Global Banks, Financial Shocks and International Business Cycles: Evidence from an Estimated Model *

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1 Federal Reserve Bank of Dallas Globalizaion and Moneary Policy Insiue Working Paper No. 120 hp:// Global Banks, Financial Shocks and Inernaional Business Cycles: Evidence from an Esimaed Model * Rober Kollmann ECARES, Universié Libre de Bruxelles and CEPR July 2012 Absrac This paper esimaes a wo-counry model wih a global bank, using US and Euro Area (EA) daa, and Bayesian mehods. The esimaed model maches key US and EA business cycle saisics. Empirically, a model version wih a bank capial requiremen ouperforms a srucure wihou such a consrain. A loan loss originaing in one counry riggers a global oupu reducion. Banking shocks maer more for EA macro variables han for US real aciviy. During he Grea Recession ( ), banking shocks accouned for abou 20% of he fall in US and EA GDP, and for more han half of he fall in EA invesmen and employmen. JEL codes: F36, F37, E44, G21 * Rober Kollmann, ECARES, CP 114, Universié Libre de Bruxelles; 50 Av. Franklin Roosevel, B-1050 Brussels, Belgium rober_kollmann@yahoo.com. Mahias Pausian conribued o his projec in is early sages--i hank him for his advice and for compuer code. I also hank Werner Roeger for many discussions. Helpful commens and suggesions were also received from Gerno Müller, Alan Suherland, Chrisoph Thoenissen, Ken Wes, Egon Zakrajšek and paricipans a several workshops. For financial suppor I hank he Naional Bank of Belgium, Universié Libre de Bruxelles (Acion de recherche concerée ARC-AUWB/ /ULB-11) and he EU Commission (CEPR projec 'Poliics, Economics and Global Governance: The European Dimensions' funded by he EU Commission under is 7h Framework Programme for Research, Conrac Nr ) The views in his paper are hose of he auhor and do no necessarily reflec he views of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem.

2 1. Inroducion The global financial crisis ha eruped in 2007 revealed he fragiliy of major financial insiuions, and i led o he sharpes global recession since he 1930s. These dramaic evens require a rehinking of he role of financial inermediaries for real aciviy. Before he crisis, sandard macro heory largely absraced from financial inermediaries. The crisis has simulaed much research ha incorporaes banks in dynamic sochasic general equilibrium (DSGE) models. Given he global naure of he crisis, ha research has frequenly focused on open economy models; see, for example, Devereux and Suherland (2011), Gamber and Thoenissen (2011), and Kollmann e al. (2011). 1 In his new class of DSGE models, bank capial is a key sae variable for domesic and foreign real aciviy negaive shocks o bank capial are prediced o increase he spread beween banks lending and deposi raes, and o rigger a fall in bank credi and real aciviy; wih a globalized banking sysem, a loan loss originaing in one counry can hus lead o a worldwide recession. So far, his new open economy macro-banking lieraure has used calibraed models--a sysemaic quaniaive empirical assessmen of he role of banks as a source of shocks and as a ransmission channel in he global economy has no ye been presened. In order o provide such an assessmen, he presen paper esimaes (using Bayesian mehods) a wo-counry DSGE model wih a global bank. Quarerly US and Euro Area (EA) macro daa and banking daa (bank loans, bank capial raio and loan spread) for he period are used. 2 The model here assumes ha each counry is inhabied by a (represenaive) worker, an enrepreneur and a governmen. The global bank collecs deposis from workers and makes loans o enrepreneurs, in boh counries. The bank has o finance a fracion of her asses using equiy (own funds). This consrain can reflec legal requiremens and, more broadly, marke pressures. I implies ha he loan rae spread 1 See also Correa e al. (2010), Davis (2010), Nguyen (2011), Andreasen e al. (2010), Perri and Quadrini (2011), Ueda (2011) and Van Wincoop (2011). Closed economy DSGE models wih banks were, i.a., presened by Aikman and Pausian (2006), Van den Heuvel (2008), de Walque e al. (2010), Gerler and Kiyoaki (2011), Del Negro e al. (2011) and Kollmann e al. (2012a,b). 2 Some previous papers have esimaed open economy DSGE models, bu hose sudies absraced from banks. Two-counry models were esimaed by de Walque e al. (2005), Rabanal and Tuesa (2006) and Le e al. (2010) who also used UE and EA daa, and by Jacob and Peersman (2011). Small open economy models were esimaed by Adolfson e al. (2009) and Jusiniano and Preson (2010). 2

3 (relaive o he deposi rae) is a decreasing funcion of bank capial, as he marginal benefi of bank capial is a decreasing funcion of bank capial. The esimaed model assumes demand and supply shocks in home and foreign labor and good markes. In addiion, here are sochasic loan losses (defauls) in he wo counries, and shocks o he required bank capial raio henceforh, I refer o hese shocks as banking shocks. The esimaion resuls sugges ha he bank capial requiremen, and he banking shocks, maer for he dynamics of macro variables. A model wih hese ingrediens ouperforms model varians wihou an operaive bank capial requiremen or wihou banking shocks. According o he baseline model esimaes, a one percenage poin fall in he global bank capial raio raises he loan rae spread by 44 basis poins. An unanicipaed US loan loss of 1$ lowers boh US and EA GDP by abou 0.15 $, on impac. An unanicipaed increase in he required bank raio by one percenage poin lowers US and EA GDP by 0.21%, on impac. The esimaed model maches key cyclical properies of US and EA macro and banking variables. In paricular, i capures he fac ha US and EA loans are more volaile han oupu, and ha loans are procyclical, while he loan spread is counercyclical. I also capures he fac ha GDP, consumpion, invesmen and bank loans are posiively correlaed across he US and he EA. Banking shocks maer more for EA macro variables han for US real aciviy. These shocks accoun for 5%-10% of US GDP volailiy, and for 10%-25% of US invesmen and employmen volailiy. By conras, banking shocks, explain 15%-30% of EA GDP volailiy, 50%-70% of EA invesmen volailiy, and 25%-50% of EA employmen volailiy. Banking shocks played a noiceable role in he Grea Recession, bu were no he dominan facor driving he fall in GDP: according o he esimaes, banking shocks accouned for abou 20% of he fall in US and EA GDP during ha recession; however, banking shocks accouned for more han half of he fall in EA invesmen and employmen. During he previous US recession (2001) banking shocks also accouned for abou 25% of he fall in US GDP and invesmen. Secion 2 presens he model. Secion 3 discusses he economeric approach. Secion 4 describes key daa feaures. Secion 5 repors he esimaion resuls. Secion 6 concludes. 3

4 2. A wo-counry world wih a global financial inermediary In each of he wo counries, called Home (H) and Foreign (F), here is a represenaive worker, an enrepreneur and a governmen. A global bank collecs deposis from workers, and makes loans o enrepreneurs, in boh counries. The bank faces a capial requiremen: a fracion of bank asses has o be financed using he bank s own funds (equiy). Enrepreneurs produce a homogenous radable good ha is used for consumpion and for capial accumulaion. All agens are infiniely-lived. Markes are compeiive. Preferences and echnologies have he same srucure in boh counries. The following exposiion focuses hus on he Home counry. Foreign variables are denoed by an aserisk Preferences, echnologies, markes The Home worker The Home worker provides labor o he Home enrepreneur and invess her savings in one-period bank deposis. Her dae budge consrain is: where C + D + T = ω N + DR, (1) W W D + 1 W C and N are he worker s consumpion and hours worked respecively. he real wage rae. D + 1 is he bank deposi held by he worker a he end of period. ω is D R is he gross ineres rae on deposis, beween -1 and. W T is a lump sum ax. The W worker s dae expeced life-ime uiliy, V, is: V = u( C ) +Ψ u( D ) Ψ N + E β V, W W D N W W wih x σ σ D ux () = ( 1), σ > 0 and Ψ > 0. The worker s marginal disuiliy of labor, Ψ > 0, is an exogenous random variable. N N Ψ will be referred o as he Home labor supply shock. Noe ha deposis provide uiliy o he worker (liquidiy services). This ensures ha, in equilibrium, he deposi rae is smaller han he loan rae, and ha workers hold deposis while enrepreneurs borrow. The worker s subjecive discoun facor is W W W W W W W decreasing in her fuure consumpion: β+ 1 β ( C+ 1), wih 0 < β ( C + 1) < 1, β '( + 1) < 0. The subjecive discoun facors of oher agens are likewise decreasing funcions of heir C 4

5 own consumpion. 3 Agens rea heir subjecive discoun facors as given, i.e. hey do no inernalize he effec of consumpion on he discoun facor I hus wrie he argumen of he subjecive discoun facor wih an upper-bar. I is assumed ha all agens have he same seady sae rae of ime preference, and he same risk aversion coefficien, σ. The Home worker maximizes her life-ime uiliy subjec o he period-by-budge consrain (1). Tha decision problem has hese firs-order condiions: W N u'( C ) ω = Ψ, (2) R E β u'( C )/ u'( C ) + Ψ u'( D )/ u'( C) = 1. (3) D W W W D The Home enrepreneur The Home enrepreneur accumulaes physical capial and uses capial and local labor o produce oupu. Her echnology is Z = K N 0< α< 1, where Z, K and α 1 α θ( ) ( ), N are oupu, capial and labor, respecively. Toal facor produciviy (TFP), θ > 0, is an exogenous random variable. The law of moion of capial sock is K+ 1 = (1 δ) K+Ξ I, where 0 δ 1is he capial depreciaion rae and I is gross invesmen. Ξ> 0 is an exogenous random shock o invesmen efficiency (Fischer (2006), Jusiniano e al. (2008)). Gross invesmen is generaed using oupu. Le Iξ ( I / I) be he amoun of oupu needed o generae I, where I is seady sae invesmen, and ξ is an increasing, sricly convex funcion wih ξ (1)= ξ '(1) = 1. Henceforh, variables wihou ime subscrips denoe seady sae values. The Home enrepreneur s period budge consrain is: LR ξ I I ω N d T L θ K N L E E α 1 α Δ +Ι ( / ) = ( ) ( ), (4) where L is a one-period bank loan received by he Home enrepreneur in period -1. is he gross ineres rae on ha loan, se a -1. In period, he Home enrepreneur L R defauls by an exogenous random amoun Δ on he amoun LR ha she owes he L bank. T is a lump sum ax. d E is he enrepreneur s dividend income a. The E 3 When subjecive discoun facors are consan, he model has a uni roo (due o marke incompleeness, ransiory shocks hen have permanen effecs on he agens relaive wealh). The endogenous discoun facors induce mean-reversion in individual wealh, and hus ensures saionariy (Kollmann (1991); Schmi-Grohé and Uribe (2003)). The numerical soluion mehod (local approximaion) and he esimaion mehod require saionariy. 5

6 E enrepreneur consumes her dividend income. Her expeced lifeime uiliy a, V, is: E E E V = u( d ) + E V, wih β + 1= β ( d + 1) < 1. Uiliy maximizaion by he enrepreneur E E E E β + 1 (subjec o (4)) yields hese firs-order condiions: (1 ) K α ω = α θ N α, (5) R + E β + u'( d + )/ u'( d ) = 1, (6) L E E E E β ( u'( d )/ u'( d )){ θ αk N + q (1 δ)} q = 1, wih q ξ '( I / I)/ Ξ. E E E α 1 1 α / The Home governmen A dae, he Home governmen makes exogenous random oupu purchases W E B financed using lump sum axes: G = T + T + T, where G ha are B T is a ax paid by he bank (see below). Each Home agen bears a consan share of he oal Home ax burden, equal o her share in Home seady sae consumpion: T = λ G for i=w,e,b where i i i i λ is imeinvarian. In seing axes, he Home and Foreign governmens assume ha 50% of he banker s consumpion akes place in counry Home. The global bank The paper focuses on he role of bank capial for he ransmission of macroeconomic and financial shocks o global real aciviy. The paper herefore adops an aggregae perspecive, and assumes a represenaive global bank ha may be hough of as he global financial sysem. 4 A, he global bank receives deposis D + 1 and D + from he * 1 Home and Foreign workers, respecively, and makes loans L + 1 and * L + 1 o Home and W * Foreign enrepreneurs, respecively. Le D D + D and L L + L denoe W * worldwide deposis and loans. The bank faces a capial requiremen: her dae capial 4 Thus, he inerbank marke is no modeled here. Fricions in ha marke would maer for aggregae aciviy if hey affeced he oal flow of funds from savers o borrowers. The model here capures empirical flucuaions in he loan spread and in he oal volume of inermediaion. To invesigae he poenial role of an inerbank marke, I sudied a model varian wih a savings bank and an invesmen bank. The savings bank ges deposis from households, and lends o he invesmen bank (inerbank marke), which lends o firms. Each bank faces a capial requiremen and charges a loan spread. However, aggregae dynamics hinges on oal bank capial--hus ha se-up is observaionally equivalen o he represenaive-bank model. 6

7 L W D should no be smaller han a fracion γ of he bank s asses L + 1. This may W W reflec a legal requiremen or, more broadly, marke pressures. 5 γ is a random variable ha is exogenous o he bank (see below). The bank can hold less capial han he W W W required level, bu his is cosly. Le x ( L + 1 D + 1) γ L + 1 = (1 γ ) L W W + 1 D + 1 denoe he W W bank s excess capial a he end of period. The bank bears a cos L φ ( x / L ) as a funcion of x, where L W is he seady sae sock of loans. φ is a convex funcion ( φ '' 0) for which I assume: φ ( ) > 0 for x < 0; φ (0) = 0. Thus, for x < 0 he bank incurs a x posiive cos; he cos is zero when he bank mees her capial requiremen. A, he bank W W also bears an operaing cos Γ ( D + 1+ L + 1), where Γ > 0 is he (consan) real marginal cos of aking deposis and making loans. The bank s period budge consrain is: L + D R +Γ ( D + L ) + L φ( x / L ) + d + T + T = L R Δ Δ + D, W W D W W W W B B B* W L * W where Δ+Δ is he bank s oal loan loss, and * T + T is he oal ax paid by he bank B B* (in he wo counries). B d is he profi (dividend) generaed by he bank a. (As he bank acs compeiively, loan raes and deposi raes are equaed across counries.) The banker B consumes her dividend income. Her expeced life-ime uiliy a, V, is: B B B V = u( d ) + E V, wih β + 1= β ( d + 1) < 1. B B B B β The banker s uiliy maximizaion problem has hese firs-order condiions: R + E β + u'( d + )/ u'( d ) = 1 Γ+ φ', D B B B R + E β + u'( d + )/ u'( d ) = 1 +Γ+ (1 γ ) φ'( x / L ). L B B B W A linear approximaion of hese Euler equaions gives: ' R L D ( / W ) 2 (0) (0) ( / W + R+ Γ γφ x L Γ γφ γφ x L ). (7) L D Hence, he loan rae spread R+ 1 R+ 1 is a funcion of he required capial raio γ and of he bank s excess capial, x. Noe ha if he bank raises deposis and loans by one uni, hen her operaing cos rises by 2Γ unis; excess bank capial falls by γ, which raises he ' '' 5 Bank capial requiremens are ofen jusified as limiing moral hazard in he presence of informaional fricions and deposi insurance (see Freixas and Roche (2008)). These issues are no explicily modeled here. Insead, I ake he capial requiremen as given, and focus on is macroeconomic effecs. 7

8 W W W penaly L φ ( x / L ) by γφ( x / L ). The bank s Euler equaions imply ha he spread ' L D beween he loan rae and he deposi rae R+ 1 R+ 1 covers he marginal cos ' W 2 Γ γφ( x / L ). Under sric convexiy of φ (i.e. φ > 0), he marginal benefi of excess capial φ ' is a decreasing funcion of (excess) bank capial, which implies ha he loan rae spread is likewise a decreasing funcion of excess bank capial. The sensiiviy of he loan rae spread o changes in bank capial is governed by φ ''. Noe ha x / W L cr γ, where cr ( W W 1 1)/ W L+ D+ L+ 1 is he bank s capial raio, i.e. he raio of bank equiy o bank asses. A one percenage poin rise in he capial raio '' lowers he loan rae spread by 4 γφ percenage poins per annum (p.a.), while a one percenage poin increase in he required bank capial raio (holding consan he spread by 4[ γφ'' φ'] percenage poins p.a.. '' cr ) raises Marke clearing Marke clearing for he oupu good requires: * * E E* B * * * * W W W W Z+ Z= C+ C+ d + d + d + Iξ( I/ I) + I ξ( I/ I ) + G+ G+ L φ ( x/ L ) + Γ ( L+ 1+ D+ 1). Forcing variables Seady sae TFP and invesmen efficiency are normalized o uniy * * ( θ= θ =Ξ=Ξ = 1). There are 11 forcing variables: Home and Foreign TFP * ( θ, θ ), invesmen efficiency * (, ), Ξ Ξ governmen purchases G G * (, ) N N*, labor supply shocks( Ψ, Ψ ), loan losses * (, ) Δ Δ and he required bank capial raio ( γ ). I refer o he firs 8 shocks are nonbanking shocks, and o he las hree shocks as banking shocks. A large number of nonbanking shocks is assumed so ha he model has he poenial o capure imporan feaures of macro daa, even in he absence of banking shocks. Oher recen esimaed DSGE models likewise assume many shocks (e.g., Smes and Wouers (2007)). Following he empirical DSGE lieraure, I assume ha each non-banking shock z follows a saionary univariae AR(1) process: z z 1 8 ln( z/ z) = ρ ln( z / z) + ε, (8)

9 z wih 0 ρ < 1, where ε z is a normally disribued whie noise. The innovaions o he nbk non-bank shocks are correlaed. Le ε denoe he vecor of innovaions o he 8 nonbanking shocks. The laws of moion of loan losses (normalized by seady sae GDP) and of he required bank capial raio are: Δ / Y= ρ Δ / Y+ ϑ ln( Y/ Y) + ε, Δ Δ Δ 1 Δ / Y = ρ Δ / Y + ϑ ln( Y / Y ) + ε, (9) * * Δ * * * Δ * * Δ * 1 γ = (1 ρ ) γ + ρ γ + ϑ ln( Y / Y ) + ε, (10) γ γ γ W W γ 1 wih * ρ ρ ρ < Y, Y and Δ Δ* γ 0,, 1. Y Y+ Y are Home and Foreign GDP and world W * GDP respecively. 6 ε Δ *, ε Δ γ and ε are normal whie noises. ε Δ * and ε Δ are correlaed, γ bk Δ Δ* γ bu independen of ε. ε ( ε, ε, ε ) is assumed independen of he vecor of non- nbk banking shocks, ε, a all leads and lags. To allow for correlaion beween γ * ( Δ, Δ, ) and he non-banking forcing variables, I assume ha * (,, γ ) Δ Δ depends on GDP and hus is parly endogenous. The independence of nbk ε and bk ε makes i sraighforward o decompose he variance of he endogenous variables ino componens due o ε, respecively (see below). bk nbk ε and o 2.2 Model soluion A linear approximaion (around he deerminisic seady sae) is used o solve he model. The soluion can be expressed as s =Λ s +Λ ε, (11) where s is a vecor consising of saes and conrols chosen (or realized) in period, nbk bk expressed as deviaions from seady sae values. ε ( ε, ε ) is he vecor of dae 6 W W The bank s operaing coss and he coss of excess bank capial L φ ( x/ L ) represen inpus used by he bank; hese coss hus have o be subraced from he enrepreneurs oupu when compuing GDP. I assume ha he resources used by Home banking Γ L ) 1+ D 1 are purchased from he Home enrepreneur, and ha ( + + W W 50% of he resource cos L φ( x / L ) is likewise purchased from he Home enrepreneur. Hence, Home 1 W W GDP is: Y Z Γ ( L + D ) L φ( x / L )

10 innovaions o he forcing variables. Λ 1 and Λ 2 are marices whose elemens are funcions of he model parameers. 3. Economeric approach The model is esimaed using quarerly ime series for 12 macro and banking variables, in 1990q1-2010q3: US and EA GDP, oal privae consumpion, invesmen, employmen, commercial bank credi (deflaed using he GDP deflaor), he loan rae spread of US commercial banks, and he capial raio of US commercial banks. The baseline esimaes use daa on oal bank credi (o all secors) by US Commercial banks and by EA Moneary financial insiuions (MFI). Below, I also repor esimaion resuls ha insead use daa on credi o he business secor. (I use oal credi for he baseline esimaes, as ha variable accouns for a greaer share of bank asses.) The measure of he US loan rae spread is he series commercial and indusrial loan raes spread over inended federal funds rae, from he Federal Reserve Board s (FRB) Survey of Terms of Business Lending (Table E.2). Daa on he EA loan rae spread are only available for he period since 2003q1; as shown in Figure 2, he available EA loan spread closely racks he US loan spread (correlaion in : 0.90). 7 I hus use he US loan rae spread as a measure of he global loan rae spread. The US Commercial bank capial raio is aken as a proxy for he capial raio of he global bank. The empirical bank capial raio measure is consruced as (oal financial asses oal liabiliies)/oal financial asses, using daa from he Flow of Funds (FRB). See he Appendix for furher informaion on he empirical variables. In esimaion, he loan spread and he capial raio are demeaned, while he oher empirical variables are linearly derended in log-form. The number of daa series used for esimaion (12) exceeds he number of shocks (11). To avoid sochasic singulariy of he model, I assume ha observed variables conain measuremen error. Allowing for measuremen error also seems imporan because (especially) he empirical banking series migh be imperfec measures of he 7 The EA spread ploed in Fig. 2 is he difference beween he EA MFI loan rae and he EONIA rae. 10

11 heoreical conceps. 8 obs The dae daa used in esimaion, y, are a subse of he saes and conrols included in he vecor s (see (11)), and are measured wih error: where Γ is a marix, and obs y =Γ s + μ, (12) μ is a vecor of Gaussian i.i.d. measuremen errors ha are independen of he rue sae variables a all leads and lags. I use a Bayesian approach o esimae a subse of he parameers, while he remaining parameers are calibraed Esimaed and calibraed parameers I esimae he following parameers: he curvaure of he bank capial penaly funcion φ '', he curvaure of he invesmen cos funcion ξ '', and he parameers of he process governing he banking shocks (9),(10). These parameers are key for he dynamic properies of he model, bu do no affec he seady sae. In addiion, I esimae he risk aversion coefficien σ, and he sandard deviaions of measuremen errors. I calibrae he remaining parameers so ha he seady sae maches long run properies of he daa. E.g. he echnology parameer 1 α is se a he mean empirical labor share, he seady sae bank capial raio is calibraed using hisorical mean capial raios ec. I would be difficul o esimae hese parameers hrough he lens of he model, unless raios of he relevan variables were used in he measuremen equaion (as poined ou by Smes and Wouers (2007)). In addiion, I calibrae he non-banking shock processes Prior parameer disribuion The means and sandard deviaions of prior parameer disribuions are shown in Cols. (1)-(2) of Table 3. The mean of he prior disribuion of σ is se a uniy. φ '' affecs he response of he loan rae spread o changes in he bank capial raio, and is hus key for he ransmission of banking shocks o real aciviy. Recall ha a one percenage poin 8 To break he singulariy, measuremen error in jus one observable is sufficien. To deermine he presence of measuremen error empirically, I allow for i in all series. Assuming measuremen error jus in banking variables gives he same resuls abou he role of banking shocks. For recen empirical DSGE models ha explicily allow for measuremen error see Ireland (2004), Boivin and Giannoni (2006), Gali e al. (2011) and de Anonio (2011). 11

12 increase in he bank capial raio lowers he loan rae spread by 4 γφ '' percenage poins per annum. As discussed below, I se he seady sae required bank capial raio a γ = I se he mean of he prior disribuion a 4 γφ '' a 0.2, a value consisen wih ime series regressions of he loan rae spread on aggregae bank capial repored by Kollmann e al. (2011). Invesmen is excessively volaile when he capial accumulaion echnology is linear ( ξ '' = 0), as hen inernaional capial flows respond very rapidly o counry-specific shocks. I se he mean of he prior disribuion of ξ '' a 1; for ha value, he raio of he sandard deviaion of invesmen divided by he sandard deviaion of GDP is abou 3 in he differen model varians discussed below, and hus roughly in he range of he relaive volailiy of EA invesmen, when he oher parameers are se a prior mean values. 9 The priors of he parameers of he banking shock processes (9),(10) are se as Δ * follows: he prior mean of he sandard deviaions of ε, ε Δ and ε γ is 0.5%; he prior mean of he correlaion beween ε Δ and * ε Δ and of he auoregressive coefficiens Δ Δ*,, ρ ρ ρ γ is 0.5; he prior mean of he GDP coefficiens, ϑ Δ γ and ϑ, is The prior Δ g* γ mean of he sandard deviaion of ε, ε and ε is in he range of esimaed sandard deviaions of innovaions o empirical measures of he non-banking shocks--see discussion below (e.g. he hisorical sandard deviaion of US and EA TFP innovaions is 0.48%, see Table 1). Empirically, TFP and oher non-banking shocks (excep he labor supply shock) are posiively correlaed across counries he prior hus assumes ha loan losses are likewise posiively correlaed across counries. The prior means and prior sandard deviaions of he sandard deviaions of measuremen errors are se a 1/4 and 1/20, respecively, of he sandard deviaions of he corresponding (demeaned/derended) empirical series. 9 The prior disribuions of σ, φ '' and ξ '' are Gamma disribuions wih sandard deviaions se a half he prior means. Thus a reasonably wide range of parameer values around he mean has non-negligible mass. 10 The prior sandard deviaions of hese parameers are se a

13 Calibraion Calibraed echnology parameers (non-finance secor), size of governmen One period in he model represens one quarer in calendar ime. As is sandard in he macro lieraure, he (quarerly) depreciaion rae of physical capial is se a δ= The elasiciy of oupu wih respec o capial is se a α=0.3, consisen wih long run average hisorical US and EA labor shares of abou 70%. The wo-counry model here absracs from US and EA rade wih hird counries; I hus use he sum of US governmen consumpion and of US ne expors o counries oher han he EA as an empirical measure of US auonomous spending, G ; EA auonomous spending is consruced analogously. During , US [EA] auonomous spending represened 14.2% of US GDP [21.2% of EA GDP], on average. I ake he US as he empirical counerpar of counry Home and se GY= / 14.2%, * * G / Y = 21.2%. Calibraed preference and bank parameers Mos DSGE sudies calibrae he subjecive discoun facor o mach average hisorical reurns. I use he same approach. As menioned above, i is assumed ha all agens have he same seady sae subjecive discoun facor, here denoed by β. β is se so ha he seady sae loan rae maches he mean US real loan rae. I use he ineres rae on commercial and indusrial loans made by all commercial banks repored by he FRB (Survey of Terms of Business Lending, Table E.2) as a measure of he nominal loan rae, from which I subrac he quarerly growh rae of he US GDP deflaor o consruc he real loan rae. The average US real loan rae was 3.440% p.a.. Accordingly, I se he (quarerly) seady sae subjecive discoun facor a β = (as L R β = 1, from he enrepreneur s Euler equaion (6)). I assume ha all agens subjecive discoun facors have he same elasiciy wih respec o consumpion, denoed by ε β. I se ε β a a small absolue value, ε β= 0.001, ha yields a saionary equilibrium, while generaing (essenially) he same shor run dynamics as a model varian wih a consan subjecive discoun facor. (Impulse 13

14 responses over he firs 100 periods are very similar across model varians wih ε β = 0 and ε β = ) The sample mean ( ) of he US loan rae spread was 2.161% p.a.. 11 I se he seady sae deposi raes in he model a 1.279% p.a., so ha he seady sae loan rae spread maches he mean hisorical spread, 2.161%. The mean EA loan spread was 2.01% in (see above), which is close o he seady sae spread assumed in he model calibraion. I se he seady sae acual and required bank capial raios a cr= γ = 11.17%, which corresponds o he average capial raio of US commercial banks during he sample D period (from Flow of Funds daa). The bank s Euler equaions imply R β = Γ+ 1 φ ' and L R β =+Γ+ 1 (1 γφ ) '. Given he seady sae deposi and loan raes, hese wo condiions pin down he bank s marginal operaing cos Γ and he seady sae slope of he bank s penaly funcion φ ': Γ= 0.25%, φ ' = 0.28%. The assumpion ha cr= γ implies ha seady sae excess bank capial is zero, x=0, i.e. W W L (1 γ) = D. I se L(1 γ) = D and L * (1 γ ) = D *, i.e. he seady sae raio of deposis o loans is he same in boh counries (as is consisen wih he daa). The raio of ousanding US commercial bank loans o annual US GDP was 53% on average in , while he mean raio of he sock of EA MFI loans divided by annual EA GDP was 87%. Thus, he US has a noiceably lower loans/gdp raio han he EA. The calibraion reflecs his: I assume ha he seady sae raios of loans o annual GDP are 53% in counry Home, and 87% in Foreign. Finally, I assume ha boh counries have he same seady sae GDP, normalized a uniy: Y= Y * = 1. These seady sae arges pin down he remaining preference parameers (he weighs of deposis in Home and Foreign 11 As menioned above, he baseline measure of he US loan rae spread is he commercial and indusrial loan raes spread over inended federal funds rae. Using he rae on shor erm Cerificaes of Deposi as a measure of he bank s marginal funding coss yields a loan rae spread ha has a 0.75 correlaion wih he baseline spread, and a sample mean of 1.929% p.a., which is close o he assumed seady sae spread. 14

15 * workers uiliy funcions, D D Ψ, Ψ, and seady sae marginal disuiliies of labor, N N* Ψ, Ψ ). 12 Calibraed non-banking shock processes. I consruc quarerly empirical measures of he 8 US and EA non-banking forcing variables ( ). Following Coeurdacier, Kollmann and Marin (2010), I use he raio of he CPI o he invesmen deflaor as a measure of invesmen efficiency. The N empirical labor supply shock is consruced as Ψ = (1 α)( Z / N )/ C, which follows from he firs order condiions (2),(5) when σ = 1 (i.e. when σ equals is prior mean). Thus, he empirical labor supply shock is proporional o labor produciviy divided by consumpion. 13 I se he sandard deviaions, and auo- and cross-correlaions of he non-banking shocks in he model equal o he corresponding momens of linearly derended logs of he empirical measures (see Table 1). The empirical DSGE lieraure--ha has largely focused on closed economies--ypically assumes uncorrelaed shocks, and i esimaes he parameers of shock processes hrough he lens of he DSGE model (joinly wih he remaining parameers). In a muli-counry model i is imporan o allow for correlaed shocks empirical measures of he shocks are srongly correlaed. I calibrae he process governing non-banking shocks, as empirical measures of he non-banking shocks can easily be consruced, and as esimaion of he correlaion marix of hese shocks hrough he lens of he model would be challenging (given he large number of crosscorrelaions). As repored in Table 1, US invesmen efficiency, US auonomous spending and he US labor supply shock are more volaile han he corresponding EA variables. The cross-counry correlaions of TFP (0.51) and invesmen efficiency (0.84) are sizable. 12 D D W σ W (3) implies Ψ = (1 R β)(( C / Y)/( DY / )). DY / is deermined by LY /, while C / Y is pinned down by raios of governmen purchases and invesmen o GDP. Y= 1 hen pins down 15 N Ψ (as N Ψ deermines he seady sae labor inpu). In seady sae, consumpion by he Home [Foreign] worker and he enrepreneur represen respecively 58.2% and 4.8% [52.3% and 3.5%] of domesic GDP, while he banker s consumpion represens 0.21% of world GDP. 13 Labor produciviy is consruced using GDP as a proxy for he enrepreneur s oupu Z. I also considered N an alernaive measure of he labor supply shock based on real wage rae daa: Ψ = ω/ C. Tha measure gives similar esimaes of model parameers and of he role of banking shocks.

16 TFP is posiively correlaed wih invesmen efficiency; US and EA TFP are srongly negaively correlaed wih US auonomous spending (G), and negaively correlaed wih he US labor supply shock. All forcing variables are highly persisen (auocorrelaions in he range ). 4. Daa plos and business cycle saisics. Figure 1 plo he (demeaned/derended) 12 empirical series used in esimaion. Macro aggregaes co-move closely across he US and he EA he synchroniciy was especially high during he recen Grea Recession. According o he NBER, ha recession began in 2007q4 and ended in 2009q2. (Shaded areas in Figures indicae NBER recessions.) Relaive o rend, US oupu fell by 8.5%, during he recession, while EA oupu fell by 7.5%; US consumpion (-7.3%) and invesmen (-35.1%) fell more sharply han EA consumpion (-4.0%) and invesmen (-15.9%). US and EA bank lending grew srongly in he years before 2008, and hen collapsed sharply. The loan rae spread fell during he hree years prior o he crisis, bu rose sharply during he Grea Recession. The bank capial raio exhibis relaively mild flucuaions--hroughou he sample period i says in a ±2% range around he sample mean of 11.17%. Figures 3a-b plo he bank capial raio, ogeher wih he baseline loan spread series and alernaive spread measures ha are used for robusness checks below (all series in Figures 3a-b are demeaned). Excep for he period of he financial crisis, he bank capial raio and he baseline loan rae spread comove negaively. While he loan rae spread rose, during he crisis (as menioned above), he bank capial raio has had a fla rend since abou i has been argued ha his may parly reflec accouning discreion, which has allowed banks o oversae he value of heir asses in he crisis (Huizinga and Laeven (2009)). The correlaion beween he bank capial raio and he baseline lending spread was during he period , bu close o zero (-0.06) over he whole sample period ( ). Figure 3a also plos he series ne percenage of banks increasing spreads of loan raes over cos of funds, from he FRB Senior Loan Officer Opinion Survey on Bank Lending Pracices, SLOOS. (The series represens he percenage of banks increasing spreads minus he percenage of banks lowering spreads; he ploed series is scaled so ha is sandard deviaion equals ha of he baseline loan spread.) Tha series is 16

17 posiively correlaed wih he baseline loan spread (correlaion 0.39 for ), and negaively correlaed wih he bank capial raio (-0.47 for ; for ). Figure 3b plos Gilchris and Zakrajšek s (2011a) excess US commercial bond premium, consruced by subracing expeced bond defaul probabiliies from he spread beween he yield on US commercial bonds and he yield on US Treasury bonds. 14 As commercial banks are key players in he commercial bond marke, he commercial bond premium migh be informaive abou credi spreads/marke condiions. 15 The excess bond premium oo is negaively correlaed wih he bank capial raio (correlaion: for ; for ). The bond premium is posiively correlaed wih he baseline loan rae spread (0.29) and wih he SLOOS ne percenage of banks increasing spreads (0.79). Overall, he daa are hus consisen wih he model s predicion ha he spread is inversely relaed o he bank capial raio (see (7)). The absence of an pronounced inverse relaion during he crisis migh be due o he fac ha he measured bank capial raio oversaes he rue capial raio during he crisis (see discussion above), or ha he required bank capial raio rose during he crisis (his could raionalize he observed increase in he loan rae spread, during he crisis, wihou a fall in he bank capial raio). Table 2 repors momens of Hodrick-Presco (HP) filered macro and banking variables, for he US and he EA ( ). GDP volailiy is very similar in he US (1.12%) and he EA (1.14%). Consumpion is less volaile han GDP, while invesmen is markedly more volaile han GDP. US invesmen is almos wice as volaile as EA invesmen. In boh counries, loans are more volaile han oupu, while he loan spread is counercyclical. Real aciviy and loans are posiively correlaed across he US and EA. 14 I hank Egon Zakrajšek for providing me wih he excess bond premium series, and wih he business loan and loan capaciy daa used below. 15 Gilchris and Zakrajšek (2011a) argue ha an increase in he excess bond premium reflecs [...] a conracion of he supply of credi wih significan adverse consequences for he macroeconomy (p.31). 17

18 5. Esimaion resuls 5.1. Poserior parameer esimaes (Table 3) Columns (4)-(6) of Table 3 respecively repor he means, he modes and he sandard deviaions of he poserior parameer disribuion, for he baseline model (poserior means and modes are very close); Cols. (7) and (8) show he 5h and 95h perceniles of he poserior parameer disribuions. 16 The daa are informaive abou he esimaed parameers: in almos all cases, he poserior parameer disribuions have lower sandard deviaions han he prior disribuions; he poserior means ofen differ noiceably from he prior means. The poserior esimae (mode) of 4 γφ '' indicaes ha a 1 percenage increase in he bank capial raio leads o a 44 basis poin reducion in he annualized loan rae spread, and ha a 1 percenage poin rise in he required bank capial raio ( γ ) increases he loan rae spread by 45 basis poins p.a.. The poserior esimaes also show ha EA loan loss shocks are more volaile han US loan loss shocks he poserior modes of he sandard deviaions of ε Δ * and ε Δ are 0.48% and 1.38%, respecively. US and EA loan loss shocks are posiively correlaed (0.34). The required bank capial raio undergoes sizable flucuaions (poserior mode of γ sd. of ε : 0.53%). The poserior means of he sandard deviaions of measuremen errors are mosly smaller han he prior means. An imporan excepion o his is he sizable sandard deviaion of measuremen error for bank capial raio (is poserior mode is 1.31%) Business cycle momens implied by poserior esimaes (Table 4) Table 4 repors model-prediced momens of HP filered US and EA variables, compued a he poserior mode of he esimaed parameers. Column (1) assumes all 11 srucural shocks, and measuremen error. Cols. (2)-(9) consider momens generaed by differen subses of he srucural shocks, in isolaion, wihou measuremen error. Specifically, 16 The means, sandard deviaions and deciles of he poserior disribuions were generaed using he Random Walk Meropolis algorihm (see An and Schorfheide (2007)). 17 The esimaed measuremen error for he bank capial raio is markedly smaller when he model is esimaed using daa on business loans; see below. 18

19 nbk Col. (2) assumes jus he 8 non-banking shocks ε, and Col. (3) assumes jus he 3 bk exogenous banking shocks ε. Cols. (4)-(9) assume jus a single ype of shock (Col.(4): jus TFP shocks; Col. (5): jus invesmen efficiency shocks; ec.). Col. (10) repors empirical momens (from Table 2). 18 The model wih all shocks and measuremen error generaes prediced saisics ha are mosly in he range of he empirical saisics. The prediced sandard deviaion of US GDP (1.30%) and of EA GDP (0.88%) are close o he empirical sandard deviaions. The model (wih all shocks) capures he fac ha invesmen and loans are more volaile han GDP. The model also maches he empirical cross-correlaions of mos variables wih domesic GDP in paricular, i correcly predics ha US and EA loans are procyclical, and ha he loan spread is counercyclical. Also, he model correcly predics ha GDP, consumpion, invesmen and loans are posiively correlaed across he wo counries he prediced cross-counry correlaion of GDP is Taken in isolaion, TFP shocks and Labour supply shocks induce by far he larges flucuaions in real aciviy (prediced sandard deviaion of US and EA GDP wih jus hese shocks: 0.94% and 0.77%, respecively). The prediced sandard deviaions of US GDP wih jus loan loss shocks and wih jus shocks o he required bank capial raio are 0.28% and 0.15%, respecively. Wih jus TFP shocks, jus invesmen efficiency shocks, and jus labor supply shocks, GDP is negaively correlaed across counries. By conras, governmen purchases shocks and he banking shocks induce posiive crosscounry oupu correlaions. Noice also ha he banking shocks induce a srong negaive correlaion beween he loan rae spread and GDP. Panel (a1) of Table 7 repors he % shares of he prediced variances of HP filered endogenous variables (wih measuremen error) ha are accouned for by he nonbanking shocks nbk ε (see rows labeled NonBk ), and by he banking shocks bk ε (rows 18 Using (11),(12), he model soluion for observables (wih measuremen error) can be wrien as: obs y = nbk bk AL () ε ν+ BL () ε ν+ μ where A() L and BL () are lag polynomials. (The momens in Table 4 perain o HP obs, HP obs nbk bk filered series, y = H() L y, where H () L is he HP filer.) By assumpion, ε, ε and μ are independen a all leads and lags. Thus he prediced variance of endogenous variables under all shocks and measuremen error (Col. (1) of Table 4) is he sum of: (i) he variance wih jus non-banking shocks (Col.(2)); (ii) he variance wih jus banking shocks (Col. (3)); (ii) he variance of measuremen error. By conras, he variances prediced under he differen individual shocks in Cols. (4)-(10) of Table 4 do no add up o he variance wih all shocks, as individual shocks are correlaed. 19

20 labeled Bank ); he remainder represens he conribuion of measuremen error o he prediced variance. (The variance shares are compued a he poserior mode of he esimaed parameers.) According o he baseline model, he banking shocks accoun for a 6% share of US GDP variance, bu explain larger shares of he variances of US invesmen (11.3% share), employmen (15.2%) and loans (28.1%). Banking shocks accoun for roughly 2-5 imes larger variance shares of EA variables--gdp: 15.5%; invesmen: 55.1%; employmen: 26.5%; loans: 76.3%. Thus, more han half of he variance of EA invesmen and loans is due o banking shocks Impulse responses (Table 5) Impulse responses (repored in Table 5) help o undersand he model s mechanics, and he prediced business cycle momens. The impulse responses are compued a he poserior mode of esimaed model parameers. Each impulse response focuses on an isolaed innovaion, assuming ha all oher exogenous innovaions are zero. 20 A posiive innovaion o Home TFP raises Home GDP and invesmen, bu leads o a fall in Foreign GDP and invesmen. The shock raises he income of he Home worker; hus ha worker saves more, and her holdings of bank deposis increase--i.e. he bank s deb rises, which lowers he bank capial raio. This raises he loan rae spread. The deposi rae falls (due o he greaer supply of deposis); he Foreign worker responds o his by consuming more, and working less, and hence Foreign GDP falls. Foreign invesmen falls likewise, as he reducion in Foreign hours worked lowers he marginal produc of capial. Counry-specific invesmen efficiency shocks and labor supply shocks likewise drive Home and Foreign GDP in opposie direcions. By conras, banking shocks induce responses of real aciviy (and of loans) ha are common across he wo counries. For example, a rise in he Home loan loss lowers he global bank s capial raio, which riggers a rise in he loan rae spread; in response o his, loans, invesmen and GDP fall in boh counries. A rise in he required capial raio ( γ ) likewise raises he loan rae 19 Banking shocks accoun for 85.5% of he variance of he loan rae spread, bu for only 13.7% of he variance of bank capial, which reflecs he sizable esimaed measuremen error in ha variable. 20 To save space, Table 5 does no show responses o EA non-banking shocks hose responses are qualiaively similar o he responses o US non-banking shocks (repored in Table). 20

21 spread (see (7)); on impac, his oo lowers loans, invesmen and real aciviy in boh counries. Noe also ha banking shocks drive he loan spread and oupu in opposie direcions. According o he baseline esimaes, an unanicipaed US loan loss of 1$ lowers boh US and EA GDP by abou 0.15 $, on impac. An unanicipaed increase in he required bank raio by one percenage poin lowers US and EA GDP by 0.21%, on impac Decomposing hisorical ime series (Figure 4) Figure 4 plos he conribuions of he banking shocks and of US and EA non-banking shocks o he hisorical ime series (he decomposiion is compued a he poserior mode of he esimaed parameers). 21 Thick coninuous lines show he hisorical daa; he hin coninuous lines indicae he conribuion of banking shocks, while he dashed-doed and dashed lines represen he conribuions of US and EA non-banking shocks, respecively. The hisorical decomposiion yields a picure ha is consisen wih he variance decomposiions. Banking shocks maer more for EA GDP han for US GDP. Banking shocks are key drivers of EA invesmen and employmen. During he 2007q4-2009q2 recession, banking shocks accoun for a 1.6% (1.7%) fall in US (EA) GDP i.e. he banking shocks capure abou 1/5 of he fall in US GDP (-8.5%) and in EA GDP (-7.5%), relaive o rend. Banking shocks also capure 25% [30%] of he fall in US invesmen [employmen], and 60% [85%] of he fall in EA invesmen and employmen. Thus, he fall in EA employmen can almos fully be accouned for by banking shocks. In he previous US recession (2001q1-2001q4), banking shocks accouned for 1/4 of he fall in US oupu and invesmen, for 1/3 of he fall in EA oupu and for 2/3 of he fall in EA invesmen. During he 1990q3-1991q1 US recession, he role of banking shocks was more mued, accouning for 1/10 of he fall in US GDP and invesmen (he EA did no experience a recession in ). Figure 4 shows ha he oupu componens accouned for by he domesic nonbanking shocks rack hisorical US and EA GDP very closely. 22 Foreign non-banking 21 Using smoohed shocks and measuremen errors, each hisorical series can be expressed as he sum of: (i) a base rajecory (dynamic effecs of predeermined saes in he iniial period) plus measuremen error; (ii) conribuions of each exogenous shock. Figure 4 shows he daa and he shock conribuions. 22 This resul parallels he finding by de Walque e al. (2005) and Le e al. (2010) ha domesic macro shocks are he main drivers of US and EA GDP. 21

22 shocks had a sabilizing effec on domesic real aciviy; eg, during he recession, EA non-banking shocks had a posiive influence on US GDP, and hus miigaed he US recession. This reflecs he fac ha, in he model here, TFP shocks and labor supply shocks are negaively ransmied inernaionally (see above) Alernaive empirical measures of banking variables As a robusness check, I esimaed he model using oher empirical measures of he loan rae spread and of bank loans. Panels (a2)-(a5) of Table 7 repor resuling esimaes of variance shares explained by banking shocks. These variance shares are higher, by up o a facor of 3, han he baseline shares discussed above (Panel (a1)). 23 (Poserior parameer esimaes obained from he alernaive daa ses are in he same range as he baseline esimaes, and are hus no repored) Alernaive proxies for he loan rae spread In Panels (a2) of Table 7, he baseline loan rae spread is replaced by he series ne percenage of banks increasing spreads of loan raes over cos of funds (from SLOOS), while Panel (a3) uses he Gilchris-Zakrajšek (2011a) excess bond premium series. When he Gilchris-Zakrajšek excess bond premium is used, 9.2% (21.8%) of he variance of US (EA) GDP is due o banking shocks. 24 Business loans and lending capaciy In Panel (a4), oal bank credi is replaced by US and EA bank loans o he non-financial business secor, while Panel (a5) uses Gilchris and Zakrajšek s (2011b) measure of US business lending capaciy in lieu of US oal credi. 25 Figures 5a-b plo hese series. Business loans are highly posiively correlaed wih oal loans, bu more volaile, 23 I also esimaed he model using an alernaive measure of he bank capial raio--he capial raio of US Securiies Brokers and Dealers (insead of he capial raio of US commercial banks). Resuls are robus o using his measure. Kollmann and Zeugner (2012) analyze he capial raio dynamics of differen subsecors of he finance indusry. 24 Using he SLOOS series ne percenage of banks ighening lending sandards in lieu of he baseline lending spread yields very similar esimaed variance shares. 25 Gilchris and Zakrajšek (2011b) poin ou ha, in he US, many business loans are offered under prior commimen (credi lines); hence, business loans respond wih a lag o shocks o bank funding. The Gilchris and Zakrajšek business lending capaciy measure is defined as he sum of loans ousanding and of unused commercial bank lending commimens--he auhors argue ha his variable is more informaive (han loans ousanding) for idenifying loan supply shifs (no comparable measure exiss for he EA). 22

23 especially in he US. US lending capaciy fell earlier and much more sharply han oal lending, during he recession. When hese alernaive lending (capaciy) series are used, hen abou 10% of US GDP variance and 25%-30% of EA GDP variance is aribued o he banking shocks. 26 The following conclusions can be drawn from he robusness analysis in Table 7: Banking shocks maer more for EA macro variables han for US real aciviy. These shocks accoun for 5%-10% of he uncondiional volailiy of US GDP, and for 10%-25% of US invesmen and employmen volailiy. Banking shocks explain 15%-30% of EA GDP volailiy, 50%-70% of EA invesmen volailiy and 25%-50% of EA employmen volailiy The role of he bank capial requiremen The presence of an operaive bank capial requiremen φ '' > 0 is key for he ransmission of banking shocks o real aciviy. Banking shocks have a negligible effec on real aciviy, bu remain imporan drivers of loans and he bank capial raio, when φ '' = 0. Columns (9)-(11) of Table 3 repors poserior parameer esimaes for a model varian wih φ '' = 0 (he priors for parameer oher han φ '' are he same as in he baseline model). 28 Table 6 repors he implied prediced business cycle momens, while Panel (b) of Table 7 shows he corresponding variance shares accouned for by non-banking/ banking shocks. In he absence of an operaive bank capial requiremen ( φ '' = 0), he prediced sandard deviaions of GDP, invesmen and he loan rae spread generaed by banking shocks are negligible (0.02% or less); by conras, non-banking shocks rigger bigger 26 Banking shocks now also accoun for a much larger share of he variance of he bank capial raio (above 60%); his is due o he fac ha he esimaed sandard deviaion of measuremen error in he bank capial raio (0.4%) is noiceably smaller han when oal credi is used in esimaion (1.3%). 27 Nolan and Thoenissen (2009) and Jermann and Quadrini (2012) use closed economy models wih collaeral-consrained firms (bu wihou banks) o consruc esimaes of shocks o firms funding consrains. The auhors argue ha hose shocks can explain up o half of he variance of US GDP. By conras, he model here assumes ha only he bank faces a collaeral consrain. 28 The poserior esimae of he invesmen echnology curvaure parameer is basically he same as in he baseline model, bu he esimaed risk aversion coefficien is slighly lower (0.57). The esimaed variabiliy of EA loan losses is again greaer han ha of US loan losses. 23

24 flucuaions of real aciviy, han in he baseline model (wih an operaive bank capial requiremen). Recall ha, in he baseline model, a posiive TFP shock leads o an increase in he loan rae spread he rise in he spread dampens hus he rise in GDP riggered by ha shock. When φ '' = 0, he dampening effec of he loan spread response is no presen anymore and real aciviy responds more srongly o TFP changes (and he oher nonbanking shocks). Wih all simulaneous shocks (and measuremen error), he prediced sandard deviaions of GDP, invesmen and employmen are hus higher han in he baseline model and higher han he corresponding empirical saisics. Model fi can be evaluaed using he marginal daa densiy, MDD (marginal likelihood). 29 The log MDD of he baseline model is , while he log MDD of he model varian wihou he operaive bank capial consrain is This implies a Bayes facor (raio of poserior odds o prior odds) of e ha massively favors he baseline model. I also esimaed a model varian wih an operaive bank capial requiremen, bu wihou banking shocks; ha model has a log MDD of , a value markedly below he log MDD of he baseline model (wih banking shocks). 30 This suggess ha boh he operaive bank capial requiremen and he banking shocks help he model o capure he dynamics of he macro and banking variables used in esimaion. Imporanly, he presence of hese model ingrediens specifically helps o beer explain he 8 US and EA macro variables used in esimaion. For hese 8 macro variables, he baseline model has a log MDD of , while he model varian wihou an operaive bank capial requiremen (bu wih banking shocks) has a log MDD of The model wih an operaing bank capial requiremen, bu no banking shocks has a log MDD of Thus, he bank capial requiremen and he banking shocks boh help explain he macro series beer. 29 The MDD measures he ou-of-sample predicive abiliy of he model (Geweke (2001)). The MDDs repored below were compued wih he Geweke (1999) harmonic mean esimaor, using he parameer draws from he Random Walk Meropolis algorihm (An and Schorfheide (2007)) 30 A model varian wihou an operaive bank capial requiremen and wihou banking shocks has a log MDD of

25 6. Conclusion This paper has esimaed a wo-counry model wih a global banking sysem, using US and Euro Area (EA) daa ( ), and Bayesian mehods. The esimaed model maches key US and EA business cycle saisics. Empirically, a model version wih an operaive bank capial consrain ouperforms a srucure wihou such a consrain. A loan loss originaing in one counry riggers a global oupu reducion. Banking shocks maer more for EA macro variables han for US real aciviy. These shocks accoun for 5%-10% of US GDP volailiy, and for 10%-25% of US invesmen and employmen volailiy. Banking shocks, explain 15%-30% of EA GDP volailiy, 50%-70% of EA invesmen volailiy, and 25%-50% of EA employmen volailiy. During he Grea Recession ( ), banking shocks accouned for abou 20% of he fall in US and EA GDP, bu for more han half of he fall in EA employmen and invesmen. 25

26 DATA APPENDIX A.1 Baseline daa se used for esimaion US GDP, privae consumpion (oal), invesmen (all a consan prices): from US Naional Income and Produc Accouns (Bureau of Economic Analysis, BEA); he invesmen series include privae and governmen invesmen. US employmen: Toal nonfarm payrolls: all employees (Bureau of Labor Saisics) US bank loans: ousanding oal bank credi by Commercial Bank, deflaed using GDP deflaor (from June 2011 Flow of Funds, Table L109). US bank capial raio: (oal financial asses-oal liabiliies)/(oal financial asses) for Commercial Banks (from June 2011 Flow of Funds, Table L109). US loan rae spread: Commercial and indusrial loan raes spread over inended federal funds rae ( All loans series, Survey of Terms of Business Lending, Table E.2, Federal Reserve Board, June 2011). EA GDP, privae consumpion (oal), invesmen (all a consan prices): from ECB Area-Wide Model (AWM) daabase (10 h updae, Sepember 2010). EA employmen: from AWM daabase. EA bank loans: MFI loans o privae secor (from ECB monhly bullein), deflaed using he GDP deflaor. A.2 Oher variables (used for esimaion of model varians) Excess bond premium: spread beween he yield on US commercial bonds and he yield on Treasury bonds, minus expeced bond defaul probabiliies, as consruced by Gilchris and Zakrajšek (2011a) using daa for a panel of individual bonds. Ne percenage of banks increasing spreads of loan raes over cos of funds : percenage of banks increasing spreads minus he percenage of banks lowering spreads, from he Senior Loan Officer Opinion Survey on Bank Lending Pracices, SLOOS (Federal Reserve Board). SLOOS repors a series (ne percenages of banks raising spreads) for loans o large and middle-marke firms and one for loans o small firms. The wo series are very similar (correlaion: 0.95). I use he average of he wo series. US business loans: ousanding commercial bank loans o he non-financial business secor, consruced by Gilchris and Zakrajšek (2011b). EA business loans: MFI loans o non-financial corporaions(nfc), from ECB monhly bullein, deflaed using he GDP deflaor. US business lending capaciy: ousanding commercial bank loans plus unused commercial bank lending commimens (credi lines) o he non-financial business secor, consruced by Gilchris and Zakrajšek (2011b). A.3 Oher variables (used for model calibraion) Auonomous spending (G): governmen purchases plus ne expors o hird counries (deflaed using GDP deflaor). Daa sources: AWM, BEA and ECB monhly bullein. Invesmen efficiency: measured as raio of CPI o Gross Invesmen Deflaor (BEA and AWM). All series are quarerly and seasonally adjused (when relevan) 26

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30 Table 1. Time series properies of non-bank forcing variables (1990q1-2010q3) (a) Sandard deviaions (in %, diagonal) and cross-correlaions (off-diagonal elemens) US TFP EA TFP US Ieff EA Ieff US G EA G US LS EA LS US TFP EA TFP US Ieff EA Ieff US G EA G US LS EA LS 1.83 (b) Auocorrelaions US TFP EA TFP US Ieff EA Ieff US G EA G US LS EA LS (c) Sandard deviaions of innovaions (in %) US TFP EA TFP US Ieff EA Ieff US G EA G US LS EA LS Noe: The Table repors sample momens of empirical measures of US and Euro Area (EA) nonbanking forcing variables (in linearly derended log form). Panel (a) repors % sandard deviaions (on main diagonal), and cross-correlaions (off-diagonal elemens). Panel (b) repors firs-order auocorrelaions. Panel (c) repors % sandard deviaions of residuals of univariae AR(1) equaions fied o each variable. TFP: oal facor produciviy ( θ ); Ieff: invesmen efficiency ( Ξ ); G: auonomous spending N (governmen consumpion plus ne expors o hird counries); LS: Labor supply shock ( Ψ ). Log TFP is esimaed as ln( Y) 0.7ln( N) where Y and N are GDP and employmen, respecively. The esimae of invesmen efficiency is he raio of he CPI o he invesmen deflaor. The esimae of he log labor supply shock is ln( Y) ln( N) ln( C), where C is privae consumpion. 30

31 Table 2. Hisorical business cycle saisics US EA Sandard deviaions (in%) GDP (Y) Consumpion Invesmen Employmen Loans Bank capial raio Loan rae spread (p.a.) Correlaions wih domesic GDP Consumpion Invesmen Employmen Loans Bank capial raio Loan rae spread Cross-counry correlaions GDP 0.56 Consumpion 0.39 Invesmen 0.45 Employmen 0.53 Loans 0.53 Loan rae spread 0.79 Noe: Momens of HP filered series are shown (GDP, consumpion, invesmen, employmen and loans were logged before applying he filer). The bank capial raio is expressed in fracional unis. The loan rae spread is expressed in fracional unis per annum. The correlaions of he bank capial raio wih domesic GDP repored in he Table are correlaions of he US commercial bank capial raio wih US GDP and EA GDP. Sample period: 1990q1-2010q3 (excep for EA loan spread: 2003q1-2010q3). 31

32 Table 3. Prior and poserior parameer disribuions for he baseline model ( φ '' > 0) and a model varian wihou operaive bank capial requiremen ( φ '' = 0) Baseline model: Model wih φ '' = 0 : Prior disribuion Poserior disribuion Poserior disribuion Parameer Mean Sd Disrib Mode Mean Sd 5% 95% Mode Mean Sd (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Behavioral parameers 4 γφ '' G ξ '' G σ G Parameers of banking shocks disribuions Sd( ε Δ ) IG * Sd( ε Δ ) IG Sd( ε γ ) IG Corr ε ε Δ Δ* (, ) B ρ Δ B * ρ Δ B γ ρ B ϑ Δ N γ ϑ N Sandard deviaions (%) of measuremen errors GDP US IG GDP EA IG C US IG C EA IG I US IG I EA IG N US IG N EA IG Loans US IG Loans EA IG Bank cap. raio IG Loan rae spread IG Noes: Cols. (1) and (2) shows he means and sandard deviaions of he prior disribuion for model parameers. Col. (3) indicaes he disribuion funcion of he prior (B: Bea; G: Gamma; IG: Invered Gamma; N: Normal). Cols. (4)-(8) show saisics of he poserior parameer disribuion, for he baseline model (means, modes, sandard deviaions, 5 h and 95 h perceniles). Cols. (9)-(11) show saisics of he poserior parameer disribuion for a model varian wihou an operaive bank capial requiremen (for ha varian, he priors in Cols. (1)-(3) are used, excep ha φ '' is se a φ '' = 0). Poserior disribuions are compued using he Random Walk Meropolis algorihm (250,000 draws of which he firs 50,000 were discarded) 32

33 Table 4. Baseline model: implied business cycle saisics Non- All banking Banking Inves. Loan Required shocks shocks shocks TFP Eff. G LabS Loss Bnk.Cap Daa (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (a) Counry Home (US) momens Sandard deviaions (in%) GDP (Y) Consumpion Invesmen Employmen Loans Bank cap raio Loan spread Correlaions wih domesic GDP Consumpion Invesmen Employmen Loans Bank cap raio Loan spread (b) Counry Foreign (EA) momens Sandard deviaions (in%) GDP (Y) Consumpion Invesmen Employmen Loans Bank cap raio Loan spread Correlaions wih domesic GDP Consumpion Invesmen Employmen Loans Bank cap raio Loan spread (c) Cross-counry correlaions GDP Consumpion Invesmen Employmen Loans Loan spread Noe: The Table shows momens of HP filered model variables, compued a he poserior mode of he esimaed parameers. The bank capial raio is expressed in facional unis. The loan rae spread is expressed in fracional unis per annum. Oher variables are normalized by seady sae values. Col. (1) assumes all 11 srucural shocks and measuremen error. In Cols. (2)-(9), subses of shocks are assumed in isolaion, wihou measuremen error (model no re-esimaed). Col. (2): jus he non-banking shocks, nbk bk ε ; Col. (3): jus banking shocks, ε. Col. (4): jus Home and Foreign TFP shocks; Col. (5): jus shocks o invesmen efficiency; Col. (6): jus shocks o governmen purchases; Col.(7): jus labor supply shocks; Col.(8): jus loan loss shocks; Col. (9): jus shock o required bank capial raio ( γ ). Col. (10) shows empirical momens (from Table 2). 33

34 Table 5. Baseline model: dynamic responses o innovaions GDP Consumpion Invesmen Employmen Loans Bank Cap. Loan Horizon US EA US EA US EA US EA US EA Raio Spread (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (a) Home counry TFP shock (1%) (b) Home invesmen efficiency shock (1%) (c) Home governmen purchases shock (1%) (d) Home labor supply shock (1%) (e) Home loan loss shock (1% of seady sae GDP) (f) Foreign loan loss shock (1% of seady sae GDP) (g) Shock o required bank capial raio (1 percenage poin) Noe: The Table shows dynamic responses o exogenous shocks, afer 0, 4 and 20 quarers (see lef-mos column labeled Horizon ), of he variables lised a he op of he Table. The responses are compued a he poserior mode of he esimaed parameers. In each case, an isolaed innovaion is considered, assuming ha all oher exogenous innovaions are zero. Panel (a): 1% innovaion o Home TFP ( θ ); Panel (b): 1% innovaion o US invesmen efficiency ( Ξ ); Panel (c): 1% innovaion o N governmen purchases ( G ); Panel (d): 1% innovaion o US labor supply preference parameer ( Ψ ); Panel (e): innovaion o Home loan loss ( Δ ) worh 1% of seady sae GDP; Panel (f) innovaion o Foreign loan loss 34 * ( Δ ) worh 1% of seady sae GDP; Panel (g) innovaion ha raises required bank capial raio ( ) γ by 1 percenage poin. Cols. (1)-(2): Responses of US and EA GDP; Cols. (3)-(4): US and EA consumpion; Cols. (5)-(6): US and EA invesmen; Cols. (7)-(8): US and EA employmen; Cols. (9)-(10): US and EA loans; Col. (11): bank capial raio; Col. (12): Loan rae spread. Responses of he bank capial raio are in basis poins. Responses of he loan spread are in bp per annum. Oher responses are in percenage poins of seady sae values.

35 Table 6. Model varian wihou operaive bank capial requiremen( φ '' = 0) : implied business cycle saisics Non- All banking Banking Inves. Loan Required shocks shocks shocks TFP Eff. G LabS Loss Bnk.Cap Daa (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (a) Counry Home (US) momens Sandard deviaions (in%) GDP (Y) Consumpion Invesmen Employmen Loans Bank cap raio Loan spread Correlaions wih domesic GDP Consumpion Invesmen Employmen Loans Bank cap raio Loan spread (b) Counry Foreign (EA) momens Sandard deviaions (in%) GDP (Y) Consumpion Invesmen Employmen Loans Bank cap raio Loan spread Correlaions wih domesic GDP Consumpion Invesmen Employmen Loans Bank cap raio Loan spread (c) Cross-counry correlaions GDP Consumpion Invesmen Employmen Loans Loan spread Noe: For he model varian wihou an operaive bank capial requiremen ( φ '' = 0), he Table shows momens of HP filered model variables, compued a he poserior mode of he esimaed parameers. The bank capial raio is expressed in facional unis. The loan rae spread is expressed in fracional unis per annum. Oher variables are normalized by seady sae values. Col. (1) assumes all 11 srucural shocks and measuremen error. In Cols. (2)-(9), subses of shocks are assumed in isolaion, wihou measuremen nbk bk error (model no re-esimaed). Col. (2): jus he non-banking shocks, ε ; Col. (3): jus banking shocks, ε. Col. (4): jus Home and Foreign TFP shocks; Col. (5): jus shocks o invesmen efficiency; Col. (6): jus shocks o governmen purchases; Col.(7): jus labor supply shocks; Col.(8): jus loan loss shocks; Col. (9): jus shock o required bank capial raio ( γ ). Col. (10) shows empirical momens (from Table 2). 35

36 Table 7. Share (%) of variance of HP filered variables due o non-banking shocks and o banking shocks GDP Consumpion Invesmen Employmen Loans Bank Cap. Loan US EA US EA US EA US EA US EA Raio Spread (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (a) Variance shares for baseline model, based on alernaive daa ses (a1) Baseline daa NonBk Bank (a2) Loan rae spread replaced by loan officer survey spread measure NonBk Bank (a3) Loan rae spread replaced by Gilchris-Zakrajsek excess bond premium NonBk Bank (a4) Toal bank loans replaced by bank loans o non-financial business NonBk Bank (a5) US loans replaced by GZ business lending capaciy; EA bank loans replaced by business loans NonBk Bank (b) Variance shares for model varian wihou operaive bank capial requiremen ( φ '' = 0) NonBk Bank Noe: The rows labeled NonBk and Bank show % shares of he variances of HP filered variables (wih measuremen error) nbk bk accouned for by he non-banking shocks ( ε ) and by he banking shocks ( ε ), respecively. The decomposiions are compued a he poserior mode of he esimaed parameers. The variance shares are shown for he variables lised above Cols. (1)-(12). Cols. (1)-(2): US and EA GDP; Cols. (3)-(4): US and EA consumpion; Cols. (5)-(6): US and EA invesmen; Cols. (7)- (8): US and EA employmen; Cols. (9)-(10): US and EA loans; Col. (11): bank capial raio; Col. (12): Loan rae spread. Panels (a1)-(a5) perain o esimaes of he baseline model, wih differen daa ses. Panel (a1) uses he baseline daa se. In Panels (a2)-(a5), he baseline measures of banking variables are replaced by alernaive measures. Panel (a2): baseline loan rae spread replaced by ne percenage of banks increasing spreads of loan raes over cos of funds from he US senior loan officer opinion survey, SLOOS. Panel (a3): baseline loan rae spread replaced by he Gilchris and Zakrajsek (2011a) excess bond premium series. Panel (a4): he baseline loan series for US and EA replaced by loans o he non-financial business secor. Panel (a5): baseline US loan series replaced by US business lending capaciy measure of Gilchris and Zakrajsek (2011b); baseline EA loan series replaced by EA bank lending o he non-financial business secor. Panel (b) considers a varian of he model wihou an operaive bank capial requiremen φ '' = 0 (he varian is esimaed using he 12-variables baseline daa se). The model is re-esimaed for each of he daases/model varians considered in his Table. 36

37 Figure 1. Time series used in esimaion Noe: The Figure shows he ime series used in esimaion. Bank capial raio and loan spread (p.a.) are demeaned. Oher variables are logged and derended. Shaded areas indicae US recessions (NBER daes). 37

38 Figure 2. US and EA loan rae spreads Noe: Loan spreads (p.a.) are no demeaned. Shaded areas: US recessions (NBER daes). Figure 3a. US bank capial, loan spread and SLOOS spread measure Noe: The solid line shows he demeaned bank capial raio; he dashed line shows he demeaned loan spread; he doed line shows a survey-based measure of he ne percenage of banks increasing spreads (from Survey of Senior Loan Officers Opinion Survey, SLOOS). Shaded areas: US recessions (NBER daes). Figure 3b. US bank capial and Gilchris-Zakrajsek (2011a) bond premium Noe: The solid line shows he demeaned bank capial raio; he dashed line shows he demeaned excess bond premium of Gilchris and Zakrajsek (2011a). Shaded areas: US recessions (NBER daes). 38

39 Figure 4. Hisorical decomposiions (baseline esimaion) 39

40 Figure 4 cd. Noe: The Figure shows he hisorical conribuions of banking shocks (hin solid lines), US non-banking shocks (dashed-doed lines), EA non-banking shocks (dashed lines) o hisorical series (hick solid lines). The decomposiions are compued a he poserior mode of he esimaed parameers. The hisorical bank capial raio and loan rae spread series (p.a.) are demeaned, he oher hisorical series are linearly derended in log form. Shaded areas: US recessions (NBER daes). 40

41 Figure 5a. US commercial banks: oal loans, business loans and business lending capaciy Noe: The solid line shows oal US bank credi (baseline measure); dashed line: business lending; dashed-doed line: US business lending capaciy (Gilchris and Zakrajsek (2011b). All series are linearly derended in log form. Shaded areas: US recessions (NBER daes). Figure 5b. EA banks: oal loans and business loans Noe: The solid line shows oal EA bank credi (baseline measure); dashed line: loans o non-financial corporaions. Boh series are linearly derended in log form. Shaded areas: US recessions (NBER daes). 41