Cross-Border Banking and Business Cycles in Asymmetric Currency Unions

Transcription

1 Deparmen Socioeconomics Cross-Border Banking and Business Cycles in Asymmeric Currency Unions Lena Dräger Chrisian R. Proaño DEP Socioeconomics) Discussion Papers Macroeconomics and Finance Series /25 amburg, 25

2 Cross-Border Banking and Business Cycles in Asymmeric Currency Unions Lena Dräger a and Chrisian R. Proaño b a Universiy of amburg b The New School of Social Research, New York. March 2, 25 Absrac Agains he background of he recen housing boom and bus in counries such as Spain and Ireland, we invesigae in his paper he macroeconomic consequences of cross-border banking in moneary unions such as he euro area. For his purpose, we incorporae in an oherwise sandard wo-region moneary union DSGE model a banking secor module along he lines of Gerali e al. 2), accouning for borrowing consrains of enrepreneurs and an inernal consrain on he bank s leverage raio. We illusrae in paricular how differen lending sandards wihin he moneary union can ranslae ino desabilizing spill-over effecs beween he regions, which can in urn resul in a higher macroeconomic volailiy. This mechanism is modelled by leing he loan-o-value LTV) raio ha banks demand of enrepreneurs depend on eiher regional produciviy shocks or on he produciviy shock from one dominaing region. Thereby, we demonsrae a channel hrough which he financial secor may have exacerbaed he emergence of macroeconomic imbalances wihin he euro area. Addiionally, we show he effecs of a moneary policy rule augmened by he loan rae spread as in Cúrdia and Woodford 2) in a wo-counry moneary union conex. Keywords: Cross-border banking, euro area, moneary unions, DSGE JEL classificaion: F4, F34, E52. Conac auhor: Lena.Draeger@wiso.uni-hamburg.de. We would like o hank Zeno Enders, Philipp Engler, Mahias offmann, Alexander Meyer-Gohde, Michael Paez and enning Weber for helpful commens and suggesions. The auhors also hank Philipp Engler, Federico Signorei and Andrea Gerali for sharing heir code. Par of his research was conduced while Chrisian R. Proaño was visiing he Research Cenre of he Deusche Bundesbank, he hospialiy of which is graefully acknowledged. The views expressed in his paper do no necessarily reflec hose of he Deusche Bundesbank. Financial suppor by he ans-böckler Foundaion is graefully acknowledged.

3 Inroducion One of he cenral feaures of he European moneary unificaion process has been he seady inegraion of financial markes across he European Moneary Union EMU) over he las hree decades, which was embedded in an unprecedened financial globalizaion process Lane and Milesi-Ferrei, 27, European Commission, 28, ECB, 2). According o he exbook heory, more inegraed financial markes improve porfolio diversificaion and faciliae he channeling of funds owards he more producive projecs, hereby promoing beer risk sharing and faser economic convergence across regions Barro e al., 995). owever, he radiional view on financial globalizaion has been significanly relaivized since he 27 global financial crisis see e.g. Kose e al., 29 for a criical review). An alernaive view sresses he imporance of a poenial link beween financial inegraion and he emergence of financial bubbles and, hus, macroeconomic insabiliy due o overly opimisic growh expecaions and excessive cross-border privae and public borrowing Blanchard and Milesi-Ferrei, 2 and Jaumoe and Sodsriwiboon, 2). The increased financial inegraion among euro area counries, driven by he eliminaion of currency risk, a fall in real ineres raes in Souhern European economies and he general economic inegraion, led o a surge in cross-border financial flows as shown in Figure. Given he well-known predominance of he banking secor in he European financial landscape, he expansion in cross-border financial aciviies ook place primarily in he form of bank-relaed capial flows BIS, 2; Kleimeier e al., 23). While iniially economic convergence processes wihin EMU seemed o be relaed o he increase in financial inegraion, cross-border banking was also a driving facor for he credi booms and housing bubbles in some European counries such as Spain and Ireland, and hereby conribued o he build-up of inra-eurozone curren accoun imbalances see e.g. Allen e al., 2 and BIS, 2). Agains his background, we invesigae in his paper he role of cross-border bank credi flows in a wo-region moneary union by incorporaing a banking secor in an oherwise sandard wo-counry DSGE framework. As he main conribuion of he paper, we evaluae he macroeconomic consequences of cross-border banking under differen lending sandards. This is modelled by leing he loan-o-value LTV) raio ha banks demand of firms as a measure of heir crediworhiness depend on eiher regional produciviy shocks, or on he produciviy shock from one dominaing region. The laer scenario, which we erm rule-of-humb banking, may capure he effec of ineres rae convergence wihin EMU shown in Figure, where he eliminaion of currency risk effecively led financial markes o apply he low risk sandards of he larges European economies hroughou he whole moneary union. Our model hus allows o evaluae he role of he financial secor for he ransmission and amplificaion of shocks hroughou he moneary union. Following Gerali e al. 2) and Gambacora and Signorei 24), he banking secor is assumed o consis of an inernaional wholesale branch, which underlies an exogenous consrain on he arge leverage raio, and regional reail

4 Toal Gross Capial Flows mill. USD) Gross Capial Flows Real ineres rae Real Ineres Rae Year Year Ausria Belgium Luxembourg Finland Ausria Belgium Finland France Germany Greece France Germany Greece Ialy Neherlands Porugal Ireland Ialy Neherlands Spain Porugal Spain Figure : Toal Gross Capial Flows and Real Ineres Raes across EMU. Source: IMF Balance of Paymens Saisics Yearbooks as assembled in Broner e al. 23) and AMECO daabase. branches providing credi o enrepreneurs and collecing deposis from households. As in Iacoviello 25), enrepreneurs are subjec o a financial consrain where credi is awarded relaive o heir ne worh, weighed wih banks desired LTV raio as a measure for firms crediworhiness. Calibraing he model o he euro area, we firs analyze he effec of a common moneary policy shock. Second, he naure of cross-border banking and rading flows in a moneary union wih differen LTV-based credi sandards is evaluaed. In he baseline scenario, bank s desired LTV raio of firms is assumed o be consan and equal across regions. The baseline scenario may hus be regarded as capuring he case wih symmeric informaion regarding firms ne worh in boh regions. In he second scenario, he parameer follows an AR) process driven by regional-specific echnology shocks. Thereby, a posiive echnology shock no only affecs firms ne worh direcly, bu also serves as a signal for banks assessmen of firms crediworhiness. ence, in his scenario banks are assumed o suffer from asymmeric informaion which hey aemp o recover using he echnology shock as a signal. The effec of he shock on bank lending is amplified, and via he rade links beween he regions, he whole moneary union is affeced. In he hird scenario, we assume ha here exiss one dominaing region providing he signal for credi worhiness. This scenario may be regarded as capuring convergence in shor-run ineres raes across EMU counries wih he inroducion of he common currency. Noably, macroeconomic volailiy is highes in he hird scenario. In a nushell, our simulaion resuls highligh he role of cross-border lending no only as an amplifying mechanism wihin a moneary union, bu also as a poenial source of macroeconomic insabiliy in he presence of asymmeric informaion. More precisely, while cross-border lending amplifies he effecs of exogenous shocks in all hree considered scenarios, in he laer one where here is a dominan region which implicily deermines he lending sandards for he whole moneary 2

5 union cross-border lending also leads o he occurrence of business flucuaions driven purely by laxer credi condiions, and no by macroeconomic fundamenals. ence, he financial secor may work o exacerbae he emergence of macroeconomic imbalances in a moneary union if banks assign lending sandards from one dominaing region o he whole moneary union. Analyzing possibiliies for moneary policy agains his scenario, we find ha a sandard inflaion argeing moneary policy rule augmened by an inermediae loan spread arge may be beneficial for reducing he volailiy of macroeconomic variables, an argumen along he lines of he proposals by Cúrdia and Woodford 2) and, more recenly, Gambacora and Signorei 24). In modern DSGE models, he financial secor has only more recenly received more aenion. While models accouning for a financial acceleraor as in Bernanke e al. 999) or Iacoviello 25) are now relaively common, mos models do no feaure a deailed banking secor. Recenly, Gerali e al. 2) se up a DSGE model wih an imperfecly compeiive banking secor subjec o an inernal leverage consrain and enrepreneurs facing a borrowing consrain. Esimaing he model on euro area daa, he auhors repor ha shocks originaing in he banking secor explain he larges share of he conracion of economic aciviy in 28, while macroeconomic shocks play only a limied role. A similar resul is obained in Kollmann e al. 2) in an esimaed wo-counry model for he US and he euro area. In a simplified version of his model, Gambacora and Signorei 24) analyse wheher moneary policy should also arge asse prices or credi in he presence of borrowing consrains on firms side and a banking secor wih a credi supply consrain. They show ha leaning-agains-he-wind policies by he cenral bank in reacion o supply side shocks allow for a beer rade-off beween oupu and inflaion sabilizaion. ence, he auhors reinforce he resuls obained by Cúrdia and Woodford 2) in a much simpler model wih exogenously inroduced ineres rae spreads. We exend he analysis in Gerali e al. 2) and Gambacora and Signorei 24) by evaluaing he effec of borrowing and credi supply consrains in a wo-region model of a moneary union, allowing us o focus on spill-over effecs of banking relaed shocks beween he regions. Moreover, our paper is relaed o he hree-counry New Keynesian model analyzed in in Veld e al. 24), which also focuses on he emergence of inernaional capial flows in a moneary union like he euro area. Specifically, in Veld e al. 24) idenify he following deerminans for he recen boom-bus cycle in Spain: a) falling risk premia on Spanish housing and non-residenial capial, b) a loosening of collaeral consrains for Spanish households and firms, and c) a fall in he ineres rae spread beween Spain and he res of he euro area. Their approach differs from ours in ha we model cross-border lending in an explici manner hrough he specificaion of an inernaional bank wih loan reail branches a he naional level, and analyze he effecs of changes in banks assessmen of firms credi-worhiness across he moneary union. Finally, our approach is more broadly relaed o oher wo-region DSGE models of a moneary union, such as Benigno 24), Gali and Monacelli 28), Beesma and Jensen 25), Duare and Wolman 3

6 28), Ferrero 29) and Engler e al. 23). While he former hree papers evaluae opimal moneary and fiscal policy rules in a moneary union, he laer hree papers focus more specifically on problems relaed wih fiscal policy in a moneary union, such as possibiliies o improve inflaion differenials wih fiscal policy, or o use fiscal devaluaion o counerac macroeconomic imbalances. The remainder of his paper is organized as follows: In secion 2 we se up a wo-region DSGE model of a moneary union wih a cross-border banking secor consising of an inernaional wholesale branch and counry-specific reail branches as in Gerali e al. 2) and Gambacora and Signorei 24). In secion 3 we discuss he properies of he resuling heoreical framework, and analyze he dynamic adjusmens of he model s main variables o unexpeced moneary policy and cos-push shocks, as well as he consequences of alernaive specificaions of he lending sandards by he banking secor. In secion 4 we invesigae he design of moneary policy in such an environmen. Finally, we draw some concluding remarks in secion 5. 2 The Model We consider a wo-region moneary union populaed by a coninuum of agens on he inerval [, ], a segmen [, n] residing in a region labeled ome), and he oher segmen living in he oher region labeled Foreign). We assume ha ome is he risky region he Souh, for he sake of illusraion), and Foreign is he safe-haven region he Norh, for he sake of illusraion). There is no labor mobiliy beween he regions. Boh regions are assumed o produce radable consumpion goods, which are considered o be imperfec subsiues due o a sandard home bias argumen. Since we model a moneary union, he nominal exchange rae beween he regions is consan and may be normalised o one. 2. ouseholds ouseholds in boh regions are infiniely-lived and have idenical preferences and endowmens wihin each region. Furher, as in Iacoviello 25) households are assumed o be more paien han enrepreneurs, ha is, ha hey have a lower discoun facor β < β E ). As a resul, households purchase a cerain amoun of new deposi conracs and enrepreneurs borrow a posiive amoun of loans in equilibrium. In oher words, in equilibrium posiive financial flows exis wih households being ne lenders and enrepreneurs being ne borrowers. In order o render he model saionary, we follow Schmi-Grohé and Uribe 23) and assume ha households face a small quadraic porfolio adjusmen cos θ D when heir deposis differ from he seady-sae level D. Capial leers denoe indices, small leers denoe single unis. 4

7 In a sandard manner, he uiliy maximizaion problem of households in ome analogous expressions apply for he F oreign households) is given by [ ) N max E β s ln Cs η+ )] s subjec o he real budge consrain ) W C + D = N P s= + + rd )D π η + + θ D 2 ) D D ) 2 + Π, 2) where C represens he households aggregae consumpion bundle o be defined below), N he households labour supply, D he ineres-earning deposis, π P /P he gross CPI inflaion rae, W /P he real wage and Π he real profis from reailers in, which are paid in a lumpsum manner o households. ouseholds hus maximize he expeced presen discouned value of ineremporal uiliy, which we assume o be separable in consumpion and leisure. ouseholds in boh ome and Foreign save in he form of bank deposis, earning a uniform deposi rae r d which for he sake of simpliciy is assumed o be equal o he shor-erm ineres rae conrolled by he moneary auhoriy of he currency union. From he FOCs of his ineremporal opimizaion problem we obain a consumpion Euler equaion and he sandard labor supply equaion: and C + C = E π + ) β + r [ d) θd D D) ] N ) η = W C P As he households in F oreign are assumed o have symmeric ineremporal preferences, we ge analogous expressions for he F oreign households: ) C+ F β + r d ) C F = E [ θd D F D) ] π F + 3) 4) 5) and N F ) η = W F C F P F 6) Following Duare and Wolman 28) and Ferrero 29), he aggregae consumpion bundle in ome analogous expressions hold for F oreign) conains counry-specific goods bundles from boh regions and is defined as C = [ ω ) σ C h ) σ σ + ω ) σ C f ) σ ] σ σ σ 7) where C h and C f represen bundles of reail consumpion goods i produced in ome and Foreign, respecively, σ denoes he elasiciy of subsiuion beween hese wo consumpion bundles and he 5

8 parameer ω represens he seady-sae impor share of households in. Given our assumpion of home bias in consumpion, i holds ha ω < n). 2 Nex, we deermine he opimal allocaion of oal consumpion expendiures of he represenaive household across he regional good bundles C h and C f. This is derived from he poin of view of a household in here, where analogous relaions apply for households in F. Assuming ha he law of one price LOP) holds, he price for idenical bundles of goods will be he same in boh regions. For insance, P h = S P h, where P h is he price of goods produced in in erms of foreign currency and S is he nominal exchange rae. Since we model a moneary union, he nominal exchange rae is fixed a one and LOP implies P h = P h and P f = P f. ouseholds in region firs allocae consumpion across individual reail goods, and hen opimally choose how o allocaion consumpion across bundles produced in region and F. We assume ha counry-specific bundles of reail goods i, produced in and in F, are packed ino consumpion bundles C h and C f wih he usual CES funcions, adjused for region size, where n is he size of region, n) he corresponding size of region F and ε denoes he elasiciy of subsiuion beween differeniaed goods: 3 C f = C h = [ n ε n [ n) ε C h i) ) ε ε This gives he usual demand funcions for individual goods: n ] ε ε di ) ε ] ε C f ε ε i) di 8) 9) C h i) = n where he reail price indices are defined as P h i) C f i) = n P h P f i) P f ) ε C h ) ) ε C f ) P h [ n n P h i) ) ε di ] ε and P f [ n n ) ] ε P f ε i) di. 2 Noe ha he assumpion of a symmeric seady sae wih equal per-capia oupu in he wo regions implies ha he amoun of home bias in boh regions is relaed o he relaive region size: ω F = n n ω. 3 When using consumers demand funcions o derive oal demand for reailers individual goods, we model he elasiciy of subsiuion as a counry-specific exogenous shock process. Thereby, a cos-push shock on reailers markup may be inroduced. To keep he model simple, we omi his assumpion here and simply rea he elasiciy of subsiuion as a parameer. 6

9 Consequenly, he cos minimizaion problem for he allocaion of consumpion across he regionspecific bundles of reail consumpion goods produced in and F gives he following demand funcions: C h = ω ) P h P ) σ C 2) C f = ω ) P f P ) σ C 3) where P [ ) ) ) ] ω P h σ σ + ω P f σ denoes he CPI price index for region. Given he assumed home bias in consumpion, he households aggregae consumpion bundles in ome and F oreign and he corresponding price indices are no necessarily symmeric. In order o ge rid of relaive prices, we can express everyhing in erms of rade. Terms of rade T are defined as follows: T P f /P h. By expanding he expression for he CPI price indices in and F, we hus derive: P h P P f P = [ ω ) + ω T σ ] σ 4) = [ ω ) T σ + ω ] σ 5) Similarly, we ge for relaive prices in region F, assuming ha he law of one price holds: P f P F P h P F = [ ω F ) + ω F T σ ] σ 6) = [ ω F ) T σ + ω F ] σ 7) Finally, in a moneary union wih fixed nominal exchange rae he real exchange rae RER is given by he relaion of foreign o home CPI price indices: RER = P F P ω F ) + ω F T σ ) σ = T ω ) + ω T σ 8) 2.2 Firms We assume ha producion akes place in wo sages. In he firs sage, firms in region and firms in region F produce he inermediae good Y h,in and Y f,in in fully compeiive markes and under credi consrains as in Iacoviello 25). In line wih Bernanke e al. 999), we hen assume ha inermediae goods are sold o reailers, who ake heir price as given and differeniae hem a no cos. Due o he differeniaion of producs, reailers are assumed o operae under monopolisic compeiion and face a quadraic cos for he adjusmen of prices as in Roemberg 982). All profis from reail aciviies are rebaed lump-sum o households in he respecive region. 7

10 2.2. Enrepreneurs Enrepreneurs in regions and F produce inermediae goods Y h,in and Y f,in under perfec compeiion. Inermediae goods are used in he producion of a final consumpion good and are assumed o be non-radable. Enrepreneurs aim a maximizing heir consumpion and use capial goods and labor for he producion of inermediae goods. We assume ha enrepreneurs consume only goods from heir own region. A he end of each period, enrepreneurs buy new capial goods from capial producers, so ha capial is only realized in he nex period. Invesmen ino new capial goods is assumed o be financed wih loans from banks. 4 Following Iacoviello 25), we assume ha enrepreneurs are credi-consrained and hus can only borrow up o a fracion of heir collaeral, i.e. heir capial asses. The resuling dynamics are similar o a financial acceleraor effec as in Bernanke e al. 999). Noe ha our assumpion of a lower discoun facor for firms ensures ha he borrowing consrain will always bind in he neighbourhood of he seady-sae. Enrepreneurs in hus maximize consumpion C E subjec o heir budge and heir borrowing consrains and o a Cobb-Douglas consan-reurns-o-scale producion funcion: s.. C E + rb + π ) W B E + P max E = βe ln CE 9) ) N d + q K K Y µ h,in + B E + q k δ k )K E 2) B E me q+ k δ k )K E + r b π + 2) Y h,in = A ) K E ξ ) N d ξ) 22) where C E rae + r b ), N d is enrepreneurs consumpion in, B E is he amoun borrowed from banks a he loan is he amoun of labor demanded by enrepreneurs, µ P h, /P h,in denoes he mark-up of reail over inermediae goods prices we assume ha he mark-up is he same in boh regions), K E is capial obained a he price q k and depreciaed wih rae δ k. Enrepreneurs discoun facor β E is assumed o be lower han households β, so ha enrepreneurs are always ne borrowers. The borrowing consrain in 2) saes ha loans canno exceed a fracion m E of he real depreciaed value of capial asses in relaion o he ineres obligaions. The parameer m E may be inerpreed as he loan-o-value LTV) raio ha banks demand of enrepreneurs and, hus, gives a measure of banks assessmen regarding firms credi-worhiness. We assume ha m E may vary across 4 This seems o be a reasonable assumpion for a model of he EMU, since bank credi is he predominan source of exernal finance for European firms, see for insance Allen e al. 2). 8

11 regions in he moneary union, reflecing differen macroeconomic condiions and differen assessmens of firms credi-worhiness by banks. While he baseline simulaion assumes symmeric borrowing consrains in boh regions, in secion 3.4 we assume ha he borrowing consrain parameer is eiher affeced by he region s own echnology shock, or banks may perceive one region s echnology shock as dominan and apply resricions o borrowing consrains in boh regions. Finally, he Cobb-Douglas producion funcion gives oupu as a funcion of capial and labour inpus, where A is an exogenous echnology process which may differ across counries. We define A as an exogenous AR) process wih persisence parameer ρ a and i.i.d. shock process ε A he real reurn of capial as R k condiions: C E s B = β E + r b q k C E W P = = ξa K ) E ξ N d ) ξ) π + ). Defining µ we hen ge he following opimaliy C E + 23) β E [ R k C+ E + + q+ k δ k ) ] + sb m E q+ k )π+ + r b 24) h,in ξ)y N d µ 25) Equaion 23) gives enrepreneurs Euler equaion, where s B denoes he Lagrange muliplier on he borrowing consrain and hus gives he marginal value of one uni of borrowing. The relaion in 24) gives he opimal relaion beween enrepreneurs consumpion and real reurns from capial, given he borrowing consrain. Finally, equaion 25) shows ha in he opimum, real wages equal he marginal produc of labor. Analogous opimaliy condiions hold for enrepreneurs in region F Capial producers As in Gerali e al. 2) and Gambacora and Signorei 24), we assume ha each period, capial producion is underaken by perfecly compeiive capial producers, which are owned by enrepreneurs. These firms buy las period s depreciaed capial sock from enrepreneurs as well as an invesmen I in he form of new final goods from reailers and use boh o produce he new capial sock. In line wih previous auhors, we assume ha old capial sock can be ransformed one-for-one ino new capial sock, while invesmen from final goods underlies a quadraic adjusmen cos for he ransformaion ino capial goods. A he end of he period, he resuling new capial sock is sold back o enrepreneurs. Since capial goods producion akes place wihin each region, we only describe he problem for capial goods producers in, bu analogous relaions hold also in F: Defining x K E δ k )K E, capial goods producers hen solve he following problem: max x,i E = Λ E k, [ q k x I ] 26) 9

12 s.. x = [ κi 2 I I ) 2 ] I, 27) where Λ E k, +k βe k U C+k E) = βk E λe, wih k =,,..., is he sochasic discoun facor from enrepreneurs, who are assumed o own capial producing firms, and λ E is he Lagrange muliplier on enrepreneur s budge consrain. The capial adjusmen cos is denoed by κ I, which we assume o be equal across regions. The FOCs hen yield an expression deermining he price of real capial, q k : ) = q k κi I 2 ) ) I 2 I κ I I I λ E I + β E E + I λ E q+ k ) + I ) 2 ) κi I + I 28) Reailers Reailers in counries and F buy inermediae goods Y h,in compeiive marke, aking heir price P h,in or P f,in or Y f,in from enrepreneurs in a as given. These inermediae goods are hen differeniaed ino final consumpion goods a no cos, so ha reailers operae under monopolisic compeiion. Addiionally, hey are assumed o face quadraic coss for he adjusmen of prices as in Roemberg 982). In our wo-region model, reailers are symmeric, bu face demand from consumers in boh regions as well as from domesic enrepreneurs. Aggregaing over households and enrepreneurs, world demand for individual reail goods for reailers in is hen derived from he demand equaions of households and from enrepreneurs, measured in unis per domesic firm. Noe ha we model he elasiciy of subsiuion for individual goods produced in as a counry-specific exogenous process ε. This gives he demand for individual good Y h i), faced by a reailer in again, analogous relaions apply for reailers in F): Y h,oal i) = Y h,oal i) = ) [ P h ε i) P h λ) ) P h ε i) [ P h [ ω ) P h P ) σ C + ω F n n λ) [ ω )[ ω ) + ω T σ P h ] σ σ C P F ) σ C F ] + ω F n n + λc E ] [ ω F ) T σ ] ] ] + ω F σ σ C F + λc E Y h,oal i) = P h i) P h ) ε C W 29) where C W denoes aggregae world demand for reail goods from region and F, respecively, and λ is he share of enrepreneurs in he economy. Individual reailers in se he price P h i) for he individual final good Y h i), and hus face he following maximizaion problem: max P h i) E = Λ k, [ P h i) P h Y h,oal i) P h,in P h Y h,oal i) κ p P h i) 2 P h i) ) 2 C W ], 3)

13 where Λ k, β k U C+k ) = βk λ +k, wih k =,,..., is he sochasic discoun facor from households uiliy maximizaion in, π h = P h /P h defines reail price inflaion and κ p denoes he adjusmen cos for changing prices. The maximizaion problem is subjec o oal demand for he final good as derived above: Y h,oal i) = P h i) P h ) ε C W 3) Imposing a symmeric equilibrium, his yields he following opimaliy condiion: ε + ε κ p π h π h µ ) [ λ + + βκ p E λ C W + C W π h + π h + )] = 32) Finally, he exogenous process for he elasiciy of subsiuion is relaed o reailers mark-up mk in region via he relaion mk = ε /ε ). We model reailers region-specific mark-up as an AR) process wih persisence ρ mk and an i.i.d. cos-push shock ε Y. 2.3 The Banking Secor For our model of cross-border banking wihin a moneary union, we build on he work of Gerali e al. 2) and Gambacora and Signorei 24). The wo papers presen DSGE models wih boh a collaeral channel from enrepreneurs credi consrain à la Iacoviello 25) and a credi-supply channel semming from a arge for banks leverage raio, which may limi he supply of credi available from banks. We follow his approach and adjus he se-up of banks in he model o allow for crossborder credi flows. Specifically, we assume ha here exiss a represenaive bank in he moneary union, which consiss of an inernaional wholesale branch and naional reail branches in each region of he moneary union. The wholesale branch is responsible for collecing deposis from households hroughou he moneary union and disribues he resuling funds o he reail branches a he inernal loan raes R b and R bf. The reail branches hen provide credi o enrepreneurs in heir counry of residence. Noe ha in his se-up, banks canno endogenously creae new credi. The wholesale branch is addiionally responsible for adhering o he exogenous consrain on he bank s leverage raio, which is modelled in he form of a quadraic cos of deviaing from he arge value ν. The value of ν could for insance be inerpreed as reflecing regulaory legislaion regarding banks equiy holdings. The credi-supply channel hus inroduces an addiional feedback loop beween real and financial condiions in he sense ha he loan raes, as well as he spread beween he loan raes and he risk-free policy rae, depends on banks leverage, heir profi and, hence, on macroeconomic condiions. Finally, reail branches in, F are assumed o operae under monopolisically compeiive condiions, and hus charge a consan mark-up µ b on he inernal loan rae R b, i.e. R bf.

14 Aggregae deposis in he moneary union and aggregae lending o enrepreneurs in boh regions are defined as follows: D nd + n)d F 33) [ ] γ ) n γ B γ ) γ + n) γ B F γ γ γ 34) B where B and B denoe he credi supply given o reail branches in region and F, respecively, and γ denoes he bank s elasiciy of subsiuion beween lending o boh regions. We hus assume ha loans o he wo regions are imperfec subsiues from he poin of view of he bank, which may be moivaed wih he noion of a hisorically more sound economic performance in one region here he Norh), as well as wih differences in he credi screening capabiliies in boh regions. Noe ha we assume no home bias in lending, because he wholesale bank is assumed o be inernaional. In our se-up, he wholesale branch hus aims a maximizing profis subjec o a quadraic cos for deviaing from heir arge leverage raio ν and o heir budge consrain: s.. max nr b B + n)r bf B F r d D θ ) K b 2 ν K b 35) 2 B B = D + K b 36) [ ] γ ) B = n γ B γ ) γ + n) γ B F γ γ γ, 37) where K b is he banks own capial and he parameer θ gives he proporion of Kb o which he cos of deviaing from arge applies. The bank s leverage raio and is budge consrain are deermined wih respec o aggregae lending B. Solving he maximizaion problem gives he inernal loan raes for credi supply o reail branches in regions and F: R b = n γ γ R bf r d B B = n) γ γ ) γ r d B B F γ n γ K b θ ν B ) γ ) K b ) 2 2γ+ ) γ B B γ γ n) γ K b θ ν B ) K b ) 2 2γ+ ) γ B B F γ 38) 39) ence, exending he closed economy se-up in Gambacora and Signorei 24) o he open economy case, i urns ou ha boh he effec of he risk-free deposi rae and of he leverage consrain on he loan rae are weighed wih he relaive share of loan supply o he respecive region, adjused for region size. This means ha loan raes in a given region will be more sensiive o deviaions from he bank s leverage arge and o changes in he policy rae if he wholesale branch disribues a larger share of is overall credi supply o his region. 2

15 As in Gambacora and Signorei 24), he reail banks are hen assumed o be able o differeniae he wholesale loans a no coss and pass hem under monopolisic compeiion on o enrepreneurs, charging a consan mark-up µ b, which we assume o be equal across regions in he moneary union: 5 r b = R b + µ b 4) r bf = R bf + µ b 4) Finally, we define aggregae banks profis J b as he sum of wholesale and reail profis and assume ha banks re-inves heir profis ino new bank capial, where a fracion δ b is used each period o pay for banking aciviies: J b = nr b B + n)r bf B F r d D θ ) K b 2 2 B ν K b 42) K b = δ b )K b + Jb 43) 2.4 Moneary Policy The cenral bank in he model conrols he nominal risk-free ineres rae r d and adjuss o inflaion as in Bernanke e al. 998). Since we model a currency union, he cenral bank arges inflaion in boh regions, where he weigh is given by heir relaive size. This resuls in he following Taylor-ype rule: + r d ) = + rd )ρ + r d ) ρ [ n π ) + n) π F )] φπ ) ρ ε rd 44) where ρ measures he amoun of ineres rae smoohing, r d he nominal seady sae ineres rae, φ π gives he srengh of inflaion argeing and ε rd is an i.i.d. moneary policy shock. 5 This assumpion implies ha hroughou he moneary union, he marke srucure among reail banks is similar. Since we assume ha he represenaive bank acs inernaionally in boh counries of he moneary union, his assumpion seems reasonable. 3

16 2.5 Equilibrium Equilibrium in our model is defined by he resource consrains and marke clearing condiions in all markes. These are given as follows for he goods marke, he labor marke and he banking secor, where Y k denoes aggregae oupu in region k: ny Y = C W + q k K E Y F = C W F + q kf K EF + n)y F = n [ C + C E + q k + n) [ C F + C EF δ)k E ) + ) + δ)k EF K E + q kf δ)k E K EF n δb K b 45) n δb K b 46) )] 47) δ)k EF )] N = N d 48) N F = N df 49) B E = B 5) B EF = B F 5) B = D + K b 52) Finally, he model is log-linearized around he seady sae and solved numerically using Dynare 4.4.3, see Adjemian e al. 2). 3 Simulaions 3. Calibraion For he following simulaions we follow Gambacora and Signorei 24) and se our model parameers mainly as in Gerali e al. 2), who calibraed heir model so as o mach key aspecs of he euro area real and financial secors. Addiionally, some parameers relaing o he open-economy aspec of he model are calibraed as in he wo-region model of he euro area of Engler e al. 23). Table repors all parameer values. 6 Accordingly, households discoun facor β P is se a.996, which implies a seady-sae policy rae of abou 2 % annualized). Enrepreneurs discoun facor β E is se a.975, as in Iacoviello 25). The inverse of he Frisch elasiciy η is se a as in Galí, 28). The share of capial in he aggregae producion funcion α is se a.2, and he depreciaion rae of physical capial δ k ) a.5 as in Gerali e al. 2). The elasiciy of subsiuion across regional goods bundles σ is se a 2 as in Engler e al. 23). Furher, we se he adjusmen cos for changing prices κ p a he 6 We also considered esimaing he curren framework wih disaggregaed euro area daa, bu decided agains i because a proper esimaion of he cross-border banking effecs a work here would be a ask beyond he scope of his paper, due o heir overlap wih he global financial liberalizaion since he 2s. We leave his for furher research. 4

17 Table : Calibraion parameers Parameer Descripion Value β P Paien household discoun facor.996 β E Enrepreneurs discoun facor.975 σ Elasiciy of subsiuion beween ome and Foreign goods bundles 2 θ D Parameer for households porfolio adjusmen cos. D Seady-sae level of deposis ω Seady-sae impor share in ome.33 ω F Seady-sae impor share in Foreign.7 n ome s relaive size.34 η Inverse of he Frisch elasiciy α Capial share in he producion funcion.2 δ k Depreciaion rae of physical capial.5 κ I Invesmen adjusmen cos parameer 5 m E Enrepreneurs LTV raio.35 κ p Adjusmen cos for changing prices γ Bank s elasiciy of subsiuion beween lending o boh regions 2 θ Bank capial adjusmen cos ν Targe capial-o-asse raio.9 δ b Cos for managing he bank s capial posiion.49 φ π Inflaion gap Taylor rule parameer.5 ρ Moneary policy ineria.77 ρ mk Persisence of reailers cos-push shocks.5 ρ a Persisence of echnology shocks.95 σmp 2 Variance of moneary policy shock. σmk 2 Variance of cos-push shock σa 2 Variance of echnology shock value esimaed by Gerali e al. 2) for he euro area, namely Concerning he invesmen adjusmen cos parameer κ I, we se i a 5 as in Gambacora and Signorei 24) in heir analysis of heir model s response o echnology shocks. 7 The required LTV raio for enrepreneurs se by he reail bank branches, m E, is se a.35 in he baseline case, which is similar o he average raio of long-erm loans o he value of shares and 7 Gambacora and Signorei 24) se κ I a.5 when analyzing cos-push shocks, bu argue ha when boh echnology and cos-push shocks hi heir model a he same ime, heir overall resuls are no affeced by he choice of a paricular value of κ I, see Gambacora and Signorei 24, p.55-56). 5

18 oher equiies for nonfinancial corporaions in he euro area, see also Gerali e al. 2) as well as Gambacora and Signorei 24). The arge leverage raio ν and he cos for managing he bank capial posiion δ b are se a 9% and.49, respecively, following again Gerali e al. 2). Due o he lack of a more direc measure, we se he bank capial adjusmen cos θ a, he value esimaed by Gerali e al. 2). Finally, he bank s elasiciy of subsiuion beween loans o ome and Foreign, γ, is se equal o he elasiciy of subsiuion beween ome and Foreign goods bundles, σ, a 2. The degree of moneary policy ineria is se a.77, and φ π is se a.5, as i is sandard in he lieraure. Finally, we se he relaive size of he ome and Foreign economies a.34 and.66, respecively, o reflec he asymmeric economic size of he regions wihin he euro area, assuming for he sake of illusraion ha ome represens he Souhern euro area counries such as Spain, Ialy, Porugal or Greece, and Foreign he Norhern euro area counries, in paricular Germany see also Engler e al., 23). 3.2 Moneary policy shock In order o illusrae he differen mechanism a work in he presen framework, in he following we discuss he dynamic adjusmens of he model s endogenous variables o an unexpeced conracionary shock on he policy rae of he moneary union s cenral bank. As summarized in Figure 2, he unexpeced increase in he policy rae of he moneary union s cenral bank affecs boh economies hrough a variey of channels. Firs, a conracionary shock o he policy rae r leads o an increase in he inernal rae of ineres beween he wholesale and he region-specific reail bank branches, and hus by exension also o an increase in he loan ineres raes R b and R bf offered o he enrepreneurs by he reail bank branches in he Souhern and Norhern regions, respecively. This pass-hrough effec from r o R b and R bf is larger han one, as he rise in he spread beween he loan rae in boh regions and he policy ineres rae clearly illusraes. A his poin i is noeworhy ha despie he fac ha he iniial shock in he policy rae affecs boh regions in an idenical fashion, he reacion of loan ineres raes, he loan spreads and by exension he aggregae amoun of awarded loans is, hough qualiaively similar, quaniaively differen in boh regions, wih a larger effec on he spread in he Souhern region. This raher unexpeced resul arises from he differen economic sizes assumed for boh economic regions and he resuling differen relaive shares of aggregae lending allocaed o each region. 8 The deerioraion in he credi financing-condiions for firms leads o a decrease in he demand for credi and hus in he amoun of loans graned in equilibrium. This resuls in a reducion in he level 8 Theoreically, if boh counries were compleely idenical in heir economic srucure and had he same relaive economic size, i.e. n =.5, hen he reacions would also be idenical and no shif in relaive prices would occur. This is indeed corroboraed by our model when n is se a.5. 6

19 .4 Moneary Policy Rae.8 Loan Raes.4 Spreads Aggregae Loans Souhern Norhern Souhern Norhern Souhern Norhern Aggregae Invesmen Aggregae Capial Aggregae Consumpion Wages Souhern Norhern Souhern Norhern Souhern Norhern Souhern Norhern Reail Inflaion.5 CPI Inflaion.5 RER x 7 2 ToT x Souhern Norhern Souhern Norhern RER ToT Aggregae Oupu.2 Union wide Deposis 2 Wholesale Bank Profis 2.5 Bank Capial Souhern Norhern Figure 2: Dynamic adjusmens afer a union-wide moneary policy shock. All raes are shown as absolue deviaions from seady sae, expressed in percenage poins. All oher variables are percenage deviaions from heir respecive seady sae levels. of aggregae invesmen and by exension in he capial accumulaion in boh economies, as illusraed in Figure 2. The increase in he policy rae leads of course also o a reducion in aggregae boh households and enrepreneurs ) consumpion by heir respecive consumpion Euler equaions which, joinly wih he reducion in aggregae invesmen, leads o an overall decrease in curren aggregae oupu, employmen and wages. Noe ha he effec of he moneary policy shock on aggregae oupu is very similar across boh regions despie larger differences in he effec on invesmen. This is because aggregae consumpion in our model is a relaively larger par of oupu compared o invesmen. The reducion in households wage income causes a ne reducion in heir bank deposis despie he 7

20 increased opporuniy coss relaed wih he increase in he deposi rae which is assumed o be equal o he policy rae). Finally, as expeced he increase in he policy rae causes a fall in boh reail and CPI inflaion in he wo regions. Since he LOP assumpion holds, inflaion in boh regions reacs symmerically o he shock, even hough he level of inflaion may differ. Turning our aenion back o he banking secor, he dynamic reacions of he wholesale bank s profis J B and capial K b illusraed in Figure 2 show clearly ha while he reducion in he quaniies of boh deposis and loans affecs he inernaional wholesale banking secor negaively, he ne effec of a policy rae increase is posiive due o he larger increase in he inernal and loan ineres raes, leading o an increase in he bank s profis and capial. 3.3 Cos-Push Shock Nex, we briefly discuss he dynamics resuling from an unexpeced cos-push shock of one sandard deviaion in he Norhern region. Figure 3 summarizes he dynamics of he main variables of he model. As can be clearly observed, an unexpeced asymmeric cos-push shock in he Norhern region leads o an immediae rise in boh reail and CPI inflaion in boh regions, as well as o a relaive hough very small in absolue erms) improvemen in he compeiiveness posiion of he Norhern economy. Noe ha since he LOP applies in our model, prices in boh regions adjus symmerically o he cos-push shock in he Norhern region, even hough he level of CPI inflaion may differ due o he asymmeric region sizes. The sandard counercyclical reacion of he moneary union s cenral bank implies a rise in he policy rae sufficien o yield an increase in he real ineres rae. Again, his effec is amplified via he banking secor, as he increase in loan rae spreads in boh regions clearly illusraes. Noe ha he larger increase in he Souhern regions loan spread is again due o he differen region sizes. owever, in he case of a cos-push shock occurring only in one region, here he Norh, only he Norhern region s economy is adversely affeced by he shock. This may be observed by he drop in reail profis due o a fall in aggregae demand for reail goods produced in he Norhern region he iniial posiive effec is because prices increase on impac, while demand is slower o adjus), leading o a fall in agregae consumpion, wages, invesmen and oupu. By conras, reail profis in he Souhern region increase, yielding a boom in he region. Therefore, even hough loan spreads increase more in he Souhern region, enrepreneurs from he Souh are awarded relaively more loans. Finally, as in he case of a moneary policy shock, he banking secor profis relaively more from he increase in loan spreads han from he drop in loans and deposis, so ha overall banking profis and capial increase. 8

21 Moneary Policy Rae x Loan Raes Souhern Norhern Spreads x Souhern Norhern Aggregae Loans Souhern Norhern Aggregae Invesmen.2 Aggregae Capial.4 Aggregae Consumpion.6 Wages Souhern Norhern Souhern Norhern Souhern Norhern Souhern Norhern Reail Inflaion x 3 5 CPI Inflaion x Enrepreneurs Consumpion 4 Reail Profis Souhern Norhern Souhern Norhern Souhern Norhern Souhern Norhern Aggregae Oupu.5 Union wide Deposis.4 Wholesale Bank Profis. Bank Capial Souhern Norhern Figure 3: Dynamic adjusmens afer a cos-push shock in he Norhern region. All raes are shown as absolue deviaions from seady sae, expressed in percenage poins. percenage deviaions from heir respecive seady sae levels. All oher variables are 3.4 Cross-Border Lending, Rule-of-Thumb Banking and Business Flucuaions ere we invesigae he implicaions of cross-border banking for macroeconomic aciviy. Indeed, as previously discussed see also CIEPR, 22), he recen experience of he housing boom-and-bus cycles in Spain and Ireland which were financed o a large exen by cross-border capial flows from Germany seems o sugges ha cross-border lending may no have been subjec o he same screening sandards for credi worhiness as inernal lending, and ha his pracice may have hus conribued decisively o he recen macroeconomic insabiliy of hose counries. 9

22 In order o model his phenomenon in he mos parsimonious manner, we assume in he following ha he LTV borrowing consrain for enrepreneurs, capured by he parameer m E, is no consan as assumed in he previous secions, bu ha i follows a ime-varying process driven by firms regionspecific oal facor produciviy TFP): m E,k = + µa k ) m E, k = {, F} 53) where µ is a proporionaliy facor, assumed here o equal.65. While his is of course a convenien modeling shorcu, he raionale behind his specificaion is sraighforward: In he real world, banks usually employ a screening mechanism o assess he profiabiliy of he invesmen projecs o be financed, and hus he crediworhiness of he loan applicans. To reflec his, we assume ha invesmen profiabiliy is given solely by TFP. Under he assumpion ha TFP shocks are observable also by he banking secor, i is naural o assume ha a posiive TFP shock leads o a relaxaion of he borrowing consrain imposed on he enrepreneurs by he banks. Obviously, he deerminaion of m E,k in ome and Foreign deermining m E would be region-specific in he normal case, wih he reail bank branches and m EF according o he observaion of A and AF, respecively. We refer o his normal case as scenario in he following. Alernaively, we consider an addiional scenario where he lending sandards in boh counries are deermined uniformly solely on he observaion of TFP in he Norhern region, i.e. This alernaive specificaion of m E,k m E,k = + µa F )m E, k = {, F}. 54) solely as a funcion of A F is mean o represen he rule-ofhumb deerminaion of lending sandard in cross-border banking wihin he euro area discussed for insance by Allen e al. 2) and CIEPR 22). In paricular, his specificaion reflecs he implici risk pooling associaed wih he esablishmen of moneary unions, and observable in he excessively low sovereign risk premia of EMU counries and resuling ineres rae convergence during he 2s, see e.g. De Grauwe and Ji 22) and Proaño e al. 24). We erm his scenario rule-of-humb banking or scenario 2. Figure 4 illusraes he dynamic adjusmen of seleced variables of our model under a consan LTV borrowing consrain baseline scenario), varying region-specific lending sandards scenario ), and rule-of-humb lending sandards scenario 2). In all cases we assume a posiive one-sandard deviaion shock in TFP in he Norhern region, A F, leaving all oher variables and especially TFP in he Souhern region) unchanged, as he firs wo graphs in he firs column of Figure 4 show. 2

23 .5 TFP Produciviy Norhern) Baseline Scenario Scenario 2.5 TFP Produciviy Souhern) Baseline Scenario Scenario LTV Consrain Norhern) Baseline Scenario Scenario 2.5 LTV Consrain Souhern) Baseline Scenario Scenario Loan Rae Spread Norhern) Baseline Scenario Scenario 2.2 Loan Rae Spread Souhern) Baseline Scenario Scenario Awarded Loans Norhern) Baseline Scenario Scenario 2.5 Awarded Loans Souhern) Baseline Scenario Scenario Wholesale Bank s Profis Baseline Scenario Scenario Wholesale Bank s Leverage Baseline Scenario Scenario Aggregae Invesmen Norhern) Baseline Scenario Scenario Aggregae Invesmen Souhern) Baseline Scenario Scenario Aggregae Consumpion Norhern) Baseline Scenario Scenario Aggregae Consumpion Souhern) Baseline Scenario Scenario Aggregae Oupu Norhern) Baseline Scenario Scenario 2.5 Aggregae Oupu Souhern) Baseline Scenario Scenario Figure 4: Dynamic adjusmens o a posiive TFP shock in he Norhern region under consan baseline), region-specific scenario ) and rule-of-humb scenario 2) lending sandards. All raes are shown as absolue deviaions from seady sae, expressed in percenage poins. All oher variables are percenage deviaions from heir respecive seady sae levels. 2

24 As furher shown in Figure 4, a posiive shock o TFP in he Norh leads o an expansion in aggregae income, consumpion and invesmen in ha region, he laer being parly financed by an expansion of lending o he enrepreneurs by he banking secor over ime. Noe ha his credi expansion akes place also in he baseline case where m E,k = cons., bu is of course larger in magniude in he wo alernaive scenarios, where m E,k is a direc funcion of TFP in he Norhern region. Due o he higher aggregae income in he Norh, here is also a higher demand for goods produced here which requires an expansion of he capial sock and hus in he producion capabiliies of he region. This effec akes place in all hree scenarios, bu is of course larges in scenario 2, where he LTV borrowing consrain assumed o be a funcion of he observed TFP in he Norhern region) is relaxed no only in he Norhern economy where indeed an increase in TFP ook place), bu also in he Souhern region. As he graphs in he las row in Figure 4 show, aggregae economic aciviy in boh regions is significanly larger paricularly in he firs periods afer he shock in scenarios and 2 relaive o he baseline scenario. Analyzing he differen effecs on dynamic adjusmens in he Souhern economy in he differen scenarios allows o disinguish beween spill-over effecs via he rade linkages and he addiional effec of rule-of-humb banking assumed in scenario 2. These emerge specifically wih respec o loans awarded o enrepreneurs and, hus, invesmen. As he Souh is awarded he same relaxaion in borrowing condiions han he Norh in scenario 2, boh loans and invesmen increase more rapidly. Finally, boh aggregae consumpion and oupu increase by more wih ime-varying LTV raios, alhough here are only marginal differences beween scenario and 2. Overall, he comparison beween scenarios and 2 shows ha wih rule-of-humb banking addiional business cycle dynamics occur in he Souhern region, which are solely relaed o relaxaions in credi availabiliy, and no backed by macroeconomic fundamenals. Loan rae spreads decrease in boh regions following he increase in loans awarded afer he Norhern TFP shock, whereas he effec is relaively larger in he Souhern region. In boh regions, he effec becomes sronger over ime as he bank adjuss he borrowing consrain o changes in produciviy. Since credi expands a he same ime, we observe again ha as in he previously discussed cases of a moneary policy or cos-push shock price effecs in his case changes in loan rae spreads) dominae over quaniy effecs i.e. loans awarded), resuling here in a negaive effec of he TFP shock on he inernaional wholesale bank s profis. Furher, as i can be clearly observed in Figure 4, he reducion in he bank s profis increases ceeris paribus he wholesale bank s leverage, as a higher quaniy of awarded loans goes hand in hand wih lower profis and, by exension, lower bank capial, see eq. 43). This resul is paricularly noeworhy as i implies ha cross-border rule-of-humb banking leads o a higher leverage in he financial sysem, and hus o a more fragile macrofinancial siuaion. 22