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 January 29, 214 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 policy 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 policy would always increase he welfare of savers, bu heir e ecs on borrowers depend on he shock ha his he economy. In paricular, macroprudenial policy 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 Pierpaolo Benigno, Helge Berger, Larry Chrisiano, Chris Erceg, Ivo Krznar, Vivien Lewis, Jesper Lindé, Olivier Loisel, Sephen Murchinson, Jorge Roldós, Thierry Tressel and paricipans a various conferences and seminars for useful commens and discussions. This paper should no be repored as re ecing he views of he Inernaional Moneary Fund. Any errors and omissions are our own. Addiional maerial on he derivaion of he model and esimaion resuls can be found a hp:// 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 2 1. Inroducion The recen nancial crisis, ha sared in he summer of 27, lead o he wors recession since World War II. 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, Kose and Terrones (29), 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). Excessive leverage has complicaed he recovery and he reurn o pre-crisis growh raes in several advanced counries, in paricular in he group of peripheral European counries known as GIIPS (Greece, Ireland, Ialy, Porugal and Spain). Developmens in hose counries since he launch of he European Economic and Moneary Union (EMU) in 1999 shared many characerisics wih he run-up o oher crises. Real exchange rae appreciaion (which in he EMU ook he form of persisen in aion di erenials), large capial in ows mirrored by large curren accoun de cis, and above-poenial GDP growh raes fuelled by cheap credi as well as asse price bubbles are he radiional sympoms of ensuing nancial, banking and balance of paymens crises in emerging and developed economies alike. 1 In addiion o all hese overheaing sympoms, he GIIPS counries faced prolonged negaive real ineres raes, which magni ed he boom side of 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 increased credi spreads ha helped o amplify he bus side of he business cycle. There is an increasing consensus 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. 2 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. 3 In paricular, a key quesion o be addressed is he role of macroprudenial regulaion. Should i be used as a counercyclical policy ool, leaning agains he wind of large credi, asse and house price ucuaions, or should i ake a more passive role and jus aim a increasing he bu ers of he banking 1 See Kaminsky and Reinhar (1999) and IMF (29). 2 See Galai and Moessner (213) and he references herein. 3 See Blanchard, Dell Ariccia and Mauro (21).

3 3 sysem (provisions and capial requiremens), hereby minimizing nancial secor risk, as currenly envisioned in Basel III? Our 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 case of he EMU, where he European Cenral Bank (ECB) has he mandae of price sabiliy a he union-wide level. Before he crisis, he GIIPS counries were no able o use moneary policy o cool down heir economies and nancial sysems, address asse and house price bubbles or abnormal credi growh. Therefore, he use of oher policy insrumens in a currency union can poenially help in sabilizing he business and nancial cycle. We provide a quaniaive sudy on how moneary and macroprudenial measures could inerac in he euro area. Early conribuions o he debae on he role of macroprudenial policies include several quaniaive sudies conduced by he Bank for Inernaional Selemens (BIS) on he coss and bene s of adoping he new regulaory sandards of Basel III (see Angelini e al., 211a; and MAG, 21a,b), and in oher policy insiuions (see Bean e al., 21; and Roger and Vlcek, 211). Oher auhors have also 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 wih borrowing consrains. Bianchi and Mendoza (211) analyze he e eciveness of macroprudenial axes o avoid he exernaliies associaed wih 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. 4 Our paper s in he recen (and growing) lieraure ha embeds nancial fricions in a DSGE model and searches for opimal moneary and macroprudenial policy rules. Closes o our conribuion are he papers by Brzoza-Brzezina, Kolasa and Makarski (213) and Rubio (213), who also sudy he role of macroprudenial policies in a wo-counry currency area, bu calibrae insead of esimae he model, as we do in his paper. Beau, Clerc and Mojon (212) and Angelini e al. (211b) analyze macroprudenial policies in an esimaed DSGE model of he euro area bu do no disinguish beween di eren counries in he union. In hese four cases, he credi fricion consiss in a borrowing consrain à la Iacoviello (25), and hence here is no defaul. Lamberini, Mendicino and Punzi (213) sudy he e ec of LTV raios on welfare in a calibraed closed economy model wih housing and risky 4 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 4 morgages, which is similar o our seup for he nancial fricion. Oher conribuions of DSGE models wih a nancial acceleraor include Unsal (213) and Medina and Roldós (214), who sudy he role of macroprudenial policy when a small open emerging economy receives large capial in ows. A common resul in his lieraure is ha he opimal macroprudenial policy is sae-dependen, and, herefore, simple operaional rules ha reac o observable variables may lead o policy misakes. For insance, if he source of a credi boom is a produciviy shock, and he macroprudenial auhoriy reacs mechanically o a credi variable (raher han o he e ecs of he shock), hen welfare migh decrease. In all hese previous conribuions, and in he presen paper, macroprudenial policies aim a reducing he volailiy e ecs of a buil-in nancial acceleraor bu do no a ec he risk-aking behavior of agens. An imporan excepion o he lieraure is he paper by Collard e al. (213), who include risky echnologies in a DSGE model, and sudy how macroprudenial policies can reduce risk-aking behavior. In Collard e al. (213), rms can eiher use a riskless or a risky echnology o produce capial goods. The risky echnology is socially ine cien because i delivers, in expeced value, a lower reurn han he riskless echnology. However, limied liabiliy and deposi insurance provides an incenive o "gamble" and collec he pro s when he risky echnology delivers a high payo. In heir model, moneary policy can only a ec he quaniy bu no he composiion of credi. The opimal macroprudenial policy ses he capial requiremen o a su cienly high level, such ha rms inernalize he riskiness of heir choices and only adop he riskless, socially opimal echnology. Hence, he opimal capial asse raio moves wih shocks ha a ec risk in he economy (such as he reurn of he risky echnology), bu i says consan when shocks do no a ec risk (such as an economy-wide produciviy shock). In his paper, we quanify he role of moneary and macroprudenial policies in sabilizing he business cycle in he euro area using an esimaed Dynamic Sochasic General Equilibrium (DSGE) model. The model includes: (i) wo counries (a core and a periphery) which 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 in he housing secor 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, as in Smes and Wouers (23) and Iacoviello and Neri (21). Basel III calls for regulaors o sep in when here is excessive credi growh in he

5 5 economy. 5 We wan o sudy he pros and cons of reacing o credi indicaors, eiher by using moneary or macroprudenial policies. 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 real oupu growh. We nd ha he opimal Taylor rule srongly reacs o deviaions of CPI in aion and oupu growh from heir seady sae values, as is ypical in he lieraure. Aferwards, we exend he moneary policy rule o reac o credi aggregaes. We nd ha he exended Taylor rule improves welfare wih respec o he original one, wih borrowers being worse o under some condiions. Nex, we inroduce a macroprudenial insrumen ha in uences credi marke condiions above and beyond curren regulaions. This insrumen arges credi spreads by a ecing he fracion of liabiliies (deposis and bonds) ha nancial inermediaries can lend. Spreads can be increased by imposing e.g. addiional capial surcharges, liquidiy raios, loan-loss provisions, or reserve requiremens, whereas he direc provision of liquidiy o he banking secor (eiher hrough convenional or unconvenial policies) can decrease spreads. 6 This could be achieved via measures such as widening of collaeral sandards, he Funding for Lending Scheme launched by he Bank of England in 212, or even liquidiy provision o he real economy as in Gerler and Karadi (211). We nd ha by inroducing macroprudenial policies welfare furher increases, bu ha here are winners and losers of including hese measures. As we discuss in Secion 4, opimal moneary and macroprudenial policies are welfare improving under housing demand or risk shocks: hese measures reduce he volailiy of real variables by o seing acceleraor e ecs riggered by hese shocks. However, when echnology shocks hi he economy, macroprudenial policies have he opposie e ec and magnify he counercyclical behavior of he lending-deposi spread. This imposes larger ucuaions of consumpion, housing invesmen and hours worked for borrowers and, hus, reduces heir welfare. Therefore, idenifying he source of he credi and house price boom is crucial for he success of policy measures ha reac o nancial variables. The res of he paper is organized as follows: Secion 2 presens he model and Secion 3 discusses he daa as well as he economeric mehodology o esimae he parameers of he model. In Secion 4, we discuss he di eren exercises of opimal 5 See Basel Commiee on Banking Supervision (211). 6 See Crowe e al. (211) and Vandenbussche, Vogel and Deragiache (212) for a discussion on he e ecs of di eren macroprudenial measures.

6 6 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, 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 in each counry) and borrowers (1 ), who di er 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 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. 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 a ec he balance shee of borrowers, which in urn a ec he defaul rae on morgages and he lending-deposi spread. There are wo ypes of nancial inermediaries. Domesic nancial inermediaries ake deposis from savers, gran loans o borrowers, and issue bonds. Inernaional nancial 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 nancial 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 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. As he foreign counry block is characerized by a similar srucure regarding credi markes, households and rms, we absrac from presening i. Unless speci ed, all shocks 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.

7 7 follow zero-mean AR(1) processes in logs. A. Credi Markes We adap he BGG 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 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 and Macroprudenial Policy Domesic nancial inermediaries collec deposis from savers S, for which hey pay a deposi rae R, and exend loans o borrowers S B for which hey charge he lending rae R L. Credi graned o borrowers is backed by he value of he housing sock ha hey own (P D D B ), where P D is he nominal house price and D B is he housing sock owned by borrowers. We inroduce risk in he credi and housing markes by assuming ha each borrower (indexed by j) is subjec o an idiosyncraic qualiy shock o he value of her housing sock,! j, ha is log-normally disribued wih CDF F (!). We choose he mean and sandard deviaion so ha E! = 1 and, hence, here is idiosyncraic risk bu no aggregae risk in he housing marke. This assumpion implies ha log(! j ) N( 2!; ; 2 2!;), wih!; being he sandard deviaion characerizing he qualiy shock. This sandard deviaion is ime-varying, and follows an AR(1) process in logs: wih u!; N(; u! ). log(!; ) = (1! ) log(! ) +! log(!; 1 ) + u!; The qualiy shock! j can lead 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 heir ousanding loan R L 1S B 1. Realizaions of! j 1 ha are low enough make households defaul on heir loans in period. Afer 8 A similar approach is aken by Suh (212) and Zhang (29).

8 8 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,! j 1P D D B. Afer paying his amoun, he household keeps her house. These deb-collecion agencies charge banks a fracion of he value of he house. The pro s 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, 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 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 ): Z! a R = E (1 )!df (!;!; ) P D +1D B +1 S B + [1 F (! a ;!; )] R L = E (1 )G (! a ;!; ) P +1D D +1 B + [1 F (! a S B ;!; )] R L ; (2) wih [1 F (! a ;!; )] = R 1 df (!;! a!; )d! being he expeced probabiliy ha he shock exceeds he ex-ane hreshold! a and G (! a ;!; ) = R! a!df (!;!; ) being he expeced value of he shock condiional on he shock being less han! a. The paricipaion consrain (2) ensures ha he opporuniy coss R are equal o he expeced reurns, which are given by he expeced foreclosure selemen as percen of ousanding credi (he rs 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, nancial inermediaries only receive a fracion (1 ) of he morgage selemen. We inroduce he macroprudenial insrumen, denoed by, ha in uences credi marke condiions by a ecing he fracion of liabiliies ha banks can lend. We discuss is properies in Secion 2.D.3. The aggregae balance shee of domesic 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 e ecs on housing and residenial invesmen. See Forlai and Lamberini (21).

9 9 nancial inermediaries in he home counry is: n 1 (S B ) = n (1 ) S B ; (3) where B are claims on nancial inermediaries in he foreign counry (as explained below). Combined wih he paricipaion consrain equaion (2), we obain he following relaionship beween he lending-deposi spread and macroprudenial policy: R L R 8 < = E : (1 )G(! a ;!;)! a 9 = + [1 F (! a ;!; )]; : (4) According o equaion (4), for a given demand of credi from borrowers, observed values of risk!;, a sance of macroprudenial policy, 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! a so ha equaion (1) and he paricipaion consrain (2) are ful lled. 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 nancial inermediaries delivers ex-ane zero pro s. However, i is possible ha, ex-pos, hey make pro s or losses. We assume ha savers collec pro s or recapialize nancial inermediaries as needed. I is worh emphasizing ha 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. Le s rs assume ha = = 1 in equaion (4), so here is no macroprudenial regulaion and in case of defaul, he nancial inermediary recovers nohing from he defauled loan. According o equaion (1), 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 he sandard deviaion!; increases he spread beween he lending and he deposi raes. When!; rises, i leads o a mean-preserving spread for he disribuion of! j : he ails of he disribuion become faer while he mean remains unchanged. As a resul, lower realizaions of! j are more likely so ha more borrowers will defaul on heir loans. More generally, when he nancial inermediary is able o recover a fracion (1 ) of he collaeral value, i can be shown (using he properies of he lognormal disribuion when E! = 1) ha he denominaor in he spread equaion (4) 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 Sørensen and Lichenberger (27) and ECB (29). Finally, we assume ha he deposi rae in he home counry equals he risk-free

10 1 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 R L, and he spread is deermined in an analogous way o equaion (2), including a macroprudenial insrumen. We explain below how he deposi rae in he foreign counry R is deermined. A.2 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 (issued a an ineres rae R ) and he foreign counry (issued a R ): R = R + # exp 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 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 > R. The parameer B denoes he risk premium elasiciy and # 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 pro s (R R ) B, which are equally spli across savers of boh counries. 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-de ned seady sae and saionariy of he ne foreign asse posiion. See Schmi-Grohé and Uribe (23).

11 11 B. Households B.1 Savers Savers indexed by j 2 [; ] maximize he following uiliy funcion: ( X 1 E " C log(c j "C 1 ) + (1 ) D log(d j ) = L j 1+' 1 + ' #) ; (6) where C j, D j, and L j represen he consumpion of he ow 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 " measuring he in uence of pas aggregae non-durable consumpion C 1. The uiliy funcion is hi by wo preference shocks, a ecing he marginal uiliy of eiher non-durable consumpion ( C ) or housing ( D ). The parameer sands for he discoun facor of savers, measures he share of non-durable consumpion in he uiliy funcion, and ' 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 = 1 C C j C 1 1 C H; + (1 ) C C j C 1 C F; C C 1 ; (7) wih 2 [; 1] denoing he fracion of domesically produced non-durables a home and C governing he subsiuabiliy beween domesic and foreign goods. Following Iacoviello and Neri (21), we inroduce imperfec subsiuabiliy of labor supply beween he durable and non-durable secor o explain comovemen a he secor level: L j = L L C;j 1+L + (1 ) L L D;j 1+L 1 1+ 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 denoing he share of employmen in he non-durable secor. Reallocaing labor across secors is cosly, and is governed by he parameer L. 11 Wages are exible and se o equal he marginal rae of subsiuion beween consumpion and labor in each secor. 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 + j ; (9) 11 Noe ha when L = he aggregaor is linear in hours worked in each secor and here are no coss of swiching beween secors.

12 12 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 consumpion C j and W D. Savers allocae heir expendiures beween non-durable and residenial invesmen I j. They 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 secor, from domesic and inernaional nancial inermediaries, and from deb-collecion agencies ha charge fees o domesic nancial 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 )D j 1 + " 1 z Ij 1 I j 2!# I j 1 (1) where denoes he depreciaion rae of he housing sock 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 >. 12 B.2 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 respecive facor of savers ( B < ), and we allow for di eren habi formaion coe ciens " B. Second, borrowers do no earn pro s from inermediae goods producers, nancial inermediaries, or deb-collecion agencies. Finally, as discussed above, borrowers are subjec o a qualiy shock o he value of heir housing sock! 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 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 >; ; (11) 12 This cos funcion allows us o replicae hump-shaped responses of residenial invesmen o shocks, and reduce residenial invesmen volailiy.

13 13 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 (equaions 7, 8, and 1). The budge consrain for borrowers di ers 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! p 1;!; 1 D B + 1 F! p 1;!; 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. 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 : (13) P D D B Since invesmen increases he housing sock wih a lag (equaion 1), D B is a pre-deermined variable. Because he lending rae is also pre-deermined 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 he fracion of loans which are 1 repaid by he borrowers, because hey were hi by a realizaion of he shock above he hreshold! p 1. Similarly, P D G! p R 1;!; 1 D B = P D! p 1!dF (!;!; 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 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 as well as saggered price seing à la Calvo (1983). Inermediae goods are no raded across counries and are bough by domesic nal goods producers. In he nal goods secor, non-durables are sold o domesic and foreign households. 13 Durable goods 13 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

14 14 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. 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 Z 1 n k Y k (h) k 1 k n dh # k k 1 ; for k = fc; Dg (14) where k represens he price elasiciy of inermediae goods. Pro maximizaion leads o he following demand funcion for individual inermediae goods: Y C (h) = P H P H (h) C Y C and Y D (h) = P D P D (h) D Y D (15) Price levels for domesically produced non-durables (P H ) are obained hrough he usual zero-pro condiion: (P D ) and durable nal goods 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 : (16) C.2 Inermediae Goods 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 goods 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 price index P C, which will be a combinaion of hese wo price levels.

15 15 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 2 [; n] (17) 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 (A ) = log (A 1 ) + " A : This shock inroduces non-saionariy o he model and consiues 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 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 : (18) Inermediae goods producers solve a sandard Calvo model pro maximizaion problem wih indexaion. As shown in appendix B, in aion dynamics in each secor depend on one expeced lead and one lag of in aion, and he secor-speci c real marginal cos. 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 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)

16 16 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. Besides equaion (3), his requires: nb + (1 n) B = : (22) 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 (23) + (1 n) P H; CH; + (1 ) CH; B np F; CF; + (1 ) CF; B ; 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 union-wide CPI in aion and real oupu growh. The cenral bank ses he deposi rae in he home counry, and he oher raes are deermined as described in he model. Le EMU be he seady sae level of union-wide CPI in aion, R he seady sae level of he ineres rae and " m an iid moneary policy shock, he ineres rae rule is given by: R = R P EMU =P EMU 1 EMU Y EMU 1 =Y EMU y 1 R R R 1 exp(" m ): (24) 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 :

17 17 D.3 Macroprudenial Policy Similar o Kannan, Rabanal, and Sco (212) we inroduce a macroprudenial ool ha aims a a ecing he credi marke condiions counercyclically. As shown in equaions (3) and (4), he macroprudenial insrumen a ecs he equilibrium in he domesic credi marke and a ecs he lending-deposi spread in each counry. We inerpre his macroprudenial insrumen as being deployed above and beyond curren rules, which are saic o a large degree. Hence, when we esimae he model, we se o a consan value of one. When we conduc an opimal macroprudenial policy exercise in Secion 4.B, we allow he insrumen o be changed in order o maximize he weighed uiliy of all he ciizens in he moneary union. A ighening of macroprudenial policies will be re eced in a higher, which will ranslae ino a higher lending-deposi spread. Alhough we leave i unspeci ed, his could be implemened via addiional capial surcharges, liquidiy raios, loan-loss provisions, or reserve requiremens ha reduce he amoun of loanable funds by nancial inermediaries. We assume ha he insrumen, in principle, can behave symmerically and i can go below one. In ha case, he cenral bank or any oher regulaory agency would provide liquidiy o he banking secor o reduce he lending-deposi spread. This could be achieved via (convenional or unconvenional) measures like a widening of collaeral sandards, he Funding for Lending Scheme launched by he Bank of England in 212, or even a direc provision of liquidiy o he real economy as in Gerler and Karadi (211). In he welfare maximizing exercise, we specify he macroprudenial insrumen as reacing o an indicaor variable ( ): = ( ) ; = ( ) : (25) We sudy wo main cases. In each counry he macroprudenial insrumen reacs o: (i) nominal credi growh, or (ii) he credi-o-gdp raio. For boh cases, he parameers and are eiher allowed o be di eren, or are forced o be he same in he moneary union. In all cases, he indicaor reacs o deviaions from seady sae values. This concludes he explanaion of he model. In Secion 3, we conduc a Bayesian esimaion of he model s parameers. In Secion 4, we examine opimal moneary and macroprudenial policy rules by obaining he opimal values of ; y; R ; and using he uiliy funcion of he four ypes of households in he moneary union (paien and impaien, in he home and foreign counries).

18 18 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, A. 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. 14 Third, he soluion of he model is expressed in sae-space form and he likelihood funcion of he model is compued using a Kalman ler 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. 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 he GIIPS counries (Greece, Ireland, Ialy, Porugal, and Spain). We use quarerly daa ranging from 1995q4-211q4 and eleven macroeconomic ime series. 16 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. 17 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 and logged equivalen variable o he model. All daa is nally demeaned. 14 Appendix B deails he full se of normalized, linearized equilibrium condiions of he model. 15 The esimaion is done using Dynare The poserior disribuions are based on 25, draws of he Meropolis-Hasings algorihm. 16 Due o he shor hisory of he EMU we face a shor ime series. We include he years o increase he sample size. During hose years mos EMU counries were conducing moneary policy in a coordinaed way. 17 See Appendix A for furher deails on he daa se.

19 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 ( = 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. 18 As a resul, he seady sae 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 he recovery raes for loans esimaed for he Unied Saes. 19 Using hese values, he zero-pro condiion for nancial inermediaries, and he consumpion Euler equaion for borrowers, we obain a discoun facor of borrowers of B = :985. As discussed in he previous secion, we se he macroprudenial insrumen o = 1 o esimae he model. The depreciaion rae is assumed o be 5 percen (annual) and equal across counries ( = = :125). 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 he same for he core and he periphery of he euro area ( = ). The assumpions of symmery and balanced rade makes 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. [Table 1 abou here] 18 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 aken from he World Bank World Developmen Indicaors daabase (hp://daa.worldbank.org/opic/ nancial-secor). 19 See Morgage Bankers Associaion (28).

20 2 C. Prior and Poserior Disribuions In Table 2 we presen he prior disribuions, he poserior mean and 9 percen credible se of seleced esimaed parameers. 2 To save space, we presen he esimaed parameers of he shock processes in Appendix C. As we face he problem of a shor sample, in addiion o calibraing some parameers, we resric ohers o be he same across counries. More speci cally, we only allow he parameers relaed o nominal rigidiies o di er across secors and counries, in order o permi quaniaively di eren ransmission channels of moneary policy. On he oher hand, he parameers relaing o preferences, adjusmen coss, and he fracion of savers are assumed o be he same in boh counries. We assume ha he AR(1) coe ciens of he shocks are he same across counries, bu we allow he sandard deviaion of he shocks o 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 are Normal iid wih mean zero. log( D ) = ;D log( D 1) + " ;D log( D ) = ;D log( D 1) + " ;D and " ;D + " ;D;COM (26) + " ;D;COM ) as well as common (" ;D;COM ) innovaions 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 larger fracion (:61) o he macro daa. 21 Ineresingly, we nd ha he habi formaion coe cien for borrowers is smaller han he one 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 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 2 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 ( and ), which is no a free parameer bu raher a funcion of ; ; ;, B ; "; " B ; and '. 21 Gerali e al. (21) calibrae his fracion o be :8 for he euro area.

21 21 elasiciy of subsiuion beween home and foreign goods (he poserior mean of 1:9 is 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 hird, which is similar o Iacoviello and Neri (21). [Table 2 abou here] 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 :2) and a high degree of ineres rae ineria (:8). We op for a gamma prior for he risk premia elasiciy B beween counries wih a mean of :1. We nd ha he risk premium elasiciy beween counries moves abou :43 basis poins wih a one percen increase in he exernal deb-o-gdp raio. 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 four quarers) and sandard deviaion of :15. 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). 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. Table C.1 in he appendix presens he prior and poserior disribuions for he shock processes. We commen on wo resuls. Firs, he common innovaions o non-durable echnology shocks and durable preference shocks are imporan, and as we discuss in he nex subsecion hey are key o mach cross-counry correlaions of some key macro variables. Second, he mean of he (log) risk shock is log(:1742) = 1:74. 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. 22 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, as re eced by he poserior. 22 See he World Developmen Indicaors daabase from he World Bank.

22 22 D. Model Fi and Variance Decomposiion We presen he sandard deviaion and rs ve auocorrelaions of he observable variables, and heir counerpar in he model implied by he poserior disribuion of he parameers, o undersand how well he model s he daa. In Table 3, he rs row for each enry 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. Finally, he model correcly implies ha credi growh in he periphery is more volaile han in he core. The model also does 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 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 3 abou here] [Table 4 abou here] 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 4 we presen he conemporaneous correlaion of seleced observable variables in he daa and in he model (9 percen con dence se). 23 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 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 does a good job in explaining he correlaion of credi wih main macroeconomic variables in he core. The model does a worse job in explaining he correlaion of credi wih oher macro aggregaes in he periphery, because i implies a correlaion ha is smaller han in he daa, while sill geing he sign righ. We brie y discuss he resuls from he variance decomposiion exercise. To save space, we presen he able wih he 9 percen con dence se for he share of he 23 Table C.2 in he appendix presens conemporaneous correlaion of all observable variables.