The Adverse Feedback Loop and the Real E ects of Financial Sector Uncertainty

Transcription

1 The Adverse Feedback Loop and he Real E ecs of Financial Secor Uncerainy Sco Davis y Vanderbil Universiy February 21 Absrac This paper presens a model ha shows he real e ecs of risk and uncerainy in he nancial secor. I inroduce a nancial secor, and mos imporanly, nancial secor uncerainy, ino an inernaional real business cycle model. The model shows ha during periods of acue nancial uncerainy, risk in he nancial secor acs as an imporan mechanism for he ransmission of real shocks. The model shows how an increase in nancial secor uncerainy leads o higher inerbank lending raes which lead o higher business cycle volailiy, persisence, and inernaional co-movemen. During periods of acue nancial uncerainy, an adverse feedback loop can arise whereby deerioraing condiions in he real economy have a derimenal e ec on condiions in he nancial secor, which has an adverse feedback e ec on he real economy. When calibraed o mach he levels of risk in he inerbank lending markes since Augus 27, he model is able o replicae many of he changes o he business cycle ha have occurred since he beginning of he nancial crisis. JEL Classi caion: E32; E44; F4; G1 Keywords: Financial acceleraor; Adverse feedback loop; nancial crises. I would like o hank Mario Crucini, Kevin Huang, Andrew Hughes Halle, and Elias Papaioannou for many helpful commens and suggesions. I would also like o hank he parisipans a he 21 ASSA meeings. All remaining errors are my own. y Deparmen of Economics, Vanderbil Universiy, VU Saion B #351819, Nashville, TN , USA, Tel.: ; fax: ; address: jonahan.s.davis@vanderbil.edu. 1

2 1 Inroducion Augus of 27 saw he beginning a full scale banking and nancial crisis ha was largely unknown in he poswar economic hisory of developed economies. Taylor and Williams (29) deail he rapid increase in counerpary risk in he inerbank lending markes beginning in Augus 27, and conemporary accouns deail he dramaic rise in nancial secor uncerainy ulimaely linked o securiized morgages. Inerbank lending spreads, he premium over he risk free rae ha banks charge one anoher for shor-erm unsecured lending, has played a cenral role in he recen nancial crisis. However mos macroeconomic models, used for boh academic and policy analysis, do no incorporae inerbank lending spreads. Boh Real Business Cycle models based on classical assumpions and models based on Keynesian assumpions assume perfec informaion and hus accep irrelevance of nancial condiions implied by he Modigliani and Miller (1958) heorem. A few papers move beyond he condiions of he Modigliani-Miller heorem and incorporae nancial fricions ino a general equilibrium model. 1 The mos noable being Bernanke and Gerler (1989) who rely upon agency coss and asymmeric informaion o produce he " nancial acceleraor". In his model, borrowing coss are inversely relaed o a borrower s ne worh. If his ne worh is procyclical, hen borrowing coss should fall in booms and rise in recessions, amplifying boh. Carlsrom and Fuers (1997) apply he agency cos problem o a quaniaive real business cycle model, and nd ha he nancial acceleraor mechanism can help explain he hump-shaped dynamic of oupu in response o a echnology shock. Furhermore, Bernanke e al. (1999) apply he nancial acceleraor in a model wih sicky prices o show how nancial fricions can a ec he economy s response o moneary shocks. In a relaed srand of lieraure, Kiyoaki and Moore (1997) show how credi marke 1 See Gerler (1988) for a survey of how he lieraure of nancial fricions arose ou of he lieraure incorporaing imperfec informaion. 2

3 fricions, in he form of collaeral requiremens, inroduce an imporan mechanism for he propagaion of echnology shocks. These papers incorporae nancial fricions, bu hey do no direcly examine he role of a nancial secor. Financial fricions a ec he producive secor of he economy. Chrisiano, Moo, and Rosagno (28) incorporae a nancial secor ino a model wih a nancial acceleraor mechanism. They show ha due o nominal deb conracs, he banking secor can play an imporan role in he ampli caion and propagaion of moneary shocks. However, for oher ypes of shocks, he nominal deb conracs are no as imporan and he banking secor plays a much less subsanial role as a propagaion mechanism. Chrisiano e al. incorporae a banking secor ino a quaniaive business cycle model wih a nancial acceleraor, bu do no speci cally allow for fricions wihin he banking secor. The dramaic rise in inerbank lending spreads in many nancial crises is a sympom of fricions a counerpary risk among banks. A few recen papers like Meh and Moran (28), Gerler and Karadi (29), and Gerler and Kiyoaki (29) incorporae nancial fricions, in he form of collaeral consrains, direcly ino he nancial secor. The model in his paper is similar o hese previous models which incorporae fricions ha can a ec a bank s cos of capial. However he nancial fricions in his paper cener on heerogeneiy across banks wih regard o heir losses on loans o he real secor. This heerogeneiy means ha some banks will be overexposed o he se of non-preforming loans and a subse of hose banks may hemselves become insolven. This possibiliy of bank insolvency means ha lenders in he inerbank marke will require a defaul-risk premium on unsecured lending. The possibiliy of defaul and hus he defaul-risk premium is inversely relaed o he size of he bank s capial cushion. This paper will show how his defaul risk in he nancial secor can give rise o a feedback loop ha acs as an inernal propagaion mechanism. This propagaion mechanism ampli es he real e ec of shocks o he economy, and in an inernaional real business cycle model his propagaion mechanism makes he real e ec of TFP shocks more severe, more persisen, 3

4 and i increases he degree of inernaional ransmission. In any model wih a nancial acceleraor, here is a feedback loop ha acs as a propagaion mechanism. In a real business cycle model, a negaive TFP shock would lower manufacuring rm pro s and hus raise rm deb raios. The deb-elasic defaul risk premium implied by he bankrupcy risk in he model would hen push up he rm s borrowing cos, which would furher lower he rm s pro s and raise heir deb raio. The model in his paper also incorporaes bankrupcy risk in he nancial secor. This leads o a similar feedback loop. The shock o TFP a ecs rms in he producive secor. Some defaul on heir deb, which resuls in a fall in he value of bank asses and an increase in heir deb-asse raios. In he presence of bankrupcy risk in he nancial secor, banks face a higher cos of capial afer heir deb-asse raio increases. Banks pass his higher cos along o rms in he form of higher raes on boh physical capial loans and working capial loans. Higher raes charged o he manufacuring secor lead o more defauls, riggering a furher erosion of bank balance shees. This paper shows ha he feedback loop arising in a nancial acceleraor model is ampli ed in when risk is incorporaed in he nancial secor. This is due o wo reasons. Firs, as discussed before, when a he banking indusry faces a higher cos of capial, hey raise heir raes on boh physical capial loans and working capial loans. This conrass wih a feedback loop concenraed in he manufacuring secor alone, where he rae on physical capial loans is he only rae a eced by he deb-elasic ineres premium. Second, and more imporanly, he nancial secor is more leveraged han he manufacuring secor. This means ha any feedback e ecs are much more pronounced when bank s don have a large capial cushion. Mos of he ime he adverse feedback loop semming from bankrupcy risk in he nancial secor is no quaniaively signi can. Normally, risk is low in he nancial secor and herefore even a bank s relaively small capial cushion is large enough o keep real shocks from leading o heighened bankrupcy risk in he banking secor. However, during periods 4

5 of acue nancial secor uncerainy, like ha experienced in he recen nancial crisis, he feedback loop associaed wih bankrupcy risk in he nancial secor can play a signi can role in he propagaion of real shocks. Making he e ecs of real shocks boh more severe and more persisen. This paper will proceed as follows. Secion 2 discusses he recen nancial crisis and wih anecdoal evidence shows how many he evens in he nancial markes since Augus 27 can be viewed as a sory of counerpary risk and uncerainy in he nancial secor. Secion 3 provides empirical evidence of an adverse feedback loop operaing hrough balance shees and risk premiums. The empirical resuls show ha risk in he nancial secor leads o a sronger adverse feedback loop han risk in he manufacuring secor. Secion 4 presens he inernaional real business cycle model used o explain how nancial uncerainy can ac as a mechanism for he propagaion of real shocks. The resuls from he model are presened in secion 5. Firs, wih impulse responses we show how nancial uncerainy can lead o greaer business cycle volailiy, persisence, and inernaional co-movemen following a produciviy shock. Then we compue business cycle momens from he model and show ha he model, calibraed o mach periods of acue nancial sress, can largely explain he changes in business cycle volailiy and co-movemen ha we have winessed in he pas few years. Finally, secion 6 concludes and o ers some suggesions for furher research. 2 Financial secor uncerainy and he crisis of The London Inerbank O ered Rae (Libor) is a money marke ineres rae ha measures he rae he larges banks charge one anoher for unsecured loans wih mauriy of a few monhs. Since hese loans are unsecured, here is risk of large losses in he even of a borrower defaul beween now and he mauriy dae. This risk is referred o as counerpary risk, and hus he spread beween he 3-monh Libor and he 3-monh T-bill rae (he TED spread) 5

6 is a measure of counerpary risk in he inerbank lending marke. Figure 1 chars his spread using daily daa from Augus 22 o Augus 29. Five key daes in he nancial crisis are also marked on he char. These are he ick marks leered a-e. They correspond o he daes, Augus 9, 27; March 14, 28; Sepember 15, 28; February 25, 29; and April 13, 29. In he ve years prior o Augus 9, 27 (poin "a" on he char) his spread averaged 29 basis poins. On Augus 8h, he spread was 57 basis poins. On Augus 9h, BNP Paribas, France s larges bank, announced ha given he high amouns of marke uncerainy and illiquid markes for cerain securiies, i was haling redempion on hree of is invesmen funds. This news solidi ed wha he marke had suspeced for monhs; he subprime morgage securiies in he U.S. backed by declining house prices were worh less han originally hough. Finance companies ha were over-exposed o he subprime morgage marke were early vicims of he crisis. However, he process of securiizaion mean ha in he early days of he crisis, a ypical bank s exposure o hese oxic asses was uncerain. An aricle from he Economis from Augus 16, 27 summed up he prevailing mood in he inerbank marke. The aricle saed ha "banks no longer rus oher banks enough o lend hem money excep on onerous erms." The aricle wen on o say ha "wih everybody having sold on he risk o everyone else - and he risk ofen being carved up, repackaged and sold again - nobody is sure where he losses are...in he inerbank marke, every counerpary was poenially vulnerable." By Augus 2h, he TED spread reached a peak of 239 basis poins. The ick mark labeled "b" corresponds o March 14h, 28, when he FED rs announced ha i was providing a nancial guaranee for JPMorgan o acquire Bear Searns. The gure shows a emporary jump in he TED spread righ around ha dae. The spread was 162 basis poins he day of he announcemen. Early he nex week, despie a 75 basis poin FED rae cu, he Libor coninued o increase, and on March 2h i reached 28 basis 6

7 poins. Following he announcemen ha he FED would ensure a smooh acquisiion of Bear Searns, one hedge-fund manager was quoed as saying, "If Bear Searns had failed, banks would no have know where hey were for days or weeks."(the Economis 28) The nex wo marks on he char, labeled "c", correspond o Sepember 15h and Sepember 29h, 28. These were he days ha Lehman Brohers led for bankrupcy and he House of Represenaives rejeced he iniial version of he TARP program, respecively. On Sepember 15, Lehman Broher led for chaper 11 bankrupcy proecion in he larges bankrupcy in U.S. hisory. This sen he message hrough he inerbank marke ha any bank, regardless of size, was vulnerable. The nex day, AIG, a major counerpary in he Credi Defaul Swap (CDS) marke received an emergency loan of $85 billion from he New York Fed. This creaed enough counerpary uncerainy in he inerbank marke ha he TED spread, which was 151 basis poins he Friday before he Lehman bankrupcy, increased o 475 basis poins by he following Thursday. The announcemen over he weekend of he Treasury s plan o purchase $7 billion of roubled asses calmed he fears in he inerbank marke and he TED spread seled o jus over 35 basis poins by Monday he 22nd. The second major shock in Sepember 28 came a week laer. On Monday he 29h, he House of Represenaives rejeced he iniial version of he Treasury s roubled asse purchase plan (TARP). Following ha news, he Libor jumped by 1 basis poins in one day. The peak of he TED spread was reached on Ocober 1h, a 574 basis poins. In prepared remarks in mid-ocober, Chairman of he Federal Reserve Ben Bernanke summed up he prevailing mood in he nancial markes when he said ha "As in all pas crises, a he roo of he problem is a loss of con dence by invesors and he public in he srengh of key nancial insiuions and markes." The inerbank marke recovered from he shocks of lae Sepember, bu he TARP program salled, and he spread sayed in a range of basis poins hroughou he winer. On February 25, 29 (poin "d" on he char), a he heigh of he bank naionalizaion 7

8 scare, he Federal bank regulaory agencies announced ha hey would conduc sress ess on banks o deermine heir capial adequacy under di eren adverse scenarios. On April 13h (poin "e" on he char), Goldman Sachs announced healhy rs quarer earnings and sold shares o gain he funds necessary o pay o he TARP funds hey had received in he fall. The increased cerainy in he inerbank marke ha came from seeing ha some banks were healhy enough o do wihou governmen suppor caused he TED spread o fall hroughou April, and on May 7h, when he sress es resuls were announced, he spread closed below 12 basis poins. I coninued o fall hroughou May and broke below 1 basis poins in early June. 3 Empirical Evidence of an Adverse Feedback Loop In he model in his paper, risk in he nancial secor creaes a feedback loop ha can amplify he e ecs of real shocks. Furhermore, his feedback loop is no nearly as srong when risk is localized in he manufacuring secor. A number of recen even sudies of previous nancial crises in developed and developing counries nd ha economic downurns ha are accompanied by banking crises end o be more severe and more proraced han ordinary recessions (See, for example Reinhar and Rogo 28 and 29, Cecchei, Kohler, and Upper 29, The IMF 29a and 29b, and Bordo and Haubrich 21). In relaed sudies Bernanke (1983), Bernanke and Lown (1991), Peek and Rosengren (2), and Gilchris e al. (29) aemp o isolae exogenous fricions in he credi markes and nd robus evidence ha disurbances arising from wihin he nancial inermediaion process can have real e ecs. This empirical evidence of how disurbances wihin he inermediaion process can have real e ecs is evidence of an adverse feedback loop. An adverse feedback loop should lead o more severe and proraced economic downurns as he iniial fall in oupu leads o a banking crisis, which leads o a furher fall in oupu. This implies ha he overall fall in 8

9 oupu should be more severe han would have been wihou a banking crisis, and he normal economic recovery mechanisms are hampered by he banking crisis and poor availabiliy of credi, prolonging he recession. To provide some empirical backing for his conclusion, and o show how his adverse feedback loop is much more pronounced when fricions arise wihin he banking secor iself, in his secion we consider he ime series relaionship beween indusrial producion, he spread on lending o he manufacuring secor, and he spread on lending o he nancial secor. We begin by esimaing a bivariae VAR(1) model wih he monh-over-monh change in he log of he index of indusrial producion, IP, and a measure of risk in lending o he real secor. RP m is he spread on lending o he manufacuring secor, he spread beween he rae on corporae bonds and he 3-monh T-bill rae. The VAR(1) model akes he following form: IP RP m = c + A 4 IP 1 RP m " (1) Negaive o -diagonial erms in he marix A would be evidence of an adverse feedback loop where a real economic slowdown causes increased risk premiums, and hese increased risk premiums cause a furher economic downurn. However he model wih he spread beween corporae raes and he risk free rae, RP m, doesn specify wheher he adverse feedback loop is due o nancial fricions in he nancial secor or fricions in he real secor. To separae he e ec of hese wo poenial fricions, we hen consider a rivariae VAR(1) model wih he monh-over-monh change in he log of he index of indusrial producion, IP, and measure of risk in lending o he real secor. However now he risk premium RP m is divided ino he spread beween corporae bonds and he 3-monh Libor, RP m, and he spread beween he 3-monh Libor and he 3-monh T-bill, RP f. Thus RP f risk premium on inerbank lending and RP m measures he measures he risk premium on lending o he 9

10 real secor IP RP m RP f 7 5 = c + A 6 4 IP 1 RP m 1 RP f " (2) The resuls from he bivariae and rivariae esimaions are presened in he ables 1 and 2. The op half of each able shows he resuls from esimaing he bivariae model in (1), and he boom half of each able shows he resuls from esimaing he rivariae model in (2). The resuls in able 1 are found using he raes on Aaa raed corporae bonds and he resuls in able 2 are found using he raes on Baa raed corporae bonds. The ables show evidence of he adverse feedback loop. In he bivariae VARs, lags of indusrial producion have a negaive e ec on he spread beween corporae bonds and reasuries. The regressions using Baa corporae risk spreads show ha lagged values of he risk spread have a signi canly negaive e ec on indusrial producion growh. This channel is no signi can in he esimaion using Aaa corporae risk spreads, however he resuls from he bivariae VAR regressions can be inerpreed as evidence of an adverse feedback loop where a fall in real economic aciviy causes an increase in risk premiums on lending o he real secor, and hese higher risk premiums cause a furher fall in real economic aciviy. 2 The rivariae VARs in he boom half of each able show he same adverse feedback loop. Lagged values of he risk premium have a negaive e ec on indusrial producion growh, however lagged values of indusrial producion growh negaively a ec he risk premium on inerbank lending bu don a ec he risk premium on lending o he real secor. This implies ha he adverse feedback loop in he bivariae VARs was primarily due o fricions in he inerbank marke. The adverse feedback loop requires ha a slowdown in real economic aciviy lead o higher risk premiums. The resuls from he rivariae VAR show ha a slowdown in real aciviy only has a signi canly e ec on inerbank spreads; 2 A leas when considering he spread on Baa raed corporae bonds. 1

11 hus in an environmen wih no fricions in he nancial secor (inerbank lending spreads are zero) here should be no evidence of an adverse feedback loop. 4 Model In order o model he real e ecs of nancial uncerainy, his paper incorporaes he nancial acceleraor mechanism from Bernanke e al. (1999) in he workhorse inernaional real business cycle model of Backus e al. (1992 and 1994) and Baxer and Crucini (1993). The model consiss of wo counries, home and foreign. In each counry here are households, a manufacuring secor, and a nancial secor. The manufacuring secor uses domesic labor and capial o produce radable consumpion goods. Banks in he nancial secor channel savings from domesic households o rms in he domesic manufacuring secor, and borrow and lend from banks in he foreign nancial secor hrough he inerbank lending marke. Manufacuring rms and banks boh face idiosyncraic shocks o he value of heir asses which may resul in bankrupcy. The probabiliy of bankrupcy is increasing in heir debasse raio. As a resul, lenders mus be compensaed by a deb-elasic defaul risk premium. This gives rise o he nancial acceleraor mechanism. In he model, he wo counries are symmeric and in wha follows we focus on he relevan equaions for he home counry, when foreign variables appear, hey are disinguished by an aserisk (). 4.1 Manufacuring Secor The home manufacuring secor is made up of a coninuum of rms, indexed by i, on he inerval [; 1]. Firm i owns a sock of physical capial K (i). This physical capial is nanced hrough equiy and a loan from he domesic banks, K (i) = E M (i) + b M (i). Firms combine his capial wih labor o produce a radeable inermediae good. Toal 11

12 producion by rm i in period is: Y (i) = A (N (i)) (K (i)) 1 (3) where Y (i) is oal producion by rm i, N (i) is he rm s labor inpu, K (i) is he capial inpu, and A is counry speci c oal facor produciviy. Inermediae goods from each rm are combined o produce an aggregae inermediae good ha can be used a home or expored: Z 1 Y (i) di = y d + y x (4) where y d are inermediae goods mean for domesic use and y x are mean for expor. Domesic and impored inermediae goods are hen combined o produce a nal good ha can eiher be used for consumpion by domesic households or invesmen in he domesic manufacuring secor: h () 1 y d 1 i + (1 ) 1 (y x ) 1 1 = C + I (5) where (1 ) is he seady sae impor share, is he impor demand elasiciy, C is household consumpion, and I is aggregae invesmen in physical capial. Aggregae invesmen is equal o he sum of invesmen by individual rms, I = R 1 I (i) di. The rm sells is oupu for a price p y. Assume ha rms pay for labor in advance, herefore he oal wage bill of he rm is (1 + r wc ) w N (i), where r wc on working capial loans. Therefore he rm s operaing pro in period is: is he ineres rae (i) = p y Y (i) (1 + r wc ) w N (i) (6) The rm s sock of physical capial evolves according o: 12

13 K +1 (i) = 1! M (i) K (i) + I (i) (7) where! M (i) is an i.i.d. shock o he rm s physical capial sock. I is lognormally disribued on he inerval ; 1 wih mean 1 and a variance 2 M. The rm speci c shock! M (i) inroduces heerogeneiy among manufacuring rms and gives rise o he possibiliy ha some manufacuring rms will receive an abnormally large shock and be forced o defaul on heir debs. Since he shock has a mean 1, i has no e ec on he aggregae capial sock, bu since his shock is unknown when he bank makes a physical capial loan o he rm, he shock inroduces incomplee informaion and hus he assumpions necessary for he irrelevance of nancial condiions implied by he Modigliani- Miller (1958) heorem are no sais ed. Afer he shock o he rm s asses in period, he rm in he manufacuring secor is bankrup if he depreciaed value of is physical capial plus is operaing pro in period is less han he value of is loan from he nancial secor plus any ineres i is o pay on ha loan in period : 1! M (i) K (i) + (i) < 1 + r M b M (i). (8) Since he variables K (i), (i), and b M (i) are all deermined before he realizaion of he idiosyncraic shock, hey are equal across all rms i. 3 Therefore he shock o he rm on he margin beween bankrupcy and coninuing operaions is:! M = K r M b M. (9) K Thus if! M (i)! M hen rm i will coninue operaions, and if! M (i) >! M hen rm i will declare bankrupcy. 3 The irrelevance of pas hisory is due o he fac ha here are no capial adjusmen coss and he he shocks! M (i) are i.i.d. If he manufacuring rm i receives a paricularly bad shock in he las period, i is able o compleely replenish is capial sock by raising funds in he equiy markes. 13

14 If a manufacuring rm defauls on is debs, equiy invesors ge nohing and lenders receive a share of he rm s remaining asses. A fracion,, of he rm s asses are los o liquaion coss, so lenders receive (1 ) 1! M (i) K + afer liquidaion. If he manufacuring rm does no defaul hen he lender receives 1 + r M b M. The nancial secor is populaed by banks engaged in perfec compeiion, so he ineres rae charged on physical capial loans, r M, is deermined by a bank s zero pro condiion: 1 + r b b M = Z! M 1 + r M b M df! M Z 1 + (1 ) 1! M K + df! M! M (1) where r b is he bank s cos of capial and F disribuion of! M.! M is he c.d.f. of he runcaed lognormal Thus he ineres rae charged by banks for physical capial loans o manufacuring rms is: 1 + r M = h 1 + r b b M (1 ) (K + ) 1 F! M F (! M ) b M K R 1! M! M df! M i (11) where F! M is he percen of manufacuring rms ha repay. This ineres rae, r M, is decreasing in F! M and hus decreasing in! M.! M is decreasing in he manufacuring rm s deb-asse raio, so r M is increasing in he rm s level of indebedness. Afer he realizaion of he shock, rms ha coninue operaions inves in new capial and reurn he res of heir ne income as dividends o shareholders, while rms ha go bankrup pay no dividends: 8 >< d M r M b M I (i) if! M (i)! M (i) = >: if! M (i) >! M. (12) Therefore he average dividend paid by rms in he domesic manufacuring secor is: 14

15 Z 1 d M = d M (!) df (!) = = r M b M F! M Z! M Z! M d M (!) df (!) (13) I (!) df (!). 4.2 Financial Secor Banks in he nancial secor serve as an inermediary beween domesic savers and rms in he domesic manufacuring secor. Furhermore, banks engage in inerbank lending and borrowing wih heir foreign counerpars. There is a coninuum of banks indexed j on he inerval [; 1]. In period he book value of he equiy of bank j is: E F (j) = B M (j) + B ib (j) b s (j) b ib (j) (14) where B M (j) are he he bank s holdings of physical capial loans o he domesic manufacuring secor, B ib (j) are foreign bank bonds purchased in he inerbank lending marke, b s (j) are savings from domesic households, and b ib (j) is inerbank borrowing from foreign banks. The same sock of bonds may be a liabiliy o a manufacuring rm bu an asse o a bank, so when a sock of bonds is an asse is wrien wih a capial B, bu when i is a liabiliy i is wrien wih a lower case b. The same is rue for inerbank borrowing and lending. The domesic bank s inerbank lending o foreign banks is represened on he bank s balance shee as B ib (j), bu he same bank s inerbank borrowing from foreign banks is represened by b ib (j). 4 4 Thus in equilibrium he oal sock of physical capial loans ha appear as liabiliies o manufacuring rms is equal o he oal sock of physical capial loans ha appear as asses o bank, R 1 bm (i) di = R 1 BM (j) dj. Similarly he oal sock of inerbank borrowing from foreign banks ha appears as a liabiliy o domesic banks is equal o he oal sock of inerbank lending ha appears as an asse o foreign banks, R 1 bib (j) dj = R 1 Bib (j) dj. 15

16 Of he bank s liabiliies, 1 are savings from domesic households and are loan from oher banks in he inerbank lending marke. Laer in his secion, we discuss how he parameer = inegraion in he daa. b ib (j) b s (j)+bib (j) is calibraed o mach levels of inernaional credi marke Because of bankrupcy in boh he domesic manufacuring secor and among foreign banks, he bank s asses, which have a book value of B M period, have a book value a he end of he period of: (j) + B ib (j) a he beginning of 1! F (j) M B M (j) + 1 F B ib (j) (15) where M is he percen of he average bank s porfolio of loans o he domesic manufacuring secor ha is los o bankrupcy and liquidaion coss, and F is he share of he bank s claims on foreign banks ha is los o bankrupcy and liquidaion coss. M is he percen of he average bank s loan porfolio ha is los o bankrupcy and liquidaion coss, bu! F (j) M is he percen of bank j s loan porfolio ha is los o bankrupcy and liquidaion coss.! F (j) is an i.i.d. shock o he bank s loan porfolio. I is h i 1 lognormally disribued on he inerval ; wih mean 1 and variance 2 M F. The shock implies ha some banks may be over-exposed o he se of manufacuring rms ha go bankrup, and hus hese banks may nd hemselves in nancial rouble. This implies ha banks do no hold fully diversi ed loan porfolios. This over exposure may be due o a regional bias in he bank s porfolio, or i may be because a bank has a cerain core compeency and is herefore overexposed o a cerain secor of he economy. 5 The bank speci c shock! F (j) preforms he same funcion in he model as he manufacuring rm speci c shock! M (i). The shock has a mean 1, so i has no e ec on aggregae loans losses, bu he shock inroduces heerogeneiy among banks, and hus ex-ane uncerainy and defaul risk. This ex-ane uncerainy ensures ha he condiions of he 5 Like he banks, many of which are now bankrup or were acquired by healhier rivals, who were overexposed o he subprime secor of he morgage marke during he recen crisis. 16

17 Modigliani-Miller heorem are no sais ed and he bank nancial condiions are imporan. In equilibrium, he zero pro condiion among perfecly compeiive banks implies ha banks demand an expeced reurn of 1+r b o loans made o he manufacuring secor. Thus E 1 + r M 1 M = 1 + r b. In he nex secion, he household s savings decision is used o deermine F. Afer he realizaion of he shock! F (j), bank j will declare bankrupcy if he value of is liabiliies exceeds he value of is asses: 1! F (j) M B M (j) + 1 F B ib (j) < b s (j) + b ib (j) (16) The variables B M (j), B ib (j), b s (j), and b ib (j) are deermined before he realizaion of he bank speci c shock! F (j), and are herefore equal across all j. Therefore he value of! F (j) for he bank on he margin beween bankrupcy and coninuing operaions is:! F = BM + 1 F B ib b s b ib M B M (17) Thus if! F (j)! F hen bank j will coninue operaions, and if! F (j) >! F hen i will declare bankrupcy. This expression for! F shows how cross-border credi marke inegraion, represened by a large = bib b s +bib, can lead o he cross-border spread of nancial crises. A crisis in he foreign nancial secor would lead o a large F. If he wo counries have well inegraed credi markes, hen B ib is a large porion of he domesic banks asses. Therefore he large number of foreign bankrupcies causes a fall in! F, which means ha he bankrupcy hreshold among domesic banks is lower, leading o more bankrupcies in he domesic nancial secor. The bank s cos of capial, r b, is deermined from home and foreign household savings decisions. The bank s liabiliies are considered unsecured, jus as he Libor measures he rae on unsecured lending in he inerbank marke. Thus if he bank does no defaul on heir 17

18 debs, heir crediors receive a gross reurn of 1 + r b. If he bank does defaul on heir debs, crediors receive nohing. The zero pro condiion among risk neural crediors implies: 1 + r f = Z! F 1 + r b dg! F (18) where r f is he risk free rae. From (18) we can solve for he bank s cos of capial, r b : 1 + r b = 1 + rf G (! F ) (19) where G! F is he percen of domesic banks ha do no declare bankrupcy. Jus as wih he ineres rae charged o manufacuring rms in equaion (11), his ineres rae, r b, is decreasing in G! F and hus decreasing in! F.! F is decreasing in he bank s deb-asse raio, so r b is increasing in he bank s level of indebedness. 6 The expression for he bank s cos of capial in (19) explains how uncerainy in he early days of he subprime crisis in Augus 27 lead o a dramaic rise in inerbank lending raes. In his model, he bank s cos of capial, r, b is essenially he Libor. Therefore he spread beween he Libor and he risk free rae is decreasing in G! F. G () is he c.d.f. of he log-normal disribuion, so for a given! F i is sricly decreasing in he variance of he idiosyncraic bank shocks! F (j). The variance of hese shocks represens nancial secor uncerainy. When he variance, 2 F, is low or zero, here is lile or no ex-ane uncerainy abou he healh of a bank s asses, so lenders do no demand a high premium over he risk free rae. When 2 F is large and banks are ex-ane uncerain abou each oher s nancial posiion, G! F risk premium in he inerbank marke increases. decreases and he 6 In addiion o inerbank lending, household savings are bank liabiliies. By assuming ha lending o he bank is unsecured, he model absracs from he role of deposi insurance. In his model wih risk neural crediors, where he proceeds from bank pro s or insolven bank liquidaion are reurned lump-sum o he household, deposi insurance would no have a quaniaive impac. If any of hese condiions were no rue, here could be a role for deposi insurance in he model. 18

19 Afer he realizaion of he shock, banks ha coninue operaions reurn he period s cash ow as dividends o shareholders, while rms ha go bankrup pay no dividends: 8 >< d F (j) = >: 1!F (j) M 1 + r b b s + b ib 1 + r M B M + 1 F 1 + r b B ib B M +1 + B ib +1 b s +1 b ib +1 1 C A if! F (j)! F if! F (j) >! F (2) The average dividend paid by domesic banks is d F = R 1= M d F (!) dg (!). 4.3 Households Households supply labor o domesic rms, own shares in domesic and foreign rms, and earn ineres income from savings wih domesic banks. The household maximizes discouned fuure uiliy, 1X U = (C ) 1 (1 N ) (21) =1 subjec o he household s budge consrain: C + B s F! M E M + 1 G! F E F = (22) w N + d M + d F + M + F + b B s +1 B s r b 1 F B s where N is he oal labor supplied o domesic rms, and B s +1 is a sock of non-coningen bonds wih he domesic nancial secor purchased in period ha pay o in period E M and E F are he book values of he equiy in he domesic manufacuring and nancial 7 Since he sock of bonds is an asse o he household, i is wrien wih a capial B s. In equilibrium, he sock of savings ha is an asse o he household is equal o he oal sock of savings ha is a liabiliy o banks in he domesic nancial secor, B s = R 1 bs (j) dj. 19

20 secors. Since 1 F! M percen of manufacuring rms and 1 G! F percen of banks declare bankrupcy, he equiy in hose rms is los and mus be replenished. M and F are losses o bankrupcy and liquidaion in he manufacuring secors ha is reurned lump-sum o he household. b represens a small quadraic ransacions cos o holding bonds. Finally, F is he percen of he household s savings wih domesic banks ha is los o bankrupcy and liquidaion coss, so of he B s in savings wih domesic banks, only 1 F B s of he principle is reurned. This principle earns a gross ineres rae of 1 + r. b In equilibrium, risk neural households demand an expeced reurn of 1+r f o heir savings. Thus E 1 + r b 1 F = 1 + r f. 4.4 Model Parameerizaion and Soluion The dynamics of he model are deermined from a rs order approximaion abou he seady sae. The seady sae of he model is deermined by he parameer values lised in able 3. Deviaions from his seady sae are driven by exogenous TFP shocks. The process describing he evoluion of hese exogenous produciviy shocks appears a he end of his secion. The rs seven parameers in able 3, he exponens in he household s uiliy funcion, he impor demand elasiciy, he discoun facor, capial s share of income, he impor share, he capial depreciaion rae, and he household s quadraic ransacion cos o holding bonds are all se o values commonly found in he lieraure. The parameer measures he percen of a bank s liabiliies are loans from foreign banks on he inerbank lending marke. This parameer is calibraed such ha in he seady sae, he raio of a counry s cross-border credi marke holdings o GDP is one. This is similar o he raio repored in Lane and Milesi-Ferrii (27). The nex wo parameers relae o he idiosyncraic manufacuring rm speci c risks, M, and he cos of bankrupcy in he manufacuring secor,. These parameers are chosen such ha in he seady sae of he model he defaul rae of manufacuring loans is 2

21 1% per quarer, manufacuring rms have a seady-sae deb-asse raio of :5, and in he seady sae, he annualized spread beween he beween bank raes and he rae paid by manufacuring rms (r M r b ) is 316 basis poins. This is he average spread beween he rae on Baa corporae bonds and he Libor beween 1984 and 27. The nal parameer, he cross bank heerogeneiy in regards o loan losses, F, is calibraed such ha in he seady sae deb-asse raio for banks is :9 and in he seady sae here is a 53 basis poin annualized spread beween he risk free rae and inerbank raes (r b r f ). This is he spread beween he 3-monh Libor and he 3-monh T-bill beween 1984 and 27. Like many real business cycle models, business cycles in he model are driven by shocks o oal facor produciviy (TFP). To esimae he process ha deermines he evoluion of counry speci c TFP shocks, we rs esimae Solow residuals in he U.S. and he U.K. using quarerly GDP, employmen, and invesmen daa from he rs quarer of 1984 o he second quarer of Afer nding he U.S. and U.K. Solow residuals, he process ha deermines he evoluion of counry speci c TFP shocks is and is described by he following VAR(1) process: 2 6 where = "US " UK ^A US +1 ^A UK = 4 "US " UK :756 :11 :14 :834 = ^A US ^A UK 1:68 :5 :5 1: "US " UK To ensure symmery, his VAR esimaion is averaged o describe he evoluion of he home and foreign TFP shocks ha drive business cycle ucuaions in he model. 8 The evoluion of he capial sock is inferred from he evoluion of gross invesmen by assuming a quarerly depreciaion rae of :25. The Solow residual is inferred from he GDP, employmen, and capial sock daa assuming a capial share of :

22 2 6 4 ^A +1 ^A = 4 :8 :8 :8 : ^A ^A " " where var(" ) =var(" ) = 1:7 1 5 and corr(" ; " ) = :3. 5 Resuls To show how increased nancial secor uncerainy can a ec he business cycle, we sar wih impulse response diagrams o show how GDP and he componens of GDP reac o a shock o oal facor produciviy (TFP). We examine hese responses under di eren levels of nancial uncerainy o show how acue nancial sress can a ec he propagaion of real shocks. The model is hen used o show he e ec of higher nancial uncerainy on he second momens of he business cycle. Speci cally we use he model o show he e ec of higher nancial secor uncerainy on he volailiy and co-movemen of GDP and is componens. We show how he behavior of he business cycle since 27 can largely be explained by his model during imes of increased nancial uncerainy. Furhermore, we show ha he impac of higher nancial secor uncerainy is parly due o he working capial channel in he model, which means ha an increase in a bank s cos of capial is passed hrough o shor erm working capial loan raes. We also show ha he propagaion mechanism eviden during imes of high nancial secor risk arises largely because of he high leverage raios in he nancial secor which magnify he feedback loop associaed wih he nancial acceleraor. 22

23 5.1 Impulse responses during imes of increased nancial uncerainy In his secion we calculae he response of GDP and is componens o a shock o TFP, and show how his response depends on he level of nancial secor uncerainy in he economy. For his we consider muliple levels of uncerainy in boh he manufacuring and nancial secors. Recall ha M is he sandard deviaion of he idiosyncraic rm speci c shocks in he manufacuring secor and F is he sandard deviaion of he idiosyncraic bank speci c shocks in he nancial secor. Thus M governs he risk premium on loans o rms in he manufacuring secor and F governs he risk premium on inerbank loans. In his and he nex secion where we examine he e ec of uncerainy on business cycle momens, we consider ve di eren cases, relaed o combinaions of M and F. 1. M = and F =. In his case here is no rm level risk in eiher he manufacuring or nancial secors. In his case, he model is a version of an inernaional real business cycle model (IRBC). 2. M = M and F =. Thus here is rm level risk in he manufacuring secor, bu here is no risk in he nancial secor. This is he classic case from he nancial acceleraor lieraure and he resuls are qualiaively comparable o Carlsrom and Fuers (1997). In boh he rs and second cases, here is no bank level risk in he nancial secor. In hese cases, he nancial secor in he model is nohing more han a bookkeeping enry. 3. M = M and F = F from able 3. As discussed in secion 4, he values of M and F are chosen such ha in he seady sae he spread beween he rae on manufacuring loans and he inerbank rae is 316 basis poins (annualized) and he spread beween he inerbank rae and he risk free rae is 53 basis poins. 23

24 4. M = M and F =1:1 F. Thus he fourh case represens a period of acue nancial sress. A 1% increase in F represens a 1% increase in nancial secor uncerainy. In he model his resuls in an average spread beween inerbank raes and he risk free rae of 163 basis poins. This is he average spread beween he 3-monh Libor and he 3-monh T-bill beween he hird quarer of 27 and he second quarer of M =1:1 M and F =. This case is mean o answer he quesion of wha if insead of hinking abou nancial secor risk, we jus increase he risk in he manufacuring secor, bu oherwise keep he same nancial acceleraor model. The response of home and foreign GDP and invesmen o a negaive home TFP shock under cases 1, 2, and 3 are found in gure 2. The gure shows ha risk in he nancial secor has almos no e ec on he response of boh GDP and invesmen, for he response under he model wih jus manufacuring risk is nearly indisinguishable from he response from he simple IRBC case. Adding nancial secor risk has a sligh a ec and makes GDP deviaions a lile more persisen, bu he e ec is small. Figure 3 shows hese same impulse responses under heighened levels of manufacuring and nancial secor risk. The impulse responses under he benchmark level of risk are included as well. These impulse responses show ha heighened manufacuring secor risk has only a small e ec on home and foreign GDP and invesmen, however heighened nancial secor risk has a large e ec and makes he iniial drop in GDP and invesmen more severe, here is greaer inernaional ransmission of he shock, and he response is 9 To highligh he role of nancial secor uncerainy as a ransmission mechanism for shocks o TFP, F, is simply a parameer. Cases hree and four are mean o highligh he role of acue levels of uncerainy in he nancial secor, so he model is simply simulaed under wo di eren parameerizaions. Gilchris e al. (29) and Bordo and Haubrich (21) empirically documen he role of shocks in he inermediaion process iself. Wihin he framework of a nancial acceleraor model, a number of recen papers, like Chrisiano e al. (28), Nolan and Thoenissen (29) and Jermann and Quadrini (29), have made he parameer governing risk in a nancial acceleraor model iself a sochasic process. In his model, credi marke shocks would be represened by sochasic ucuaions in F. This is beyond he scope of his paper bu is an ineresing direcion for furher research. 24

25 much more persisen. Wihou he heighened nancial secor risk, home and foreign GDP and invesmen have nearly reurned o heir seady sae levels afer 4 quarers, bu wih heighened nancial secor risk, home and foreign GDP is sill signi canly below seady sae levels even afer 4 quarers. The reason behind his increased inernaional ransmission and persisence can be found by examining he e ec on risk premiums in gures 4 and 5. Speci cally, he gures show he response of he spread beween home and foreign inerbank raes and he risk free rae, and he spread beween home and foreign manufacuring raes and inerbank raes. In gure 4, hese responses are ploed for he case of no bankrupcy risk in eiher he manufacuring of nancial secors (IRBC), he case of bankrupcy risk in he manufacuring secor, and bankrupcy risk in he manufacuring and nancial secors. Firs, he gure shows ha he risk premiums are consan and zero in he classic IRBC case. Furhermore, he spread beween inerbank raes and he risk free rae is consan and zero when here is bankrupcy risk only in he manufacuring secor. The gure shows ha risk premiums increase in response o he negaive home TFP shock, alhough he earlier impulse responses of GDP and invesmen show ha under normal levels of risk in he nancial secor, bankrupcy risk fails o ac as a mechanism for he propagaion of TFP shocks. However, gure 5 shows ha under heighened level of nancial secor risk, he responses of hese risk premiums become much greaer and much more persisen. This explains why he responses of GDP and invesmen is much greaer and more persisen under heighened levels of nancial secor risk. 5.2 Financial uncerainy and business cycle volailiy and comovemen The impulse responses presened in he las secion seem o sugges ha greaer nancial uncerainy should lead o greaer business cycle volailiy and greaer inernaional cyclical 25

26 co-movemen. In his secion he model presened in secion 4 is simulaed under di eren values of M and F, he wo parameers ha represen rm level uncerainy, and herefore exernal nance premiums in he manufacuring and nancial secors. The resuls from he benchmark parameerizaion of he model are presened in able 4. The able presens he average or seady sae values of he wo key ineres rae spreads in he model, he sandard deviaion of GDP and he wo ineres rae spreads, he relaive volailiy of cerain macro aggregaes, he correlaion beween hose aggregaes and GDP, and cross-counry correlaions. In he rs wo columns, he momens are calculaed from U.S. daa, and he las ve columns conain he heoreical momens implied by he model. 1 The rs column presens momens calculaed from U.S. daa from he rs quarer of 1984 o he second quarer of 27. In he second column, hese same momens are calculaed wih daa from he hird quarer of 27 o he second quarer of 29, he ime of he curren nancial crisis and recession. Admiedly, he daa in he second column is calculaed from a small sample, bu i is clear ha he nancial crisis has lead o a dramaic increase in he level and volailiy of ineres rae spreads, a nearly 15% increase in GDP volailiy, a similar increase in he volailiy of he oher componens of GDP, and higher co-movemen across he board, wheher i be co-movemen beween a variable and GDP or cross-counry co-movemen. The hird column presens he resuls from he model when M = and F =. This "urns-o " he nancial acceleraor mechanism in he model, and risk spreads drop o zero. When hese wo variances are se o zero, he model is a version of he benchmark inernaional real business cycle model. In he fourh column, he sandard deviaion of he idiosyncraic bank shocks is se o zero, bu he sandard deviaion of shocks in he manufacuring secor is se o is benchmark level, M, in able 3. This implies ha here is no spread beween he inerbank rae and he 1 The daa in he rs wo columns is calculaed from U.S. daa and he cross-counry correlaions and calculaed beween he U.S. and he EU

27 risk free rae, bu here is a spread beween he rae a which manufacuring rms borrow and he inerbank rae. Now he model becomes an inernaional version of he nancial acceleraor model in Carlsrom and Fuers (1997). There is a nancial secor, bu wihou nancial secor risk he nancial secor is nohing more han a bookkeeping enry in his model wihou nominal rigidiies. Comparing columns hree and four shows ha adding a nancial acceleraor and manufacuring secor risk in his real model has lile e ec on he business cycle. The one place where he manufacuring secor risk seems o have an e ec is in invesmen volailiy. Risk in he manufacuring secor and hus a posiive and volaile risk premium, a ecs rms borrowing coss and hus a ecs heir invesmen decision, bu i has lile direc e ec on he res of he economy. In he fh column M = M and F = F. The idiosyncraic defaul risk in boh he manufacuring and nancial secors is calibraed o mach he Baa-Libor spread and he Libor-Tbill spread over he period from he rs quarer of 1984 o he second quarer of 27. A comparison of he fourh and fh column shows ha inroducing a small amoun of nancial secor risk ino he model has some e ec on business cycle volailiy and comovemen, bu no much. The able shows ha GDP volailiy is abou 1% higher when nancial secor risk is aken ino accoun, and here is lile change in business cycle comovemen, eiher he co-movemen of a variable wih GDP or cross-counry co-movemen. The only major di erence is now he spread beween he inerbank rae and he risk free rae is non-zero and very counercyclical. In he sixh column, he variance of he bank speci c shock, F, is higher by 1%. This implies ha here is greaer uncerainy, and hus greaer risk, in he nancial secor. The spread beween he inerbank rae and he risk free rae increases afer he increase in nancial secor uncerainy. Comparing he rs row in columns wo and six shows ha his 1% increase in uncerainy is su cien o mach he increase in he TED spread ha occurred during he recen crisis. 27

28 Comparing columns ve and six shows ha he model predics a 7% increase in GDP volailiy following a 1% increase in nancial secor uncerainy. Thus he model is able o replicae nearly half of he increase in GDP volailiy observed in he recen crisis. The model can replicae he fac ha in he recen crisis, mos macro aggregaes have become more procyclical. The model also is able o replicae he fac ha ineres rae spreads, boh he Baa-Libor spread and he Libor-Tbill spread, become more counercyclical during imes of high nancial uncerainy. Comparing cross-counry correlaions shows ha he model is able o replicae he increase in cross-counry business cycle co-movemen during he recen crisis. Moving from a sae wih low nancial secor uncerainy o one wih high nancial secor uncerainy resuls in a 25 percenage poin increase in cross-counry GDP co-movemen. To show ha he business cycle e ecs of an increase in nancial secor uncerainy are acually due o increased uncerainy in he nancial secor and no jus an overall increase in risk, in column seven uncerainy in he nancial secor, F, is se o zero, bu uncerainy in he manufacuring secor is 1% higher han is benchmark level. Thus in column seven, he model is he usual model of he nancial acceleraor, bu wih higher han normal risk. Wihou idiosyncraic defaul risk in he nancial secor, he nancial secor acs as a bookkeeping enry in his real business cycle model. The higher uncerainy in he manufacuring secor leads o a 15 basis poin increase in he risk premium for loans o he manufacuring secor. However, comparing he resuls in column four o hose in column seven shows ha GDP volailiy barely increases following an increase in defaul risk in he usual nancial acceleraor model wih exible prices. The only clear e ec of he higher uncerainy is he higher invesmen volailiy The e ec of he working capial channel In able 5 he same resuls are calculaed, bu wihou a working capial channel in he model. Thus rms are no required o pay employees ahead of ime, r wc =. When 28