International Transmission of Financial Shocks * Sami Alpanda a, Uluc Aysun b

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1 Inernaonal Transmsson of Fnancal Shocks Sam Alpanda a, Uluc Aysun a Bank of Canada, Oawa, Onaro, Canada Unversy of Cenral Florda,Orlando, FL386 Augus, Asrac Ths paper nvesgaes he ransmsson mechansm of fnancal shocks across large economes. To quanfy hese effecs, we consruc a wo-counry open economy DSGE model wh nomnal and real rgdes. We model he fnancal sde of he economes usng he fnancal acceleraor mechansm of Bernanke e al. (999). We esmae he model usng US and Euro area daa and Bayesan mehods. We fnd ha he aselne model does no generae a large Euro area oupu response o U.S. moneary, cred supply and ne worh shocks. Allowng for cross-regonal correlaon n ne worh, reurns-o-capal and neres rae shocks mproves he model s aly o replcae he spll-over effecs of U.S. fnancal shocks. In he second half of he paper, we exend he aselne model y ncorporang he lendng channel of moneary ransmsson and generae an endogenous, cross-regonal correlaon of cos of capal. Smulaons ndcae ha U.S. shocks have a much larger mpac on Euro area oupu compared o he effec predced y he aselne model. JEL Classfcaons: E3, E44, E5. Keywords: DSGE, fnancal acceleraor, nernaonal usness cycles We hank he parcpans of he Mdwes Macroeconomcs Meengs for helpful commens and dscussons.

2 . Inroducon The recen fnancal crss ha orgnaed n he U.S. has clearly demonsraed ha frcons caused y asymmerc nformaon n fnancal markes can have a sgnfcan mpac on spendng decsons and he level of economc acvy even n maure markes. One oher characersc of he curren crss was ha he conraconary effecs of he fnancal shock were no confned o he U.S., and counres wh exposure o U.S. asse markes were negavely and sgnfcanly affeced. Alhough he declne n economc acvy n he U.S. was a facor n he cross-counry spll-over effecs hrough rade, he mmedae response of foregn economes were promped y her exposure o U.S. asse markes. Furhermore, here s evdence (Fgures and ) ha he correlaon eween U.S. and Euro area oupu, coss of capal and sock prce ndces are que hgh; any realsc large open economy model would e expeced o replcae and accoun for hese hgh levels of correlaons. The amplfcaon mechansm ha fnancal frcons have generaed durng he curren crss s no a novel sujec n macroeconomcs. There s a long-sandng leraure (c.f. Bernanke, Gerler and Glchrs, 999; Carlsrom and Fuers, 997) ha provdes ample evdence and a useful framework o sudy hese effecs. In conras, he role ha hese frcons play n nernaonal usness cycles has een pu under scruny y a fewer numer of sudes. The analyss n hs paper conrues o he leraure y quanfyng he spllover effecs of fnancal shocks and sudyng her sgnfcance for nernaonal usness cycles. To do so, we uld a wo counry open economy DSGE model ha s characerzed y he fnancal acceleraor mechansm of Bernanke, Gerler and Glchrs (999). In hs framework, fnancal frcons generae he amplfcaon mechansm menoned aove y allowng macroeconomc shocks o affec orrowng coss and cred spreads pro-cyclcally. We esmae hs model usng a Bayesan

3 mehodology and U.S. and Euro area daa. In our smulaons we denfy he conruon of he fnancal acceleraor mechansm y measurng he mpulse responses n an economy wh hgh and low levels of fnancal frcons. We hen allow some fnancal varales o e correlaed across counres and measure he mplcaons for he spll over effecs. Our smulaon resuls from he aselne model show ha he spllover effecs from U.S. shocks on he Euro Area macroeconomc varales are small. Specfcally, we measure he response of Euro area real varales such as oupu and nvesmen o U.S. moneary polcy, cred supply and ne worh shocks and fnd small spllover effecs. Ths resul s more or less he same for economes wh hgh and low degrees of fnancal frcons. The cenral resul n hs paper s ha he model s only ale o generae hgher cross-correlaons n oupu and fnancal varales when fnancal shocks (shocks o ne worh, neres raes and cos of capal) are allowed o e correlaed across he wo regons. When we esmae hese correlaons, usness cycle properes of he model are also more smlar o hose oserved n he daa, and hsorcal decomposons llusrae ha U.S. shocks, fnancal and real, explan a larger share of Euro area oupu volaly. In he second half of he paper, we exend he aselne model o nvesgae one reason why fnancal shocks could e correlaed across regons. Usng hs model, we generae an endogenous correlaon eween fnancal shocks and compare he resuls wh hose oaned from he model wh ad-hoc, esmaed correlaons. In dong so, we focus on he shocks o cos of capal (or cred spreads) and more rgorously model he supply sde of capal y allowng for ankng acvy o e gloal and resrcng anks o pay a premum n rasng loanale funds over he rsk free rae. Ths premum s caused y an dosyncrac ne worh shock ha anks face and, smlar o he premum pad y he enrepreneur n he fnancal acceleraor framework,

4 s an ncreasng funcon of anks fnancal leverage. The opmaly condons from hs model ndcae ha anks no only consder he orrowers leverage u also her own leverage when choosng lendng raes. Therefore, f here s an ncrease (decrease) n he demand for loans n one regon hs ncreases (decreases) he rsk premum n oh regons snce anks leverage s now hgher (lower). Shocks o anks ne worh have a smlar, symmerc effec on rsk premums n oh regons. The mpulse responses oaned from hs demonsrae a large response of Euro area oupu o U.S. shocks and model oupu correlaon across regons s more conssen wh he daa compared o he aselne model. The res of he paper s organzed as follows: Secon presens he model. Secon 3 descres he daa and he Bayesan esmaon sraegy. Secon 4 dscusses he resuls. Secon 5 descres he model wh cross-regonal ankng and presens he resuls. Secon 6 concludes.. The model. General Overvew The model s a wo-counry open economy verson of he sandard New Keynesan DSGE model (Smes and Wouers, 7, and Chrsano e al, 5) appended wh a fnancal acceleraor mechansm (Bernanke e al., 999, Gerler e al., 7, and Glchrs e al., 9). Monopolscally compeve real frms are prce-seers n he goods marke, and households are wage-seers n he laor marke. Nomnal rgdes are nroduced hrough saggered prce and wage-seng as n Calvo (983) and hrough ndexaon of prces and wages o pas nflaon. The model feaures nermedares n each counry whch mpor consumpon and nvesmen goods from aroad and sell hem domescally n he local currency; saggered prce-seng for hese nermedares resul n ncomplee exchange rae pass-hrough (Gerler e al., 7). Each counry also has fnancal nermedares whch accep deposs from households and lend o 3

5 domesc enrepreneurs n order o fnance her nvesmen. They charge a rsk-premum on her lendng ased on he ne worh of he enrepreneurs; hs resuls n a fnancal acceleraor mechansm (Bernanke e al., 999). In wha follows, we refly descre he equaons ha characerze he equlrum of he model afer all varales are log-lnearzed around her seady-sae. Furher deals of he mcrofoundaons of he model can e found n Smes and Wouers (7), Gerler e al. (7), Glchrs e al. (9), Bernanke e al. (999) and Alpanda (9).. Log-lnearzed Equlrum Condons Consumpon demand s characerzed y a parally forward-lookng IS curve whch s oaned from he frs-order-condon of he households' maxmzaon prolem wh respec o consumpon and he Euler condon: / / c c Ec l El r E / / / c,, () where ndexes me, c s consumpon, l s laor, r s he nomnal neres rae se y he cenral ank, and s he nflaon rae. s he (exernal) ha parameer n he household uly funcon, s he seady-sae per-capa growh rae of he economy, s he nverse of he neremporal elascy of susuon, and s a level parameer n he households uly funcon whch, whou loss of generaly, wll e calraed o ensure he seady-sae value of laor s equal o. c, s a consumpon demand shock whch follows an AR() process characerzed y c, c c, c, where c s he perssence parameer, and c, s he shock 4

6 nnovaon whch s dsrued..d. normal wh mean and sandard devaon c. The IS curve saes ha curren consumpon s nversely relaed o he ex-ane real neres rae, posvely relaed o demand shocks, and s nfluenced y pas and expeced fuure consumpon and laor servces. Consumpon s a compose of he home-produced consumpon good, c h,, and mpored consumpon good, c f,, as c h, c f, c c c, () where c s he share of domesc goods n he consumpon aggregaor funcon. In equlrum, he consumpon of domesc and foregn goods are relaed o each oher as c c s, (3) h, f, c where c s he nraemporal elascy of susuon eween home and foregn goods n he consumpon aggregaor, and s pf, ph, s he erms-of-rade where p f, and p h, are he domesc prces assocaed wh he foregn-produced and home-produced goods respecvely. gven y Invesmen demand s derved from he frs-order condons of capal-producers and s ~ (4) ~ ~ E ~ q, where s nvesmen, q s he real prce of capal relave o he consumpon good, and, s a shock o nvesmen-specfc echnologcal change shock whch follows an AR() process. ~ s For revy, we om he equaons for he res of he shocks ha follow AR() processes. We wll use for he perssence parameers, and for he sandard devaon of he nnovaons of hese shocks wh approprae suscrps. 5

7 he adjused me-dscoun facor, and s equal o where s he smple me-dscoun facor of households, and s he populaon growh rae. s an nvesmen adjusmen cos parameer, and regulaes he elascy of nvesmen demand wh respec o he prce of capal. Smlar o he consumpon good, he nvesmen good s also a compose of domescally-produced nvesmen goods, h,, and mpored consumpon goods,, h, f,, (4) f, as where s he share of domesc goods n he nvesmen aggregaor funcon. In equlrum, he nvesmen of domesc and foregn goods are relaed o each oher as s, (5) h, f, where s he nraemporal elascy of susuon eween home and foregn goods n he nvesmen aggregaor. Domesc oupu s characerzed y he followng producon funcon: y p a, z k l, (6) where y s oupu, a, s a producvy shock followng an AR() process, z s he ulzaon rae of capal, and k s he capal sock. The parameer regulaes he share of capal servces n producon, and p s he gross mark-up of home-good prces over margnal cos a he seady-sae, whch also equals one plus he seady-sae share of fxed coss n producon. In equlrum, he margnal produc of capal, and real wages, w, as mpk, s relaed o he capal-laor rao 6

8 mpk z k l w, (7) and capal ulzaon s relaed o he margnal produc of capal as z mpk, (8) where s an elascy parameer. The law of moon of capal s gven y k k, ~, () where s he deprecaon rae of capal. The reurn on capal, alernavely he realzed orrowng cos, r k,, s defned over capal gans and margnal produc of capal: r k, ~ q ~ mpk q. () The requred reurn demanded y fnancal nermedares nclude an exernal fnance premum whch depends nversely on he ne worh of enrepreneurs, n : k, k, Er re q k n, (9) where s he elascy of he rsk-premum wh respec o leverage, and k, s an exogenous rsk-premum shock followng an AR() process. The ne worh of enrepreneurs evolve accordng o K n ene rk, rk, E rk, n,, () N where e s he survval proaly of enrepreneurs, K/N s her seady-sae capal o neworh rao, and n, s an AR() shock o ne worh. 7

9 The home-goods producers prolem yelds a parally forward-lookng New Keynesan Phllps curve for home-goods prce nflaon: ~ ~ h h 3.5 h h, ~ h, ~ h, ~ h h h h a, z k l w h,, (4) where h, ph, ph, s he nflaon rae assocaed wh home-good prces, and h, s a cospush shock whch follows an ARMA(,) process gven y h, h h, h, h h,. The parameer h deermnes he degree o whch prces are ndexed o pas domesc prce nflaon, and h s he proaly ha frms canno adjus her prces n any gven perod. The aove Phllps curve es curren home-good nflaon rae o pas and expeced fuure nflaon as well as he margnal cos (.e. he dfference eween he real wage and he margnal produc of laor) of frms. Smlarly, foregn-goods prce nflaon s descred y a forward-lookng Phllps curve: ~ f f f 3.5 ~, () f f, ~ f, ~ f, ~, f f f f where f, pf, pf, s he nflaon rae assocaed wh foregn-good prces, and f, s a cos-push shock whch follows an ARMA(,) process gven y f, f f, f, f f,. The parameer f deermnes he degree o whch prces are ndexed o pas foregn-good prce nflaon, and f s he proaly ha mporer nermedary frms canno adjus her prces n any gven perod. gven y p f, e ph, s he devaon of mpored-good prces from he law-of-one-prce and s, where e s he nomnal exchange rae (n uns of home-currency per The 3.5 erm n he denomnaor comes from he Kmall aggregaor funcon used y fnal goods producers a he calraed values n Smes and Wouers (7). 8

10 un of foregn currency) and p s he home-goods prce of he foregn counry (.e. he prce a h, whch he mporer nermedares n he home counry mpor he foregn good). 3 Overall consumer prce nflaon n he home counry s gven y ( ). () c h, c f, The relaonshp eween nomnal wage nflaon, w,, consumer prce nflaon and real wages can e expressed as w w. (3) w, Saggered wage-seng y households yelds he followng wage nflaon Phllps curve: w, w ~ E w, w ~ w 6 w w w ll c / c w,, (8) where w, s a cos-push shock followng an ARMA(,) process w, w w, w, w w,. f s he parameer deermnng he degree of nflaon ndexaon of nomnal wage nflaon, s he nverse of he elascy of laor supply, and w s he proaly ha households canno adjus her wages n any gven perod. The wage Phllps curve es curren wage nflaon o he dfference eween real wages and he margnal rae of susuon eween consumpon and lesure, as well as pas and presen prce nflaon, and expeced fuure wages. l Moneary polcy s conduced va a Taylor rule for he nomnal neres rae: y y r, r r ( )[ r r y r y y ], (4) 3 As a convenon, we wll desgnae he foregn economy varales and parameers wh he same names as her counerpars n he home counry, u wh an asersk () superscrp. 9

11 where s he neres-rae smoohng parameer, r, r y and r y are he long-run response coeffcens of he cenral ank o nflaon, oupu, and oupu growh respecvely, and r, s an exogenous AR() process capurng shocks o moneary polcy. The uncovered neres pary (UIP) condon s gven y Ed r r, (5) d, where d e e s he nomnal deprecaon rae of home currency, r s he nomnal neres rae se y he cenral ank of he foregn counry, and d, s an exogenous shock followng an AR() process and capures currency deprecaon and counry rsk. The real exchange rae s defned as rer e p p, whch afer frs-dfferencng can e wren as rer rer d. Frs-dfferencng he devaons from he law of one prce for he mpored goods yelds f, h, d. (6) Smlarly, frs-dfferencng he erms-of-rade yelds s s. (7) f, h, The feasly condon for he domesc economy s gven y y C c ch, I h, G g, c C c f, I f,, (8) Y Y Y Y Y

12 where c f, and f, are expors from he home counry o he foregn counry, and g, s governmen expendure whch s gven y an AR() process. 4 For each of he equlrum condons ()-(3), excep for he UIP condon (), here s a correspondng equaon for he foregn economy where he foregn varales and parameers are now desgnaed wh an asersk. The UIP condon (), as well as he currency deprecaon varale, d, and currency deprecaon rsk shock, d,, are common o oh counres. Also noe ha snce we defned he exchange rae n uns of home currency per foregn currency, he foregn equvalen of equaon () reads: d. (9) f, h, 3. Daa and esmaon 3. Daa and Esmaon We follow Smes and Wouers (7), and esmae he model parameers usng Bayesan lkelhood mehods. 5 The model ncludes shocks n oal; here s a currency deprecaon rsk shock whch s common o oh counres, and each counry has 3 demand shocks (consumpon, nvesmen and governmen expendure), producvy shock, moneary shock, 3 cos-push shocks (home-goods prce, mpored-goods prce and wage), and fnancal shocks (exernal fnance premum shock and ne worh shock). 4 Noe ha model conssen gross domesc produc (GDP) ncludes he mark-up of mporer nermedares over mpor prces as well as he value of domesc oupu. Snce hs mark-up does no conrue sgnfcanly o he varaon n GDP, we rea domesc oupu as GDP n wha follows. Also noe ha echncally, he feasly condon of he model should also nclude he consumpon of enrepreneurs who do no survve he perod, real coss ncurred due o he ulzaon of capal, and coss of fnancal nermedaon. We gnore hese componens snce hey are small. 5 The use of Bayesan prors have ecome commonplace n he leraure due o he scarcy of macroeconomc daa and denfcaon\n prolems. See An and Schorfhede (7) and Fernandez-Vllaverde (9) for more on Bayesan esmaon of DSGE models. We use Dynare o esmae and smulae our model.

13 Followng Glchrs e al. (9), we shu down he nvesmen shocks n oh economes snce hese presen an denfcaon prolem for he role of fnancal shocks. Accordngly, we use 9 quarerly daa seres n our esmaon from he U.S. and he Euro zone, for he perod 995q o 9q3. The daa seres (and her model counerpars) are, he nomnal deprecaon rae of U.S. dollar agans he Euro d for he Euro zone; namely real oupu real governmen expendure prce nflaon, exernal fnance premum E r, and daa seres each for he U.S. and 8 daa seres y, y, real consumpon c, c, real nvesmen, g, g, laor hours l, l, he real wage rae w, w,, consumer, he shor-erm nomnal neres rae argeed y he cenral ank r, he k, r, and he real sock marke ndex n, n. 6 The exernal fnance premum was proxed y he spread eween corporae onds (Baa raed for he U.S.) followng Glchrs e al. (9). Smlarly, he ne worh of enrepreneurs n each counry was denfed y he value of he sock marke (S&P 5 for he U.S. and he Dow Jones Euro Soxx 5 Prce Index for he Euro zone) as n Chrsano e al. (9). All daa seres were seasonally adjused (f needed), frs-dfferenced (excep for he deprecaon rae, he nflaon rae, he nomnal neres rae, and he exernal fnance premum), and demeaned pror o esmaon. 7 Appendx A conans furher nformaon regardng he daa seres used n he esmaon. 3. Calraed Parameers Snce he daa used n he esmaon do no conan nformaon aou parameers ha deermne he frs momens of model varales, we calraed some of he level parameers pror o 6 The real wage rae and he real sock marke ndex were oaned y deflang her correspondng nomnal seres wh he consumer prce deflaor, n lne wh he nflaon seres used n he esmaon. The quarerly deprecaon rae, nflaon rae and he neres raes refer o quarerly non-annualzed raes n accordance wh he model. 7 In oher words, we specfy anoher se of varales n he model whch are conssen wh he frs-dfferenced oserved varales.

14 esmaon o ge more reasonale seady-saes (Smes and Wouers, 7, and Alpanda, 9). We se hese calraed parameers o dencal values for oh counres. The populaon growh facor,, and he per-capa growh of oupu,, are se o.5 and.5 mplyng (near) % populaon growh and % oupu growh on an annual ass. The adjused me-dscoun facor, ~, s se o.99 whch mples a (near) 4% annualzed real neres rae (.e. rsk-free rae) along he alanced growh pah of he model. 8 We se he capal share parameer n he producon funcon,, o.3 whch mples a seady-sae share of laor ncome of 7%. The deprecaon rae of capal,, s se o.5 whch mples a (near) % annual deprecaon rae. We assume ha he share of governmen expendure n oal oupu along he seady-sae, G/Y, s.. We also se he neremporal elascy of susuon,, o mplyng logarhmc uly wh respec o consumpon. The seady-sae wage mark-up, w, s se o.5 as n Smes and Wouers (7). For he seady-sae rao of he capal sock o ne worh of enrepreneurs, K/N, we follow Glchrs e al. (9), and se hs rao o.7 mplyng a de-equy rao of.7 a he seady-sae. Also followng Glchrs e al. (9), he survval proaly of enrepreneurs, e, s se o.99. Smlarly, we se he elascy of he exernal fnance premum o leverage,, o.7 ased on he pror dsruon n Glchrs e al. (9). We se he home-as parameers, c and, o.9 mplyng % mpor (and expor) o oupu rao along he seady-sae. The nraemporal elascy of susuon parameers n he 8 Noe ha we do no need o se a value for he acual me-dscoun facor,, whch s relaed o he adjused facor wh, snce does no ener any of he log-lnearzed condons y self. 3

15 consumpon and nvesmen aggregaors, c and, are se equal o and.5 respecvely followng Gerler e al. (7). 3. Pror Dsruons The pror dsruons for he parameers are lsed n Tales and for home-counry and foregn-counry parameers respecvely. We used prors smlar o Smes and Wouers (7) and Glchrs e al. (9) for he parameers ha are no relaed o he open economy feaures of he model. The ha parameer,, has a ea-dsruon pror wh a mean of.7 and a sandard devaon of.. The parameer l has a normal pror wh a mean of (reflecng a Frschelascy of laor supply of.5) and a sandard devaon of.75. The laor level parameer n he household uly funcon,, s no esmaed, u s rerced o equal he followng expresson o ensure ha laor servces, l, s equal o a he seady-sae: w / C/ Y. () The capacy ulzaon elascy parameer,, has a ea pror wh mean.5 (whch mples un elascy of ulzaon wh respec o he margnal produc of capal) and sandard devaon.. The nvesmen adjusmen-cos parameer,, has a normal pror wh mean 4 (reflecng an elascy of nvesmen wh respec o he prce of capal of aou.5) and sandard devaon.5. The Calvo parameers regulang prce and wage sckness,, and w, all have ea prors wh mean.5 (.e. an average of -quarer prce and wage sckness) and sandard devaon.. The prce and wage ndexaon parameers, h, f and w, have ea h f 4

16 prors wh a mean.5 and sandard devaon of.5. The prce mark-up a he seady-sae, p, s assumed o have a normal pror wh mean.5 and sandard devaon.. For he Taylor rule parameers, we assume ha he pror for he long-run nflaon reacon coeffcen, r, has a normal dsruon wh a mean of.5 and sandard devaon.5. Smlarly, he long-run reacon coeffcen on oupu and oupu growh, r y and r y, have normal dsruons wh mean.5 and sandard devaon.. The pror for he neres rae smoohng parameer,, has a normal dsruon wh a mean of.75 and a sandard devaon of.. The prors for he auoregressve and movng average erms n all shocks have ea dsruons wh mean.5 and sandard devaon.. The prors for he sandard devaons of all he shocks are also farly unnformave, wh nverse-gamma dsruons wh mean.5% and nfne varance. 4. Resuls Fgures, 3 and 4 dsplay he mpulse responses (along wh 95% confdence ands) from he esmaed aselne model o moneary polcy, cred supply and ne worh shocks respecvely. The domesc varales response o hese shocks have he expeced sgns and are sgnfcan n general. In response o a moneary polcy shock, oh domesc and expor demand decreases. The drop n foregn oupu makes foregn enrepreneurs more leveraged and ncreases he rsk premum. Ths fnancal response amplfes o nal, foregn rade-nduced drop n oupu. Smlar responses and he amplfcaon mechansm are oserved when here s a domesc ne worh and cred supply shock. The common aspec of hese responses are ha he mpac on foregn varales s ypcally small compared o he magnude of he domesc varale 5

17 responses. To es wheher allowng for cross-regonal correlaon eween neres rae, ne worh and cred supply shocks amplfy he effecs on foregn varales, we esmae and smulae he model wh correlaed shocks. The responses are dsplayed n Fgure 5 and sugges ha allowng for correlaon, despe havng a smaller mpac on domesc varales, sgnfcanly amplfes he mpulse responses of he foregn economy varales. For example, he maxmum response of foregn oupu o a one sandard devaon domesc ne worh shock s approxmaely mes hgher han n he aselne model. I s mporan o noe however ha he daa used n esmaon were lmed and ha a more exensve daa se may e helpful n oanng more accurae poseror values. Fnally, we es he sgnfcance of he fnancal acceleraor mechansm for he cross counry ransmsson of moneary polcy shocks n he aselne model y shung off he fnancal acceleraor mechansm (seng equal o zero). The resuls, also dsplayed n Fgure 6, sugges ha alhough responses (especally domesc varales) are smaller whou he fnancal acceleraor, he decrease n he response of foregn varales s mmaeral. 5. Cross-regonal ank lendng In hs secon we exend he aselne model o endogenously generae a cross-regonal correlaon eween cred spreads. We do so y assumng ha here s cross-regonal ank lendng and ha anks canno rase loanale funds a he rsk free rae and have o pay a premum ha depends on he anks fnancal leverage. These assumpons allow us o lnk cred spreads across regons snce oh shocks o economc acvy and shocks o he anks ne worh affec her fnance coss whch n urn mpacs cred spreads n oh regons. We egn exendng our model y assumng ha here s a connuum of dencal gloal ank holdng companes (BHCs) ha lend oh n he U.S. and n he Euro area. These BHCs 6

18 lend hrough her susdares whch offer conracs o enrepreneurs ha are defned y he wo equaons elow. a l k Fa R v Q K N a R Q K R Q K N (6) a R k Q K R v Q K N (7) where s he share of lendng y BHC and a s he dosyncrac reurns o capal shock ha enrepreneurs face. If hs shock s smaller han he cuoff value, a, defned n equaon (7) he enrepreneur defauls and he ank recovers he remanng funds of he enrepreneur afer payng ankrupcy coss (governed y he parameer, ). To compensae hese ankrupcy coss enrepreneur pays a orrowng premum of ha s an ncreasng funcon of her fnancal leverage. Ths premum allows BHCs o equae her reurns from lendng o her coss of rasng loanale funds, E R so ha k e QK R R. (8) N These equaons are smlar o hose used o derve he cos of capal condon n Secon (equaon ()) and equaon (8) s smlarly oaned y aggregang over he connuum of enrepreneurs. We devae from hs usual pracce y assumng ha he BHCs canno rase loanale funds a he rsk free rae and have o orrow from nerank markes and pay a premum of R R (where R s he average rsk free nerank marke rae). To smplfy compuaons, we assume ha he consumers n each regon pool her savngs n her local nerank marke and collec he domesc rsk free rae of reurn. These funds are hen orrowed y he BHCs o fnance her lendng n ha regon. More specfcally, le D and 7 D denoe he

19 oal savngs of consumers n he wo regons hen, D QK N and D Q K N. These assumpons allow us o derve he average rsk free nerank marke rae, R, as a weghed average of he wo rsk free raes n he wo regonal nerank markes as follows: BB BB R NB QK N QK N R QK N NB BB Q K N Q K N Q K N BB (9) R NB QK N R R BB Q K N BB R (3) where BB QK N Q K N s he oal amoun orrowed y all he BHCs and NB denoes he ne worh of all he BHCs. Here we assume ha BHCs have an equal share ( ) of he loans and he ne worh of all he BHCs, and ha he monorng echnology and hus he level of fnancal frcons s he same across he wo nerank markes. The source of fnancal frcons here s ha he BHCs experence an dosyncrac ne worh shock (lognormally dsrued across BHCs wh an expeced value of ) afer enrepreneurs pay ack her loans and he BHCs pool he revenues from her susdares. Smlarly, f hs shock s elow a ceran cuoff value, he BHC fals o pay ack s loans from he nerank marke. The nerank marke hen ncurs ankrupcy coss n recoverng a fracon of he ad loans. To compensae for he chance of defaul and he ankrupcy coss, he nerank markes charge a orrowng premum over he rsk free rae. Gven hese assumpons, he followng wo equaons defne he conrac ha he BHCs agree o: F R x BB NB R x BB R BB NB (8) 8

20 R x BB NB R x BB (9) where BB QK N Q K N s s s. Gven ha he BHCs are dencal n every aspec excep he dosyncrac shock, as n he conrac wh he enrepreneurs, every BHC s charged he same premum. Therefore, le R R x hen he BHCs orrowng coss can e derved y susung equaon (9) no equaon (8), BB R R v (3) NB BB NB where v F df NB NB NB BB BHCs evolves as follows: 9 NB BB BB BB NB. The ne worh of he NB F (3) These ankrupcy coss smlarly generae a wedge eween he rsk free rae and he BHCs cos of orrowng. The cos of capal can hen e derved as follows: R e R BB v v NB e QK N (3) In Appendx B, we derve hs equaon from he opmzaon prolem of he BHC. The key feaure of hs prolem s ha he BHC, n deermnng he lendng premum, no only consders he leverage of he orrower u also s own leverage (snce affecs s own orrowng coss). In Appendx B we also lnearze equaon (33) o produce he followng cos of capal condon: 9 BHC specfc ne worh equaons, NB NB F, are aggregaed (assumng ha he expeced value of he dosyncrac shock s equal o ) o derve equaon (3). 9

21 QK N R Q K N N N n n R r r q k n q k BB BB QK (33) Q K r k 3 One desrale feaure of he exensons n hs secon s ha hey do no confound he analyss sgnfcanly. Compared o he aselne model we only modfy he cos of capal equaon for each regon and add he evoluon of BHC ne worh. 5.. Resuls The resuls dsplayed n Fgure 6 show ha he foregn varale responses o a ass pon domesc neres rae shock n he model wh cross-regonal ankng are consderaly larger n magnude compared o he aselne model responses. These resuls ndcae ha an mporan share of he foregn spllover effecs of domesc shocks can e explaned y he correlaon of cred spreads endogenously deermned y he gloal scale of ankng acvy. Smlar conclusons are drawn when he hsorcal decomposons from he aselne model (Fgure 7) and he model wh cross-regonal ankng (Fgure 8). In he model wh cross-regonal ankng U.S. shocks explan a much large share of oupu varaon. 6. Concluson Our prelmnary resuls ndcae ha he sandard wo counry model requres correlaed fnancal shocks o accoun for he oserved hgh correlaons n real and fnancal varales n he daa, and o generae a sgnfcan spll-over of fnancal shocks from one large counry o anoher. Focusng on one reason why fnancal shocks may e correlaed, we fnd ha crossregonal ankng acvy s an mporan channel hrough whch U.S. fnancal shocks are ransmed o he Euro area. Ths model can e exended o endogenze he correlaon of ne worhs (perhaps hrough corss-equy holdng) and polcy raes o more fully undersand and quanfy how fnancal shocks are ransmed nernaonally.

22 APPENDIX A To e compleed (daa descrpon)

23 APPENDIX B. Cos of capal wh cross-regonal ank lendng In hs appendx we derve he cos of capal relaonshp when here s cross-regonal ankng y solvng he opmzaon prolem of he BHCs. As n Bernanke ee al. (999) we egn y defnng a BHC s share of revenues as, a Fa a a dfa a (B.) Gven he BHC s conrac wh he nerank marke hen s opmzaon prolem can e represened as, Max K k a R QK a BB a NB (B.) s.. k a dfa R QK R v QK N a a a hen he opmaly condons can e represened as follows: Le u a df a : ' ' u a (B.3) k BB : u R QK R v QK N NB (B.4) k v a u R R k v K : (B.5) NB where v k s he paral dervave of v wh respec o k. Le u u a hen usng hese condons we can derve he cos of capal as,

24 3 QK N u u NB v R u R k k / (B.6) Accordng o equaon (B.6), he BHC no only consders he leverage of he orrower u also how much s own orrowng coss wll ncrease f lends an addonal un of capal o he enrepreneur. Equaon (B.6) can e expressed n he followng lnearzed form, n n K Q N k q n QK N k q r BB N K Q R r BB N QK R r k 3 (B.7) where he upper case and lower case varales denoe he seady sae values, and he devaons from seady sae, respecvely and /, / K Q NB v u u K Q N u u BB R QK NB v u u QK N u u BB R k k. 3 NB v k Gven ha he nerank rae s he same when solvng for he opmal amoun of lendng n each regon, can e shown usng equaons (B.5) and (B.6) ha n k q u u QKu Nu N QKN n k q.

25 REFERENCES ALPANDA, S. (9). Idenfyng he Role of Rsk Shocks n he Busness Cycle Usng Sock Prce Daa, mmeo, Amhers College. AN, S. and SCHORFHEIDE, F. (7). Bayesan analyss of DSGE models. Economerc Revews, 6: 3:7. BERNANKE, B., GERTLER, M. and GILCHRIST, S. (999). The Fnancal Acceleraor n a Quanave Busness Cycle Framework. In Taylor, J.B. and Woodford, M., ed., Handook of Macroeconomcs. Vol. C, pp Amserdam: Elsever Scence, Norh-Holland. CHRISTIANO, L. J., M. EICHENBAUM, and EVANS, C. L. (5). Nomnal Rgdes and he Dynamc Effecs of a Shock o Moneary Polcy, Journal of Polcal Economy, 3, -45. CHRISTIANO, L. J., R. MOTTO, and M. ROSTAGNO (9). Fnancal Facors n economc Flucuaons, mmeo, Norhwesern Unversy. FERNANDEZ-VILLAVERDE, J. (9). The economercs of DSGE models, mmeo, Unversy of Pennsylvana. GERTLER, M., S. GILCHRIST, AND F. M. NATALUCCI (7). Exernal Consrans on Moneary Polcy and he Fnancal Acceleraor, Journal of Money, Cred and Bankng, 39, GILCHRIST, S., ORTIZ, A., and ZAKRAJSEK, E. (9). Cred Rsk and he Macroeconomy: Evdence from an Esmaed DSGE Model,. JUSTINIANO, A., and PRESTON, B. (8). Moneary Polcy and Uncerany n an Emprcal Small Open Economy Model. Journal of Appled Economercs, forhcomng. SCHMITT-GROHE, S., and URIBE, M. (5). Closng small open economes. Journal of Inernaonal Economcs, 6: SHAPIRO, M., and WATSON, M. (989). Sources of Busness Cycles Flucuaons. NBER Workng Paper No SMETS, F. and WOUTERS, R. (7). Shocks and frcons n US usness cycles: A Bayesan DSGE approach. Amercan Economc Revew, 97: TOVAR, C. E. (8). DSGE models and cenral anks. Bank for Inernaonal Selemens Workng Paper No

26 Tale. Esmaes of srucural parameers Poseror Means l p h f w h f w c r r y r y 3 4 Baselne low level of frcons Correlaed fnancal shocks Cross-regonal ankng Pror Denses Home Foregn Home Foregn Home Foregn Home Foregn B (.7,.) B (.7,.) N (.5,.37) N (,.75) N (.5,.) B (.5,.) N (4,.5) B (.5,.5) B (.5,.5) B (.5,.5) B (.5,.) B (.5,.) B (.5,.) G (,.) G (.5,.) N (.75,.) N (.5,.5) N (.5,.) N (.5,.) B (.7,.) B (.7,.) B (.7,.) B (.7,.) Noes: a The arevaons used for he pror dsruons are: B = ea, N = normal, G = gamma. The mean and sandard devaons of he pror denses are dsplayed n parenheses. 5

27 Tale. Esmaes of shock parameers c g a r h f w k n d Poseror Means Baselne low level of frcons Correlaed fnancal shocks Cross-regonal ankng Pror Densy a Home Foregn Home Foregn Home Foregn Home Foregn B (.5,.) B (.5,.) B (.5,.) B (.5,.) B (.5,.) B (.5,.) B (.5,.) B (.5,.) B (.5,.) B (.5,.) B (.5,.) Shock sandard devaons/correlaons c IG (.5%, nf) IG (.5%, nf) g IG (.5%, nf) a IG (.5%, nf) r IG (.5%, nf) h IG (.5%, nf) f IG (.5%, nf) w IG (.5%, nf) k IG (.5%, nf) n IG (.5%, nf) d IG (.5%, nf) corr(r, r) B (.5,.) corr(n, n) B (.5,.) corr(k, k) B (.5,.) Noes: a The arevaons used for he pror dsruons are: B = ea, IG = nverse gamma. The mean and sandard devaons of he pror denses are dsplayed n parenheses. Tale 3. Daa versus pos-esmaon smulaons wh fnancal wh fnancal wh fnancal Daa acceleraor, whou correlaon acceleraor, wh correlaon acceleraor, endogenous correlaon σ(c)/σ(y) σ()/σ(y) σ(l)/σ(y) ρ(y,c) ρ(y,) ρ(y,l) ρ(y,y) ρ(,) ρ(n,n) ρ(r,r) ρ(rk,rk)

28 Fgure : US and Euro area ond yelds and growh raes of oupu and sock marke ndces.%.5%.%.5%.% -.5% % -.5% US oupu Euro area oupu -.% -.5% S&P 5 -. Dow Jones Euro Moody's U.S. Baa quarerly ond yeld. Euro area quarerly corporae ond yeld, up o years

29 Fgure. Impulse responses o a ass pons domesc neres rae shock (aselne model).5 Oupu.5 Hours Ineres rae Rsk premum Inflaon.5 Wages Foregn oupu Foregn hours Foregn rsk premum.5 Foregn neres rae Foregn nflaon..5.4 Foregn wages

30 Fgure 3. Impulse responses o a percen cred supply shock (aselne model)....3 Oupu...3 Hours Ineres rae Rsk premum Inflaon. Wages Foregn oupu.4.6 Foregn hours Foregn rsk premum Foregn neres rae Foregn nflaon.5. Foregn wages

31 Fgure 4. Impulse responses o a percen posve ne worh shock (aselne model).8.6 Oupu.8.6 Hours Ineres rae Rsk premum Inflaon.. Wages Foregn oupu..5 Foregn hours Foregn rsk premum Foregn nflaon Foregn neres rae Foregn wages

32 Fgure 5. Shock correlaon, hgh/low fnancal frcons ( ass pon neres rae shock) Oupu Hours Ineres rae Inflaon Foregn rsk premum low frcon hgh frcon ----correlaed shocks Foregn oupu... low frcon hgh frcon correlaed shocks... low frcon hgh frcon ----correlaed shocks... low frcon hgh frcon correlaed shocks... low frcon hgh frcon correlaed shocks Foregn nflaon... low frcon hgh frcon ----correlaed shocks Rsk premum Wages Foregn hours... low frcon.4 hgh frcon correlaed shocks Foregn neres rae low frcon hgh frcon ----correlaed shocks... low frcon hgh frcon ----correlaed shocks... low frcon hgh frcon correlaed shocks... low frcon hgh frcon correlaed shocks Foregn wages... low frcon hgh frcon correlaed shocks

33 Fgure 6. Cross-regonal ankng ( ass pon neres rae shock) Oupu aselne exogenous correlaon... endogenous correlaon Ineres rae aselne exogenous correlaon... endogenous correlaon Inflaon aselne exogenous correlaon... endogenous correlaon Foregn oupu Hours aselne exogenous correlaon... endogenous correlaon Rsk premum aselne exogenous correlaon... endogenous correlaon Wages aselne exogenous correlaon... endogenous correlaon Foregn hours 4 aselne exogenous correlaon... endogenous correlaon Foregn rsk premum aselne exogenous correlaon... endogenous correlaon Foregn nflaon aselne exogenous correlaon... endogenous correlaon aselne exogenous correlaon... endogenous correlaon Foregn neres rae Foregn wages aselne exogenous correlaon... endogenous correlaon aselne exogenous correlaon... endogenous correlaon

34 Fgure 7. Hsorcal decomposon of foregn oupu whou fnancal correlaon Foregn shocks U.S. shocks Foregn oupu Fgure 8. Hsorcal Decomposon of foregn oupu wh fnancal correlaon Foregn shocks U.S. shocks Foregn oupu