The Adverse Feedback Loop and the Effects of Risk in both the Real and Financial Sectors *

Transcription

1 Federal Reserve Bank of Dallas Globalizaion and Moneary Policy Insiue Working Paper No. 66 hp:// The Adverse Feedback Loop and he Effecs of Risk in boh he Real and Financial Secors * Sco Davis Federal Reserve Bank of Dallas November 21 Absrac Recessions ha are accompanied by financial crises end o be more severe and are followed by slower recoveries han ordinary recessions. This paper inroduces a new Keynesian model wih financial fricions on boh he demand and supply side of he credi markes ha can explain his empirical finding. Following a shock ha leads o a decline in economic aciviy, an adverse feedback loop arises where falling profis and asse values lead o increased defauls in he real secor, and hese increased defauls lead o increased loan losses in he banking secor. Following his increase in loan losses, financial fricions in he banking secor imply ha he banking secor iself may face difficuly obaining funds. This disrupion in he inermediaion process leads o a furher decline in oupu and asse prices in he real secor. In simulaions of he model i is found ha his feedback loop operaing hrough he balance shees of financial inermediaries can lead o as much as a 2% increase in business cycle volailiy, and impulse response analysis shows ha in he presence of financial fricions he pah back o he seady sae afer a shock is much slower. JEL codes: E32, E44, F4, G1 * Sco Davis, Federal Reserve Bank of Dallas, 22 N. Pearl Sree, Dallas, TX Sco.davis@dal.frb.org. I would like o hank Mario Crucini, Kevin Huang, Andrew Hughes Halle, Enrique Marinez-Gracia, Elias Papaioannou, and Michael Plane for many helpful commens and suggesions. I would also like o hank he paricipans a he 21 ASSA meeings, he 21 Midwes Macro Meeings, and he 6h Annual Dynare Conference. The views in his paper are hose of he auhor and do no necessarily reflec he views of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem.

2 1 Inroducion Ensconced in he comfor of he Grea Moderaion, macroeconomiss largely ignored he process of nancial inermediaion and fel comforable o rea nance simply as a "veil", unil he Grea Panic and Grea Conracion of dramaically changed he way we view he inerplay beween nance and he macroeconomy. 1 In he wake of he nancial crisis, a number of auhors have looked o he hisory of nancial crises o nd evidence of heir macroeconomic e ecs. Papers like Reinhar and Rogo (28 and 29), Cecchei, Kohler, and Upper (29), The IMF (29a and 29b), Bordo and Haubrich (21), Claessens e al. (21) and Reinhar and Reinhar (21) all nd ha an economic downurn accompanied by a nancial crisis ends o be more severe and more proraced han an ordinary recession. This paper presens a simple, highly racable model o explain he severiy of a recession ha is accompanied by a nancial crisis. In he model, a shock (eiher real or nominal) leads o a fall in economic aciviy, which causes a fall in asse prices and increased defauls in he real secor of he economy. These increased defauls in he real secor lead o loan losses in he nancial secor. This deerioraion in boh real and nancial secor balance shees leads o a reducion in he supply of credi o boh secors, causing an even greaer fall in economic aciviy and a furher fall in asse prices. This ampli caion mechanism, also called he adverse feedback loop, may explain a large par of he Grea Conracion following he Grea Panic of However i is absen from mos macroeconomic models, for 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. Some papers move beyond he condiions of he Modigliani-Miller heorem and incorporae 1 In his 29 Schumpeer Lecure o he Congress of he European Economic Associaion, Charles Bean predics ha in all probabiliy, he evens of will join he Grea Depression of he 193 s and he Grea In aion of he 197 s as "discipline-de ning evens" (Bean 29) 2 In congressional esimony, Federal Reserve Chairman Ben Bernanke referred o "he desrucive power of he so-called adverse feedback loop, in which weakening economic and nancial condiions become muually reinforcing." (Bernanke 29) 2

3 nancial fricions ino a general equilibrium model. 3 In he rs example of nancial fricions in a general equilibrium, Bernanke and Gerler (1989) 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 fricions, in he form of collaeral requiremens, inroduce an imporan mechanism for he propagaion of echnology shocks. In addiion, Iacoviello (25) and Chrisiano e al. (28) consruc models wih a nancial acceleraor and nominal deb conracs o highligh he deb-de aion channel from Fisher (1933). They show how he non-indexaion of deb combined wih nancial fricions can serve o amplify he e ecs of demand shocks ha produce a posiive co-movemen beween oupu and in aion and dampen he e ec of supply shocks, which produce a negaive co-movemen. In hese papers, which form he "core" of he nancial acceleraor lieraure, here is no a speci c role for nancial inermediaries. However, o model he macroeconomic e ecs of a crisis in he nancial secor i is necessary o incorporae nancial fricions in he inermediary secor iself. In addiion, many empirical sudies have produced resuls ha seem o conras wih he irrelevance of nancial condiions in he inermediary secor. 4 Absracing from he condiions of he Modigliani and Miller heorem, Holsrom and Tirole (1997), Sein (1998), Chen (21) and von Peer (29) presen models where he bank ne worh maers for he quaniy of inermediaion. 3 See Gerler (1988) for a survey of how he lieraure of nancial fricions arose ou of he lieraure incorporaing imperfec informaion. 4 The relevance of nancial condiions in he inermediary secor is a cenral par of he bank-lending channel of moneary policy ransmission Bernanke and Gerler Bernanke (1983), Bernanke and Lown (1991), Peek and Rosengren (2), Lown and Morgan (26), 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. Kashyap and Sein (1995 and 2) nd ha he impac of moneary policy on a paricular bank s lending behavior depends on is balance shee srengh, and hey inerpre his as evidence ha a bank s funding cos depends on is nancial condiions. In addiion Hubbard e al. (22) shows ha here is a relaionship beween a borrower s cos of funds and he healh of his bank s balance shee. 3

4 Moivaed by he recen crisis and he cenral role of he increase in inerbank lending spreads (see Taylor and Williams 29), a number of recen papers incorporae nancial fricions wihin he inermediary secor in a quaniaive business cycle model (see e.g. Aikman and Pausain 26, Gerler and Karadi 29, Gerler and Kiyoaki 21, Gilchris e al. 29, Curdia and Woodford 29, Hirakaa, Sudo, and Ueda 29 and 21, Dib 21, and Meh and Moran 21 and see Woodford (21) for an excellen discripion of he ways ha he recen crisis has a eced he course of macroeconomic and business cycle research). Adrian and Shin (28) and Adrian, Monench, and Shin (21a and 21b) deail he e ecs of endogenous changes in he size of nancial secor balance shees as banks and oher nancial inermediaries change he raio of deb o equiy on heir balance shee in response o changes in he cos of deb. In addiion, Van Den Heuvel (29) wries speci cally of he "bank capial channel" of moneary policy ransmission (as opposed o he "bank lending channel") whereby moneary policy leads o changes in a bank s ne worh and in he presence of nancial fricions in he banking secor, his change in ne worh a ecs he supply of lending from he inermediary secor. Inspired by his research ino he macroeconomic e ecs of changes in a bank s ne worh, his paper presens a model wih nancial fricions in boh he real and nancial secors, which are linked hrough he balance shees of nancial inermediaries. In he model, a shock ha leads o a decline in oupu and asse prices leads o a fall in ne worh in he real secor of he economy. This, combined wih nancial fricions in he real secor, will lead o a feedback look where worsening balance shees lead o increased credi risk, and hus lenders curail lending or charge higher raes, leading o a furher decline in economic aciviy and asse prices. Bu when fricions are also inroduced wihin he nancial secor, he power of his feedback loop is signi canly enhanced. In he model, nancial inermediaries (banks) make loans o he real secor. Increased credi risk and increased defauls in he real secor lead o a worsening of balance shees in he nancial secor. As in Sein (1998) here is uncerainy abou he healh of a paricular bank s balance shee. This uncerainy forms he basis of nancial fricions in he nancial secor. Thus in addiion o he rs feedback loop ha resuls solely from fricions in he real secor, 4

5 a second feedback loop arises from he combinaion of nancial fricions in boh he real and nancial secors. The iniial shock leads o increased credi risk and increased defauls in he real secor, which leads o a worsening of balance shees in he banking secor. As bank balance shees deeriorae, crediors become relucan o lend o banks and inerbank raes increase. When banks receive less funding, or are forced o pay a higher rae, hey pass his on o heir borrowers, leading o a curailmen of lending o he real secor and hus a furher decline in oupu and asse prices. Thus wo ypes of nancial fricions give rise o wo ypes of feedback loops. Boh of hese feedback loops lead o he ampli caion of shocks, which increases he severiy of he economic downurn following he iniial shock and slows he recovery. However he model in his paper will show how he second feedback loop, ha has o do wih he healh of a bank s balance shee, is sronger han he rs. This is due o wo facors ha are paricular o he nancial secor. Firs, nancial fricions in he real secor alone primarily a ec access o longer erm physical capial nancing. Bu he nancial secor also plays an imporan role in providing shor erm working capial nancing o rms. As demonsraed in he crisis of 28, when here are problems in he nancial secor, rms have rouble ful lling heir working capial needs as well. The model in his paper shows how a signi can porion of he exra ampli caion due o nancial fricions in he inermediary secor is due o he e ec of hese fricions on he marke for shor erm nancing. The second facor ha makes he feedback loop due o fricions in he inermediary secor so poen is he fac ha banks have relaively small capial cushions. Firms in he non- nancial secor mainain much higher capial-asse raios han rms in he nancial secor. This implies ha hey are more cushioned agains a fall in he value of heir asses. By examining simulaions of he model under alernaive scenarios relaed o he nancial secor s capial-asse raio, his paper shows how he srengh of he feedback loop arising because of fricions in he inermediary secor is direcly proporional o nancial secor leverage. This paper will proceed as follows. Secion 2 presens he model used o explain how recessions accompanied by nancial crises end o be longer and more severe han ordinary recessions. The model is a muli-counry new Keynesian model, wih nancial fricions inroduced in boh he real and nancial secors ha enable he model o move away from he irrelevance of balance shees implied by he Modigliani and Miller heorem. Then he calibraion of he model is discussed 5

6 in secion 3. The resuls from simulaions of he model are presened in secion 4. The resuls are presened in hree pars. Firs, impulse responses show how nancial fricions can lead o greaer business cycle volailiy and persisence following boh produciviy and moneary policy shocks. Second, we compue he volailiy and co-movemen of GDP is componens and show how he second momens of he business cycle change beween versions of he model where we "urn-on" various nancial fricions. Thirdly, we consider a new ype of shock, ied o fricions in he inermediary secor, ha can be hough of as an exogenous shock o nancial risk. Finally, secion 5 concludes and o ers some suggesions for furher research. 2 Model In he model here are ve ypes of agens: rms, enrepreneurs, capial builders, banks, and households. There is also a cenral bank ha ses he risk free nominal rae of ineres. Firms use capial and labor inpus o produce radeable oupu ha is used for consumpion and invesmen. Each rm produces a di ereniaed good and ses prices according o a Calvo (1983) syle price seing framework, hus giving rise o nominal price rigidiy. Enrepreneurs own physical capial and ren i o rms. This physical capial is nanced parially hrough deb and parially hrough equiy. In every period, an individual enrepreneur faces an idiosyncraic shock o he value of heir physical capial asses. While hese shocks have no direc aggregae e ecs, hey inroduce heerogeneiy among enrepreneurs. The shock is uninsurable, and a fracion of enrepreneurs may experience an abnormally large shock o he value of heir physical capial sock and be pushed ino bankrupcy, while mos will no. The uncerainy over which enrepreneurs will be pushed ino bankrupcy and which will no is a ype of nancial fricion in he real secor. The raio of deb o equiy on an enrepreneur s balance shee deermines heir abiliy o wihsand an abnormally large shock o he value of heir capial sock. Crediors use he enrepreneur s deb-equiy raio o deermine he riskiness of lending o he enrepreneurial secor, giving rise o a defaul risk ineres premium ha depends on he deb-equiy raio. 5 Capial builders purchase nal goods from rms for physical capial invesmen. There are diminishing marginal reurns o physical capial invesmen. In periods when invesmen is high, 5 The fac ha his idiosyncraic shock is uninsurable provides he necessary violaion of he complee markes assumpion necessary o overcome he implicaions of he Miller and Modigliani heorem. 6

7 he marginal reurn of ha invesmen in producing new physical capial is low, and vice versa. This gives rise o a procyclical relaive value of physical capial. Banks channel savings from households o rms in he form of working capial loans and o enrepreneurs in he form of physical capial loans. A bank nances is asse porfolio parially hrough equiy and parially hrough deb, which is made up of deposis from domesic and foreign households. Due o bankrupcies in he real secor, a porion of a bank s porfolio of physical capial loans will go ino defaul in any given period. While hese loan losses are no grea enough o push he enire banking secor ino insolvency, here is heerogeneiy among banks wih regards o heir exposure o he se of non-performing loans. A few banks may be over-exposed o he se of bad loans, and hey hemselves may be pushed ino insolvency. The uncerainy abou which banks are over-exposed o he se of non-performing loans and which are no is a ype of nancial fricion in he banking secor. The raio of deb o equiy on a bank s balance shee deermines heir abiliy o absorb loan losses, so he deb-equiy raio deermines he ex-ane riskiness of a paricular bank. This gives rise o an environmen where he spread beween inerbank lending raes and he risk free rae is increasing in he leverage raio of he banking secor. Households supply labor o rms and consume nal oupu. Furhermore hey supply a di ereniaed ype of labor and se wages according o a Calvo-syle wage seing process, giving rise o nominal wage rigidiy. Finally, he cenral bank ries o sabilize oupu and prices by conrolling he risk free nominal rae of ineres. The remainder of his secion presens he acual deails of he model. The model is a wocounry, wo-good model. In secion 4 we will examine he model in he case of a closed economy, wo large open economies, and a small open economy. In he model s noaion, he relaive size of he home counry is n and he relaive size of he foreign counry is 1 n. The small open economy is modeled as he home counry where n!. The closed economy is he foreign counry under he same parameerizaion (and hus 1 n! 1). In he case of wo large economies, n = 1 2. In wha follows, all variables are wrien in per capia erms and foreign variables are disinguished by an aserisk (*). Relaive counry size is he only source of cross-counry heerogeneiy in he model, so foreign equaions have been omied for breviy excep where absoluely necessary. 7

8 2.1 Firms In he home counry, inermediae goods producing rms, indexed i 2 [ n], combine capial and labor, k (i) and h (i) o produce a unique inermediae good Y (i). The rm s producion funcion is: Y (i) = A h (i) 1 k (i) (1) where A is an exogenous counry speci c sochasic TFP parameer ha is common o all rms and is a xed cos parameer ha is calibraed o ensure ha rms earn zero pro in he seady sae. The oupu from rm i can be sold o he domesic marke or sold as impors in he foreign marke: Y (i) = y d (i) + y m (i) where y d (i) is oupu from rm i ha is sold domesically and y m (i) is he oupu ha is impored ino he foreign counry. Inermediae goods from domesic and foreign rms are hen combined ino one aggregae nal good. As in Chari, Kehoe, and McGraan (22), domesically supplied and impored inermediae goods are aggregaed by he following: y = " () 1 R n yd (i) R 1 di + f 1 n ym (i) 1 # di (2) where is he elasiciy of subsiuion beween domesic varieies and is he elasiciy of subsiuion beween home and foreign varieies. From his aggregaor funcion he demand in he home counry for he inermediae good from domesic rm i, where i 2 [ n], as a funcion of aggregae demand is: y d (i) = (n) P d (i) P d y (3) P Similarly, he demand in he home counry for he inermediae good from foreign rm i, where P d 8

9 i 2 (n 1], as a funcion of aggregae demand is: 1 n y m (i) = f (1 n) P m (i) P m P P m y (4) where P d (i) is he price in he domesic marke for he inermediae good from rm i, P d = R n P d (i) di is a price index of domesically produced inermediae goods, P m = 1 1 nr 1 n (P m (i)) 1 di 1 1 price level is given by P = is a price index of impored inermediae goods, and he aggregae h (n) 1 1 P d 1 + f (1 n) 1 1 (P m ) 1 i 1 1. Firm i can discriminae when seing prices for he domesic or foreign marke. Thus hey can se separae prices for he domesic and expor markes. In period, he rm will be able o change is price in he domesic marke wih probabiliy 1 p. If he rm canno change prices hen hey are rese auomaically according o P d (i) = 1 P d 1 (i), where 1 = P 1 P 2. Thus if allowed o change heir domesic price in period, he rm will se a price o maximize: max 1P E P d(i) = o p + n ;+ P d (i) y+ d (i) MC + y+ d (i) where is he marginal uiliy of income in period. As discussed in his paper s echnical appendix, he rm ha is able o change is domesic price in period will se is price o: P d (i) = 1P E = 1 1P E = ;+ P d p + MC + + P+ d P y+ + ;+ P d p + + ;+ P+ d P y+ + If prices are exible, and hus p =, hen his expression reduces o: P d (i) = 1 MC which says ha he rm will se a price equal o a consan mark-up over marginal cos. Wrie he domesic price se by he rm ha can rese prices in period as ~ P d (i) o denoe ha i is an opimal price. Firms ha can rese prices in period will all rese o he same level, so P ~ d (i) = P ~ d. Subsiue his opimal price ino he price index P d = 1 R n n P d (i) di. Since a rm has a probabiliy of 1 p of being able o change heir price, hen by he law of large 9

10 numbers in any period 1 p percen of rms will reopimize prices, and he prices of p percen of rms will be auomaically rese using he previous periods in aion rae. Thus he domesic price index, P d, can be wrien as: P d = 1 p 1; P d p P ~ d The full deails of his derivaion as well as he derivaion for prices se for he foreign marke is locaed in he appendix. The rm hires labor and capial inpus, where W is he wage rae paid for labor inpu and R is he capial renal rae, boh of which he rm akes as given. Furhermore he rm mus pay heir wage bill in advance. To do so hey borrow b wc (i) = W h (i). The rm s income afer paying for capial and labor inpus is: d f (i) = P d (i) y d (i) + P x (i) y x (i) W h (i) R k (i) r wc b wc (i) (5) where P x (i) is he expor price for he inermediae good from rm i, and r wc on working capial loans. is he ineres rae Since here is no defaul risk from lending working capial o rms, compeiion in he banking secor forces he rae on working capial loans down o he bank s own cos of capial, r wc = r b. 6 The aggregae income from all rms is reurned o households as a lump sum paymen, d f = R n df (i) di. The rm will choose h (i) and k (i) o maximize pro in (5) subjec o he producion funcion in (1). The working capial requiremen implies ha he cos of he labor inpu is W (1 + r wc ) and he cos of he capial inpu is R. Given hese prices, he rm s demand for labor and capial inpus are: 6 As will be discussed laer in he paper, his implies ha a rm s access o shor erm working capial nancing is ied o he healh of he banking secor and he bank s cos of funds. When presening he resuls we will run alernae simulaions of he model where rms can borrow working capial a he risk free rae, and hus a rm s access o shor erm nancing is no ied o he healh of he nancial sysem. 1

11 where MC = 1 A W(1+r wc ) 1 MC h (i) = (1 ) W (1 + r wc ) Y (i) (6) k (i) = MC Y (i) R 1 R. 2.2 Enrepreneurs Enrepreneurs, indexed j 2 [ n], buy capial from capial builders and ren i o rms. A he beginning of period, enrepreneur j has a sock of capial, K (j), ha he will ren o rms in period a a renal rae R. In equilibrium, he aggregae sock of capial supplied by all domesic enrepreneurs j is equal o he aggregae sock of capial demanded by all domesic rms i, R n K (j) dj = R n k (i) di. Enrepreneurs nance his sock of capial parially hrough deb. The enrepreneur borrows b e (j) from domesic banks o nance heir capial sock K (j). Thus he marke value of he asses and liabiliies for enrepreneur j a he beginning of period are: Asses: P K K (j) Liabiliies: b e (j) (7) where P K is he price of exising capial. The end of he period he value of he non-depreciaed capial sock for he average enrepreneur is P K (1 ) K. However during he period, he individual enrepreneur j receives an idiosyncraic draw ha a ecs he relaive price of heir exising capial, so for enrepreneur j he end of period value of heir non-depreciaed capial sock is:! e (j) P K (1 ) K (j) where! e (j) is a i.i.d. draw from a lognormal disribuion on he inerval [; 1) wih mean 1 and variance 2 e. Since his draw has a mean 1, i has no e ec on he aggregae capial sock. I simply inroduces 11

12 heerogeneiy among enrepreneurs, and in any given period a fracion of enrepreneurs receive a draw ha has a large adverse e ec on he value of heir exising capial (a small! e (j)) and hus a he end of he period, he value of heir liabiliies exceeds he value of heir asses. During he period he enrepreneur rens his capial sock o rms for a renal rae of R. The enrepreneur nances his capial sock wih a loan from he bank wih an ineres rae r e. Thus a he end of he period, afer he realizaion of! e (j), he nominal marke value of enrepreneur j s asses is! e (j) P K (1 ) K (j) + R K (j). A he end of he period he nominal value of he enrepreneur s liabiliies is (1 + r e ) b e (j). Thus, afer he realizaion of! e (j), enrepreneur j is bankrup if:! e (j) P K (1 ) K (j) + R K (j) < (1 + r e ) b e (j) (8) Thus he hreshold value of! e (j) below which he enrepreneur goes bankrup in period and above which hey coninue operaions is:! e = (1 + re ) be (j) K (j) P K (1 ) R (9) where DA e (j) = be (j) K (j) is he raio of he book value of deb o he book value of asses on an enrepreneur s balance shee. The hisory of individual enrepreneur j will in uence he level of b e (j) and K (j), bu he raio DA e (j) = be (j) K (j) is equal across all enrepreneurs. This is a key resul for aggregaion, for i implies ha he bankrupcy cuo value! e does no depend on an enrepreneur s hisory. More inuiion behind his resul is presened a he end of his secion and a formal proof is presened in he appendix. If enrepreneur j does no defaul in period, he crediors receive a reurn of r e. If he enrepreneur defauls, crediors receive a share of he enrepreneur s remaining asses, less he bankrupcy cos e. The hreshold value! e in equaion (9) deermines wheher or no an enrepreneur goes ino defaul. Thus he payo o crediors condiional of he realizaion of he shock! e (j) is: (1 + r e ) (b e (j)) if! e (j)! e (1 e )! e (j) (1 ) P K K (j) + R K (j) if! e (j) <! e (1) Perfec compeiion in he banking secor implies ha he bank s expeced pro is zero. So 12

13 he no defaul rae he bank charges on physical capial loans is se such ha he expeced reurn, afer facoring in he cos of bankrupcy, is equal o he bank s cos of capial, r b : Z! e 1 + r b b e (j) = (1 e )! e (j) (1 ) P K K (j) + R K (j) df (! e )+ Z 1! e (1 + r e ) b e (j) df (! e ) where F (! e ) is he c.d.f. of he lognormal disribuion of! e. Thus he ineres rae charged by banks for physical capial loans is: h 1 + r e = 1 + rb (1 e ) R F (! e ) + (1 1 F (! e ) ) P K (1 F (! e )) be (j) K (j) R i! e! e df (! e ) (11) where F (! e ) is he percen of manufacuring rms ha declare bankrupcy. Holding all else equal, his ineres rae, r e, is increasing in F (! e ). If here are nancial fricions in he enrepreneurial secor, F (! e ) is increasing in! e.! e is increasing in he manufacuring rm s deb-asse raio. Thus when here are nancial fricions in he enrepreneurial secor, he ineres rae on physical capial loans is increasing in he level of deb on an enrepreneur s balance shee. The cuo value of! e (j) in equaion (9) combined wih he ineres rae expression in (11) demonsraes he feedback loop associaed wih nancial fricions in he enrepreneurial secor. When he price of exising capial, P K falls, he cuo value! e rises. This implies ha more rms will receive draws of! e (j) below his cuo value and be forced ino bankrupcy. When more rms go ino bankrupcy, F (! e ) increases, and r e increases as banks now demand a higher ineres rae o compensae for he increased bankrupcy risk. This higher r e means higher ineres expenses and lower pro for he enrepreneur, which leads o a furher increase in he cuo value! e. The end of period ne worh for he rm ha survives is he rm s pro in ime plus he value of heir non-depreciaed capial sock: ~N e (j) = r k K (j) (1 + r e ) b e (j) +! e (j) P K (1 ) K (j) The rm will pay a dividend o shareholders of d e (j) and begin he nex period wih ne worh N e +1 (j) = ~ N e (j) d e (j). Firms ha declare bankrupcy in period pay no dividend and drop ou of he marke, hey are replaced wih new rms, which are endowed wih sar up capial of 13

14 N e. Thus he ne worh of he enrepreneurial secor a he beginning of nex period is: N e +1 = Z! e = N e F (! e ) + N e +1 (j) df (! e ) + Z 1! e N e +1 (i) df (! e ) (12) Z 1 r k K (1 + r e ) b e d e (1 F (! e )) + P K (1 ) K! e! e df (! e ) A he beginning of any period, enrepreneurs have di eren levels of ne worh N +1 (j) ha will depend on he enrepreneur s hisory of idiosyncraic shocks! e (j). The enrepreneur will acquire capial up o he poin where he ineres rae on bank loans is equal o he expeced reurn o holding a uni of capial: r e +1 = E R +1 +! e +1 (j) (1 ) P K +1 P K! Since! e +1 (j) is i.i.d. and E! e +1 (j) = 1, he lef hand side of he above expression is he same across all enrepreneurs j, which implies ha r e +1 is he same across all enrepreneurs. 2.3 Capial Builders The represenaive capial builder convers nal goods, given by equaion (2), ino he physical capial purchased by enrepreneurs. A he end of period, he non depreciaed physical capial sock is (1 ) K, and he physical capial sock a he beginning of he nex period is K +1. The evoluion of he physical capial sock is given by: I K +1 (1 ) K = K K where > and < implying ha here are diminishing marginal reurns o physical capial invesmen. Capial builders purchase nal goods for invesmen a a price P and sell exising capial o enrepreneurs a a price P K. Thus he pro s of he represenaive capial builder are given by: d c = P K (K +1 (1 ) K ) P I 14

15 In a compeiive capial building secor, pro maximizaion implies ha he relaive price of exising capial is: Since <, when I K P K 1 = I P K is high, I K is low, so P K P is high. This implies ha during imes of high physical capial invesmen, when he raio of invesmen o he exising capial sock is high, he relaive price of exising capial is high. Since invesmen is highly procyclical, capial adjusmen coss imply ha he relaive price of capial is highly procyclical as well. 2.4 Banks Banks, indexed k 2 [ n] make physical capial loans o domesic enrepreneurs. They nance his loan porfolio parially wih equiy and parially wih borrowing from domesic and foreign households. A he beginning of period, he value of he bank s asses is B e (k), which is he bank s sock of loans o enrepreneurs. The value of he bank s liabiliies is b s (k) + b sf deposis of domesic households and b sf (k) are he deposis of foreign households. 7 (k), where b s (k) are he The bank also makes working capial loans o rms in order o nance he rm s wage bill. This however is no lised as a beginning of period asse for he bank. By assumpion his loan is made afer he beginning of he period and repaid before he end of he period. If he sock of working capial loans were o appear as a asse for he bank a he beginning of period, ha would imply ha he loan was made in period 1, which implies ha he rm made a decision abou period s labor inpu in period 1. Bankrupcy in he enrepreneurial secor in period means he bank s asses are worh less a he end of he period. The value of he average bank s asses a he end of he period is (1 e ) (1 + r e ) B e, where e is he share of he average bank s physical capial loan porfolio ha is los o bankrupcy and liquidaion coss. 7 The same sock of bonds ha is a liabiliy o one pary is an asse o anoher. Throughou his paper, when a sock of bonds is an asse, i is wrien wih a capial B, when he sock of bonds is a liabiliy i is wrien wih a lower case b. Thus marke clearing in he bond marke requires ha he sum of physical capial loans across all banks equals he sum of borrowing by enrepreneurs, R n Be (k) dk = R n be (j) dj. 15

16 e represens he share of he average bank s physical capial loan porfolio ha is los o bankrupcy and liquidaion coss, however banks don hold fully diversi ed loan porfolios. Some banks may be overexposed o he se of non-performing loans o he enrepreneurial secor. This overexposure 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. 8 The percen of he bank k s loan porfolio ha is los o bankrupcy or liquidaion coss is h i! b (k) e, where! b (k) is an i.i.d. draw from a lognormal disribuion on he inerval 1 e wih mean 1 and sandard deviaion b. If bank k receives a large draw! b (k), i implies ha he bank is overexposed o he se of non-performing loans and may iself face insolvency. The bank is insolven if he end of period value of is asses is less han he end of period value of is liabiliies: 1! b (k) e (1 + r e ) B e (k) < 1 + r b (k) b s (k) + b sf (k) The hreshold value of! b (k) above which bank k is forced o declare bankrupcy and below which he bank will coninue operaions is:! b = (1 + re ) 1 + r b (k) bs (k)+bsf (k) B e(k) e (1 + r e ) (13) Bank k s hisory of idiosyncraic draws,! b (k), hus is hisory of exposure o non-preforming secors of he economy, will deermine he levels of B e (k), b s (k), and b sf (k). However, a he beginning of he period, all banks will have he same raio of oal deb o oal asses, DA b (k) = b s (k)+bsf (k) B e(k) and will have he same cos of capial, r b (k). This resul is key for he aggregaion of balance shee variables across a coninuum of individual banks, for his implies ha he cuo value! b is common across all banks. The formal proof of his claim is presened in he appendix. When deciding how much o lend o bank k in he nex period and a wha rae, he bank s crediors facor in he fac ha if he bank does no defaul, hey receive a gross ineres rae 1 + r b +1 (k). If bank k defauls, crediors receive nohing.9 Thus he expeced payo o a bank s 8 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 nancial crisis. 9 The assumpion ha crediors receive nohing in he case of bank defaul is because he model is laer calibraed such ha he spread beween he inerbank rae, r b, and he risk free rae, i, in he seady sae of he model is equal 16

17 crediors condiional on he bank s exposure o he se of non-preforming loans is: 1 + r+1 b (k) b s +1 (k) + bsf +1 (k) if! b +1 (k) <!b +1 if! b +1 (k)!b +1 (14) Domesic and foreign deposiors will exend bank k credi up o he poin where he expeced reurn, afer facoring in he probabiliy of defaul is equal o he risk free rae: Z! b (1 + i +1 ) b b +1 (k) + b bf +1 (k) +1 = 1 + r+1 b (k) b b +1 (k) + b bf +1 (k) dg! b +1 This condiion can be used o solve for he ineres rae on inerbank lending o bank k: 1 + r+1 b (k) = 1 + i +1 G! b (15) +1 where G! b +1 is he c.d.f. of he lognormal disribuion of! b +1, and hus measures he proporion of banks ha do no go bankrup in period + 1. Since DA b +1 (k) = bs +1 (k)+bsf +1 (k) B e +1 (k) is consan across all banks, he inerbank lending rae, and hus banks cos of capial, is consan across all banks. The expressions for he cuo value! b +1 in (13) and he inerbank ineres rae in (15) shows how he feedback loop menioned earlier ha occurs because of bankrupcy risk in he enrepreneurial secor is worse when we also consider insolvency risk in he banking secor. If he expeced bankrupcy rae in he real secor is high, he expeced loan losses for he average bank, E e +1, is high. When E e +1 increases,! b +1 decreases. If bank k receives a draw of! b +1 (k) above!b +1, hen he bank is overexposed o he se of non-performing loans and ha bank becomes insolven. When! b +1 falls, more banks are expeced o receive a draw above he cuo value, and hus he expecaion of more insolvencies in he real secor lead o he expecaion of more insolvencies in he nancial secor. The greaer chance of insolvency causes an increase in inerbank ineres raes, r b +1.1 o he hisorical average of he spread beween he 3-monh Libor and he 3-monh T-bill. The Libor is an inerbank index rae ha is based on he ineres rae for unsecured lending o banks. 1 An increase in E e +1 can be hough of as he special kind of bad news discussed in Geanakoplos (29). An increase in aggregae loan losses no only lowers expecaions abou he value of a bank s asses, bu i leads o more uncerainy abou he value as well. 17

18 When inerbank ineres raes increase, banks are forced o pass on his higher cos of capial by charging higher ineres raes on loans o he enrepreneurial secor. This squeezes enrepreneurial secor balance shees, as discussed earlier in secion 2.2, leading o more bankrupcies in he enrepreneurial secor. Thus a second feedback loop occurs due o fricions in he banking secor ha complimens he earlier feedback loop ha was due o fricions in he enrepreneurial secor. The end of period ne worh of he bank ha is no over-exposed o he se of non-preforming loans and is able o coninue operaions is: ~N b = 1! b (k) e (1 + r e ) B e (k) 1 + r b b s (k) + b sf (k) The bank will pay a dividend o shareholders and begin he nex period wih a ne worh N b +1 (k) = ~ N b (k) d b (k). Banks ha were overexposed o he se of non-preforming loans and hus were forced ino bankrupcy end he period wih no ne worh and drop ou of he marke. They are replaced wih new banks ha are endowed wih sar up capial N b. Thus he ne worh of he enire banking secor a he beginning of nex period is: N b +1 = Z 1! b = N b 1 G Z! b N+1 b (i) dg! b +! b (1 + r e ) B e e Z! b + (1 + r e ) B e! b dg! b N+1 b (k) dg! b 1 + r b b s + b sf d b G! b (16) 2.5 Households Households, indexed l 2 [ n], supply heerogeneous labor o rms and consume from heir labor income, ineres on savings, and pro income from rms, enrepreneurs, capial builders, and banks. The household maximizes heir uiliy funcion: max 1 P = ln (C (l)) (H (l)) 1+ H H (17) subjec o heir budge consrain: 18

19 P C (l) + B+1 s (l) + S B sf +1 (l) + F (!e ) N e + 1 G = W (l) H (l) + d f (l) + de (l) + d c (l) + d b (l) + 1 b + 1 b 1 + r b S B sf (l) + e + b b 2! b N b 1 + r b B s (l) S B sf (l) S B sf 2 (18) where C (l) is consumpion by household l in period, H (l) is he household s labor e or in he period, B s (l) is he household s sock of deposis wih domesic banks a he beginning of he period, B sf (l) is he sock of deposis wih foreign banks, W (l) is he wage paid for he household s heerogenous labor supply, b ( b ) represens he small share of deposis o he home (foreign) banking secor ha are los o bankrupcy and liquidaion coss, and d f (l), de (l), d c (l) and d b (l) are he household s share of period pro s from rms, enrepreneurs, capial builders and banks, respecively. 11 The household pays a small quadraic ransacions cos o holding oher han he seady sae level of deposis wih foreign banks, b 2 B sf (l) B sf 2. Each household supplies a di ereniaed ype of labor. The funcion o aggregae he labor supplied by each household ino he aggregae sock of labor employed by domesic rms is: Z n H = H (l) 1 1 dl (19) where H = R n h (i) di. Since he household supplies a di ereniaed ype of labor, i faces a downward sloping labor demand funcion: W (l) H (l) = H W In any given period, household j faces a probabiliy of 1 w of being able o rese heir wage, oherwise i is rese auomaically according o W (l) = 1 W 1 (l). If household j is allowed o rese heir wages in period hey will se a wage o maximize he 11 Marke clearing in he marke for deposis requires ha he sum of deposis wih domesic banks across all domesic households equals he sum of borrowing from domesic households across all domesic banks, R n R Bs (l) dl = n bs (k) dk, and ha he sum of deposis wih foreign banks across all domesic households equals he sum of borrowing from domesic households across all foreign banks, R n Bsf (l) dl = R 1 n bsf (k) dk. 19

20 expeced presen value of uiliy from consumpion minus he disuiliy of labor. E 1P = ( w ) + ;+ W (l) H + (l) (H + (l)) 1+ H H Thus afer echnical deails which are locaed in he appendix, he household ha can rese wages in period will choose a wage: W (l) H +1 = 1 + H 1 H (W ) H E = 1P ( w ) 1P E ( w ) + ;+ = + W + H ;+ W (H+ ) 1+ H H W+ ;+ W H+ If wages are exible, and hus w =, his expression reduces o: W (l) = 1+ H H (H ) 1 H 1 Thus when wages are exible he wage rae is equal o a mark-up, ( 1), muliplied by he marginal disuiliy of labor, 1+ H H (H ) 1 H, divided by he marginal uiliy of consumpion,. Wrie he wage rae for he household ha can rese wages in period, W (l), as ~ W (l) o denoe i as an opimal wage. Also noe ha all households ha can rese wages in period will rese o he same wage rae, so ~ W (l) = ~ W. All households face a probabiliy of (1 w ) of being able o rese heir wages in a given period, so by he law of large numbers (1 w ) of households can rese heir wages in a given period. The wages of he oher w will auomaically rese by he previous periods in aion rae. Subsiue ~ W ino he expression for he average wage rae W = derive an expression for he evoluion of he average wage: W = 1 1 w ( 1; W 1 ) (1 w ) ~W R n W (l) 1 dl 1 1, o 2.6 Moneary Policy The moneary policy insrumen is he shor erm risk free rae, i, which is deermined by he cenral bank s Taylor rule funcion: 2

21 1 + i 1 + i ss = 1 + i i n o 1 1 i 1 + i ss ( ) p (1 + OG ) y m (2) where = P P 4, OG = GDP A GDP ss 1, and m is an exogenous shock o he nominal ineres rae. 3 Parameer Values The model in he previous secion is solved wih a rs-order approximaion and he resuls are found from simulaions of he calibraed model. This secion will begin by presening he basic parameer values used in his calibraion. Then we will describe he various ypes of exogenous shocks ha will drive he simulaions of he model and he esimaion of hese di eren shock processes. The full lis of he model s parameers and heir values is found in able 1. The rs eigh parameers: he discoun facor, he capial depreciaion rae, capial s share of income, he elasiciy of subsiuion beween home and foreign goods, he bond adjusmen cos parameer, he labor supply elasiciy, he elasiciy of subsiuion beween goods from di eren rms, and he elasiciy of subsiuion beween labor from di eren households are all se o values ha are commonly found in he lieraure. The capial adjusmen cos parameer,, describes he curvaure of he capial adjusmen funcion I K. I is he elasiciy of he relaive price of capial wih respec o changes in he invesmen-capial raio. This parameer preforms he imporan funcions of lowering he relaive volailiy of invesmen and ensuring he procyclicaliy of he price of capial. Empirical esimaes of his parameer vary, bu he value of :375 is in he middle of he range of empirical esimaes and ensures ha he relaive volailiy of invesmen in he model is near wha we see in he daa. The nex wo parameers in he able are he Calvo price and wage sickiness parameers. The wage sickiness parameer is chosen such ha on average a household adjuss heir wages once a year. The price sickiness parameer implies ha prices are a lile more exible han wages and is aken from he DSGE esimaion lieraure (see e.g. Chrisiano e al. 25). The nex se of parameers describe exponens in he cenral bank s Taylor rule funcion. The ineres rae smoohing parameer, he weigh on lagged in aion, and he weigh on he oupu gap are all se o values ha are commonly found in he lieraure. 21

22 The nex four parameers are all deermined so ha he seady sae of he model is able o mach cerain feaures of he daa. The and f parameers from he funcion ha aggregaes home and foreign goods in (2) are se such ha he home counry in he model has a seady sae impor share of 25%. Noe ha his value will depend on wheher we are considering he closed, he large open, or he small open economy. 12 The nex wo parameers, and are he xed cos in he producion of inermediae goods and he weigh on he disuiliy from labor in he household s uiliy funcion, respecively. These are se o ensure ha in he seady sae, inermediae goods rms earn zero economic pro and he household s labor supply is uniy. Finally he las hree parameers in he able relae o he risk of bankrupcy and liquidaion coss in eiher he banking or enrepreneurial secors. The parameer b measures he seady sae level of uncerainy in he nancial secor. This parameer is deermined o ensure ha in he seady sae of he model, when banks have a deb-asse raio of abou :9, here is a 13 basis poin spread beween inerbank raes and he risk free rae, he average spread beween he 3-monh Libor and he 3-monh T-bill from 1984 o 27. The cos of liquidaion and he idiosyncraic bankrupcy risk in he enrepreneurial secor, e and e are joinly deermined. These parameers ensure ha in he seady sae of he model, when rms in he enrepreneurial secor have a deb-asse raio of :5, an enrepreneur faces a 2% probabiliy of bankrupcy and he seady sae spread beween he ineres rae on physical capial loans and he bank s cos of capial is approximaely 7 basis poins Exogenous Shock Processes In his model here are hree ypes of shocks. The rs wo, counry speci c shocks o oal facor produciviy (TFP) in (1) and counry speci c moneary policy shocks ha appear in he cenral bank s Taylor rule funcion in (2) are common feaures of many real business cycle or new Keynesian models. The hird shock is a shock o he uncerainy abou he healh of a bank s 12 From he demand funcions for domesically supplied inermediae inpus and impors, equaions (3) and (4), he seady sae impor share is: m = Z 1 P m (i)ym (i) Z n n Z 1 = f 1 (1 n) P d(i)yd (i)+ P m(i)ym (i) (n) 1 + f (1 n) 1 n 13 The calibraion ha enrepreneurs have a seady sae deb-asse raio of abou :5 and banks have a seady sae deb-asse raio of abou :9 is based on he hisorical average deb-asse raios for U.S. non- nancial and nancial rms as repored in he Federal Reserve s Flow of Funds Accouns. 22

23 asses, b, and is unique o a model wih nancial fricions in he banking secor. 14 Recall ha b measures he cross-secional heerogeneiy among banks wih regard o heir exposure o loan losses. This erm can also be hough of as he uncerainy abou a paricular bank s exposure o he se of non-preforming loans. Holding all else equal, an increase in b will cause crediors o demand a higher rae when lending o banks. Thus a shock o b is a direc shock o he cos of capial in he banking secor. However before we consider his new and unfamiliar ype of shock, le s discuss he esimaion of he processes governing TFP and moneary policy shocks. Shocks o TFP are given by: ^A = ^Y (1 ) ^N ^K where ^Y, ^N, and ^K, are counry-speci c ime series of deviaions of GDP, employmen, and he capial socks, from an HP lered rend. The series for home and foreign TFP ucuaions are hen used o esimae a VAR(1) process: ^A +1 ^A = A 6 4 ^A ^A ^"a ^" a where A 6 = 4 ^"a ^"a 7 5 is he covariance marix of he innovaions, ^" a ^" a ^" a and ^" a. Alernaively we can consider shocks o he risk free ineres rae in he cenral bank s Taylor rule funcion. Firs aking he log of each side of he of he policy funcion in (2): (i i ss ) = i (i 1 i ss ) + (1 i ) ( p + y OG ) + m where i,, and OG are counry speci c ime series of he overnigh ineres rae, he in aion rae, and he oupu gap. Apply he benchmark parameerizaion, i = :9 and p = 1:5 and y = :5 o calculae he residual erm m, which is a ime series of counry speci c moneary policy shocks. 14 Recenly auhors have begun o incorporae risk shocks ino nancial acceleraor models, see references in secion 4.3 for examples. 23

24 The series for home and foreign moneary policy shocks are hen used o esimae a VAR(1) process: m +1 m = M m m ^"m ^" m where M 6 = 4 ^"m ^"m 7 5 is he covariance marix of he innovaions, ^" m ^" m ^" m and ^" m. Since we consider hree ypes of models, a closed economy, wo large open economies, and a small open economy, we need o esimae a few shock processes. The shock processes for he model wih wo large open economies is esimaed from daa for he U.S. and he Eurozone from 1995:1 o 27:2. The processes for he small open economy and he closed economy are esimaed from daa for he U.S. and he UK from 1984:1 o 27:2. We rea he U.S. as he large economy and he UK as he small economy. We impose he resricion ha here is no spillover from he UK o he U.S. (one of he o -diagonal erms in A and M is equal o zero. This resricion means ha he esimaed shock processes for he UK are for a small open economy and hose for he U.S. are for a closed economy. The processes for he TFP and moneary policy shocks are presened in able 2. Since he nancial secor uncerainy shocks, b, are new and unfamiliar, we will no aemp o esimae a process for hese shocks bu will insead es he model s reacion o a nancial secor uncerainy shock under a number of alernaive parameerizaions Resuls To show he cyclical e ecs of he feedback loop caused by fricions in boh he enrepreneurial and banking secors, we will rs discuss some impulse responses o examine he impac of a shock on balance shees and he see how in a model wih nancial fricions, balance shee changes have real e ecs. Secondly, in an aemp o quanify he feedback loop resuling from nancial fricions, we will see how cerain second momens of he business cycle (volailiy and co-movemen) are a eced by he inroducion of nancial fricions ino he model. Lasly, we will inroduce nancial secor risk shocks ino he model and show how in an environmen wih nancial fricions in he banking 24

25 secor, exogenous ucuaions in risk arising ou of he nancial secor can be an independen source of ucuaions. In wha follows we will presen he resuls from hree versions of he model, a version where he nancial fricions in boh he enrepreneurial and banking secors have been "urned o " and hus he condiions of he Miller and Modigliani heorem hold, where he nancial fricion in he enrepreneurial secor has been "urned on" bu sill here are no fricions in he banking secor, and a version where here are fricions in boh secors. When a nancial fricion is "urned o ", he risk spread, r e r b or r b i is held a is seady sae level hrough dynamic simulaions of he model. The seady sae value of he spread, and hus he oher variables in he model, is he same in all hree versions of he model, wheher or no he nancial fricion is "urned on" or "urned o ". 4.1 Impulse Responses The adverse feedback loop in a closed economy The responses of he relaive price of capial, enrepreneurial secor deb-asse raios, he risk spread on physical capial loans, and he inerbank lending spread in a closed economy o moneary policy shock are presened in gure 1. Following an exogenous increase in he risk free rae, he relaive price of capial falls due o he capial adjusmen coss ha impose diminishing marginal reurns o invesmen. When invesmen falls, as i does following an exogenous increase in ineres raes, he marginal reurn o invesmen increases, so he relaive price of exising capial falls. This 1% fall in he relaive price of capial leads o a similar increase in enrepreneurial secor deb-asse raio. When here are no nancial fricions in he model, balance shees don maer and his increased leverage has no e ec, bu when here are nancial fricions in he model, his increase in borrower leverage makes lending o enrepreneurs appear riskier. Thus when here are nancial fricions in he model, he defaul risk premium charged by banks increases by 15 2 basis poins. The increase in enrepreneurial leverage leads o more loan defauls. This leads o a fall in he value of asses on a bank s balance shee and hus leads o a decline in a bank s ne worh. In a model wih nancial fricions in he banking secor, his make banks appear riskier. The gure 25