Leverage Constraints and the International Transmission of Shocks. Michael B. Devereux University of British Columbia NBER CEPR

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1 Leverage Consrains and he nernaional Transmission of Shocks Michael B. Devereux Universiy of Briish Columbia NBER CEPR James Yeman Bank for nernaional Selemens Augus 0, 2009 Absrac Recen macroeconomic experience has drawn aenion o he imporance of inerdependence among counries hrough financial markes and insiuions, independenly of radiional rade linkages. This paper develops a model of he inernaional ransmission of shocks due o inerdependen porfolio holdings among leverage-consrained financial insiuions. n he absence of leverage consrains, inernaional porfolio diversificaion has no implicaions for macro-economic co-movemens. When leverage consrains bind, however, he presence of diversified porfolios in combinaion wih hese consrains inroduces a powerful financial ransmission channel which resuls in a high correlaion among macroeconomic aggregaes during business cycle downurns, quie independen of he size of inernaional rade linkages. Keywords: Leverage, nernaional Transmission, Porfolios JEL Classificaion: F3, F32, F34. Devereux hanks he Bank for nernaional Selemens, Bank of Canada, SSHRC and he Royal Bank of Canada for financial suppor. The views expressed here are hose of he auhors and do no necessarily reflec hose of he Bank for nernaional Selemens or of he Bank of Canada. We hank, wihou implicaion, Phil Wooldridge for advice on daa and seminar paricipans a he JMCB/Board of Governors Conference Financial Markes and Moneary Policy, June 4-5, and People s Bank of China Bank for nernaional Selemens Conference The nernaional Financial Crisis and Policy Challenges in Asia and he Pacific, Augus 6-8, 2009, for commens, including in paricular he discussans, Paolo Peseni and Kyungsoo Kim. This paper was wrien while he firs auhor was visiing he Reserve Bank of Ausralia and he Bank for nernaional Selemens. He is graeful for he warm hospialiy and resources provided by boh insiuions.

2 . nroducion The curren inernaional financial crisis has highlighed he criical role of financial markes in he propagaion of business cycle shocks, boh in ransmiing shocks from one counry o anoher and in magnifying he effecs of hose shocks. One key aspec of his linkage, seen in boh he curren crisis as well as he Asian and Russion crises a decade ago, is he imporance of balance shee linkages among firms and financial insiuions across counries. This implies ha asse price collapses in one counry are ransmied inernaionally hrough deerioraions in he balance shees of insiuions in counries holding porfolios of similar asses. is widely agreed ha high financial leverage a high raio of asses o underlying capial is a criical facor in he magnifying effecs of financial crises. As asse values decline, highly levered financial insiuions find heir ne worh sharply eroded. These insiuions are forced o shed asses o avoid unaccepable risks of insolvency. Bu asse sales drive asse values down furher, adversely impairing he balance shees of oher insiuions. These insiuions in urn are forced o sell asses, creaing a vicious cycle of balance shee deerioraion and asse sales. While he financial dynamics of such balance shee adjusmens have been widely discussed elsewhere, i is less well undersood how his process affecs macroeconomic oucomes, or ha his process alone may generae an immediae and powerful inernaional ransmission of shocks. A clear pre-requisie for balance shee adjusmens o have powerful macroeconomic effecs is he presence of some ype of financial fricions or disorions in credi markes. Afer all, in a Modigliani-Miller world, leverage is irrelevan. Thus, in order o capure he dynamics of he financial meldown, financial fricions will be of criical imporance. 2

3 n he conex of he inernaional ransmission of business cycles, however, oher puzzles arise. Mos models of business cycle ransmission sill rely on inernaional linkages due o rade flows. While global rade has been growing a remarkable raes over he pas wo decades, i is sill he case ha he major world regions he Unied Saes, Asia and Europe are o a large exen closed economies, wih he expor share from one region o anoher represening only a small proporion of overall GDP. Kose and Yi (2006) find ha using convenional inernaional real business cycle models, i is hard o accoun for he magniude of business cycle comovemens among counries. n addiion, here is evidence ha business cycle co-movemen is greaer beween counries wih greaer financial inegraion (mbs 2004, 2006). Neverheless, in he sandard inernaional business cycle model, enhanced inernaional financial inegraion acually ends o reduce business cycle co-movemen (Heahcoe and Perri 2002, 2005). Bu Krugman (2008) suggess ha radiional muli-counry business cycle models lack a criical inernaional finance muliplier, by which financial shocks in one counry affecs invesmen boh in he original counry and in oher counries hrough financial or balance shee linkages. This paper develops a heoreical model of a balance shee channel for he inernaional ransmission of shocks. The model emphasizes how a process of balance shee conracions, generaed by a downurn in one counry, is spread around he globe hrough iner-conneced porfolios. n he presence of leverage consrains, we show ha his gives rise o a separae financial ransmission mechanism of business cycle shocks ha is compleely independen of rade linkages. n fac, we work wih a highly sripped down one world good model in which, in seady sae, here are no rade linkages across counries a all. n he recen lieraure, for example Krugman (2008), he adjusmen of balance shees is someimes referred o as de-leveraging. This erm is inaccurae as a descripion of our model, since, as in Kiyoaki and Moore (997), he leverage raio is consan. Noneheless, he process of saisfying leverage consrains in he wake of asse price 3

4 The paper s main conribuion is o compare how macro shocks are ransmied under wo financial marke srucures. We do no aemp o provide an inegraed explanaion of he recen crisis, bu insead highligh how he join process of balance shee consrains and porfolio inerdependence generae an imporan cross-counry propagaion effec. We develop a wocounry model in which invesors borrow from savers in each counry, and inves in fixed asses. nvesors also diversify heir porfolios across counries and hold equiy posiions in he asses of he oher counry, as well as heir own. nvesors canno commi o repay savers, however, and in order o enforce paymen, may face limis on he maximum amoun of leverage on heir balance shees. We look a one environmen where leverage limis do no bind. n his case he inernaional ransmission of shocks is quie limied. Specifically, here is no inernaional ransmission due o balance shee adjusmens. A negaive produciviy shock, which leads o a fall in he value of asses in one counry, will cause financial insiuions o sell some asses and reduce heir deb exposure, bu his does no affec oher counries. n fac, in oher counries, invesors increase heir borrowing. More broadly, business cycle flucuaions across counries are essenially uncorrelaed in he absence of limis on leverage. When leverage consrains are binding, however, here is a powerful ransmission of shocks across counries. A fall in asse values in one counry forces an immediae and large process of balance shee conracions in ha counry s financial insiuions. Bu he fall in asse values leads o balance shee deerioraion in oher counries ha have inernaionally diversified asse porfolios, causing a sell-off in asses and a forced reducion in borrowing around he globe. This, in urn, drives a furher sell-off in he firs counry, esablishing a feedback loop. The end declines does impar a magnificaion effec on real aciviy. The endogenizaion of he leverage raio represens a separae issue, beyond he scope of his paper. For a recen conribuion, see Geanakoplos (2009). 4

5 resul is a large magnificaion of he iniial shock, a large fall in invesmen, and highly correlaed business cycles across counries during he resuling downurn. The scale of he propagaion linkages depends no jus on he presence of leverage consrains, bu also on he degree of inernaional porfolio diversificaion. We show ha greaer financial inegraion, which faciliaes more diversified porfolios, will increase he degree of common business cycle co-movemen of shocks. n his sense here is a rade-off beween he benefis of inernaional risk-sharing and he magnified inernaional propagaion mechanism. Finally, he model has implicaions for gross capial flows. We show ha a negaive shock ha reduces invesmen in fixed asses in one counry causes a scaling back of gross posiions, leading o a fall in he holdings of foreign equiy and an increase in he holding of home equiy. Bu he magniude of his gross capial flow conracion is much bigger in he presence of binding leverage consrains. The model draws heavily on a number of separae lieraures. Firs, and mos imporanly, we follow Kiyoaki and Moore (997) in imposing leverage limis on invesors. This leads o a wedge beween he effecive reurns faced by invesors and savers, and can ac as an amplificaion mechanism for business cycle shocks. 2 Second, we emphasize he linkages among counries hrough he presence of iner-conneced porfolios. Porfolio linkages, in a somewha differen conex, have for some ime been seen as imporan in he conagion effecs of financial shocks (see Rigobon 2003 and Pavlova and Rigobon 2008, for example). Finally, we inroduce 2 An alernaive mechanism where balance shees play a key role in business cycles is he financial acceleraor model of Bernanke e al. (999). This has been exended o a muli-counry seing by Gilchris (2004). 5

6 endogenous porfolio inerdependence hrough he recenly developed echniques of Devereux and Suherland (2009a). 3 The paper is organized as follows. The nex secion provides some evidence of he imporance of a financial channel in he recen business cycle downurn. We hen develop he basic wo-counry model in which invesors and savers inerac, bu invesors may be limied by leverage consrains. n secion 4 we explore he effecs of a negaive produciviy shock in one counry, and demonsrae he role of balance shee adjusmens in he propagaion of business cycle shocks across counries. We hen conclude. 2. Empirical evidence We presen some empirical evidence ha suppors our conenion ha balance shee conracions may have been an imporan propagaion mechanism for he curren inernaional crisis. Firs, Figure documens he global naure of he economic crisis, demonsraing a remarkably synchronous collapse in economic growh raes for a sample of OECD counries. is unlikely ha rade linkages alone could accoun for he simulaneous downurns in all regions. f we ake he US economy as he ulimae source of he financial crisis hen i would be easy o explain he scale of he downurn in Mexico, for insance. Bu Figure illusraes dramaic reducions in economic growh in many European economies, only marginally linked o he US hrough rade flows. 3 Dedola and Lombardo (2009) develop an ineresing model similar o he presen paper based on he financial acceleraor model, incorporaing endogenous porfolios as in he presen paper. They emphasise a somewha differen ype of ransmission effec, unique o he financial acceleraor model, coming from he direc connecion beween risk-premia across counries. 6

7 Figure Real GDP growh 7.5 n per cen US CA MX GB DE FR ES T NL TR PL CH Year-over-year changes in real GDP. US = Unied Saes, CA = Canada, MX = Mexico, GB = Unied Kingdom, DE = Germany, FR = France, ES = Spain, T = aly, NL = Neherlands, TR = Turkey, PL = Poland, CH = Swizerland. Source: naional daa n addiion here is clear evidence ha US banks reduced heir ousanding claims on he res of he world. Table conains shor-erm claims of US banks, for all OECD counries for which daa is available. This is he oal sock among US reporing banks of all claims on he desinaion economy wih less han one year remaining unil mauriy. Under normal circumsances new claims are issued and many mauring exising claims are rolled over each quarer. A rapid decline in less han one year, hen, implies lile new issuance, and few exposures being rolled over. There is a clear paern overall ha he larges OECD economies (by size of claims) have experienced a subsanial fall in shor-erm US bank claims during n paricular France, Germany, reland, aly, Korea and Luxembourg all experienced major wihdrawals over Furher, oal claims across all counries declined by more han 20 percen, wih half of ha decline occurring in he final quarer. 7

8 Table Shor erm claims of US banks on OECD economies $US millions Desinaion of Funds 2007Q4 2008Q 2008Q2 2008Q3 2008Q4 Ausria 4,79 4,207 4,84 3,574 2,256 Belgium 8,742 3,9 7,453 5,762 5,567 Czech Republic Finland 3,9 2,837 2,386 3,024 2,928 France 57,952 69,098 4,790 44,355 55,287 Germany 56,90 65,933 48,407 4,295 39,266 Greece 3,947 4,857 3,005 2,30 2,428 Hungary 894, ,3 49 reland 28,37 27,47 28,082 27,767 23,550 aly 25,80 25,52 26,25 8,67 7,243 Korea 26,254 27,435 28,027 29,873 2,58 Luxembourg 26,050 24,730 22,826 2,650,943 Mexico 6,492 7,752 7,497 6,784 7,734 Neherlands 43,32 46,995 52,07 47,67 37,230 Poland 2,356 2,254 2,279 2,308 2,52 Porugal 2,86 2,33 2,054,740,226 Spain 28,267 28,367 25,370 8,79 8,420 Turkey 7,320 6,96 7,04 6,00 5,07 Source: BS Consolidaed Banking Saisics Aside from bank balance shees, we can also find evidence consisen wih balance shee conracions in oher insrumens. Equiies in paricular were believed by some policymakers o be a vecor of conagion, as he following quoe by Rakesh Mohan, Depuy Governor of he Reserve Bank of ndia, indicaes: Our problems are mainly due o he sell-off by foreign insiuional invesors in he domesic equiy markes leading o a sharp reducion in ne capial inflows and he sharp slowdown in global economic aciviy and exernal demand. (Mohan 2009) This view is consisen wih he daa on inernaional capial flows capured by he Treasury nernaional Capial Sysem (Figure 2). The crisis has seen a fall in boh inflows and ouflows of capial from he US, a he aggregae level. The scale of he fall in flows in early 8

9 2009 is unprecedened over he full sample of aggregae TC daa going back o 980. n he model we will see ha he balance shee conracions implied by his, when combined wih binding leverage consrains among financial insiuions, can impar an independen inernaional ransmission of shocks. nflows Ouflows Figure 2 US capial inflows and ouflows n billions of US dollars 5,000 4,000 3,000 2,000, Source: US Deparmen of Treasury. 0 Financial linkages versus rade linkages The effecs of global balance shee adjusmens should be expeced o vary by counry. Some economies are more dependen on capial inflows han ohers, and counries wih low credi raings may suffer more from a sudden reducion in flows han higher raed counries, for example. Evidence of he effecs of a financial channel should accoun for he difference in vulnerabiliies across counries. We demonsrae he imporance of balance shee conracions as a propagaion mechanism for he crisis using regression analysis. As a rough measure of he inernaional effec of he crisis, we use he change in he growh rae of real GDP beween he year ended December 2007 and December The vulnerabiliy of counries o a sudden ouflow of capial is calculaed as oal capial inflows from he US, as a percen of 2007 GDP, using US Treasury 9

10 nernaional Capial daa (labeled TC). Our sample includes all members of he OECD for which TC daa is available. We also include rade linkages, measured using expors o he US in 2007 as a percen of GDP (X). Finally, we inerac each of hese variables wih he sovereign credi raing of he economy (CR), o capure he idea ha capial wihdrawals are likely o affec lower raed economies more heavily han higher raed ones, due o fligh o qualiy. Based on he Sandards and Poor s sovereign foreign currency credi raing in December 2007, we conver he credi raing o a numerical scale where a value of 0 corresponds o a AAA-raing, o a AA+ raing, and so on, down o 2 for a BB- raing. Table 2 Explaining he slowdown () (2) (3) (4) (5) X (0.844) (0.982) (0.662) CRX (0.775) (0.44) TC (0.035) (0.006) (0.005) CRTC (0.022) (0.009) Adj. R Obs Dependen variable: real GDP growh rae in he year o 2008Q4, less he growh rae in he previous year. P-values are in parenheses; bold indicaes significance a he 5% level. X equals expors o he US and TC is gross capial inflows from he US, each as a percenage of GDP, in CRX and CRTC are ineracive erms, where CR is S&P sovereign foreign currency credi raing in CR=0 corresponds o a AAA-raing, for AA+, and so on, o 2 for BB-. The resuls are given in Table 2, and provide srong suppor for our argumen ha financial flows were a srong causal facor in he propagaion of he crisis, while rade channels 0

11 appear less imporan. Firs he expor variables (X and CRX) are never economically or saisically significan, and someimes ener wih he wrong sign. Second our measure of capial flows (TC) is saisically significan in all cases. Third, when we include an ineracive erm beween he credi raing and he size of capial inflows from he US, his no only eners significanly, consisen wih fligh-o-qualiy, bu i also furher srenghens he saisical suppor for TC. Finally, he size of he adjused R-squared saisics is supporive of capial inflows playing an imporan role in explaining he downurn, while rade channels are of less imporance. n summary, his evidence suggess he possibiliy ha a financial channel may be imporan for he inernaional propagaion of shocks. Moreover, i is difficul o explain he scale and synchroniciy of he global downurn based on rade alone. 3. The model n his secion we describe a basic wo-counry model wih levered borrowers and lenders in each counry. The counries are called home and foreign. Wihin each counry here are invesors and savers, boh of whom use he same fixed asse and have infinie horizons. nvesors purchase he fixed asse and ren i o producion firms, receiving a risky reurn in exchange. We may hink of his invesmen as he purchase of an equiy claim in he producion firm. nvesors are more impaien han savers, so hey will borrow from savers in order o inves in he fixed asse. 4 Savers also make use of he fixed asse in home producion. Savers herefore choose a porfolio in which hey hold he deb of invesors and he fixed asse. By assumpion, savers do no hold domesic or foreign equiy. n he curren version, we assume ha savers do no lend o foreign invesors. Because he model is symmeric, his makes lile difference for he resuls. 4 Because hey are more impaien han savers, invesors will never accumulae enough resources o cover he cos of invesmen in any period.

12 nvesors in eiher counry, however, may rade claims wih invesors in he oher counry so as o diversify heir porfolio of equiy holdings. Thus invesors in each counry hold levered invesmens, bu also have equiy porfolios ha are iner-conneced across counries. Finally, boh invesors and savers in each counry supply labor inelasically o producion firms. nvesors We normalize he populaion of each counry o uniy, wih a measure n of invesors and n savers. The represenaive invesor in he home counry maximizes: () E θ su( Cs), s= where C s is consumpion of he final good. To keep he analysis solely focused on financial iner-linkages beween counries, i is assumed ha here is jus one world good. Adding an endogenous erms of rade o he analysis would enrich he response, bu would no fundamenally aler he cross-counry ransmission of balance shee adjusmens modeled here, so long as he elasiciy of subsiuion across home and foreign goods is no close o uniy. 5 We define he discoun facor for invesors such ha: wih β '( ) 0, where C s θ = ( ), '( s+ β Cs θs β Cs ) 0, C s is he economy-wide average consumpion of invesors. Thus he invesor s ime preference is increasing in consumpion, bu he rae of ime preference is aken as given by he individual invesor. The assumpion of endogenous ime preference for invesors plays he usual role of ensuring a saionary wealh disribuion among groups, boh wihin 5 As is well known, wih an elasiciy of subsiuion equal o uniy, here is a high cross-counry correlaion of consumpion purely due o he risk sharing implicaions of erms-of-rade adjusmen. This is seen, for insance, in he paper by Dedola and Lombardo (2009). Aghion e al. (2004) explore he imporance of erms-of-rade movemens in affecing borrowing consrains in an emerging marke economy framework. Exending our model o a seing wih endogenous erms-of-rade would affec borrowing consrains hrough he impac of a erms-of-rade adjusmen on ne worh in a similar way o he effecs of asse price changes in he presen version of he model. 2

13 counries and across counries. Bu i also plays a key role in allowing for a comparison of an economy in which financial consrains bind wih one where hey do no bind, as we discuss below. nvesors receive income from heir curren holdings of domesic and foreign equiy, as well as labor income from working in he domesic producion firm. n addiion, hey mus repay heir debs owed o domesic savers. They hen issue new deb, purchase equiy claims on home and foreign invesmens and consume. The home counry invesor s budge consrain is wrien as: (2) C 2 2 ( ) ( 2 2 ) q k q k W q R K k q R K k2 B R B + + = , where q and q represen he price of he fixed asse (or equiy) in he home and foreign 2 counry respecively, and and k are he porfolio holdings of he fixed asses in each counry k 2 held by he home invesor. The fixed asse of he home (foreign) counry earns a reurn of R K R ). is wage income for he invesor, who supplies one uni of labor. Finally, ( 2K W B is he deb issued o domesic savers and R B is paymen on previously incurred deb. One may quesion why only invesors can purchase he fixed asses, which are hen used by final goods firms. As in Bernanke e al. (999), we could assume ha invesors (or, in heir model, enrepreneurs) have some special capabiliy for ransforming a uni of he fixed asse ino a usable facor of producion ha is rened o producion firms. Lenders canno do his, and so may gain only indirecly from he invesmen, by lending o he invesors. n addiion o consrain (2), we assume ha invesors face a consrain on oal leverage due o an inabiliy o commi o repaymen, as in Kiyoaki and Moore (997). Toal deb is 3

14 assumed o be resriced o be no greaer han κ imes he marke value of equiy asses, where κ <. Thus home invesors choices are consrained by: (3) B κ qk qk 2 2 ( + ). The full leverage rae (he value of asses o capial) for invesors is hen / ( κ ) in he case where he leverage consrain (3) is binding. We ake κ as a free variable in our analysis. Leverage consrains in he form of (3) have been used quie widely in he lieraure on asse prices (Aiyagari and Gerler 999), emerging marke crises (Mendoza and Smih 2006), borrowing in a small open economy (Uribe 2006) and moneary policy wih credi fricions (acoviello, 2005). Kiyoaki and Moore (997) show ha κ may depend on he borrowing rae and expeced capial gains on equiy under some circumsances. nvesors in he home counry choose invesmen in he home equiy and he foreign equiy, as well as borrowing, o maximize heir expeced uiliy subjec o heir budge consrain (2) and leverage consrain (3), giving he condiions: (4) (5) ( q + R ) U'( C ) = Eβ ( C ) U'( C ) + κμ, + K+ + q ( q + R ) U'( C ) = Eβ ( C ) U'( C ) + κμ, 2+ 2K+ + q2 (6) U'( C ) ( ) '( = Eβ C U C+ ) R + μ, where μ is he muliplier on he leverage consrain, or equivalenly he uiliy benefi of an exra uni of deb o he invesor. f his is posiive, i means ha he invesor would like o borrow more, bu is consrained by (3). Therefore curren marginal uiliy is less han expeced fuure marginal uiliy imes he reurn on invesing in eiher he home or foreign counry. Thus μ is a 4

15 measure of he value of he opporuniy o make a levered invesmen. To show his, pu (4), (5) and (6) ogeher o obain: (7) μ ωr + ( ω ) r R Eβ ( C ) U'( C ) κ,, + 2, + = + where q, k, q, k, q2, k2, ω = /( + ) is he share in home equiy, r, + = ( q, + + R K, + )/ q, is he reurn on he home equiy and r 2, + = ( q 2, + + R )/ 2 K, + q 2, is he reurn on he foreign equiy. Equaion (7) shows ha, for a given disribuion of excess reurns and consumpion, μ is higher he higher is he leverage rae. also implies ha, when μ > 0 porfolio, up o he firs-order, exceeds he cos of borrowing., he expeced reurn on he Noe ha he leverage consrain does no direcly affec he invesors incenive o diversify equiy holdings across counries, since (3) applies equally o borrowing for domesic or foreign equiy purchases. Thus we may pu (4) and (5) ogeher o ge he sandard porfolio selecion condiion: ( q + R ) ( q + R ) '( ) = 0. + K+ 2+ 2K+ (8) EU C+ q q2 Given ha he porfolio choice may be wrien in he form (8), we can use he recen mehods described in Devereux and Suherland (2009a) o derive he opimal equiy porfolio of each counry s invesors. This involves using a second-order approximaion of condiion (8) in conjuncion wih a linear approximaion of he remaining aspecs of he model. We discuss he deails involved in porfolio choice more fully below. Savers Savers have preferences given by: S S (9) E θ U( C ). s s s= 5

16 Again, as for invesors, we define he discoun facor such ha θ S = S ( S ) S s β C θ, wih + s s S β '( ) 0, where C s C s is he economy-wide aggregae consumpion of savers. We make he assumpion ha savers are inherenly more paien han invesors in he sense ha: S (0) β () x > β () x, for all feasible values of x. Assumpion (0) ensures ha savers will lend o invesors, even in a seady sae where he leverage consrain (3) is no binding. 6 Savers purchase he fixed asse, and buy deb from invesors. They receive wage income from working in he final goods secor, and reurns on heir lending o invesors. n addiion, hey have a residual home producion funcion ha uses he fixed asse. Thus an individual saver owning S of he fixed asse produces ( S ) in erms of home producion, where G'( k S ) < 0. k, Gk,, For simpliciy, we assume ha home producion is perfecly subsiuable wih he final good in savers preferences. Wih his assumpion, we may wrie he saver s budge consrain as: () C S S S S ( S ) S q k W q k G k B R B S + = Noe ha, by assumpion, savers purchase only he domesic fixed asse. They do no have access o he same invesmen opporuniies as invesors and herefore only have use for he domesic fixed asse, as i may be uilized in home producion. On he oher hand, savers purchases of deb from invesors are unconsrained. The firs-order condiions for he opimal choice of k S and S B are simply: (2) S S S S ( q + G'( k U '( C ) = Eβ ( C ) U '( C+ ) q S +, + ), 6 An alernaive, bu considerably more difficul, approach o achieving an equilibrium wih levered invesmen is o assume ha invesors are less risk averse han savers. Solving a model wih leverage based on risk preferences would be subsanially harder han he approach we follow, because we would need o solve he full sochasic model o a higher order of approximaion. 6

17 (3) U '( C S ) S ( S ) '( S = Eβ C U C+ ) R. Producion firms Producion firms in each counry hire capial and fixed asses in order o produce. Firms are compeiive, and maximize profis given he producion funcion: (4) Y = AF( L, K ), where L is effecive employmen and K is he firm s use of he fixed asse. We allow for labor supplied by invesors and savers o have differen fixed producive conen. Thus L S = η L + η L, where η and η are fixed effecive produciviy facors. Profi maximizaion S S hen implies ha: (4) W = η AF ( L, K), (5) W S =η AF (, ) L K, S (6) R K, = AF (, ) 2 L K. Equilibrium Equilibrium of he wo-counry world economy enails marke clearing for he world marke of he fixed asse, as well as each counry s deb marke. Thus, for he home economy, i mus be he case ha: * S (7) nk + nk + ( n) k =,,,, S (8) nb + ( n) B = 0, 7

18 * where k represens foreign counry invesors real holdings of he home asse a he beginning of ime, +. n addiion, he world marke clearing condiion mus be saisfied: (9) nc C n C C AF n n nk k * S * S S * ( + ) + ( )( + ) = ( η + η ( ), (, +, )) + AF( η n+ η ( n), nk ( + k )) + ( n)( Gk ( ) + Gk ( )). * * * S * S * S 2, 2,, 2, This condiion incorporaes he fac ha he oal labor supply of invesors and savers is n and n respecively, and oal use of he fixed facor by final goods firms is equal o oal holdings by domesic and foreign invesors. The full equilibrium is hen described by equaions (2)-(6) and ()-(8) for boh he home and foreign counry, and he world marke clearing condiion S * *S S (9). This gives 27 equaions in he 26 variables,,,, k, k 2,, k,, C C C C, k, *, k, * 2, k * S 2,, B, S B, * B, B,, q,, R, μ, *S q, 2, * R S * *S μ,,,,, R and R 2 K,, wih * W W W W K, one equaion redundan by Walras law. Properies of he seady sae Before examining he dynamics of balance shee adjusmens wihin he model, we firs discuss some properies of he non-sochasic seady sae. This is paricularly easy in he case of * μ = μ = 0, which is when leverage consrains do no bind. Then i follows from a combinaion of (4) and (6), ogeher wih (2) and (3), ha he fixed asse is allocaed efficienly beween he final good secor and home producion. Tha is, for he home economy, we have: S (20) '( ) (, ˆ G k AF L nk ), ˆ = 2 * where k = k + k represens he oal quaniy of he fixed asse used in he final goods producion secor. Thus he fixed asse is allocaed efficienly in he sense ha is marginal produc is equalized beween home producion and final goods producion. 8

19 n combinaion wih he resource consrain ˆ S nk + ( n) k =, his uniquely deermines he allocaion of asses in final goods producion. Therefore here is no inerdependence across counries in asse allocaion in seady sae when leverage consrains do no bind. Hence oupu levels are independen across counries a permanen increase in produciviy A affecs home oupu, bu no foreign oupu. n fac, we can exend his resul furher. n he case where leverage consrains never bind, i is easy o see ha here is no ineracion beween asse allocaions across counries a all, a leas up o a firs-order approximaion. This can be seen by aking a linear approximaion of (4), (6), (2) and (3) o obain he condiion: dk γ dkˆ = +, S, + da +, + E S γ2 ˆ k A k where γ and γ 2 are consan coefficiens. Hence he dynamic pahs of asse allocaions are independen across counries in he absence of balance shee consrains. 7 Noe ha his holds despie he fac ha, up o a firs-order, expeced reurns on all asses are equalized boh wihin and across counries. A more general feaure of his environmen is ha porfolio holdings have no feedback effec on asse allocaions. Tha is, allocaion of he fixed asse beween home producion and invesmen in he final good is independen of he ownership of equiies. This propery will no hold in an economy wih binding leverage consrains. When leverage consrains bind, we again use (4), (6), (2) and (3) o obain he seady sae condiion: 7 Of course his is no a robus feaure, and would be alered in a model wih endogenous labor supply or capial accumulaion. Bu he main poin here is o show ha he presence of balance shee consrains inroduces subsanial addiional forces for cross-counry correlaions ha would oherwise be absen. 9

20 S S β ( β ) (2) '( ˆ G k ) = AF2( L, nk ) S S β ( β ) κ( β β ) S S S From condiion (3) i mus be rue ha β ( β ) / [ β ( β ) κ( β β )] < so i follows ha, under binding leverage consrains, he final goods secor has an inefficienly low level of he fixed asse. More generally, however, since discoun facors are endogenous, he allocaion of fixed asses across secors will no longer be independen across counries. Asse allocaion in he home counry will depend on he level of produciviy in he foreign counry. nuiively his holds because, wih free rade in equiies across counries, reurns o invesors mus be equal in boh counries. Since reurns inerac wih movemens in consumpion hrough he endogenous rae of ime preference, (2) shows ha he division of resources beween home producion and final goods mus be linked across counries as well. herefore follows ha, unlike he case wihou binding leverage consrains, he cross-counry ownership of equiy holdings will in general have implicaions for he allocaion of invesmen in fixed asses. Even in he case of consan ime preference, however, he presence of leverage consrains would sill imply a dynamic ineracion beween oupu levels across counries ha is absen wihou hese consrains, because produciviy shocks o one counry will affec he ighness of leverage consrains across all financial markes. We explore his in deail below. Porfolio choice We have already solved for he overall allocaion of he fixed asse in each counry in seady sae, bu no he ownership srucure of equiies. Thus, while k ˆ is deermined by (20) or * (2) wih non-binding or binding leverage consrains respecively, k and k are no ye deermined. Clearly, in order o analyze he dynamic response o produciviy shocks in one counry, i is necessary o undersand he srucure of equiy holdings. To do his, we follow. 20

21 Devereux and Suherland (2009a) in using a second-order expansion of (8) o obain an approximaion of opimal porfolio holdings. Since only invesors have access o equiy markes by assumpion, i is sufficien o look a he porfolio decisions of home and foreign invesors. To illusrae he applicaion of Devereux and Suherland (2009a) o he presen model, ake he budge consrain for home counry invesors (). This may be rewrien as: (22) where C + NFA = W + R kˆ q ( kˆ kˆ ) + r NFA + r q ( k kˆ ) + B R B K 2 x NFA denoes ne foreign asses, defined as ˆ NFA = q2k2 q ( k k ), and r x is he, excess reurn on he porfolio: q + R q + R rx = r r2 q q K, 2 2 K, 2 For given, he porfolio choice may be described as he choice of ( ˆ = q k k ), NFA α which is he ne holding of home counry equiy by home agens. f α < 0, he invesors diversify in he sense ha less han 00 percen of all home equiy is owned by home invesors. Devereux and Suherland (2009a) show ha, when he model is analyzed up o a firs-order approximaion, α is a consan and is deermined by a combinaion of a second-order approximaion of (8), ogeher wih a firs-order approximaion of he res of he model. n he soluion below, following Tille and van Wincoop (2007), we exend (8) o allow for ransacions coss of inernaional financial rade ha effecively limi inernaional porfolio diversificaion. This represens a brue-force echnique for generaing an equilibrium wih home equiy bias. n paricular, we assume ha an iceberg cos facor given by exp( τ ) reduces he reurns ha home invesors receive from foreign invesmen so ha condiion (8) becomes:. 2

22 ( q + R ) ( q + R ) '( ) exp( τ ) = 0. + K+ 2+ 2K+ (8 ) EU C+ q q2 n addiion, we follow Tille and Van Wincoop in assuming ha τ is a small, second-order erm. This means ha while i does affec he soluion for he equilibrium porfolio, which is evaluaed using a second-order approximaion of (8 ), i does no impac on he firs-order dynamics of he model, excep insofar as i affecs he choice of he porfolio iself. Noe ha given he revised definiion of ne foreign asses, he leverage consrain for home counry invesors becomes: (23) ˆ B κ( NFA + q k ). Thus, holding home asse prices consan, an increase in ne foreign asses generaed by eiher a curren accoun surplus or a capial gain on he exernal porfolio will loosen he leverage consrain. Bu since * NFA + NFA = 0, his will simulaneously ighen he leverage consrain facing foreign invesors. Thus he degree o which leverage linkages govern he ransmission of shocks across counries depends on he dynamics of ne foreign asses, and hese in urn are linked o he porfolio choices made by home and foreign invesors. Calibraion Because he model is such a sripped-down represenaion of a full-scale DSGE framework, lacking capial accumulaion and dynamics in he labor supply and conaining only a single world good, here are many dimensions in which he model s predicions will depar from realiy. The aim of he exercise is solely o explore he way in which financial leverage consrains affec he cross-counry dynamics of asse prices, asse allocaions and levered invesmens, and o invesigae he inernaional ransmission of balance shee conracions. To do his, however, we need o choose parameer values for preferences, producion echnologies 22

23 and he leverage consrain iself. Table 3 gives he se of parameer values used in he baseline model. We assume ha he measure of invesors and savers is equal, so ha n = 0.5. n he leverage consrained economy, his accords wih he esimaes of Campbell and Mankiw (990) regarding he share of households ha are subjec o credi consrains in he US economy. Table 3 Calibraion Parameer Value Parameer Value n 0.5 ε 0.5 η 0.0 ω 0.36 ζ Discoun facors 0.96 and 0.94 σ 5 κ 0.5, 0.8. ρ 0.9 We assume a discoun facor defined as: β( C) = ζc η. We se η = 0.0, and choose ζ so ha, in a seady sae wih binding leverage consrains, lenders and borrowers have discoun facors of 0.96 and 0.94 respecively. The parameer κ direcly deermines he oal value of new asses ha invesors can borrow. Since he model is calibraed in a symmeric way, ne foreign asses are zero in seady sae so ha invesors ne worh, measured as oal asses less deb, equals ˆ qk ( κ ). Toal leverage (invesmen relaive o capial) is equal o/( κ ). This leverage raio has a significan affec on he model s dynamics quaniaively. We examine wo alernaives. Firs we choose a relaive low raio of 2 ( κ = 0.5 ), as in Bernanke and Gerler (999). n response o 23

24 he discussion of he high raes of leverage seen in he financial sysem in recen years we also explore he implicaions of a higher value of κ = 0.8, corresponding o oal leverage of 5. From a qualiaive poin of view, we will see ha he resuls are very similar for boh leverage raios. We assume a Cobb-Douglas final goods producion echnology, and le F( LK, ) = LK ε ε. n order o have subsanial propagaion effecs from leverage consrains, Kiyoaki and Moore (997) require ha producion in he borrowing secor is linear in he fixed asse. Kocherlakoa (2000) shows ha, wih a more convenional calibraion allowing for decreasing reurns, credi consrains have much less impac. We se ε = 0.5, implying subsanial decreasing reurns, ye find subsanial effecs of leverage consrains, as we will see. Our choice of ε implies ha fixed asses are slighly more imporan han convenional measures of capial s share in calibraions of he US economy. 8 n addiion we assume ha effecive labor produciviy of savers and lenders S is iniially equal, so ha η = η =. Regarding he home producion secor, we assume ha G= Z( k S ) ω and ω = 0.36, implying ha he fixed asse is less imporan in his secor, consisen wih convenion. We se A = Z = in seady sae. The combinaion of hese assumpions implies ha, in seady sae, 80 percen of he fixed asse is employed in final goods producion. We follow he asse pricing lieraure (see, for example, Bansal and Yaron 2004) in seing a relaively high degree of risk aversion wih σ = 5 in UC ( ) = C σ /( σ ). Lower values of σ reduce he volailiy of asse prices, bu have lile qualiaive effec on he resuls oherwise. We focus on shocks o he produciviy of final goods in each counry. The sochasic process for final goods produciviy is modeled as: (24) log( A) = ρ log( A ) + υ, 8 For many emerging marke economies, however, esimaes of capial share equal o 50 percen are quie common. 24

25 2 2 where ρ = 0.9, E υ = 0 and σ = We assume ha foreign produciviy is driven by he υ same process, and foreign and domesic produciviy shocks are uncorrelaed. 4. Effecs of produciviy shocks n his secion we look a how he join process of balance shee consrains wih porfolio inerdependence affecs he model s response o a produciviy shocks in one counry. The focus on a produciviy shock is no of cenral imporance. The main elemens of he propagaion mechanism hold also for oher shocks. The key aspec of he model is o show ha he wo feaures of porfolio inerdependence and balance shee consrains inroduce a subsanial process of macroeconomic co-movemen ha is absen when hese feaures are no presen. No leverage consrains We firs examine he impac of a percen negaive produciviy shock in he home counry, in he environmen wihou leverage consrains. Figures 3 and 4 describe he impac of he shock on consumpion of invesors, asse prices, lending by savers, asse allocaion, he inernal lending rae and he consumpion of savers. Figure 3 represens he case where porfolio diversificaion is resriced by second-order ransacions coss as described above, while Figure 4 describes he case of unresriced porfolios. n he unresriced case, invesors in he home counry choose values for and k o saisfy (8 ), evaluaed up o second-order, wihτ = 0. k 2 This involves home invesors having a bias agains home equiies. nvesors are exposed o nondiversifiable risk from wage income, which is posiively correlaed wih he reurn on home equiy. Wih an unresriced porfolio, hey will hedge his risk by aking a larger posiion in foreign equiy han home equiy, as discussed in Baxer and Jehrmann (997). Given he calibraion of he model, in an unresriced equilibrium.2 ˆ k = k. Tha is, home invesors would 25

26 hold only 20 percen of oal home equiy (i.e. 20 percen of he fixed asses which are invesed in he home final goods echnology), wih foreign invesors holding he remaining 80 percen. Figure 3 No leverage consrains, parial diversificaion (a) nvesors consumpion C C* (b) Asse prices q q (c) Borrowing B B* (d) Asse holdings k k (e) Lending rae (f) Savers consumpion 26

27 R C S C* S Figure 4 No leverage consrains, full diversificaion (a) nvesors consumpion C C* (b) Asse prices q q (c) Borrowing B B* (d) Asse holdings k k (e) Lending rae (f) Savers consumpion 27

28 R C S C* S Since his is clearly counerfacual, we use he iceberg cos variable τ as a crude mechanism o mach he opimal porfolios more closely wih observed home bias in equiy holdings. n Figure 3 τ has been chosen so ha.75 ˆ k = k, implying ha home invesors hold 75 percen of home equiy. Figure 4, by conras, illusraes he counerfacual case where here is full consumpion risk sharing for invesors due o unresriced diversificaion. The responses o a produciviy shock are quie similar in each of he figures. Wihou leverage consrains, he impac of a fall in home counry produciviy is o reduce consumpion of invesors in boh counries, by idenical amouns in he case of unresriced diversificaion. The shock represens a emporary fall in consumpion. Since consumpion is expeced o increase in he fuure, real ineres raes mus rise. The combinaion of a lower reurn on he home asse and rising real ineres raes means ha he home asse price mus immediaely fall. Wihou leverage consrains, all reurns are equalized, a leas up o a firs-order approximaion, for invesors o be willing o hold all asses in heir porfolios. Thus he price of foreign asses mus also fall. Tha is, arbirage implies ha he rae of reurn o lenders rises by he same amoun in boh counries, even hough lenders do no direcly engage in inernaional borrowing or lending. Bu he paern of lending moves in differen direcions in he wo counries, as do lenders porfolios. n he home counry, here is a fall in invesmen in he fixed 28

29 asse in he final goods secor simply because his secor has suffered a persisen negaive echnology shock. This leads o an increase in he holdings of he fixed asse by lenders. They shif he composiion of heir porfolios from deb owards increased holdings of he fixed asse. Thus lending falls in he home counry. n he foreign counry, by conras, here is no change a all in he allocaion of he fixed asse. Bu lending in he foreign counry acually rises, as invesors borrow more from lenders in order o cushion agains he emporary fall in heir invesmen income. A differen way o see his is ha in he foreign counry, lenders are offered a higher rae of reurn on heir lending, and are willing o purchase more deb from foreign invesors. Eiher way we look a i, lending rises in he foreign counry, while i falls in he home counry. n his sense, here is no inernaional ransmission of balance shee conracions. The impac of he shock on lenders consumpion in he wo counries also moves in opposie direcions. Lenders in he home counry lose, since hey suffer a direc fall in heir wage income. Lenders in he foreign counry gain, since hey lend more a higher ineres raes, and heir wage income and holdings of he fixed asse are unaffeced. Clearly lenders canno achieve full consumpion risk-sharing, since hey canno direcly hold a claim on he equiy of he oher counry. n he economy wihou leverage consrains, hen, he inernaional ransmission of shocks is limied, and clearly counerfacual, relaive o he discussion of he empirical evidence of financial spillovers in secion 2. A negaive produciviy shock in he home counry leads o balance shee conracions domesically, as invesors reduce boh heir borrowing and holdings of fixed asses. Bu here are no foreign balance shee conracions. nvesmen in fixed asses is compleely unaffeced in he foreign counry, and foreign invesors acually increase heir 29

30 borrowing. More criically, here is no inernaional ransmission of he shock o GDP a all. Since he foreign asse allocaion is unaffeced by he domesic shock, foreign oupu is unchanged. Thus, in he absence of credi marke imperfecions, he possibiliy for he inernaional ransmission of shocks hrough balance shee conracions is limied. Leverage consrains and inernaional ransmission Figures 5-8 show he impac of a negaive produciviy shock in he home counry in he model when leverage consrains bind in boh counries. Figures 5 and 6 illusrae he case where he leverage raio is 5, he former when invesors porfolios are only parly diversified due o he presence of ransacions coss and he laer wih unresriced porfolio diversificaion. Figure 5 High leverage consrains, parial diversificaion (a) nvesors consumpion C C* (b) Asse prices q q (c) Borrowing B B* 0 (d) Asse holdings k k

31 (e) Lending rae R R* (f) Savers consumpion C S C* S Figure 6 High leverage consrains, full diversificaion (a) nvesors consumpion C C* (b) Asse prices q q (c) Borrowing B B* 0 (d) Asse holdings k k (e) Lending rae (f) Savers consumpion 3

32 R R* C S C* S Figures 7 and 8 illusrae he case of a lower leverage raio of 2, in he case of parial and full porfolio diversificaion respecively. n all cases here is a clear paern of global balance shee conracions in response o he shock. Wih high leverage and unresriced porfolios (Figure 6), he home invesor wishes o hold only 47 percen of oal home equiy. While here is sill some foreign equiy bias here, i is far less han in he economy wihou leverage consrains. Tha is, in equilibrium wihou porfolio ransacions coss, invesors wish o hold more of heir own equiy when here are leverage consrains han when here are no. The reason is ha he ransmission of balance shee conracions across counries wih binding leverage consrains will make equiy reurns more posiively correlaed, as we see below. As a resul, he gains from equiy diversificaion are lessened. n Figure 5 we calibrae τ so ha invesors hold 75 percen of domesic equiy, as in Figure 3. Wihou leverage consrains, he fall in home counry produciviy leads o a fall in asse prices in boh counries, and a fall in invesors consumpion. Bu now he fall in asse prices leads o a ighening of he leverage consrain, boh in he home and foreign counries. The resul is a reducion in borrowing by invesors in boh counries, and a consequen reducion in invesmen in fixed asses. Noe ha, for he foreign counry, here is no direc fall in he 32

33 produciviy of he domesic final goods secor. The fall in invesmen akes place purely hrough balance shee linkages. n addiion, he price of foreign equiy falls. Bu in spie of here being no direc shock o R 2 K, +, and a fall in he price of he asse, here is sill a fall in demand for he asse by invesors in boh counries. This is he essence of he invered demand curve for asses ha characerizes episodes of balance shee conracions, emphasized by Aiyagari and Gerler (999). Here i is aking place as a spillover from one levered invesor o anoher, as emphasized by Krugman (2008). Tha is, a fall in he price of he asse held by one invesor leads o a ighening of leverage consrains and a fall in demand for boh he original asse and oher asses held in he porfolio. Even in he case where porfolios are only parly diversified, here is a very high correlaion across counries in borrowing and invesmen. The balance shee conracion is so grea ha he inernal lending rae in each counry immediaely falls. Again, noe ha his is in response o a emporary shock so ha fuure consumpion of invesors is expeced o increase. Bu because invesors are subjec o leverage consrains, he pah of heir consumpion is delinked from he pah of ineres raes. To see his more clearly, noe from (6) ha here is a conflic beween he Fisherian deerminans of real ineres raes and he effec of binding leverage consrains. Since consumpion falls for boh home and foreign invesors, bu is expeced o rise in he fuure, real ineres raes should rise. Bu his effec is more han offse by he increase in he shadow price of borrowing due o he leverage consrain. The fall in asse prices leads o such a large balance shee conracion in boh counries, and correspondingly a large rise in he shadow price of borrowing, ha he real ineres rae offered by lenders falls raher han rises. 33