Working Paper No. 479 Financial factors and the international transmission mechanism

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1 Working Paper No. 479 Financial facors and he inernaional ransmission mechanism Abigail Haddow and Mariya Mileva Augus 213 Working papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. Any views expressed are solely hose of he auhor(s) and so canno be aken o represen hose of he Bank of England or o sae Bank of England policy. This paper should herefore no be repored as represening he views of he Bank of England or members of he Moneary Policy Commiee or Financial Policy Commiee.

2 Working Paper No. 479 Financial facors and he inernaional ransmission mechanism Abigail Haddow (1) and Mariya Mileva (2) Absrac The aim of his paper is o invesigae heoreically how financial facors affec he inernaional ransmission mechanism. We build a wo-counry dynamic sochasic general equilibrium model wih sicky prices and financial fricions. To add o he lieraure we exend he model o include wo ypes of credi spread shocks ha are micro-founded; a mean preserving shock o he dispersion of firms idiosyncraic produciviy (risk shock) and a shock o financial agens ne worh (financial wealh shock). We find ha he source of he shock o he credi spread maers; credi spread shocks of equivalen size, bu driven by differen innovaions, have differen consequences for oupu and inflaion in he home and foreign economy. In general risk shocks generae more realisic spillovers o aciviy han a financial wealh shock. Key words: Inernaional ransmission mechanism, financial fricions, financial shocks, DSGE model. JEL classificaion: E37, F41, F42, F44. (1) Bank of England. abigail.haddow@bankofengland.co.uk (2) Kiel Insiue for he World Economy. mariya.mileva@ifw-kiel.de The views expressed are hose of he auhors and do no necessarily reflec hose of he Bank of England or members of he Moneary Policy Commiee or Financial Policy Commiee. We are graeful o Emilio Coregudo-Fernandez, Giancarlo Corsei, Luca Dedola, Mahias Pausian and Jumana Saleheen for useful commens. This paper was finalised on 15 July 213. The Bank of England s working paper series is exernally refereed. Informaion on he Bank s working paper series can be found a Publicaions Group, Bank of England, Threadneedle Sree, London, EC2R 8AH Telephone +44 () Fax +44 () publicaions@bankofengland.co.uk Bank of England 213 ISSN (on-line)

3 Summary Two sriking feaures of he Grea Recession of 28-9 are he speed and synchroniciy of he collapse in world oupu and rade in he wake of he sub-prime crisis. These observaions provide compelling evidence ha spillovers of shocks across naional boundaries can be large. Bu sandard macroeconomic models are unable o accoun for such srong linkages in real aciviy across counries. There is also lile consensus in previous work on he impac ha financial marke shocks have on real aciviy and how hey migh spill over from one counry o anoher. The aim of his paper is herefore o invesigae heoreically he impac ha financial fricions have on he ransmission of shocks across counries and o invesigae if incorporaing financial facors ino an open economy model could help hese models o accoun for he large and synchronised declines in cross-counry real aciviy, ofen observed following financial crises, no only he recen one. I also analyses how he naure of financial marke shocks affec he way ha shocks spill over o real aciviy. To invesigae he impac of financial facors on he ransmission of shocks across counries we build a wo-counry model, wih sicky prices and financial fricions. Our analysis is wofold. Firs we build a shadow version of he model wihou financial fricions ha is used in conjuncion wih he baseline fricion model o analyse how financial fricions affec he way ha shocks propagae across counries. Then we inroduce wo financial marke shocks ha affec he premium which borrowers pay on heir loans, he credi spread, o sudy how he source of he shock o his credi spread affecs is impac on real aciviy. We inroduce a risk shock and financial wealh shock ha are calibraed o mach he increase in credi spreads seen in he Unied Saes over he recen financial crisis period. These are used o consider wheher he model's prediced movemens in macroeconomic variables are similar o he rapid crosscounry declines in oupu and rade seen over he recen recession period. Using his modelling framework, we find ha he inernaional spillovers of shocks are driven by movemens in he real exchange rae and erms of rade. Boh he real exchange rae and erms of rade deermine he responses of real inernaional economic variables o shocks, such as expors and impors. Under cerain condiions, we find ha inroducing financial fricions can magnify movemens in hese inernaional relaive prices and herefore he spillovers of shocks o real inernaional economic variables. The source of he shock o he credi spread also maers. Resuls sugges ha credi spread increases of equivalen size, bu driven by differen shocks, have differen consequences for oupu and inflaion in he Home and Foreign economy. Our model can generae synchronised declines in oupu across he wo economies, similar o ha seen afer financial crises such as he Grea Recession, bu he inernaional spillovers following all shocks are relaively small. In addiion, here is lile evidence ha financial variables across counries end o move ogeher in his model, even in response o shocks which are financial in naure. To generae spillovers more in line wih he 27-1 period he model requires a coinciden widening of he credi spread across he wo economies. This could be inerpreed in wo ways. On one hand, a richer framework ha incorporaes direc inernaional linkages beween financial secors is needed o analyse how financial shocks spillover o aciviy across economies. On he oher hand, our resuls could be consisen wih he view ha he global reach of he recen Grea Recession is due o a common inernaional shock raher han a conagious spread of a counry-specific even. Working Paper No. 479 Augus 213 ii

4 1 Inroducion The Grea Recession has challenged academics and policy makers o undersand beer iner-linkages across economies and beween nancial and real variables. Sandard New Open Economy models have sruggled o accoun for he speed and severiy of he cross-counry declines in oupu and rade seen in he wake of he subprime crisis hrough sandard inernaional ransmission channels. There is also lile consensus in he heoreical lieraure on he impac ha nancial marke shocks have on real aciviy. These are imporan issues for policy makers, no leas because of he implicaions hey have for he ransmission of shocks across economies. This paper addresses wo quesions; rs in a simple heoreical model i invesigaes how nancial fricions a ec he ransmission of shocks o he real economy, boh domesically and across economies, second, i explores he ransmission of counry-speci c credi marke shocks. There is a vas lieraure in his area; many sudies focus on resolving some of he well known "oupu co-movemen puzzle" by inroducing a greaer role for nancial facors in he ransmission mechanism. Our paper adds o ha lieraure in is examinaion of he impac of nancial fricions on he inernaional ransmission mechanism. I also exends he curren knowledge on how nancial facors a ec economic ucuaions by invesigaing how he source of shocks o he credi spread a ec he way ha shocks propagae o he real economy which, as far as we are aware, has no been done in an open economy model before. In order o address hese quesions we build a wo-counry Dynamic Sochasic General Equilibrium (DSGE) model wih nancial fricions and sicky prices. In our simulaion hree separae shocks are inroduced o he Home economy; a oal facor produciviy (TFP) shock and wo credi spread shocks. The dynamic responses of he Home and Foreign economy variables o a TFP shock in he Home economy are compared in he model wih nancial fricions urned on and o. These are used o invesigae he e ec ha nancial fricions have on he propagaion of shocks. Nex we compare he way ha wo credi marke shocks propagae o he real economy. The rs shock ha we inroduce is a "risk shock" ha increases he dispersion of reurns on invesmen; i a ecs he curren sae of invesmen risk in he economy and herefore in uences nancial inermediaries propensiy o lend. The second is a " nancial wealh" shock ha changes he value of nancial agen s oal wealh. Boh shocks are calibraed so ha he increase in credi spreads mach he quarerly increase seen in he Unied Saes over he recen nancial crisis period. The purpose of his exercise is o invesigae he srengh of he inernaional propagaion channels in he model. We analyse he model s abiliy o generae an endogenous inernaional ransmission mechanism ha is su cienly srong o produce a large and synchronised decline in cross-counry nancial variables and real aciviy in response o an asymmeric credi spread shock ha originaes in one counry. The resuls of our analysis sugges ha movemens in inernaional relaive prices are a key channel for he propagaion of shocks o he real economy. In he model s framework inernaional spillovers of shocks are driven by movemens in he real exchange rae and erms of rade, which deermine he responses of real inernaional economic variables o shocks (expors and impors). Financial fricions end o magnify movemens in inernaional relaive prices and herefore increase inernaional spillovers following asymmeric TFP shocks bu here are some signs of sensiiviy o he speci caion of nancial conracs. The source of he shock o he credi spread also maers. Resuls sugges ha credi spread increases of equivalen size, bu driven by di eren innovaions, have di eren consequences for oupu and in aion in he Home and Foreign economy. In our model framework movemens in he credi spread driven by a risk shock lead o more realisic spillovers o aciviy in boh he Home and Foreign economy, han shocks o nancial wealh. Tha said, whils he model can accoun for he posiive cross-counry oupu co-movemen seen afer nancial crises such as he Grea Recession, he inernaional spillovers following he hree shocks remain small. There is also limied co-movemen in cross-counry nancial variables, so a widening of credi spreads in one economy does no generae a signi can widening of credi spreads in he oher. To generae spillovers in line wih he period he model requires a coinciden widening of credi spreads across he wo economies. This could be inerpreed in wo ways. On one hand, a richer framework ha incorporaes direc inernaional linkages beween nancial secors is needed o analyse nancial shocks in he conex of an open-economy macroeconomic model. On he oher hand, our resuls could be consisen wih he view ha he global reach of he Grea Recession is due o a common inernaional disurbance raher han a conagious spread of a counry-speci c even. A number of researchers have sudied he impac of inroducing nancial facors o New Open Economy models. These have predominanly focused on examining how he nancial secor propagaes shocks originaing in he real secor (Gerler and Kiyoaki (21), Goodfriend and MacCallum (27), Faia (27)). The paper mos closely relaed o ours is Faia (27) who also incorporaes a nancial acceleraor ino a wo-counry DSGE model. Faia (27) aims o explain why business cycles are more correlaed among coun- 1 Working Paper No. 479 Augus 213

5 ries ha have similar nancial srucures. Her analysis shows ha cross-counry oupu, consumpion and invesmen co-movemen increase when nancial parameers are similar. In conras, our analysis explores how nancial facors a ec he ransmission mechanism. Our conribuion o his srand of he lieraure is o develop a shadow version of he model wihou nancial fricions and explicily compare is resuls o he ones implied by he model wih nancial fricions in order o invesigae he e ec of nancial fricions on he inernaional ransmission mechanism. A newer lieraure also invesigaes he impac of inroducing more complex cross-counry nancial linkages, hrough sock marke and cross-counry balance shee exposure (Dedola and Lombardo (212)). Bu hese have focused less on how he naure of nancial disurbances a ec spillovers o he real economy and across economies. One explanaion for he recen recession is ha nancial marke shocks drove declines in invesmen and aciviy implying nancial facors may drive business cycle ucuaions. And here is empirical evidence ha shocks o he US banking sysem during he recen nancial crisis had consequences for lending and aciviy in advanced and emerging economies (Ceorelli and Goldberg (212)). There has been lile research o invesigae he macroeconomic impac of direc disurbances o he nancial secor in open economy frameworks. Chrisiano e al (21) use a version of he Bernanke e al. (1999) model, BGG henceforh, o consider he imporance of nancial disurbances for business cycle ucuaions. They esimae ha nancial facors are responsible for a subsanial proporion of economic ucuaions, accouning for more han one hird of he volailiy in euro area invesmen and 6 percen in he US bu hese are in a closed economy framework. The resuls of Chrisiano e al.(21) sugges ha nancial facors are criical for business cycle ucuaions boh in he US and he Euro area which suggess ha undersanding how nancial facors spill over o foreign economies is an imporan quesion. To invesigae how credi marke shocks propagae o he real economy boh domesically and inernaionally we inroduce wo shocks o he credi spread which are analogous o he risk and ne worh shock of Chrisiano e al. Previous sudies by Dedola and Lombardo (212) and Chrisiano e al (21) suggess ha credi spread shocks generae a quaniaively signi can e ec on real aciviy. However, here is lile undersanding o how he di eren ypes of shocks spillover o foreign aciviy. For example, here is some evidence ha shocks o nancial wealh can be sensiive o model se up. Financial fricions are inroduced via a nancial acceleraor mechanism along he lines of BGG (1999). Invesors pay an exernal nance premium (EFP) o borrow funds from households via nancial inermediaries. Collaeral consrains, of he ype inroduced by Kiyoaki and Moore (1997), have also been used o capure nancial acceleraor e ecs in open economy DSGE models (Devereux and Suherland (211)). Whils hese may beer capure balance shee e ecs associaed wih he process of nancial deleveraging, we are ineresed in nding a model which replicaes daa observaions. Brzoza-Brzezina e al(21) sugges EFP ype consrains ouperform collaeral consrains in daa so we favour using an EFP in our model. The paper is srucured as follows: Secion 2 presens he model, including he processes ha drive our economy; secion 3 discusses he calibraion of he model parameers before presening he key resuls and sensiiviy analysis and secion 4 concludes. 2 Model overview This secion oulines he baseline DSGE model ha we use in our analysis. I closely resembles Faia (27), bu i is modi ed in wo dimensions. Firs, we consider he impac of nancial facors on he propagaion of shocks by building a shadow version of he model ha excludes nancial fricions; second, we consider he role of credi spread shocks. The model comprises of wo counries and wo-raded goods. The Home (H) and Foreign (F) economy are symmeric bu are subjec o asymmeric shocks. Each economy comprises opimising households; monopolisic inermediae goods producing rms ha can se prices in Calvo fashion and nal goods producing rms ha are perfecly compeiive; capial producers ha ransform oupu ino un nished capial goods; enrepreneurs ha purchase his capial, ren i o rms and are subjec o a nancial fricion; nancial inermediaries ha channel household savings ino loans for enrepreneurs; and a policy maker ha ses ineres raes. Variables for he foreign economy are denoed wih an aserisk. Inernaional linkages are beween nal good rms who produce and sell a coninuum of domesic varieies o households and enrepreneurs in boh economies. Households engage in he inernaional rade of risk-free real bonds. In wha follows we consider he problems faced by each agen. 2 Working Paper No. 479 Augus 213

6 2.1 Model Households The household maximises is expeced discouned sum of uiliy obained from consumpion and hours worked: ( 1!) X C 1 +i H 1+ +i max E i U (1) i= where is he discoun facor, is he coe cien of risk aversion, he Frisch elasiciy of wages wih respec o he labour supply, H oal hours worked and C he nal goods consumpion baske. The consumpion index (C ) is de ned by C = h(1 ) 1 a C a 1 a f; + 1 a C a 1 i a a 1 a h; where C h; and C f; are he amouns of domesic and impored Foreign goods he household consumes. is he home bias parameer and a he elasiciy of subsiuion beween he wo goods. Households spend heir resources on consumpion (P C ) and saving in he form of real domesic deposis (D ) and risk-free real bonds denominaed in Home currency (B h; ) and in Foreign currency (B f; ). They also pay fees for adjusing heir holding of inernaional bonds 2 P (B h; ) (B f; ) 2. We assume convex fees for inernaional porfolio adjusmen in order o ensure ha our model has a unique seady sae and is saionary. 1 Funds are comprised of labour income (W H ) and nancial income obained from real deposi holdings (D 1 R D 1), inernaional Home bonds holdings (R 1 B h; 1 ) and inernaional Foreign bond holdings (R 1B f; ) held from he previous period, dividend income ( ) from owning rms and an inernaional bond fee rebae P h;. Accordingly he budge consrain is given by: P C + P D + P B h + P B f; e r + 2 P (B h; ) 2 + P 2 e r (B f; ) 2 W H + P R D 1D 1 +P R 1 B h; 1 + P R B f; 1 1 e r + + P h; (2) where e r and e are he real and nominal exchange rae, e r = ep P, e = P h; P h; = P f; P f; and h; = 2 (B h;) (B f; ) 2 is he rebae of inernaional bond adjusmen fees. The nominal and real exchange rae are 2 e r de ned he UK way so a rise in e r represens an appreciaion of he Home currency. The household maximises 1 subjec o 2 in he sandard way in order o choose quaniies fc ; B h; ; B f; ; D ; H g 1 = aking prices P ; R ; R ; R D ; W 1 = and he iniial wealh endowmens (D 1; B h; 1 ; B f; 1 ) as given. The opimal condiions ha govern he behaviour of households follow: E P e r H C = W (3) P! R D C+1 C = 1 (4) (C ) (1 + B h ) = R E (C +1 ) (5) (C ) (1 + B f ) = R E (C +1 ) e r e r +1 They include a labour supply condiion (3) which equaes he real wage o he marginal rae of subsiuion beween leisure and consumpion and hree Euler condiions ha deermine he saving decisions on deposis (4), inernaional Home (5) and Foreign (6) bond holdings. 1 Inernaional asse markes are incomplee as only risk-free bonds are raded across counries. This implies indeerminacy of seady sae ne foreign asses and non saionariy. To solve his problem we assume ha agens mus pay fees when adjusing heir holdings of boh Home and Foreign bonds. We assume ha hese fees are a quadraic funcion of he sock of bonds, where 2 B 2 h; is he fee paid on Home bonds and 2 B 2 f; on Foreign bonds. is a parameer ha describes how sensiive hese coss are o changes in he socks of bonds. These pin down he seady sae and deliver saionary model dynamics in response o emporary shocks. Realisic choices of parameer values for imply ha he cos of adjusing bond holdings has a very small impac on model dynamics. Revenues from bond-adjusmen fees are rebaed o domesic households each period as a lump ransfer h;. (6) 3 Working Paper No. 479 Augus 213

7 2.1.2 Firms There are wo sages o producion in each economy. Inermediae rms produce an idenical inpu which nal goods rms di ereniae a no exra cos o obain a radeable nal good. Inermediae rms Inermediae rms operae in a perfecly compeiive environmen. They use capial (K ) and labour (N ) which hey ren from enrepreneurs a renal rae (R k ) and hire a a nominal wage (W ) and (W e ) from households and enrepreneurs. Labour is a funcion of hours worked by households (H ) and enrepreneurs(h e ) 2 : N = (H e ) (H ) 1 (7) where is he fracion of enrepreneurial labour. Producion echnology displays consan reurns o scale: Y w Y w = A K N 1 : (8) is he gross oupu of he rm. A is a oal facor produciviy (TFP) shock which follows an AR(1) process wih persisence parameer A and sandard deviaion A. Inermediae goods are sold a price P w, so pro maximisaion implies he following opimal condiions: R k = P w Y P h; P h; K W Y = P w (1 ) (1 ) (1) P h; P h; H W e = P w (1 ) Y P h; P h; H e : (11) (9) Final goods rms Final goods producers are monopolisically compeiive and use a Calvo pricing mechanism, where! denoes he fracion of rms who canno change heir prices in a given period. The opimisaion problem is sandard and delivers he following rule for he opimal price: 8P Ph; o b < 9 1 (i) = (b 1) E i=!i i C +i P +i w (P h;+i) b X h;+i + Xh;+i = : P 1 i=!i i C +i (P h;+i) b X h;+i + Xh;+i ; : The law of one price is assumed o hold for each variey of good, which can be aggregaed for he home and foreign goods secor so ha P h; = e P h; and P f; = e P f; Un nished capial producers A compeiive secor of capial producers combines invesmen and depreciaed capial sock o produce un nished capial goods. The capial producers purchase nal goods for invesmen I boh from Home and Foreign nal producers. We assume ha hey combine he home and foreign goods in he same aggregae good baske as households such ha: I = h(1 ) 1 a I a 1 a f; + 1 a 1 a I a h; i a a 1 : The producion of un nished capial is subjec o physical adjusmen coss. Un nished capial producers have a consan reurns o scale producion funcion I K 1 K 1 ; where (:) is increasing and convex in 2 he invesmen o capial raio. We assume a quadraic funcional form I I 2 K 1 K 1, which implies he following capial accumulaion equaion: 2 I K = (1 ) K 1 + I K 1: (12) 2 K 1 2 In calibraions we keep he share of income going o enrepreneurs small (of he order.1) so his modi caion does no have a signi can e ec on he resuls. This deviaes from Faia(27) seup bu is in line wih BGG(1999). 4 Working Paper No. 479 Augus 213

8 De ning Q as he re-sell price of he capial good, capial producers maximize heir pro s 2 Q I I 2 K 1 K 1 P I and choose how much o inves based on he following opimal condiion: Q I = 1 P K 1 : (13) Enrepreneurs To inroduce nancial fricions we follow BGG (1999). There is a coninuum of risk neural enrepreneurs, indexed by j, who purchases un nished capial from he capial producers a he price q = Q P, and ransforms i ino nished capial wih linear producion echnology, (a e (j) K (j)); ha is subjec o idiosyncraic produciviy shocks a e (j) : The idiosyncraic produciviy shocks are assumed o be independenly and idenically disribued (i.i.d) across enrepreneurs and ime, and o follow a log normal disribuion, namely a e (j) log N(1; 2 a); wih cumulaive disribuion funcion denoed by F (a e ). Noice ha, for he soluion of he enrepreneurial problem, we ake he variance of a e as a given parameer. Bu, as we show in secion 2.1.7, allowing for ime variaion in 2 a will consiue a major source of shock in our model. This is Chrisiano e al. (21) risk shock. To nance he purchase of un nished capial enrepreneurs employ inernal funds, heir ne worh (NW ), bu hey also need o acquire an exernal loan (L ) from he nancial inermediary; q K (j) = L (j) + N W (j) (14) where K (j) is he amoun of capial purchased. To characerise he enrepreneurs problem we rs de ne he expeced gross reurn from holding one uni of nished capial. In period he enrepreneur buys one uni of capial a price (q ) and a period + 1, he ges income from rening i ou o inermediae producers a renal rae Rk P and from re-selling he un-depreciaed capial o capial producers a price q +1. So he expeced gross reurn is he sum of renal income and he capial gain from reselling undepreciaed capial: 2 3 E R+1 e = E 4 q +1 (1 ) + R k P 5 : (15) q The opimal loan conrac The nancial conrac beween he enrepreneur and nancial inermediary assumes he form of an opimal deb conrac, based on Gale and Hellwig (1985). Speci cally, he idiosyncraic shock o enrepreneurs is privae informaion for he enrepreneur. To observe his, he lender mus pay an audiing cos ha is a xed proporion 2 [; 1] of he realised gross reurn o capial held by he enrepreneur. The opimal loan conrac will induce he enrepreneur o no misrepor his earnings and will minimise he expeced audiing coss incurred by he lender. The conrac lass one period and is renegoiaed every period. The opimal conrac can be described in erms of he amoun of capial produced and he cu o level of produciviy a which he enrepreneur defauls. The enrepreneur is able o repay he loan a he conracual rae (R L ) if he reurn from invesmen is higher han he amoun hey mus repay on heir loan, R+1a e e +1q K > R+1(q L K NW ), or if heir produciviy is higher han some cu-o value for he idiosyncraic produciviy shock, a e +1,de ned as: a e +1 = RL +1 (q K NW ) R e +1 q K : (16) The paricipaion consrain ha ensures he nancial inermediary eners he marke is: Z 1 a e +1 R L +1 L df a e +1 + (1 ) Z a e +1 R e +1 q K a e +1 df a e +1 R D L (17) where is he monioring cos, inuiively speaking 17 saes ha he nancial inermediary will only paricipae if heir expeced reurn from lending is equal o he opporuniy cos of nance. 5 Working Paper No. 479 Augus 213

9 The conrac maximises he expeced reurn o enrepreneurs subjec o 17 and gives an opimal pair of a e +1 ; K Aggregaing yields a wedge beween he gross reurn on capial for enrepreneurs and he risk free real ineres rae. This is he exernal nance premium (EF P ), or credi spread over he risk free rae, ha R e +1 enrepreneurs pay o borrow funds from nancial inermediaries, where efp E. The opimal R D condiions for he conrac problem imply: where = Z ae raio Z ae a e df (a e ) + a e 1 efp = ( G )(1 )= + ( G ) ; (a e efp ) > ; (18) Z 1 a e df (a e ) is he expeced gross share of pro s going o he lender and G +1 = a e df (a e ) - he expeced monioring coss. Anoher opimal condiion relaes he enrepreneurs leverage qk NW o he produciviy disribuion of enrepreneurs: = 1 + h ( G )i ( G )(1 ) ; (a e ) > : (19) Combining equaions 18 and 19 allows us o wrie he credi spread as an increasing funcion of he leverage raio: efp = v ( ): (2) Noe ha equaion 2 implies a negaive relaionship beween ne worh and credi spreads. Inuiively, an increase in ne worh causes a decrease in he leverage raio which reduces he opimal cu-o value, as shown by equaion 19. As a resul, he fracion of defauling enrepreneurs falls which lowers he bankrupcy coss and he credi spread The evoluion of ne worh To ensure ha enrepreneurs do no accumulae enough funds o nance heir expendiures on capial enirely wih ne worh, we assume ha hey have a nie lifeime. In paricular, we assume ha each enrepreneur survives o he nex period wih probabiliy s. Enrepreneurs who die in period are no allowed o purchase capial, bu insead consume heir accumulaed resources and depar he marke. The ne capial gain ha enrepreneurs obain from invesing in capial is: " V = R e q 1 K 1 R D 1 + R e # a a e; df (a e; )q 1 R e K 1 (q 1 K 1 NW 1 ) : (21) (q 1 K 1 NW 1 ) So enrepreneurs who survive will accumulae ne worh a he end of period according o he following equaion: Source of shocks in he model NW = s V + W e P : (22) There are hree processes which drive he model economy. As is sandard in he lieraure, we assume ha TFP follows an auoregressive process ha is subjec o shocks: A = A A 1 + A " A (23) where " A follows a N(; 1) process and he parameer A conrols he size of he TFP shock which drives our economy. In addiion o he TFP shock, we assume ha wo addiional exogenous processes a ec he credi spread, or EFP, charged o enrepreneurs and ha hese forces drive our model economy; a risk and nancial wealh shock. 3 We assume capial producion and monioring echnology are linear which makes aggregaion possible since marginal coss are consan. 6 Working Paper No. 479 Augus 213

10 The risk shock a ecs he dispersion of enrepreneurs idiosyncraic produciviy. Following Chrisiano e al. (21) we allow he variance of he idiosyncraic produciviy shocks o change over ime. This shock is used o proxy for a sudden re-appreciaion of marke risk, similar o ha seen over he recen nancial crisis period. Each period enrepreneurs face an idiosyncraic produciviy shock which convers heir purchase of un nished capial goods ino nal capial, (a e (j) K (j)). We inroduce a posiive shock f ha changes he dispersion of produciviy across enrepreneurs. The shock is AR(1) wih persisence parameer f and sandard deviaion f. I is mean preserving so he average produciviy of he enrepreneur does no change, bu he number of enrepreneurs wih he likelihood of very high or low produciviy increases. A change in f herefore has an impac on he condiions in he enrepreneurial loans markes. An increase in f implies a higher probabiliy ha enrepreneurs go bankrup. Figure 1 displays he e ec of an increase in he dispersion of he produciviy disribuion of he enrepreneurs. For illusraive purposes we increase he dispersion of enrepreneurs produciviy from is seady sae level of a = :35 o a = :45: The immediae impac is ha he ails of he produciviy disribuion become faer. For a given seady sae cu-o produciviy of a e = :52, his implies an increase in he probabiliy of defaul of abou four percen. The yellow area o he righ of he cu-o produciviy line and under he shifed disribuion represens his increase in he defaul probabiliy. Given he informaion asymmery beween banks and enrepreneurs, his a ecs he level of he loans rae and, herefore, capial demand. The second credi spread shock a ecs he ne worh of enrepreneurs and herefore he oal nancial wealh of he model economy. I is a shock o he survival rae of enrepreneurs, so i a ecs he number of enrepreneurs exiing he marke each period. A random and ime varying fracion of enrepreneurs, (1 s ), exi he marke each period and an equal fracion ener. s is a shock o he survival rae, i follows an AR(1) process wih a persisence parameer s and sandard deviaion s. A negaive realisaion reduces he survival probabiliy of enrepreneurs and means ha here are fewer enrepreneurs who produce nished capial. This ype of shock o he credi spread has wo e ecs on he economy; rs here is an immediae increase in enrepreneurial consumpion, as he dying enrepreneurs consume heir ne worh. An inuiive way o hink of his is ha dying enrepreneurs pay an equiy dividend in he las period which is used for consumpion. Second, over he longer erm, he shock reduces he aggregae ne worh of enrepreneurs because hey become more impaien and consume more oday which a ecs he credi spread, or EFP, ha enrepreneurs mus pay for loans Moneary policy and marke clearing Moneary policy follows a Taylor rule wih ineres rae smoohing: R n R n = R n 1 R n r y 1 r 1 + Y (24) 1 + Y 1 where r re ecs he persisence of ineres rae changes and and y are he weighs on oupu and in aion volailiy. Noe ha he Fisher equaion implies he following relaionship beween he nominal ineres rae and he real ineres rae paid on deposis: R D = E R n The following marke clearing condiions hold in equilibrium. following resource consrains: : Home and Foreign nal goods imply he X h; + Xh; = Y (25) X f; + Xf; = Y : (26) Noe ha oal demand includes household consumpion, enrepreneurial consumpion, demand for invesmen goods and goods demanded by nancial inermediaries for monioring X = C + C e + I + R a e a e; df (a e; )Q 1 R e K 1 : Ne rade in inernaional bonds mus be zero in equilibrium: Noe ha he Home curren accoun is de ned as: B h; + B h; = B f; + B f; = : (27) CA = B h; B h; + (B f; B f; 1 ) =e r : (28) 7 Working Paper No. 479 Augus 213

11 Finally he loanable funds marke requires ha he real quaniy of deposis equals he volume of loans, boh a Home D = L and a Foreign D = L. 2.2 Mehod Parameerisaion and soluion of he model Parameers associaed wih he real secor of he economy are mosly calibraed based on Faia (27) bu parameers peraining o he nancial secor are calibraed di erenly. Srucural parameer values are repored in Table A. One period in he model is one quarer. We assume ha he fracion of rms allowed o adjus prices every period is.6 which implies an average price duraion of 2.5 quarers. Noe ha we assume home bias on inernaional rade in nal goods ( = :7) which implies ha purchasing power pariy does no hold in our model and he real exchange rae deviaes from uniy. Anoher imporan parameer is, which deermines he sensiiviy of inernaional adjusmen on bond fees o he sock of bonds. We se i a.25 in line wih Ghironi and Meliz (25), a low value ha does no a ec our resuls bu high enough o saionarise he model. Finally, we assume ha he inverse of he Frisch labour supply elasiciy is 1=3, which implies an elasiciy of 3. This is high bu i follows BGG (1999) and is in line wih macroeconomic sudies. Anoher di erence in our model compared o Faia is ha he enrepreneurs work and receive a wage. The fracion of hours of enrepreneurial labour in oal labour employed by inermediae rms is 1%. In Faia s model his is a lump sum ransfer o enrepreneurs bu here we follow BGG (1999) o ensure ha he enrepreneurs income ucuaes wih he business cycle. We se he hree parameers ha govern he behaviour of he nancial secor variables o closely mach he long-run developed counries esimaes for credis spreads, defaul raes, leverage raios and elasiciy of he credi spreads wih respec o leverage. The monioring cos parameer is.15, he volailiy of he produciviy disribuion of enrepreneurs a is.35, and he survival rae of enrepreneurs is.966. These values imply a seady sae credi spread of abou 123 basis poins which is close o he 187 basis poins used by Carlsrom and Fuers (1997). The seady sae leverage raio = QK NW is 2.1 which is close o he value rs used in BGG (1999) and henceforh, became sandard for nancial fricion models. The seady sae probabiliy of defaul for enrepreneurs is 3% and he elasiciy of he credi spread o he leverage raio efp is.5, a value also in line wih BGG (1999). In quarerly space he sandard deviaions of he shocks o he credi spread are calibraed in order o generae an increase in he spread of 37 basis poins on impac which is broadly consisen wih he rise in US corporae credi spreads seen over he iniial sages of he recen nancial crisis. The persisence of he credi spread shocks are based on Chrisiano e al. (21) who esimae a nancial fricions model on US and Euro area daa. Key seady sae values are repored in Table B. The nonlinear model is linearised around he seady sae o he rs order. The rs order linearisaion does no derac from he dynamic analysis of responses o nancial shocks because he nancial acceleraor mechanism creaes rs order e ecs which spill over from he EFP o he ne worh of enrepreneurs, hence from he nancial o he real secor of he economy. The linearizaion and he dynamic simulaion are execued wih DYNARE. 3 Resuls 3.1 The e ec of nancial fricions on he inernaional ransmission mechanism Before looking a he e ecs of credi spread shocks, we invesigae how nancial fricions e ec he ransmission of shocks o real aciviy in boh he Home and Foreign economy. Figure 2 shows he impulse responses of Home and Foreign economy variables o a one sandard deviaion shock o TFP in he Home economy wih (solid lines) and wihou (dashed lines) nancial fricions. The impulse responses are repored as deviaions from he seady sae in unis of he respecive variables. Only variables measured in percenage poins are convered o basis poins. 4 As in sandard models he TFP shock propagaes o he Home economy as a supply shock. Home oupu falls and in aion increases, re ecing reduced produciviy and rising marginal coss. The fall in wealh, associaed wih he fall in oupu, resuls in weaker consumpion and invesmen demand. Rising in aion a Home promps an increase in he policy rae and an appreciaion of he Home real exchange rae. 4 A lis of he non-linear equaions describing he shadow model wihou nancial fricions can be found in he Appendix. 8 Working Paper No. 479 Augus 213

12 In our model he inernaional spillovers o Foreign oupu and in aion operae via ne rade and he erms of rade. Changes in he erms of rade reduce Foreign supply which is only parially o se by a boos o oupu from ne rade, so overall Foreign oupu falls and in aion rises. The rise in Home in aion makes Foreign goods relaively more compeiive which resuls in a boos o Foreign ne rade. Bu he Foreign economy erms of rade also depreciaes because he price of Foreign impors rise relaive o heir expors. The depreciaion in Foreign erms of rade reduces he value of he marginal producs of Foreign capial and labour in erms of Home oupu which promps a fall in Foreign producers demand for capial and labour. As a resul here is a supply conracion in he Foreign economy, so Foreign oupu falls and in aion rises. Comparing he dashed lines o he solid lines summaries he impac of nancial fricions on hese responses. We use an EFP o inroduce nancial fricions, which generae a nancial acceleraor ype e ec. In he fricion world he Home TFP shock causes a fall in asse prices and he ne worh of enrepreneurs which pushes up on heir coss of borrowing, shown by he rise in he EFP. This leads o an acceleraor e ec so ha boh invesmen and oupu fall by more han in he non fricion world. This resul is in line wih sandard BGG ype models. As in he non fricion world he negaive TFP shock reduces supply in he Home economy; Home oupu falls and in aion rises, which causes an appreciaion of he real exchange rae. There is a larger crowding ou of expors, as boh he real exchange rae and erms of rade adjus by more when nancial fricions are presen. As a resul inernaional prices play a greaer role in he adjusmen process afer he TFP shock in he nancial fricion world. The response of he Foreign variables o he Home TFP shock remain similar o hose in he non-fricion world, bu he shif in he foreign aggregae supply curve is larger wih nancial fricions because he inernaional erms of rade e ec is magni ed by he presence of he nancial acceleraor. 3.2 Credi spread shocks Nex we inroduce wo credi spread shocks o he model. These are used o examine how he source of he shock o he credi spread e ecs he ransmission mechanism and is e ec on key variables. The shocks are calibraed o mach he rise in spreads seen in he US over he recen nancial crisis period because we also wan o examine wheher he model can generae a large and synchronised decline in nancial and real aciviy as ofen observed following nancial crises, such as he Grea Recession. One noable feaure of ha period is he high cross-counry correlaion beween real and credi markes variables. Panel A and B in gure 3 plo a measure of annual GDP growh and credi spreads for he UK, US and Euro Area, which show he high degree of synchronisaion across counries. In he following analysis we compare cross-counry correlaions beween oupu and credi spreads, as a proxy for hese measures, o see how he model performs relaive o he recession period as well as examining he ransmission mechanism Risk shock Figure 4 presens he impulse responses associaed wih an idiosyncraic produciviy shock, or risk shock, a Home. The risk shock operaes via reducing demand for (capial) invesmen and hen propagaes o he res of he Home economy as a demand shock, via sicky prices, and o he Foreign economy as a ne rade shock, via he real exchange rae. The risk shock a Home increases he dispersion of he enrepreneurs produciviy, which means here is an increase in he dispersion of reurns o invesmen. This is consisen wih a re-appreciaion of marke risk, so nancial inermediaries propensiy o lend falls because more enrepreneurs may defaul on heir loans. Over he recen nancial crisis period here was a similar fall in nancial inermediaries desire o lend because of a re-appreciaion of general marke risk. Consisen wih ha our model predics ha credi condiions ighen in he Home economy in response o he re-appreciaion of marke risk and he EFP charged on loans rises from 123 basis poins in seady sae o 16 basis poins on impac. These are quarerly increases so hey are consisen wih a 15 basis poin rise in he annualised credi spread which we saw in he iniial sages of he nancial crisis. Focusing rs on he impac on he Home economy: as expeced we nd a nancial muliplier e ec which operaes mainly hrough he capial marke. The increase in he dispersion of he enrepreneurs produciviy raises he probabiliy of enrepreneurial defaul and, due o asymmeric informaion, increases he EFP charged by Home nancial inermediaries. Capial demand from enrepreneurs falls because i is more cosly o acquire funds o purchase new capial, which pushes down on he capial sock and he asse 9 Working Paper No. 479 Augus 213

13 price of capial 5. In addiion falling asse prices reduce he enrepreneurs ne worh. The decline in capial demand resuls in lower invesmen expendiure. The capial sock in he economy falls slowly over ime as invesmen is lower for a number of periods and he exising capial sock depreciaes. Weaker invesmen spending resuls in a decline in oupu and hence, demand which via sicky prices pushes down on in aion. I is noable ha he overall fall in Home aggregae demand response is small compared o he fall in oupu observed over he recen nancial crises across a number of economies, in our model he peak fall in oupu is.1% compared o seady sae. Wha are he spillover e ecs o he Foreign economy? Our resuls sugges ha he inernaional ransmission is dominaed by changes in he real exchange rae and ne rade. Falling Home in aion makes Home goods relaively less expensive and leads o a depreciaion in he erms of rade and real exchange rae. Declining real ineres raes in he Home economy also suppor a depreciaion of he real exchange rae, via UIP. The depreciaion of he exchange rae means Home expor prices (denominaed in foreign currency) fall bu impor prices rise acing o boos Home ne expors, so ha he demand for Foreign goods falls. The Foreign economy experiences a fall in aggregae demand because of he decline in heir expors o he Home economy which pulls down on Foreign oupu and in aion. So he risk shock leads o oupu co-movemen across he wo economies, alhough i is noable ha he foreign economy oupu response is small compared o he Home economy. The generaed correlaion in oupu and in aion across he wo economies is also low compared o ha seen during he crisis period (able C). There is very lile co-movemen in EFPs across he wo economies as he Foreign EFP is una eced by a risk shock in he Home economy. Capial markes are closed in his model which means ha enrepreneurs in he Home economy do no borrow from he Foreign nancial inermediary. Therefore a rise in defaul risk a Home has no impac on Foreign nancial inermediaries behaviour or he Foreign EFP. So in our framework he main inernaional spillover is dominaed by he movemens in inernaional relaive prices and nancial spillovers are limied Financial wealh shock Figure 5 shows he impulse responses associaed wih a shock o he survival rae of enrepreneurs in he Home economy. A reducion in he survival rae of enrepreneurs means ha here are fewer enrepreneurs who produce nished capial. As a resul here is an increase in he number of enrepreneurs who exi he marke for nished capial. This change in behaviour has a signi can impac on he aggregae ne worh of enrepreneurs who deermine aggregae nancial wealh in he Home economy. So his shock operaes like a nancial wealh shock in he Home economy and propagaes o he Foreign economy as an exchange rae shock, via ne rade. As expeced, nancial wealh falls a Home in response o he shock o he enrepreneurs survival rae. The ne worh of exiing enrepreneurs is redisribued owards consumpion; his is analogous o enrepreneurs paying an equiy dividend o hemselves when hey exi he marke ha hey spend on consumpion raher han nished capial goods. So he aggregae ne worh of enrepreneurs and, herefore, aggregae nancial wealh fall as fewer enrepreneurs wish o produce nished capial. The fall in nancial wealh propagaes o he Home economy via aggregae demand channels. Bu his shock generaes some couner inuiive resuls in he rs few periods. On impac aggregae demand rises because dying enrepreneurs consume heir equiy which creaes upward pressure on in aion. In he rs few periods producion increases enough o suppor he rise in enrepreneurs consumpion bu i is no enough o suppor invesmen and household consumpion which is crowded ou in response o he higher real ineres raes. Afer a few periods he posiive boos o he enrepreneurs consumpion dies away, as he shock o he survival rae dissipaes, bu he negaive e ecs of he nancial wealh shock persis so overall aggregae demand a he Home economy begins o fall. Enrepreneurs ne worh coninues o fall for a few periods as declines in he asse price of capial reduce he value of enrepreneurs asses. This leads o nancial acceleraor ype e ecs. The EFP rises in response o he declines in ne worh which resuls in weaker (capial) invesmen demand because i is more cosly o borrow funds for invesmen purposes. The capial sock in he economy falls slowly over ime as invesmen is lower for a number of periods and he exising capial sock depreciaes over several periods. I is noable ha he impac of he nancial wealh shock is large; is e ecs on aciviy are quaniaively larger han hose of he risk shock. This is parly driven by he magniude of he associaed wealh shock. To generae a 37 basis poin increase in he credi spread he nancial wealh of agens falls by around 13% on impac. 5 There is evidence ha invesmen is sensiive o credi spread shocks as he impulse responses are large in comparison o he overall movemen in oupu. 1 Working Paper No. 479 Augus 213

14 Again, his analysis suggess ha movemens in inernaional relaive prices are a key channel for he propagaion of asymmeric nancial shocks o he real economy. The nancial wealh shock spills over o he Foreign economy via ne rade due o movemens in inernaional relaive prices. Rising Home in aion makes Home goods relaively more expensive and leads o an appreciaion in he erms of rade and real exchange rae. Rising real ineres raes in he Home economy also suppor an appreciaion of he real exchange rae, via UIP. The appreciaion of he exchange rae means Home expor prices rise bu impor prices fall acing o reduce Home ne expors, so ha he demand for Foreign goods rises. The Foreign economy experiences a rise in aggregae demand because of an increase in heir expors o he Home economy which pushes up on Foreign oupu and in aion. There is lile evidence of co-movemen across nancial variables in response o he nancial wealh shock. The response of Foreign nancial variables is mued in comparison o he Home economy and Foreign spillovers are driven via movemens in inernaional prices Comparison of he credi spread shock o he observaions over he recen nancial crisis Table C compares momens under he wo di eren credi spread shocks relaive o hose observed in he daa. I shows ha he nancial wealh shock generae variable responses ha are much larger han he risk shock. Consisen wih his, he volailiies of Home and Foreign oupu and he EFP afer he wo shocks are much larger in response o he nancial wealh shock. Oupu correlaions afer he nancial wealh shock are also more similar o hose observed in he daa over he recession period. Tha said, in he previous secion we showed ha he negaive risk shock leads o more realisic spillovers o real aciviy since here is a negaive response of boh Home and Foreign oupu which is consisen wih he large cross-counry declines in oupu following he nancial crisis. In conras Home and Foreign oupu rise in response o he negaive nancial wealh shock. In addiion he resuls for he nancial wealh shock show some signs of insabiliy. More generally, i is sriking ha boh he credi spread shocks are unable o generae oupu and credi spread responses ha are of a similar magniude o hose observed during he recen nancial crisis and ensuing recession. The magniude of he declines in oupu and rise in he credi spread and he volailiy of he variables following he shocks are much smaller han observed over his period. This could be aribued o he fac ha a he seady sae he nancial fricion is calibraed o mach long-run developed counries esimaes for key nancial variables. In closed economy model wih a nancial acceleraor Gilchris and Zakrajsek (forhcoming) show ha he response of he real secor following a credi spread shock increases in size when he srengh of he nancial fricion doubles. Our sensiiviy analysis also suggess ha increasing he srengh of he nancial imperfecions increases he response of oupu o credi spread shocks a leas in he Home economy. However, we need a large increase in he srengh of he nancial imperfecion in order o generae signi can change in he quaniaive response of oupu. 3.3 Sensiiviy analysis Our resuls sugges ha movemens in inernaional relaive prices are a key channel for he propagaion of asymmeric nancial shocks o he real economy. In paricular, he response of he exchange raes and erms of rade o counry-speci c shocks deermines he inernaional spillovers o he Foreign economy, and herefore a ec he labour supply decisions of agens. Given he imporance of he labour supply decision for he propagaion of shocks, we now examine how sensiive he resuls are o di eren values for he Frisch elasiciy. We also analyse he sensiiviy of our resuls o di eren parameerisaions of he nancial fricion o see how hese a ec he propagaion of he credi spread shocks. And, nally, we explore he e ec of an alernaive speci caion of he nancial conrac on our resuls. More recen papers from Chrisiano e al. (21) and von Heideken (29) sugges he specifying deb conracs in nominal erms can inroduce a powerful Fisher deb de aion mechanism ha, under cerain condiions, can reduce he ampli caion e ec associaed wih nancial fricions. So we explore his hypohesis in our wo-counry framework. Frisch elasiciy We assume a Frisch labour supply elasiciy of 3 which is in line wih macro sudies bu high relaive o some sudies based on micro-level daa. The Frisch elasiciy governs he response of labour supply o changes in he wage rae so i is an imporan parameer in our model. The mos recen paper, Dyrda e al. (212), claims ha a Frisch elasiciy of.7 is in line wih micro-evidence. We check he sensiiviy of our resuls o a lower assumed Frisch labour supply elasiciy. Resuls of his exercise are shown in Figure 6. We nd ha reducing he Frisch elasiciy does no impac he direcion of our resuls, bu does a ec he quaniaive response of key variables. A lower Frisch elasiciy implies ha 11 Working Paper No. 479 Augus 213