Work in Progress. Global Banks, Financial Shocks and International Business Cycles: Evidence from Estimated Models

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1 Work in Progress Global Banks, Financial Shocks and Inernaional Business Cycles: Evidence from Esimaed Models Rober Kollmann (*) ECARES, Universié Libre de Bruxelles and CEPR Mahias Pausian Bank of England Ocober 27, 2011 The global financial crisis ha eruped in 2007 has simulaed much research ha incorporaes financial inermediaries ino dynamic open economy models. So far, his research has focused on sylized, calibraed models. This paper pus ha class of models o he US and Euro Area (EA) daa, using Bayesian economeric mehods. The esimaion resuls sugges ha global financial inermediaries srenghen he posiive inernaional ransmission of real economic disurbances. Shocks ha originae in he banking secor accoun for roughly 20% of he forecas error variance of invesmen, and abou 5% of he forecas variance of US and EA GDP. Bank shocks explain beween 5% and 10% of he fall in US and EA real aciviy, during he Grea Recession. Key words: financial crisis, financial inermediaries, real aciviy, invesmen, Bayesian economerics. (*) Corresponding auhor. Addresses: R. Kollmann, ECARES, CP 114, Universié Libre de Bruxelles; 50 Av. Franklin Roosevel; B-1050 Brussels, Belgium; rober_kollmann@yahoo.com. Mahias Pausian, Moneary Assessmen and Sraegy Division, Bank of England, Threadneedle Sree, London EC2R 8AH, Unied Kingdom; mahias.pausian@bankofengland.co.uk This paper is being prepared for he conference The Financial Crisis: Lessons for Inernaional Macroeconomics (Paris, Ocober 28-29, 2011). R. Kollmann hanks he Naional Bank of Belgium and he EU Commission for financial suppor (CEPR projec 'Poliics, Economics and Global Governance: The European Dimensions' funded by he EU Commission under is 7h Framework Programme for Research, Conrac Nr ) 1

2 1. Inroducion In he years before he recen ( ) financial crisis, he leverage of many major financial insiuions increased seadily, and reached unprecedened levels. The crisis revealed he fragiliy of he financial secor, and of many highly indebed non-financial firms and households, and i has riggered he sharpes global recession since he 1930s. Before he crisis, srucural macro models largely absraced from financial inermediaries. Recenly, much effor has herefore been developed o he developmen of macro models ha include financial inermediaries; see, e.g., Davis (2011), Gamber and Thoenissen (2011), Devereux and Suherland (2011), In Veld e al. (2011), Kollmann e al. (2011), Nguyen (2011), Pausian and Sondergaard (2010), Perri and Quadrini (2011), Perri and Kalemli-Ozcan (2011), Ueda (2011) and van Wincoop (2011) who presen open economy models wih banks. 1 In hese models, he ne worh of banks is a key sae variable for real aciviy. This lieraure has highlighed several imporan mechanisms hrough which he presence of banks affecs he ransmission of macroeconomic and financial shocks. For example, a negaive shocks o bank capial will end o raise he spread beween banks lending and deposi raes, and hus lower lending and real aciviy; hus, shocks in one counry ha lower global banks capial can rigger a worldwide recession. So far, however, his research has focused on relaively sylized, calibraed models. A key conribuion of his paper is o ake his new class of models o he daa. Specifically, we esimae a wo-counry DSGE model wih a financial inermediary, using US and EA daa, by Bayesian economeric mehods. 2 In accordance wih he inuiion discussed above, he esimaion resuls sugges ha global financial inermediaries srenghen he posiive inernaional ransmission of real economic disurbances. Shocks direcly linked o he banking secor accoun for roughly 20% of he forecas error variance of invesmen, bu a much smaller share of he forecas variance of US and EA 1 Closed economy macro models wih banks were, i.a., presened by Aikman and Pausian (2006), Van den Heuvel (2008), Gerler and Kiyoaki (2009), Dib (2009), Adrian and Shin (2010), de Walque e al. (2010), and Challe e al. (2011). 2 There exiss a small lieraure ha esimaes open economy DSGE, bu ha lieraure has absraced from banks; also, ha lieraure has mainly focused on small open economies (e.g. Jusiniano and Preson (2010)). Two-counry models were esimaed by de Walque e al. (2005) and Peersman and Jacob (2011). 2

3 GDP. Bank shocks explain abou 5% of he fall in real aciviy, during he Grea Recession. Secion 2 presens he model ha we esimae. Secion 3 discusses he economeric approach. Secion 4 describes key daa feaures. Secion 5 repors he esimaion resuls. Secion 6 concludes. 2. A wo-counry world wih a global financial inermediary We consider a wo-counry model ha builds on Kollmann e al. (2011). 3 There is a represenaive global bank. In each of he wo counries, Home and Foreign, here is a represenaive worker, an enrepreneur and a governmen. All agens are infiniely lived. The bank collecs deposis from Home and Foreign workers, and makes loans o Home and Foreign enrepreneurs. The bank faces a collaeral consrain, ha ies he maximum amoun of deb ha he bank can issue o he bank s ne worh. 4 There is a final good ha is produced by Home and Foreign enrepreneurs using local labor and capial. The good can freely be raded. I is used for consumpion, and for capial accumulaion (by enrepreneurs). All markes are compeiive. Preferences and echnologies have he same srucure in boh counries. The following exposiion hus focuses on he Home counry. Foreign variables are denoed by an aserisk. The Home worker The Home worker consumes he final good, provides labor o he Home enrepreneur and invess her savings in one-period bank deposis. Her dae budge consrain is: where C and used as numéraire). C + D + T = WN + DR, (1) W D + 1 W are her consumpion and he wage rae, respecively (he final good is W T is a lump sum ax. N are hours worked. D + 1 is he bank deposi held by he Home worker a he end of period. D R is he gross ineres rae on deposis, beween -1 and ( R is se a -1). The worker s expeced life-ime uiliy a dae is: D 3 The model here is differen in ha, i.a., a governmen, and a lager number of exogenous shocks are assumed. 4 To focus on he role of banking fricions, we assume ha oher agens (workers, enrepreneurs) do no face collaeral consrains. 3

4 E [ u( C ) u( D ) ( N )], (2) s D N β s 0 + s +Ψ + 1+ s Ψ χ = + s where 1 ux () = ( x σ 1)/(1 σ) and 11/ + ( N) ( N η D χ = )/(1+ 1/ η), σ > 0, η > 0. Ψ > 0 is a consan. N Ψ is an exogenous sochasic ase shock ha affecs he worker s labor supply. 0< β < 1 is he subjecive discoun facor. Workers, enrepreneurs and he banker have he same subjecive discoun facor. We assume ha deposis provide uiliy o he worker (liquidiy services). This allows us o calibrae he model in such a way ha, in seady sae, he deposi rae is smaller han he lending rae, and ha workers hold deposis while enrepreneurs borrow. The Home worker maximizes (2) subjec o he period-by-budge consrain (1). Tha decision problem has hese firs-order condiions: N R Eβu'( C )/ u'( C) + Ψ u'( D )/ u'( C) = 1, u'( C ) W =Ψ χ '( N ). D D The Home enrepreneur The Home enrepreneur accumulaes physical capial and uses capial and local labor o produce he final good. Home final good oupu, denoed Z, is produced using he α 1 α Cobb-Douglas echnology Z= θ( K) ( N), wih 0< α< 1. K is he capial sock used a. Home TFPθ is an exogenous random variable ha follows an AR(1) process (see below). The law of moion of he Home capial sock is K+ 1 = (1 δ) K+Ξ I, where 0 δ 1is a depreciaion rae and I is gross invesmen. Ξ > 0 is an exogenous shock o invesmen efficiency (see Fischer, 2002, 2006; Greenwood e al., 1997; Jusiniano e al., 2007). Gross invesmen is generaed using he final good. Le ξ ( I ) be he amoun of he final good needed o generae I, wih ξ( I) I, ξ '( I) > 0, ξ "( I) 0. The Home enrepreneur s period budge consrain is: LR T ξ( K (1 δ) K) WN d L θ ( K ) ( N) L E E α 1 α Δ = + 1+, (3) where L is a one-period bank loan received by he Home enrepreneur in period -1. is he gross rae on ha loan, se a -1. We assume ha in period, he bank defauls on an exogenous amoun Δ on he conraced amoun LR ha she owes he bank. L L R E T is a 4

5 lump sum ax paid by he enrepreneur. E d is he enrepreneur s dividend income a. The enrepreneur consumes her dividend income. Her expeced lifeime uiliy a is s E E β u( d ), s= 0 + s Maximizaion of ha life-ime uiliy subjec o (3) yields hese firsorder condiions: W (1 ) K α = αθ N α, L E E R+ 1Eβu'( d+ 1)/ u'( d ) = 1, (4) Eβ( u'( d )/ u'( d )){ θ αk N + q (1 δ)} q = 1, E E α 1 1 α where q ξ '( K+ 1 (1 δ) K) is he marginal cos of gross invesmen a dae. / The Home governmen A dae, he Home governmen makes exogenous final good purchases G. These purchases are financed using he lump sum axes levied on he Home household, he Home enrepreneur, and by a lump sum ax levied on he global banker (see below): W E B G = T + T + T, where B T is he Home ax paid by he bank. The oal ax burden is divided beween hese agens, according o heir shares in seady sae consumpion, i.e. T = λ G for i=w,e,b where λ i is a ime-invarian facor ha equals agen i s i i i consumpion share in oal counry H consumpion. 5 The global bank In period, he global bank receives deposis D + 1 and D + from he Home and Foreign workers, respecively, and makes loans L + 1 and L * + 1 o he Home and Foreign W * enrepreneurs. Le D D + D and L L + L be worldwide socks of deposis and W * loans a he end of period. The bank faces a capial requiremen: her dae capial L W D should no be smaller han a fracion γ of he bank s asses L. + 1 One may W W view his as an implici requiremen reflecing marke pressures, or as a legal requiremen. γ is an exogenous random variable. Bank can hold less capial han he * 1 5 E.g. λ H = C/( C+ d E + d B /2), where o occur in counry H). S d s he banker s seady sae consumpion (of which 50% is assumed 5

6 W W W required level, bu his is cosly. Le x ( L+ 1 D+ 1) γ L+ 1 = (1 γ ) W W L+ 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 we assume: φ ( ) > 0 for x < 0; φ (0) = 0. Thus, for x < 0 he bank x incurs a posiive cos. The cos is zero when he bank mees is capial requiremen. A, W W he bank also bears an operaing cos Γ ( D+ 1+ L+ 1), where Γ > 0 is he real marginal cos of aking deposis and making loans. The bank s period budge consrain is: L + D R +Γ ( D + L ) + L φ({ L (1 γ ) D }/ L ) + T + T + d = L R + D, (5) W W D W W W W W W B B* B W L W where B d is he profi (dividend) generaed by he bank a. T B B* + T is he oal ax paid by he bank. Loan raes and deposi raes are equaed across counries (due o compeiion). The banker does no have access o oher asses, and hus she consumes her dividends. Her expeced life-ime uiliy a is: E s= 0 s B β u( d ).The banker maximizes life-ime uiliy subjec o (5). Ruling ou Ponzi schemes, ha problem has hese firs-order condiions: D B B L B B R+ 1Eβu'( d+ 1)/ u'( d ) = 1 Γ+ φ', R+ 1Eβu'( d+ 1)/ u'( d ) = 1 +Γ+ (1 γφ ) ', W W W wih φ' φ'({(1 γ ) L+ 1 D+ 1}/ L ). + s Marke clearing Marke clearing for he final good requires: ( ) Z + Z = C + C + d + d + d + ξ( I ) + ξ( I ) + G+ G + L φ { L (1 γ ) D }/ L. * * E E * B * * W W W W Loan rae spreads and bank capial L D The bank s Euler equaions imply R 1/ 1 (1 (1 ) '}/{1 ' + R+ = +Γ+ γ φ Γ+ φ} ; hence, ' R L D ( / W ) 2 (0) (0) ( / W + R+ Γ γφ x L Γ γφ γφ x L ). W Noe ha x/ L cr cr, where cr ( W W 1 1)/ W L+ D+ L+ 1 is he bank s capial raio a. Hence, he curvaure of he bank s penaly funcion φ ''(0) governs he sensiiviy of he ' '' 6

7 loan spread o change in he bank s capial raio. A 1 percenage poin increase in he capial raio lowers he loan spread by 4 γφ ''(0) percenage poins per annum. As deposis provide liquidiy services o workers, and as financial inermediaion is cosly, he seady sae deposi rae is lower han he seady sae loan rae. This implies ha φ '(0) < 0 has o hold, for a seady sae o exis. A rise in excess bank capial W W L D x L+ 1(1 γ ) D+ 1 lowers he loan rae spread R+ 1 R+ 1 when he cos of excess capial W W is sricly convex, φ '' > 0. Holding consan oal loans and deposis L+ 1, D+ 1, a rise in he benchmark bank capial raio likewise raises he loan spread. Forcing variables There are 11 exogenous forcing variables: Home and Foreign TFP * ( θ, θ ), invesmen efficiency * (, ), Ξ Ξ governmen purchases * ( G, G ) N N*, labor supply shocks( Ψ, Ψ ), loan defauls * (, ) Δ Δ and he benchmark bank capial raio ( γ ). We allow for a large number of non-bank relaed shocks, o give he model he chance o explain he daa, in he absence of banking shocks. The recen empirical esimaes of DSGE models sugges ha many shocks are needed o enable hese models o adequaely capure he daa (Smes and Wouers (2007)). There is also a echnical reason for assuming many shocks wihou measuremen error, he number of fundamenal shocks has o a leas as large as he number of empirical variables used in esimaion (oherwise he model is sochasically singular). As is sandard in he empirical DSGE lieraure, we assume ha he forcing x x variables follow univariae AR(1) processes: ln( x/ x) = ρ ln( x 1/ x) + ε for exogenous variable x ( x is he value of he variable in a deerminisic seady sae). 6 ε x is i.i.d. and normally disribued wih mean zero. We allow for cross-counry correlaion of he same ype of forcing variable, bu differen ypes of shocks are uncorrelaed. 7 6 The curren version of our simulaion code assume ha loan defaul has mean zero; he defaul of he Δ Δ Home enrepreneur follows Δ / Y= ρ Δ 1/ Y+ ε, where Y is seady sae Home GDP. 7 E.g. Home and Foreign TFP innovaions may be correlaed, bu Home and Foreign TFP innovaions are uncorrelaed wih, say, Home and Foreign governmen purchases (by conras, he empirical DSGE 7

8 2.2 Model soluion We ake a linear approximaion of he model equaions around a deerminisic seady sae. The soluion of he linearized model is given by s = Λ 1s 1+Λ 2ε, where s is a vecor consising of saes, conrols and forcing variables chosen (or realized) in period, expressed as in deviaion from he deerminisic seady sae. ε is he vecor of dae innovaions o he forcing variables. Λ 1 and Λ 2 are marices whose elemens are funcions of he srucural parameers Economeric approach The esimaion uses empirical informaion on a subse of he variables included in he vecor s. Le z be he vecor of variables used for he esimaion: z =Λ 3 s, where Λ 3 is a selecion marix. The economerician is assumed o observe he vecor z given by z = z + ω, where ω is a vecor of Gaussian i.i.d. measuremen errors ha has mean zero (measuremen error is independen across variables). Given he assumpion ha srucural innovaions and measuremen errors are Gaussian, he likelihood funcion of he daa ZT { z } = 1,.., T can easily be derived. See, e.g., Hamilon (1994, ch.13) and Schmi-Grohé and Uribe (2011). Le LZ ( Θ ) denoe he likelihood funcion, where Θ is he vecor of model parameers. The model is esimaed using quarerly daa for he US and he EA, for he period 1990q1-2010q3. The following 12 empirical series are used for esimaion: US and EA GDP, privae consumpion, invesmen, employmen, he sock of US and EA commercial bank loans (deflaed using he GDP deflaor), he loan spread of US commercial banks, and he capial raio of US commercial banks (based on Flow of Funds daa). EA loan spreads are only available for he period since 2003q1; as prediced by he model, he EA loan spread closely racks he US loan spread (see below). We hus use he US loan spread as a measure of he global loan spread. We also ake he US bank T lieraure generally assumes ha shocks are independen). An imporan avenue for fuure research is o allow for richer dynamics of he forcing variables, and a richer paerns or shock correlaions. A promising avenue would be o assume a facor srucure. 8 We use Chris Sims MATLAB proc gensys.m o solve he linearized model (see Sims (2000)). 8

9 capial raio as a proxy for he capial raio of he global bank. For esimaion, he capial raio is linearly derended, he loan spread is demeaned. The oher variables are linearly derended in log-form. (EA daa are aken from he ECB s Euro-Area-Wide-Model daa base, and from he ECB Monhly Saisical Bullein. See he Daa Appendix for a more deailed descripion of he daa.) We calibrae parameers whose values are unconroversial and/or pinned down by (banking) regulaions and/or average long run feaures of bank balance shees. Following much of he recen lieraure on he esimaion of DSGE models, we follow a Bayesian approach o esimae he remaining parameers (e.g., Orok (2000), Smes and Wouers (2007)). Le p( Θ ) be a prior densiy of Θ. According o Bayes law, he poserior densiy of Θ is p( Θ ZT) = L( ZT Θ) p( Θ )/ L( ZT), where LZ ( T) LZ ( T Θ) p( Θ) dθ is he marginal daa likelihood of he model. For each model varian discussed below, we repor he mode and sandard deviaion of he poserior parameer densiy, and he marginal likelihood (a measure of model fi). Calibraed parameers The elasiciy of final good oupu wih respec o capial is se a α=0.3, while he (quarerly) depreciaion rae of physical capial is se a δ= We consider a baseline specificaion in which all agens have log uiliy, σ = 1, and labor supply is infiniely elasic, η= ; hese values of σ, η have widely been used in macro model (Hansen and Rogerson (1995)), and hey are especially useful in he model here as hey imply ha N Ψ = WC / (from he worker s firs order condiion), which allows direc esimaion of N he labor supply shock Ψ. The mean value of he required bank capial raio is se a γ = Empirically, he capial raios of he major EA banks and of major US invesmen banks (i.e., raios of bank equiy o oal (non risk-weighed) asses) have ypically ranged beween 3% and 5% in he period , while he capial raios of US commercial banks have generally been in he range of 7%-8%. The seady sae deposi rae and he loan rae are se a 1% and 2.5% per annum. L We hus se he (quarerly) subjecive discoun facor a β = (as β R = 1, from he 9

10 D enrepreneur s Euler equaion). The bank s Euler equaions imply R β = Γ+ 1 φ ' and L R β =+Γ+ 1 (1 γφ ) '. This pins down he seady sae penaly funcion slope φ '. We assume ha excess bank capial is zero in seady sae, W W L (1 γ) = D, and se he loans o physical capial raio a 1/3: * * LK / = L/ K = 1/3. This calibraion pins down he workers preference parameer D Ψ, and he seady sae value of he labor supply N parameer Ψ. I also enails ha he raio of loans o annual GDP is 81% in seady sae. Empirically, he mean raio of bank loans o non-financial businesses divided by annual GDP was abou 45% in he US, and 90% in he EA, during he pas decade. The seady sae raio in he model lies beween hese empirical raios. 9 In he firs esimaion exercise discussed below, we direcly esimae (by OLS) he parameers of he AR(1) ime series processes of TFP, invesmen efficiency, he labor supply shock, and governmen purchases, using empirical measures of hese quaniies; we use he esimaed auocorrelaions, cross-counry correlaions and sandard deviaions of hese forcing variables in he model calibraion. The moivaion for his approach is ha i is easy o measure hese 8 forcing variables. Insead of drawing inference abou he law of moion of hese forcing variables hrough he lens of he model, i seem ineresing o sar by using direc informaion abou he forcing variables. The esimaed ime series parameers are repored in Table 2 below (where a descripion of he empirical measures used in esimaion can also be found). TFP, invesmen efficiency (measured as he raio of he CPI o he invesmen price index), he labor supply shock (measured as he raio of wage earnings o consumpion) and exogenous demand (he sum of governmen spending and a counry s ne expors vis-à-vis hird counries) are all highly persisen (AR coefficiens in he range ). US innovaions o invesmen efficiency, he labor supply shock and exogenous demand are more volaile ha he corresponding EA innovaions. Exogenous demand is negaively correlaed across he US and EA (-0.13), he oher forcing variable are posiively correlaed across he US and EA. In he firs se of esimaed discussed below, we hus only esimae he ime series processes of defauls, and of he benchmark (required) bank capial raio, as well as 9 In seady sae, he raio of he capial sock o annual GDP is 2.41, while he consumpions of he worker, he banker and he enrepreneur represen 71.56%, 0.11% and 4.01% of GDP, respecively. 10

11 seleced behavioral parameers (see below), using he full DSGE model. In a second esimaion exercise below, he parameers of all exogenous processes are esimaed hrough he lens of he model. Esimaed behavioral parameers 2 We assume ha he cos of invesmen is given by ξ ( I ) = I Ξ ( I / I 1), where Ι is seady sae Home invesmen. The curvaure parameer Ξ conrols he volailiy of invesmen. When Ξ= 0, hen invesmen is excessively volaile. We esimae Ξ using he Bayesian mehod. We likewise esimae he curvaure of he bank s penaly funcion, φ '', using he Bayesian approach. As our model feaures 11 shocks, we need o assume ha a leas one of he 12 empirical series used for esimaion is measured wih error (in order o ensure ha he model is non-singular). One se of resuls repored below assumes ha he four empirical banking variables (US and EA loans, he loan spread and he bank capial raio) are measured wih error. Anoher se of resuls assumes measuremen error in all empirical series. Assuming measuremen error seems jusified, as (especially he) banking daa are probably only rough proxies of he heoreical variables. For example, he empirical measure of bank capial is based on accouning daa on bank asses and bank equiy hose accouning daa may differ from marke values. 4. Daa plos and business cycle saisics. Figure 1-3 plo key macro/financial series. Given he key role of he bank capial raio, in he model, Figure 1 compares differen measures of leverage. 10 Figure 1 shows quarerly ime series for leverage, based on Flow of Funds daa, for hree broad US financial secors: insurance companies, INS; securiies brokers-dealers, SBD; commercial banks, CB (also shown: leverage for households, HH, and for non-financial corporae businesses, BUS). Asse and liabiliies repored in he FoF are parly measured a book 10 Leverage is defined as he oal asses/(oal asses financial liabiliies), i.e. leverage is he inverse of he capial raio. 11

12 values, and may hus differ from marke values. 11 We hus complemen he FoF leverage measures using he raios of (book-value) asses o he marke value of equiy, for US financial companies included in hree Dow Jones sock price indices (as repored by Daasream): US-Banks, US-Insurance and US-Financial Services ; 12 we refer o hese secors as BNK-MV, INS-MV and FIN-MV, respecively (where MV sands for marke value). The sample averages of FoF-based leverage raios of households (1.2) and of non-financial corporaions (2.0) are much lower han hose of he financial secors (CB: 8.9; INS: 7.7; SBD: 27.3). The sample averages of he financial secor leverage measures based on he marke value of equiy are lower han he FoF-based finance secor leverages (BNK-MV: 5.9; INS-MV: 4.0; FIN-MV: 2.6). 13 Noe also ha hese hree leverage measures, and securiies brokers-dealers (SBD) leverage (from FoF), undergo much bigger flucuaions han he oher leverage series. SBD leverage grew very srongly unil he crisis, reaching a peak of 55 in 2008q3, and hen (afer he Lehman bankrupcy) collapsed o abou 20. BNK-MV, INS-MV and FIN- MV leverage likewise grew srongly, and peaked in 2009q2 (i.e. a he poin in ime when bank equiy prices reached heir lowes values, during he recen crisis), before falling noiceably. 14 By conras, FoF-based commercial-bank leverage has had a fla rend since abou 2005, and held up well during he crisis. 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 (e.g., Huizinga and Laeven, 2009). 11 Deviaions from marke values are likely o be smalles when he balance shees in a given secor are marked o marke and when asses and liabiliies are shor erm. 12 Daasream provides he aggregae marke valuaion of he firms included in each of hese indices, as well as he corresponding (book-value) asses. The US-Banks index includes commercial banks; US- Financial Services includes invesmen banks, credi card issuers, and insiuions specializing in consumer loans, and hus overlaps only parially wih he FoF securiies brokers-dealers (SBD) caegory. These indices only include he major financial insiuions, while Flow of Funds daa cover all firms in a given secor. 13 This parly reflecs he fac ha he marke value of equiy is generally greaer han is book value. Leverage measures based on book-value equiy (also available from Daasream) are much closer o FoFbased leverage measures: 13.8, 7.5 and 14.0, respecively, for US-Banks, US-Insurance and US- Financial Services (1993q3-2010q3). 14 These movemens of he BNK-MV, INS-MV, FIN-MV and SBD leverage measures are largely driven by he sizable flucuaions in hese secors equiy. BNK-MV, INS-MV, FIN-MV leverage are also highly negaively correlaed wih he overall sock marke (he correlaion of year-on-year growh of hese hree leverage measures and he annual Fama-French sock marke reurns is abou -0.7). 12

13 Kollmann and Zeugner (2011) conduc a deailed saisical analysis of he link beween hese US leverage variables, and real aciviy; hey find ha he join informaion in secoral leverage series is more relevan for predicing fuure real aciviy han he informaion conained in any individual leverage series he marke-value based leverage measures do no dominae he Flow of Funds series. The curren version of he presen paper uses US Commercial Bank leverage, based on Flow of Funds daa, as a measure of he global bank s leverage. (Fuure versions of he paper will consider alernaive empirical leverage measures.) Figure 2 plos linearly derended logged bank loans, loan spreads (% p.a. no demeaned or derended) and loan loss raes (wrie-downs, as an annualized % fracion of he sock of loans), for US commercial banks and EA Moneary and Financial Insiuions (MFIs). (EA loan losses and loan spreads are only available for 2003q1-2010q3). Loans and loan spreads are highly posiively correlaed across he US and EA Loans rose srongly (relaive o rend), during he five years preceding he crisis, and hen fell sharply. Loan loss raes in he US have likewise increased srongly since 2007, especially in he US (he EA loan loss rae series exhibis sizable shor-erm movemens). Loan spreads have risen sharply since he sar of he crisis, boh in he US and EA; he correlaion beween US and EA loan spreads (underended) is Figure 3 plos linearly derended (log) GPD, privae consumpion, invesmen and employmen. In he second half of 2008, hese variables conraced sharply, in he US and EA. US and EA oupu fell roughly by he same amoun (-6%) beween 2007q4 and 2009q4. Consumpion and invesmen fell much more sharply in he US han in he EA (e.g. US invesmen was 34% below rend in 2009q2, while EA invesmen was 8% below rend in he same quarer). Table 1 repors momens of HP filered key macro and banking variables, for he US and he EA (1990q1-2010q3). Oupu 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. 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. The variables considered in he Table are posiively correlaed across he US and EA. 13

14 5. Model esimaes 5.1. Baseline specificaion Table 3 repors he priors and he poserior esimaes, for he baseline se-up. Prior disribuions The priors on he parameers (ha are no calibraed) are shown in column (1). We se he mean of he prior disribuion of φ '' (slope coefficien of he bank s penaly funcion) a 0.6, which implies ha a 1 percenage poin increase in he bank capial raio lowers he loan spread by 12 basis poins p.a., a value in he range of prior empirical esimaes of he sensiiviy of he loan spread (e.g., Hubbard e al. (2002), Sanos and Winon (2009)). The mean of he prior disribuion of Ξ is se a 1. The sandard deviaions of hese prior disribuions are se a half of he mean of he disribuion, which (for he gamma prior disribuion assumed here) implies ha a wide range of parameer values around he mean has non-negligible mass. The prior disribuions of he sandard deviaions of innovaions o loan defaul (normalized by seady sae GDP) and o he benchmark (required) bank capial raio are all se a 0.5%, which is in he range of he sandard deviaions of he innovaions o he oher forcing variables. The sandard deviaion of he prior is se a 0.1%. 15 The priors of he AR(1) correlaion coefficiens and cross-counry correlaions are bea disribuions wih mean 0.5 and sandard deviaion 0.1. As menioned above, he baseline esimaion se-up allows for i.i.d. measuremen error in four of he empirical daa series (US and EA loans, loan spread and bank capial raio). The prior disribuion of he sandard deviaion of measuremen error is invered gamma, wih a mean equal o 1/4 of he sandard deviaion of he corresponding empirical series, and a sandard deviaion ha is se a 1/5 of he mean. Poserior esimaes Columns (2) and (3) of Table 3 repor he mode of he poserior parameer disribuion, and he sandard deviaion of he poserior. 16 The daa are informaive abou he esimaed 15 The prior disribuion of he sandard deviaions of shock innovaions is invered gamma (IG). The IG has faer ails han he normal disribuion. Hence, a 0.1% sandard deviaion of he prior is no very resricive. A sensiiviy analysis shows ha he empirical resuls o no depend very much on ha 0.1% prior sd. 16 The mode of he poserior disribuion is he parameer vecor Θ ha maximizes he poserior disribuion; he sandard deviaions of he poserior repored here are based on a Normal approximaion of he poserior disribuion; see, e.g., Canova (2007), p

15 parameers: in mos cases, he poseriors have lower sandard deviaions han he priors, and he poserior esimaes (modes) differ noiceably from he priors. The poserior mean and sandard deviaion of he curvaure φ '' are 0.63 and 0.016, respecively. This is consisen wih a small bu significan effec of changes in he bank capial raio on he loan spread. Ineresingly, he model suggess ha US defauls are less volaile han EA defauls (poserior sd. 0.56% and 1.13%, respecively). The required bank capial raio undergoes sizable flucuaions (poserior sd.: 0.8%). Business cycle momens implied by poserior esimaes Table 4 implies business cycle saisics (of HP filered heoreical variables) implied by he poserior parameer mode. The repored momens perain o counry 1, which we ake as he heoreical counerpar of he US (he prediced momens for he EA are similar). Column (1) allows for all 11 srucural shocks. In Columns (2)-(7), only one ype of shocks is considered (he model is no re-esimaed). Column (8) repors empirical momens (from Table 1). The model wih all shocks generaes momens ha are broadly in he range of he empirical momens. The prediced sandard deviaion of GDP, 1.55% is larger han he empirical sandard deviaion, 1.12% (when he parameers of all forcing variables are esimaed hrough he lens of he model, hen he model maches more closely he sandard deviaion of GDP, as migh be expeced see below). The model (wih all shocks) capures he fac ha invesmen and US employmen are more volaile han GDP. The model also capures he cross-correlaions of he variables wih domesic GDP i correcly predics ha he loan spread is counercyclical. Finally, he model correcly predics ha he variables considered in he Table are posiively correlaed across he US and he EA--alhough i underpredics he cross-counry correlaion of GDP, and generaes a prediced cross-counry consumpion correlaion (0.72) ha is higher han he empirical correlaion (0.39). The model varians wih jus one ype of shock show ha TFP shocks and Labour supply shocks are he main drivers of GDP flucuaions (prediced sd. of GDP wih jus hese shocks: 0.99% and 1.07%, respecively), followed by defaul shocks (0.40%). Invesmen efficiency shocks and governmen purchases shocks induce much smaller flucuaions in GDP (prediced sd: 0.16% and 0.25%, respecively). 15

16 All ypes of shocks generae posiive cross-counry correlaions of oupu. Bu i should be noe ha he prediced cross-counry correlaions of GDP induced by jus TFP shocks, jus invesmen efficiency shocks, and jus labor supply shocks are smaller han he assumed cross-counry correlaions of hese shocks (see Table 2). Hence, hese shocks do no endogenously generae a posiive comovemen of real GDP (see discussion of he impulse responses below). Ineresingly, loan defaul shocks do induce srong posiive endogenous cross-counry comovemens: wih jus defaul shocks, GDP, invesmen and employmen ha are (almos) perfecly correlaed across he wo counries. This is due o he fac ha a defaul by Home enrepreneurs (say) lowers he bank s capial, which riggers a rise in he world-wide loan spread--loans, invesmen and GDP fall in boh counries. Forecas variance decomposiion Table x [o be added] decomposes he forecas error variance of GDP, consumpion, invesmen, employmen, loans, and spreads. Banking shocks (i.e. he defaul shocks and he shocks o he required bank capial raio) accoun for abou 5% of he forecas error variance of counry 1 and counry 2 GDP, and for abou 20% of he forecas error variance of invesmen, a horizons ranging beween 1 and 100 quarers. Slighly less han half of each counry s GDP forecas variance is accouned for by foreign defaul shocks. The banking shocks accoun for 99% of he forecas error variance of he loan spread and of counry 2 loans, and for 65% of he forecas error variance of counry 1 loans (a all horizons). Decomposing hisorical ime series A decomposing he hisorical ime series ino conribuions of he differen shocks yields a picure ha is consisen wih he forecas error variance decomposiions. Banking shocks accoun for a small componen of he hisorical ime series on GDP and invesmen. Figures 4 and 5 show he conribuion of GDP and invesmen series ha can be accouned for by banking shocks. The banking shocks accoun for abou 10%-15% of he fall in he variables during he financial crisis. The conribuion of banking shocks o he decline in EA invesmen is more sizable close o 50%. 16

17 Does global banking maer for he (inernaional) ransmission of shocks? While bank-specific shocks only play a relaively modes role for flucuaions in GDP, he exisence of (global) banks maers for he ransmission of shocks o GDP. Hence, banks do no maer primarily as a source of disurbance, bu because hey affec he ransmission mechanism. When we (essenially) eliminae he bank, by eliminaing he bank-specific shocks, seing he seady sae loan spread a a very small number, and seing he curvaure of he bank s penaly φ '' very close o zero, so ha he loan spread is (essenially) consan (and close o zero), hen he model here behaves like a sandard inernaional RBC model wih a bonds-only-srucure (Kollmann (1996)). The crosscounry correlaion of GDP and invesmen drop o and (compared o 0.32 and 0.59 in he baseline model wih banks). These prediced correlaions are obained by swiching off he bank, in he baseline mode, wihou re-esimaing he non-banking parameers. Re-esimaing a model varian in which he bank is a veil yields much lower prediced cross-counry oupu correlaions (-0.40). The marginal likelihood of he baseline model (wih banking fricion) is , while he marginal likelihood of he model wihou a bank is Thus, he model wih a global bank is overwhelmingly preferred o he model wihou bank. To be added: Resuls are robus o esimaing he ime series parameers of all forcing variables and also oher behavioral parameers (risk aversion, labor supply elasiciy ec.). Oher exensions: allow for richer correlaions beween shocks (e.g. i migh be imporan o allow for correlaion beween TFP and defaul shocks) Model wih an inernaional invesmen bank The model above assumes make loans whose reurns are non-sae coningen (excep for defaul). Ye, banks do hold vas amouns of sae-coningen asses. We hus also consider a model varian wih an invesmen bank ha purchases physical which she rens o he enrepreneur. Hence, he reurn on he bank s asses now is direcly ied o TFP and he oher macro shocks. Thus, bank capial plays a much more imporan role in 17 We compue he marginal likelihood using a Laplace approximaion. 17

18 he ransmission of hese shocks. There is a form of defaul oo in his world, as someimes he enrepreneur seals some of he physical capial ha he rened from he bank. [To be compleed] 6. Conclusion Shocks originaing in he banking sysem were no a major source of flucuaions in US and EA GDP (bu hese shocks maer more for invesmen). However banking has a noiceable effec on he ransmission of oher macro shocks. Global banking leads o more synchronized naional business cycles. DATA APPENDIX To be added 18

19 REFERENCES Adrian, T., A. Esrella and M. Shin (2010), Moneary Cycles, financial cycles and he business cycle. Federal Reserve Bank of New York Saff Repor No 421. Aikman, D. and M. Pausian (2006). Bank capial, asse prices and moneary policy. Bank of England Working Paper No Canova, F. (2007), Mehods for Applied Macroeconomic Research. Princeon Universiy Press Davis, S. and K. Huang, (2010) "Opimal Moneary Policy under Financial Secor Risk," Globalizaion and Moneary Policy Insiue Working Paper No. 85, June Davis, S. (2010) "The Adverse Feedback Loop and he Effecs of Risk in boh he Real and Financial Secors," Globalizaion and Moneary Policy Insiue Working Paper No. 66. Devereux, M. and A. Suherland (2011) Evaluaing inernaional financial inegraion under leverage consrains. European Economic Review. 55, 3, p Gerler, M. and N. Kiyoaki (2009). Financial Inermediaion and Credi Policy in Business Cycle Analsysis. De Walque, G, O. Pierrard and A. Rouabah (2010). Financial (In)Sabiliy, Supervison and Liquidiy Injecion: A Dynamic General Equilibrium Approach. Economic Journal, Vol. 120(549), pp De Walque, G., F. Smes and R. Wouers (2005). An Esimaed Two-Counry DSGE Model for he Euro Area and he US Economy. Working Paper. Dib, A. (2010). Banks, Credi Marke Fricions, and Business Cycles. Working Papers 10-24, Bank of Canada. Dib, A. (2010). Capial Requiremen and Financial Fricions in Banking: Macroeconomic Implicaions. Working Papers 10-26, Bank of Canada. Fisher, J (2002)."Technology shocks maer," Working Paper Series WP-02-14, Federal Reserve Bank of Chicago. 19

20 Fisher, J. (2006). The Dynamic Effecs of Neural and Invesmen-Specific Technology Shocks. Journal of Poliical Economy, Vol 114 No. 3, pp Hubbard, R., K. Kuner, and D. Palia (2002). Are here bank effecs in borrowers' coss of funds? evidence from a mached sample of borrowers and banks. Journal of Business 75 (4), Huizinga, H. and L. Laeven (2009). "Accouning discreion of banks during a financial crisis," CEPR Discussion Papers 7381, C.E.P.R. Discussion Papers. Jusiniano, A, and B. Preson (2010). Moneary Policy and Uncerainy in an Empirical Small Open Economy Model, Journal of Applied Economerics, 25(1), pp Jusiniano, A, G. Primiceri and A. Tambaloi (2008). Invesmen Shocks and Business Cycles. Journal of Moneary Economics, 57(2), March 2010, pp Kollmann, R., Z. Enders and G. Müller (2011). "Global banking and inernaional business cycles," European Economic Review, Vol. 55(3), pp Kollmann, R. and S. Zeugner (2011) "Leverage as a Predicor of Real Aciviy and Volailiy". CEPR Discussion Paper Nguyen, H., "Inernaional Crisis Transmission and Asymmeric Recoveries", Working Paper, World Bank. Peersmann, G. and J. Punnoose (2011) "Dissecing he Dynamics of he US Trade Balance in an Esimaed Equilibrium Model", Working Paper Gen Universiy. Perri, F. and V. Quadrini (2011), "Inernaional Recessions", Working Paper, Universiy of Minnesoa and USC. Sanos, J. A. and A. Winon (2008). Bank loans, bonds, and informaion monopolies across he business cycle. Journal of Finance 63 (3), 1315{1359. Van den Heuvel, S. (2008). 'The Welfare Cos of Bank Capial Requiremens,'' Journal of Moneary Economics, vol.55, pp Van Wincoop, E. (2011), "Inernaional Conagion hrough Leveraged Financial Insiuions", Working Paper, Universiy of Virginia. 20

21 Figure 1. Leverage raios (Asses/Ne worh) (a) Insurance, commercial banks (FoF) (b) Securiies brokers-dealers (FoF) (c) Households, non-financial business (FoF) (d) Banks, insurance, fin. services (equiy mk val.) The Figure plos he ime series of leverage raios for he following secors CB: commercial banks (from Flow of Funds, FoF); INS: insurance (FoF); SBD: securiies brokers and dealers (FoF); HH: households (FoF); BUS: non-financial corporae businesses (FoF); BNK-MV, INS-MV, FIN-MV: Banks, insurance and financial services, respecively, based on equiy marke values. Sample period: 1993q3-2010q3. Shaded areas indicae NBER recessions. 21

22 Figure 2. Bank loans, loan spreads, loan loss raes Bank loans (derended) Loan spreads p.a US EA US EA 0.03 Loan Loss Rae p.a US EA 22

23 Figure 3. Macro daa gdp US EA consumpion US EA 0.2 invesmen 0.04 hours US EA US EA 23

24 Figure 4. US and EA GDP and he conribuion of banking shocks 0.08 US GDP 1990q2 2010q GDP Due o banking shocks 95q1 00q1 05q1 10q1 EA GDP 1990q2 2010q GDP Due o banking shocks 95q1 00q1 05q1 10q1 24

25 Figure 5. US and EA invesmen and he conribuion of banking shocks 0.3 US Invesmen 1990q2 2010q Invesmen Due o banking shocks 95q1 00q1 05q1 10q1 0.3 EA Invesmen 1990q2 2010q Invesmen Due o banking shocks 95q1 00q1 05q1 10q1 25

26 Table 1. Hisorical business cycle saisics, 1990q1-2010q3 US EA Sandard deviaion (in%) GDP (Y) Relaive sandard deviaions (sd(x)/sd(gdp)) Consumpion Invesmen Employmen Loans Loan spread Correlaion wih domesic GDP Consumpion Invesmen Employmen Loans Loan spread Cross-counry correlaions GDP 0.56 Consumpion 0.39 Invesmen 0.45 Employmen 0.53 Loans 0.64 Loan spread 0.79 Noe: momens of HP filered series are shown (GDP, consumpion, invesmen, employmen and loans were logged before applying he filer). The Loan spread is expressed in decimal fracions). Sample period: 1990q1-2010q3 (excep for EA loan spread: 1997q3-2010q3). 26

27 Table 2. Esimaed parameers of exogenous processes (1990q1-2010q3) AR Sandard deviaions Correlaion wih coefficiens of innovaions foreign counerpar US TFP % 0.65 EA TFP % 0.65 US invesmen efficiency % 0.84 EA invesmen efficiency % 0.84 US labor supply shock % 0.46 EA labor supply shock % 0.46 US exogenous demand % 0.46 EA exogenous demand % Noe: The Table repors he ime series parameers if of linearly derended logged forcing variables. Log TFP is esimaed as ln( Y) 0.7ln( N) where Y and N are GDP and employmen, respecively. Our esimae of invesmen efficiency is he raio of he CPI o he invesmen deflaor. N Our esimae of he labor supply shock is Ψ = WC /, where W is wage earnings per employee, while C is per capia consumpion. Our measure of US exogenous demand is he sum of governmen consumpion and of US ne expors o counries oher han he EA (EA exogenous demand is defined analogously). 27

28 Table 3. Prior and poserior disribuion of parameers baseline specificaion Parameer Prior Disrib. Poserior disribuion Mode Sd.dev. (1) (2) (3) Bank capi. penaly φ '' G(.6,.3) Invesmen cos curv. Ξ G(1,.5) % Sandard deviaiions of srucural shock innovaions Home defaul Δ IG(.5,.1) * Foreign defaul Δ IG(.5,.1) Required Bk Cap Raio, γ IG (.5,.1) AR coefficiens Home defaul Δ B(.5,.1) * Foreign defaul Δ B(.5,.1) Required Bk Cap Raio, γ B(.5,.1) Cross-counry correlaion Defaul B(.5,.1) % Sandard deviaions of measuremen errors L D Spread US R R IG(.03,.006) Loans US L IG(.95,.19) Loan EA * L IG(.83,.17) Bank cap. raio US cr IG(.20,.04) Noes: Column (1) shows he prior disribuion for he differen parameers. G(m,s), B(m,s) and IG(m,s) indicae he gamma, bea and invered gamma disribuions, wih mean m and sandard deviaion s, respecively. Column (2) repors he mode of he poserior disribuion (i.e. he parameer vecor Θ ha maximizes he poserior disribuion); Column (3) repors sandard deviaions of he poserior disribuion (based on a Normal approximaion of he poserior disribuion; see Canova (2007, p.340)). 28

29 Table 4. Counry 1 ( US ) business cycle saisics implied by poserior mode of model parameers baseline esimaion Jus shocks o: All Benchmark shocks TFP Inv Eff G LabS Defaul BkCap DATA (1) (2) (3) (4) (5) (6) (7) (8) Sandard deviaion (in%) GDP (Y) Relaive sandard deviaions (sd(x)/sd(gdp)) Consumpion Invesmen Employmen Loans Loan spread Correlaion wih domesic GDP Consumpion Invesmen Employmen Loans Loan spread Cross-counry correlaions GDP Consumpion Invesmen Employmen Loans Noe: The Table shows momens of HP filered model variables, for he mode poserior esimae of he model parameers. The momens perain o counry 1, which we ake as he heoreical counerpar of he US. Column (1) allows for all 11 srucural shocks. In Columns (2)-(7), only one ype of shocks is considered (he model is no re-esimaed). Column (8) repors empirical momens * (from Table 1). Col. (2): jus TFP shocks ( θ, θ ) ; Col. (3): jus shocks o invesmen efficiency * * ( Ξ, Ξ ) ; Col. (4): jus shocks o governmen purchases ( G, G ) ; Col.(5): jus labor supply shocks N N* * ( Ψ, Ψ ); Col.(6): jus loan defaul shocks ( Δ, Δ ) ; Col. (7): jus shock o benchmark bank capial raio ( γ ). Col. (8): hisorical momens for US. 29