z;C Technology, non-durables Bea [.76,.94] Z;D Technology, durables Bea [.84,.95] ;C Preference, non-durables Bea [.58,.83] ;D Preference, durables Bea [.96,.99]! Risk shock, durables Bea [.79,.89] # Risk premium, core-periphery Bea [.57,.87] Sd. Dev. Shocks (in percen) Z Technology, EMU-wide Gamma [.41,.69] C Z Tech., non-durables, core Gamma [.37,.79] C Z Tech., non-durables, periphery Gamma [.64,1.22] C;COM Z Tech., non-durables, common Gamma [.42,.78] D Z Tech., durables, core Gamma [1.7,1.76] D Z Tech., durables, periphery Gamma [1.17,1.83] C Preference, non-durables, core Gamma [1.42,2.54] C Pref., non-durables, periphery Gamma [1.5,2.18] D Pref., durables, core Gamma [2.25,4.2] D Pref., durables, periphery Gamma [2.76,4.55] D;COM Pref., durables, common Gamma [.92,2.74] m Moneary Gamma [.1,.14] # Risk premium, inernaional Gamma [.9,.31] u!; Risk shock, durables, core Gamma [8.55,15.4] u!; Risk shock, durables, periphery Gamma [17.7, 28.67] model implied by he poserior disribuion of he parameers. In Table 4, he rs row in each case is he daa, he second row is he 9 percen con den se implied by he model esimaes. The model does reasonably well in explaining he sandard deviaion of all variables in he periphery. However, he model overpredics he volailiy of prices and quaniies in boh secors in he core of he euro area, despie having allowed for di eren degrees of nominal rigidiies, indexaion, and di eren sandard deviaions of shocks. I appears ha business cycles are less pronounced in he core, a leas for he ime period we sudy. Finally, he model correcly implies ha credi growh in he periphery is more volaile han in he core, bu a he same ime i overpredics he volailiy of credi growh in he core. The model does also a beer job in explaining he persisence of variables in he periphery han in he core, and does a good job in predicing he persisence of ineres raes. I slighly overpredics he persisence of CPI in aion in he periphery, and sligh underpredics he persisence of residenial invesmen, consumpion 24

25 growh, and house prices. In he core, he model has a harder ime ing he lack of persisence in CPI in aion, residenial invesmen and consumpion growh. Table 4: Poserior Second Momens in he Daa and in he Model Sd. Dev. Auocorrelaion R [.22,.29] [.84,,91] [.65,.8] [.48,.68] [.34,.59] [.24,.5] p C [.35,.45] [.46,.6] [.12,.3] [-.2,.15] [-.7,.7] [-.8,.4] log C [.6,.76] [.44,.54] [.13,.26] [-.1,.8] [-.8,-.1] [-.11,-.6] log Y D [1.95,2.59] [.47,.65] [.15,.39] [-.1,.2] [-.9,.8] [-.11,.] p D [.88,1.13] [.57,.68] [.2,.37] [-.1,.17] [-.9,.5] [-.11,-.2] log S [.92,1.14] [.6,.74] [.2,.37] [-.1,.17] [-.9,.5] [-.11,-.2] p C [.34,.43] [.54,.67] [.22,.4] [.5,.23] [-.3,.13] [-.6,.6] log C [.53,.68] [.45,.57] [.15,.29] [.,.12] [-.7,.2] [-.1,-.3] log Y D [2.19,2.88] [.44,.65] [.11,.4] [-.4,.2] [-.9,.7] [-.11,.] p D [.97,1.27] [.61,.73] [.24,.4] [.,.16] [-.11,.2] [-.14,-.5] log S [1.42,1.8] [.51,.67] [.39,.54] [.27,.42] [.17,.31] [.9,.21] Noes: For each variable, he op row denoes second momens in he daa, and he boom row denoes poserior second momens in he esimaed model (9 percen credible se). Sandard deviaions for all variables are in percen erms. The model capures mos of he comovemen beween main aggregaes wihin and across counries of he euro area, which is especially imporan for he design of opimal moneary and macroprudenial policies. In Table 5 we presen he conemporaneous correlaion of he observable variables in he daa and in he model (9 percen con dence se). Among he successes, we noe ha he model explains he correlaion beween house prices and residenial invesmen wihin each area well. The model also s well he correlaion of CPI in aion, house price in aion, consumpion growh and residenial invesmen growh across counries. The model can explain he comovemen beween consumpion and residenial invesmen in he core, bu fails a explaining he comovemen in he periphery. Finally, he model 25