bernankegertlergilchrist.macrohandbook1999

8/7/2019 BernankeGertlerGilchrist.MacroHandbook1999

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A ppend i x B . H ouseho l d , r e t a i l and gove rnmen t s ec t o r sB . 1 . H o u s e h o l d sB . 2 . T h e r e t a i l s e c t o r a n d p r i c e s e t t i n gB . 3 . G o v e r n m e n t s e c t o r

R e f e r e n c e s

B . S. B e r n a n k e e t al .

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Abstrac tThi s chap t e r deve l ops a dynami c gene ra l equ i l i b r i um mode l t ha t i s i n t ended t ohe l p c l a r i f y t he ro l e o f c r ed i t marke t f r i c t i ons i n bus i nes s f l uc t ua t i ons , f r om bo t ha qual i t a tive and a quant i t a t ive s tandpo int . Th e mod el i s a synthes i s o f the leadin gapproaches in the l i t e ra ture . In par t icular , the f ramework exhibi t s a "f inancia lacce l e r a t o r " , i n t ha t endogenous deve l opment s i n c r ed i t marke t s w ork t o ampl i fy andpropaga t e shocks t o t he macroeconomy. In add i t i on , w e add seve ra l f ea t u r e s t o t hemode l t ha t a r e des i gned t o enhance t he empi r i ca l r e l evance . F i r s t , w e i ncorpora t emoney and p r i ce s t i ck i nes s , w h i ch a l l ow s us t o s t udy how c r ed i t marke t f r i c t i onsm ay i n f l uence the t r ansmi s s i on o f m on e t a ry po l i cy . I n add i t ion , w e a l l ow fo r lags i ni n v e st m e n t w h i ch e n a b le s t h e m o d e l t o g e n e r a t e b o th h u m p - s h a p e d o u t p u t d y n a m i c sand a l ead - l ag r e l a t i on be t w een a s se t p r i ces and i nves t men t , a s i s cons i s t en t w i t h t heda t a. F i na ll y , w e a l l ow fo r he t e rogen e i t y am ong f irms t o cap t u r e t he f ac t t ha t bo r row e r shave d i f f e r en t i a l acces s t o cap i t a l marke t s . U nder r easonab l e pa r ame t r i za t i ons o ft he m ode l , t he f i nanc i a l acce l e r a t o r has a s i gn if i can t in f l uence on bus i nes s cyc l ed y n a m i c s .

Keywordsf i nanc ia l acce l e r a to r , bus i nes s f l uc tua t i ons , mo ne t a ry po l i cyJ E L c l a s s i f i c a t i o n : E 3 0 , E 4 4 , E 5 0


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C h . 2 1 : T h e F i n a n c i a l A c c e l e r a t o r in a Q u a n t i t a t i v e B u s i n e s s C y c l e F r a m e w o r k 13431 . I n t r o d u c t i o n

T h e c a n o n i c a l r e a l b u s i n e s s c y c l e m o d e l a n d t h e t e x t b o o k K e y n e s i a n I S - L M m o d e ld i f f e r i n m a n y f u n d a m e n t a l w a y s . H o w e v e r , t h e s e t w o s t a n d a r d f r a m e w o r k s f o rm a c r o e c o n o m i c a n a l y s is d o s h a r e o n e s t r o n g im p l i c a t io n : E x c e p t f o r th e t e r m s t r u c tu r eo f r ea l i n t e r e s t r a t e s , wh ich , t oge the r wi th ex pec t a t i ons o f fu tu re payou t s , de t e rm inesrea l a s se t p r i ces , i n t hese mode l s cond i t i ons i n f i nanc i a l and c r ed i t marke t s do no ta f f e c t t h e r e a l e c o n o m y . I n o t h e r w o r d s , t h e s e t w o m a i n s t r e a m a p p r o a c h e s b o t h a d o p tt h e a s s u m p t i o n s u n d e r l y i n g t h e M o d i g l i a n i - M i l l e r ( 1 9 5 8 ) t h e o r e m , w h i c h i m p l i e s t h a tf in a n c i al s t r u c t u re i s b o t h i n d e t e r m i n a t e a n d i r r e l e v a n t to r e a l e c o n o m i c o u t c o m e s .

O f c o u r s e , i t c an b e a r g u e d t h a t t h e s t a n d ar d a s s u m p t i o n o f f i n a n c ia l -s t r u ct u r ei r r e l evance i s on ly a s im p l i f i ca ti on , no t t o be t aken l it e ra l ly , and no t ha rm fu l i f t he" f r i c t i ons" i n f i nanc i a l and c r ed i t marke t s a r e su f f i c i en t ly sma l l . However , a s Ger t l e r(1988) d i scusses , t he re i s a l ong- s t and ing a l t e rna t ive t r ad i t i on in macroeconomics ,beg inn ing wi th F i she r and K eyne s i f no t ea r l i e r au tho r s , t ha t g ives a mor e cen t r a l ro l e t oc red i t -m arke t cond i t i ons i n t he p ro pag a t ion o f cyc l i ca l f l uc tua t ions . I n t h is a l t e rna t ivev iew, de t e r io ra t i ng c r ed i t -m arke t cond i t i ons - sha r p i nc reases i n in so lven c i e s andbankrup tc i e s , r i s i ng r ea l deb t bu rdens , co l l aps ing a s se t p r i ces , and bank f a i l u r e s -a r e n o t s i m p l y p a s s i v e r e fl e c ti o n s o f a d e c l i n i n g r e a l e c o n o m y , b u t a r e i n t h e m s e l v e sa ma jo r f ac to r dep res s ing economic ac t iv i t y . Fo r example , F i she r (1933) a t t r i bu t edt h e s e v e r i t y o f t h e G r e a t D e p r e s s i o n i n p a r t t o th e h e a v y b u r d e n o f d e b t a n d e n s u i n gf inanc i a l d i s t r e s s a s soc i a t ed w i th t he de f l a ti on o f the e a r ly 1930s , a t hem e t aken uph a l f a c e n t u r y l a t e r b y B e r n a n k e ( 1 9 83 ) . M o r e r e c e n tl y , d i st r e s s e d b a n k i n g s y s t e m s a n da d v e r s e c r e d i t- m a r k e t c o n d i t io n s h a v e b e e n c i te d a s s o u r c e s o f s e r io u s m a c r o e c o n o m i ccon t r ac t ions i n Scand inav ia , La t in Amer i ca , J apan , and o the r Eas t As i an coun t r i e s . I nt h e U S c o n t e x t, b o t h p o l i c y - m a k e r s a n d a c a d e m i c s h a v e p u t s o m e o f t h e b l a m e f o rt h e s lo w r e c o v e r y o f t h e e c o n o m y f r o m t h e 1 9 9 0 -1 9 9 1 r e c e s si o n o n h e a v y c o r p o r a ted e b t b u r d e n s a n d a n u n d e r c a p i t a l i z e d b a n k i n g s y s t e m [ s e e , e . g . , B e r n a n k e a n d L o w n( 1 99 2 )] . T h e f e e d b a c k s f r o m c r e d i t m a r k e t s t o th e r e a l e c o n o m y i n t h e s e e p i s o d e sm a y o r m a y n o t b e a s s t r o n g a s s o m e h a v e m a i n t a i n e d ; b u t i t m u s t b e e m p h a s i z e d t h a tt h e c o n v e n t i o n a l m a c r o e c o n o m i c p a r a d i g m s , a s u s u a l ly p r e s e n t e d , d o n o t e v e n g i v e u sw a y s o f t h i n k i n g a b o u t s u c h e f fe c t s.

T h e p r i n c i p a l o b j e c t i v e o f th i s c h a p t e r i s t o s h o w t h a t c r e d i t - m a r k e t i m p e r f e c t i o n sc a n b e i n c o r p o r a t e d i n t o s t a n d a r d m a c r o e c o n o m i c m o d e l s i n a r e l a t i v e l y s t r a i g h t f o r -ward ye t ri go rou s way . Bes ides o u r des i r e t o be ab l e t o eva lua t e t he ro l e o f c r ed it -m a r k e t f a c t o r s in t h e m o s t d r a m a t i c e p i s o d e s , s u c h a s th e D e p r e s s i o n o r t h e m o r e r e c e n tc r i s e s ( such a s t hose i n Eas t As i a ) , t he re a r e two add i t i ona l r ea sons fo r a t t empt ing tob r in g s u c h e f f e c ts i n to m a i n s t r e a m m o d e l s o f e c o n o m i c f l uc t u a ti o n s . F i rs t, i t a p p e a r st h a t i n t r o d u c i n g c r e d i t - m a r k e t f r i c t i o n s i n t o t h e s t a n d a r d m o d e l s c a n h e l p i m p r o v ethe i r ab i l i t y t o exp la in even " ga rden-va r i e ty" cyc l i ca l f l uc tua t ions . I n pa r t i cu l a r , i nt h e c o n t e x t o f s ta n d a r d d y n a m i c m a c r o e c o n o m i c m o d e l s , w e s h o w i n t h is c h a p t e rt ha t c r e d i t -m a r k e t f ri c ti o n s m a y s i g n i f ic a n t ly a m p l i f y b o t h r e a l a n d n o m i n a l s h o c k st o th e e c o n o m y . T h i s e x t r a a m p l i f ic a t i o n is a s t e p t o w a r d r e s o l v i n g t h e p u z z l e o f h o w


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1344 B . S. B e r n a n k e e t a l.r e l a t i ve l y sma l l shocks (modes t changes i n r ea l i n t e r e s t r a t e s i nduced by mone t a rypo l i cy , f o r exampl e , o r t he sma l l ave rage changes i n f i rm cos t s i nduced by evena r e l a t i ve l y l a rge movement i n o i l p r i ces ) can neve r t he l e s s have l a rge r ea l e f f ec t s .I n t roduc i ng c r ed i t -marke t f r i c ti ons has t he added advan t age o f pe rm i t ti ng t he s t anda rdm o d e l s t o e x p l a i n a b r o a d e r c l a ss o f i m p o r t a n t c y c l i c a l p h e n o m e n a , s u c h a s c h a n g e si n c r ed i t ex t ens ion an d t he sp r eads b e t w e en sa f e and r i sky i n t e re s t r a te s .

T h e s e c o n d r e a s o n f o r i n c o r p o r a t i n g c r e d i t -m a r k e t e f f e c ts in t o m a i n s t r e a m m o d e l sis t h a t m o d e r n e m p i r ic a l r e s e a r c h o n t h e d e t e r m i n a n t s o f a g g re g a t e d e m a n d a n d ( toa l e s se r ex t en t ) o f aggrega t e supp l y has o f t en a sc r ibed an i m por t an t r o l e t o va r iousc r ed i t -marke t f r i c t i ons . R ecen t empi r i ca l w ork on consumpt i on , f o r exampl e , hase m p h a s i z e d t h e i m p o r t a n c e o f l i m i t s o n b o r r o w i n g a n d t h e c l o s e l y - r e l a t e d " b u f f e rs t ock" behav i o r [M ar i ge r (1987) , Ze l des (1989) , J appe l l i (1990) , D ea t on (1991) , Ebe r l y(1994) , G our i nchas and Pa rke r ( 1995) , Enge l ha rd t ( 1996) , C a r ro l l ( 1997) , Ludv i gson(1997) , B acch e t t a and G er l ach (1997) ]. I n t he i nves t men t l i te r a t u re , desp i te so me r e cen tr ehab i l i ta t i on o f a r o l e f o r neoc l a s s i ca l cos t -o f - cap i t a l e f f ec t s [C umm i ns , H asse t t andH ubbard (1994) , H asse t t and H ubbard (1996) ] , t he r e r ema i ns cons i de r ab l e ev i dencefo r t he v i ew t ha t ca sh f l ow , l eve rage , and o t he r ba l ance - shee t f ac t o r s a l so havea ma j o r i n f l uence on i nves t men t spend i ng [Fazza r i , H ubbard and Pe t e r sen (1988) ,H osh i , K ashyap and Scha r f s t e i n (1991) , Whi t ed (1992) , G ros s (1994) , G i l ch r i s t andH i m me l be rg (1995) , H ubba rd , K ash yap and W hi t ed (1995) ] 1. S i mi l a r conc l us i onsa r e r e a c h e d b y r e c e n t s tu d ie s o f t h e d e t e r m i n a n t s o f i n v e n to r ie s a n d o f e m p l o y m e n t[C an t o r ( 1990) , B l i nde r and Macc i n i ( 1991) , K ashyap , Lamont and S t e i n (1994) ,Sha rpe (1994), C a rpen t e r , Fazza r i and Pe t e r sen (1994) ]. A g grega t e m ode l i ng , i f it ist o desc r i be t he dyn am i cs o f spend i ng and p ro duc t i on r ea l is t ica ll y , needs t o t ake t heseemp i r ica l f ind i ngs i n t o accou n t 2 .

H ow does one go abou t i ncorpora t i ng f i nanc i a l d i s t r e s s and s i mi l a r concep t s i n t omacroeconomi cs? Whi l e i t s eems t ha t t he r e has a l w ays been an empi r i ca l ca sefo r i nc l ud i ng c r ed i t -marke t f ac t o r s i n t he ma i ns t r eam mode l , ea r l y w r i t e r s f ound i td i f f icu l t t o b r i ng such ap pa ren t l y d i ve r se and chao t i c phenom ena i n t o t he i r f o rm a lana l yses . A s a r e su l t, adv ocac y o f a r o l e f o r t hese f ac t o r s i n aggrega t e dy nam i csf e l l f o r t he mos t pa r t to econ om i s t s ou t s i de the U S academ i c ma i ns t r eam, such a sH ym an M i nsky , and t o som e fo r ecas t e r s and f i nanc i a l -marke t p r ac t i t ione r s , such a sO t t o Eck s t e i n and A l l en S i na i ( l 986) , A l be r t W oj n i low er (1980) , and H en ry K aufm a~(1986) . H ow ever , ove r t he pas t t w en t y - f ive yea r s , b r eak t h roug hs i n t he eco nom i cso f i n c o m p l e t e a n d a s y m m e t r i c i n f o r m a t i o n [ b e g in n i n g w i th A k e r l o f (1 9 7 0 ) ] a n dt he ex t ens ive adop t i on o f t hese i deas i n co rpora t e f i nance and o t he r app l i ed f i e lds[ e . g . , J ensen and Meck l i ng (1976) ] , have made poss i b l e more fo rma l t heore t i ca l

1 A critique of the cash-flow literature is given by Kaplan and Z ingales (1997). See Chirinko (1993)for a broa d survey of the em pirical literature in inveslment.2 Contemporarymacroeconometric orecasting mo dels, such as the MPS m odel used by the FederalReserve, typically do incorporate factors such as borrowing constraints and cash-flow effects. See forexamp le Bray ton et al. (1997).


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C h. 2 1 . " T h e F i n a n c ia l A c c e l e ra t o r i n a Q u a n t it a t iv e B u s i n e s s C y c l e F r a m e w o r k 1345ana l yses o f c r ed i t -marke t i mper f ec t i ons . I n pa r t i cu l a r , i t i s now w e l l unde r s t ood t ha ta s y m m e t r ie s o f i n f o n n a I i o n p l a y a k e y r o l e i n b o r r o w e r - l e n d e r r e la t io n s h ip s ; t h a tl end i ng i ns t i t u t i ons and f i nanc i a l con t r ac t s t yp i ca l l y t ake t he fo rms t ha t t hey do i no rde r t o r educe t he cos t s o f ga t he r i ng i n fo rma t i on and t o mi t i ga t e p r i nc i pa l - agen tp r o b l e m s i n c r e d i t m a r k et s; a n d t h a t th e c o m m o n f e a t u re o f m o s t o f t h e d i v er s ep rob l em s t ha t can occur i n c r ed it ma rke t s i s a w or sen i ng o f i n fo rma t i ona l a symm et r i e sand i nc r eases i n t he a s soc i a t ed agency cos t s . B ecause c r ed i t -marke t c r i s e s ( and l e s sd rama t i c ma l func t i ons ) i nc r ease t he r ea l cos t s o f ex t end i ng c r ed i t and r educe t hee f f i c i ency o f t he p roces s o f ma t ch i ng l ende r s an d po t en t i a l bo r row er s , t hese even t smay have w i desp read r ea l e f f ec t s . I n shor t , w hen c r ed i t marke t s a r e cha rac t e r i zedb y a s y m m e t r i c i n f o r m a t i o n a n d a g e n c y p r o b l e m s , t h e M o d i g l i a n i - M i l l e r i r r e l e v a n c et heorem no l onge r app l i e s .D raw i ng on i ns i gh t s f r om t he li t e ra t u r e on a symm et r i c i n fo rma t i on and a gency cos t si n l end i ng r e l a t i onsh i ps , i n t h i s chap t e r w e deve l op a dynami c gene ra l equ i l i b r i ummo de l t ha t w e ho pe w i l l be use fu l f o r unde r s t and i ng t he ro l e o f c r ed it -marke t f r ic t i onsi n cyc l i ca l fl uc tua t i ons . The m ode l i s a syn t hes i s o f s eve ra l approaches a l r eady i n t hel i t e r a t u r e , and i s pa r t l y i n t ended a s an expos i t o ry dev i ce . B u t because i t combi nesa t tr ac ti ve f ea t u re s o f s eve ra l p r ev i ou s mode l s , w e t h i nk t he f r am ew o rk p r esen t ed he r ehas somet h i ng new t o o f f e r , hnpor t an t l y , w e be l i eve t ha t t he mode l i s o f some use i nas ses si ng t he q uan t i t at i ve imp l i ca ti ons o f c r ed i t -marke t f r i c t ions fo r ma croe con om i canalysis .

I n pa r t i cu l a r , ou r f r amew ork exh i b i t s a " f i nanc i a l acce l e r a t o r " [B ernanke , G er t l e rand G i l ch r i s t ( 1996) ] , i n t ha t endogenous deve l opment s i n c r ed i t marke t s w ork t op r o p a g a te a n d a m p l i f y sh o c k s t o th e m a c r o e c o n o m y . T h e k e y m e c h a n i s m i n v o lv e s th el in k b e t w e e n " e x t e r n a l f in a n c e p r e m i u m " ( th e d i f f e r e n c e b e t w e e n t h e c o s t o f f u n d sr a i s ed ex t e rna l l y and t he op por t un i t y cos t o f f unds i n t e rna l t o t he f i rm) and t he ne tw o r t h o f po t en t i a l bo r row er s (de f i ned a s the bo r ro w er s ' l i qu i d a s se ts p l us co l l a t e r a lva lue of i ll iquid asse t s l ess outs tan ding o bl iga t ions) . Wi th c redi t -ma rket f r ic t ionsp resen t , and w i t h t he t o t a l amo un t o f fi nanc i ng r equ i r ed h e l d cons t an t , s t anda rd mod e l so f l e n d i n g w i t h a s y m m e t r i c i n f o r m a t i o n i m p l y t h a t t h e e x t e r n a l f i n a n c e p r e m i u mdepends i nve r se l y on bor row er s ' ne t w or t h . Th i s i nve r se r e l a t i onsh i p a r i s e s because ,w hen bor row er s have l i t t l e w ea l t h t o con t r i bu t e t o p ro j ec t f i nanc i ng , t he po t en t i a ld i ve rgence o f i n t e re s t s be t w een t he b o r row er and t he supp l i e rs o f ex t e rna l f unds i sg r ea t e r, imp l y i ng i nc r eased agenc y cos t s; i n equ i li b r i um, l ende r s mu s t be com pens a t ed~br h i gh e r age ncy cos t s by a l a rge r p r emi um . To t he e x t en t tha t bo r row er s ' ne t w o r t h i sp rocyc l i ca l ( because o f t he p rocy c l i ca l i t y o f p ro f i ts and a s se t p r i ces , f o r exampl e ) , t heex t e rna l f i nance p r emi um w i l l be coun t e r cyc l i ca l , enhanc i ng t he sw i ngs i n bo r row i ngand t hus i n i nves t men t , spend i ng , and p roduc t i on .

We a l so add t o t he f r amew ork seve ra l f ea t u r e s des i gned t o enhance t he empi r i ca lr e l evance . F i r s t , w e i ncorpora t e p r i ce s t i ck i nes s and money i n t o t he ana l ys i s , u s i ngmode l i ng dev i ces f ami l i a r f r om N ew K eynes i an r e sea r ch , w h i ch a l l ow s us t o s t udyt he e f f ec t s o f mo ne t a ry po l i cy i n an econ om y w i th c r ed i t -mark e t f ri c ti ons . I n add i t ion ,w e a l l ow fo r dec i s i on l ags i n i nves t men t , w h i ch enab l e s t he mode l t o gene ra t e bo t h


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1346 B . S. B e r n a n k e e t al .h u m p - s h a p e d o u t p u t d y n a m i c s a n d a l e a d - l a g r e l a t io n s h i p b e t w e e n a s s e t p r i c e s a n dinves tmen t , a s i s cons i s t en t w i th t he da t a . F ina lly , we a l l ow fo r he t e ro gene i ty am on gf i rms to cap tu re t he r ea l -wor ld f ac t t ha t bo r rower s have d i f f e r en t i a l acces s t o cap i t a lm a r k e t s . A l l t h e se i m p r o v e m e n t s s i g n if i ca n t ly e n h a n c e t h e v a l u e o f th e m o d e l f o rquan t i t a t i ve ana lys i s , i n ou r v i ew.

T h e r e s t o f th e c h a p t e r i s o r g a n i z e d a s f o ll o w s . S e c t i o n 2 i n t r o d u c es t h e m o d e lana ly zed in t he p re sen t chap te r . S ec t ion 3 cons ide r s t he sou rce o f t he f i nanc i a la c c e l er a t o r: a c r e d i t - m a r k e t f r i c ti o n w h i c h e v o l v e s f ro m a p a r ti c u l a r f o r m o f a s y m -m e t r i c i n f o r m a t i o n b e t w e e n l e n d e r s a n d p o t e n t i a l b o rr o w e r s . I t t h e n p e r f o r m s a p a r ti a le q u i li b r iu m a n a l y s is o f t h e r e s u lt i n g t e r m s o f b o r r o w i n g a n d o f f i r m s ' d e m a n d f o rc a p i t a l , a n d d e r i v e s t h e l i n k b e t w e e n n e t w o r t h a n d t h e d e m a n d f o r c a p i t a l t h a t i st h e e s s e n c e o f t h e f i n an c i al a c c e l e ra t o r. S e c t i o n 4 e m b e d s t h e c r e d i t - m a r k e t m o d e li n a D y n a m i c N e w K e y n e s i a n ( D N K ) m o d e l o f t he b u s i ne s s c y c l e, u si n g t h e d e v i c ep r o p o s e d b y C a l v o ( 1 9 8 3 ) t o i n c o r p o r a t e p r i c e s t i c k i n e s s a n d a r o l e f o r m o n e t a r ypo l i cy ; i t a l so cons ide r s s eve ra l ex t ens ions , such a s a l l owing fo r lags i n i nves tm en t andfo r d i f f e r en ti a l c r ed i t acces s ac ro s s f i rms . Se c t ion 5 p re sen t s s im u la t ion r e su l t s , d r awingc o m p a r i s o n s b e t w e e n t h e c a s e s in c l u d i n g a n d e x c l u d i n g t h e c r e d i t - m a r k e t f ri c ti o n . H e r ew e s h o w t h a t t h e f i n a n c i a l a c c e l e r a t o r w o r k s t o a m p l i f y a n d p r o p a g a t e s h o c k s t o t h eec on om y in a quan t i t a ti ve ly s ign i f i can t way . Sec t ion 6 t hen g ives a b r i e f and se l ec t ivesu rv ey tha t desc r ibes how the f r am ew ork p re se n t f it s i n the l i t e ra tu re . Sec t ion 7 thendesc r ibes s eve ra l d i r ec t i ons fo r fu tu re r e sea rch . Two append ices con ta in add i t i ona ld i s c u s s io n a n d a n a l y s i s o f t h e p a r t ia l - e q u i l i b r iu m c o n t r a c ti n g p r o b l e m a n d t h e d y n a m i cg e n e r a l e q u i l i b r i u m m o d e l i n w h i c h t h e c o n t r a c t i n g p r o b l e m i s e m b e d d e d .

2 . T h e m o d e l : o v e r v i ew a n d b a s ic a s s u m p t i o n sO u r m o d e l is a v a ri a nt o f t h e D y n a m i c N e w K e y n e s i a n ( D N K ) f r a m e w o r k , m o d i f i e dt o a l l o w f o r f i n a n c i a l a c c e l e r a t o r e f f e c t s o n i n v e s t m e n t . T h e b a s e l i n e D N K m o d e li s e s s e n t i a l l y a s t o c h a s t i c g r o w t h m o d e l t h a t i n c o r p o r a t e s m o n e y , m o n o p o l i s t i cc o m p e t i t i o n , a n d n o m i n a l p r i c e r i g id i ti e s. W e t a k e t h i s f r a m e w o r k a s th e s t a r ti n g p o i n tfo r s eve ra l r ea sons . F i r s t, t h i s app ro ach has b eco m e wide ly accep ted in the l i t e r a tu re 3I t h a s t h e q u a l it a ti v e e m p i r i c a l a p p e al o f t h e I S - L M m o d e l , b u t i s m o t i v a t e d f r o m f ir s tp r i n ci p l es . S e c o n d , i t i s p o s s i b l e to s t u d y m o n e t a r y p o l i c y w i t h t h i s fr a m e w o r k . F o r o u rpurposes , t h i s means t ha t i t i s pos s ib l e t o i l l u s t r a t e how c red i t marke t imper fec t ionsi n f lu e n c e th e t r a n s m i s s i o n o f m o n e t a r y p o l ic y , a t h e m e e m p h a s i z e d i n m u c h o f t h erecen t l i te r a tu re 4 . F ina l ly , i n t he l imi t i ng case o f pe r f ec t p r i ce f l ex ib il it y , the cyc l i ca lp r o p e r t i e s o f th e m o d e l c l o s e l y r e s e m b l e t h o s e o f a re a l b u s in e s s c y c l e f r a m e w o r k . I n

3 See G oodfriend and K ing (1997) for an exp osition of the DN K approach.4 For a review of the recent literature on the ro le of c redit ma rket fiqctions in the transmission ofmo netary policy, see B ernanke and Gertler (1995).


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C h . 2 1 : T h e F i n a n c i a l A c c e l e r a t o r in a Q u a n t i t a t i u e B u s i n e s s C y c l e F r a m e w o r k 1347t h i s a p p r o x i m a t e s e n s e , t h e D N K m o d e l n e s t s t h e r e a l b u s i n e s s c y c l e p a r a d i g m a s as pec i a l c a s e . I t t hus h a s t he v i r t ue o f ve r s a ti l it y .E x t e n d i n g a n y ty p e o f c o n t e m p o r a r y b u s i n e ss c y c l e m o d e l t o in c o r p o r a t e f in a n c ia lacce l e r a to r e f f ec t s i s , how eve r , no t s t r a igh t f o r w a r d . The r e a r e tw o gene r a l p r ob l ems :F i r s t , b e c a u s e w e w a n t l e n d i n g a n d b o r r o w i n g t o o c c u r a m o n g p r i v a t e a g e n t s i ne q u i l ib r i u m , w e c a n n o t u s e t h e r e p r e s e n t a ti v e a g e n t p a r a d i g m b u t m u s t i n s te a d g r a p p l ew i t h th e c o m p l i c a t i o n s i n t ro d u c e d b y h e t e r o g e n e i t y a m o n g a g e n t s . S e c o n d , w e w o u l dl i ke t he f i nanc i a l con t r ac t s t ha t agen t s u s e i n t he mode l t o be mo t iva t ed a s f a r a spos s ib l e f r om f i r s t p r i nc ip l e s . S ince f i nanc i a l con t r ac t s and i n s t i t u t i ons a r e endoge nous ,r e s u l t s t ha t h inge on a r b i t r a r y r e s t r i c t i ons on f i nanc i a l r e l a t i ons h ip s may be s u s pec t .M o s t o f th e n o n s t a n d a r d a s s u m p t i o n s th a t w e m a k e i n s e t t i n g u p o u r m o d e l a r ed e s i g n e d t o f a c i l i t a t e a g g r e g a t i o n ( d e s p i t e i n d i v i d u a l h e t e r o g e n e i t y ) a n d p e r m i t a nendogenous f i nanc i a l s t r uc tu r e , t hus add r e s s ing t he s e tw o key i s s ue s .

T h e b a s i c s t ru c t u r e o f o u r m o d e l i s a s f o l lo w s : T h e r e a r e t h re e t y p e s o f a g en t s , c a l le dhous eho ld s , en t r ep r eneu r s , and r e t a i l e r s . H ous eho ld s and en t r ep r eneu r s a r e d i s t i nc tf r o m o n e a n o t h e r i n o r d e r t o e x p l i c i t l y m o t i v a t e l e n d i n g a n d b o r r o w i n g . A d d i n gr e t a i l e r s pe r mi t s u s t o i nco r po r a t e i ne r t i a i n p r i c e s e t t i ng i n a t r a c t ab l e w ay , a s w ed i sc u s s. I n a d d i t io n , o u r m o d e l i n c l u d e s a g o v e r n m e n t , w h i c h c o n d u c t s b o t h f i s c al a n dm o n e t a r y p o l i c y .

H o u s e h o l d s l i v e f o r e v e r ; t h e y w o r k , c o n s u m e , a n d s a v e. T h e y h o l d b o t h r e a l m o n e yb a l a n c e s a n d i n t e r e s t - b e a r i n g a s s e t s . W e p r o v i d e m o r e d e t a i l s o n h o u s e h o l d b e h a v i o rbe low.

Fo r i nduc ing t he e f f ec t w e r e f e r to a s t he f i nanc i a l a cce l e r a to r , en t r ep r eneu r s p l a y thek e y r o l e i n o u r m o d e l . T h e s e i n d iv i d u a ls a r e a s s u m e d t o b e r i s k -n e u t r a l a n d h a v e f i n it eho r i zons : Spec i f i c a l l y , w e a s s ume tha t e ach en t r ep r eneu r ha s a cons t an t p r obab i l i t y yo f s u r v i v i n g t o th e n e x t p e r i o d ( i m p l y i n g a n e x p e c t e d l i f e t i m e o f 1 @ )" T h e a s s u m p t i o no f fi n it e h o r i z o n s f o r e n t r e p r e n e u rs i s i n t e n d e d t o c a p t u r e t h e p h e n o m e n o n o f o n g o i n gb i r t h s and d ea th s o f f i r ms , a s w e l l a s t o p r ec lude t he po s s ib i l i t y t ha t t he en t r ep r eneu r i a ls e c t o r w i l l u l t i m a t e l y a c c u m u l a t e e n o u g h w e a l t h t o b e f u l l y s e l f - f i n a n c i n g . H a v i n gthe s u r v iva l p r o bab i l i t y be cons t an t ( i ndepende n t o f age ) f a c i l it a t e s agg r ega t i on . Wea s s u m e t h e b i r t h r a te o f e n t r e p re n e u r s t o b e s u c h t h a t t he f r a c t i o n o f a g e n t s w h o a r een t r ep r eneu r s i s cons t an t .

I n each pe r iod t en t r ep r eneu r s a cqu i r e phys i ca l c ap i t a l. ( En t r ep r eneu r s w ho "d i e "i n p e r i o d t a r e n o t a l l o w e d t o p u r c h a s e c a p i t a l , b u t i n s t e a d s i m p l y c o n s u m e t h e i ra c c u m u l a t e d r e s o u r c e s a n d d e p a r t f r o m t h e s c e n e .) P h y s i c a l c a p i t a l a c q u i r e d i n p e ri o dt is u s ed i n co m bina t i on w i th h i r ed l ab o r t o p r odu ce o u tpu t i n pe r iod t + 1 , byme ans o f a cons t an t - r e tu r n s t o s ca l e te chno logy . A cq u i s i t i ons o f c ap i t a l a r e f i nancedb y e n t re p r e n e u r i a l w e a l t h , o r " n e t w o r t h " , a n d b o r r o w i n g .

T h e n e t w o r t h o f e n tr e p r e n e u r s c o m e s f r o m t w o s o u r ce s : p r o f it s ( in c l u d in g c a p i ta lg a i ns ) a c c u m u l a t e d f r o m p r e v i o u s c a p i t a l i n v e s t m e n t a n d i n c o m e f r o m s u p p l y i n g la b o r( w e a s s u m e t h a t e n t r e p re n e u r s s u p p l y o n e u n i t o f l a b o r i n e l a s t ic a l ly t o t h e g e n e r a ll abo r ma r ke t ) . A s s t r e s s ed i n t he li t e r a tu r e , en t r e p r en eu r s ' n e t w or th p l ays a c ri t ic a l r o l ei n t h e d y n a m i c s o f t h e m o d e l . N e t w o r t h m a t t e r s b e c a u s e a b o r r o w e r ' s fi n a n ci a l p o s i t i o n


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1348 B . S. B e r n a n k e e t a l.i s a k e y d e t e r m i n a n t o f h i s c o s t o f e x t e rn a l f i n a n ce . H i g h e r l e v e l s o f n e t w o r t h a l l o wfor i nc reased se l f - f i nanc ing ( equ iva l en t ly , co l l a t e r a l i zed ex t e rna l f i nance ) , mi t i ga t ingt h e a g e n c y p r o b l e m s a s s o c i a t e d w i t h e x t e r n a l f i n an c e a n d r e d u c i n g t h e e x t e r n a l f i n an c ep r e m i u m f a c e d b y t h e e n t r e p r e n e u r i n e q u i l i b r i u m .

T o e n d o g e n o u s l y m o t i v a t e t h e e x i s t e n c e o f a n e x t e r n a l fi n a n ce p r e m i u m , w ep o s t u l a t e a s i m p l e a g e n c y p r o b l e m t h a t i n tr o d u c e s a c o n f li c t o f in t e r e st b e t w e e na bo r rower and h i s r e spec t ive l ende r s . The f i nanc i a l con t r ac t i s t hen des igned tom i n i m i z e t h e e x p e c t e d a g e n c y c o s t s . F o r t r a c t a b i l i t y w e a s s u m e t h a t t h e r e i s e n o u g ha n o n y m i t y i n f i n a n c i a l m a r k e t s t h a t o n l y o n e - p e r i o d c o n t r a c t s b e t w e e n b o r r o w e r s a n dl e n d e r s a r e f e a s i b l e [ a s i m i l a r a s s u m p t i o n i s m a d e b y C a r l s t r o m a n d F u e r s t ( 1 9 9 7 ) ] .A l l o w i n g f o r l o n g e r - t e r m c o n t r a c t s w o u l d n o t a f f e c t o u r b a s ic r e s u l ts 5. T h e t b r m o ft h e a g e n c y p r o b l e m w e i n t r o d u c e , t o g e t h e r w i t h t h e a s s u m p t i o n o f c o n s t a n t re t u r n sto s ca l e i n p roduc t ion , i s su f f i c i en t ( a s we sha l l s ee ) t o gene ra t e a l i nea r r e l a t i onsh ipb e t w e e n t h e d e m a n d f o r c a p it a l g o o d s a n d e n t r e p re n e u r i a l n e t w o r th , w h i c h f a c il i ta t e sa g g r e g a t i o n .

One compl i ca t ion i s t ha t t o i n t roduce the nomina l s t i ck ines s i n t r i n s i c t o t heD N K f r a m e w o r k , a t l e a s t s o m e s u p p l i e r s m u s t b e p r i c e s e t t e r s , i . e . , t h e y m u s tf a c e d o w n w a r d - s l o p i n g d e m a n d c u r v e s . H o w e v e r , a s s u m i n g t h a t e n t r e p r e n e u r s a r ei m p e r f e c t c o m p e t i t o r s c o m p l i c a t e s a g g r e g a t i o n , s i n ce i n th a t c a s e th e d e m a n d f o rc a p i t a l b y i n d i v id u a l f i r m s i s n o l o n g e r l i n e a r in n e t w o r t h . W e a v o i d th i s p r o b l e m b yd i s t i ngu i sh ing be tw een en t r ep reneu r s an d o the r agen t s , ca l l ed ' r e t a il e r s . En t r e p rene ur sp r o d u c e w h o l e s a l e g o o d s i n c o m p e t i t iv e m a r k e t s , a n d t h e n s e ll th e i r o u t p u t t o r e ta i l er sw h o a r e m o n o p o l i s t i c c o m p e t i t o r s . R e t a i l e r s d o n o t h i n g o t h e r t h a n b u y g o o d s f r o men t r ep reneur s , d i f f e r en t i a t e t hem (cos t l e s s ly ) , t hen r e - se l l t hem to househo lds . Them o n o p o l y p o w e r o f r e ta i le r s p r o v i d e s t h e s o u r c e o f n o m i n a l s t i c k in e s s i n t h e e c o n o m y ;o the rwi se , r e t a i le r s p l ay no ro l e . W e as sum e tha t p ro f i ts f rom re t a i l ac t i v i t y a r er e b a t e d l u m p - s u m t o h o u s e h o l d s . H a v i n g d e s c r i b e d t h e g e n e r a l s et u p o f th e m o d e l ,w e p r o c e e d i n t w o s te p s . F ir s t, w e d e r iv e t h e k e y m i c r o e c o n o m i c r e la t i o n s h i p o f t h em o d e l : t h e d e p e n d e n c e o f a f i r m ' s d e m a n d f o r c a p it a l o n th e p o t e n t i a l b o r r o w e r ' s n e tw o r t h . T o d o s o , w e c o n s i d e r t h e f i r m ' s ( e n tr e p r e n e u r 's ) p a r t ia l e q u i l i b ri u m p r o b l e m o fj o i n t l y d e t e r m i n i n g i ts d e m a n d f o r c a p i ta l a n d t e r m s o f e x t e r n a l fi n a n c e in n e g o t i a t i o nw i t h a c o m p e t i t i v e l e n d e r ( e . g . , a f i n a n c i a l i n t e r m e d i a r y ) . S e c o n d , w e e m b e d t h e s er e l a t i o n s h i p s ! n a n o t h e 1 ~ i s e c o n v e n t i o n a l D N K m o d e l . O u r o b j e c t i v e i s t o s h o w h o wf l u ct u a ti o n s in b o r r o w e r s ' n e t w o r t h c a n a c t t o a m p l i f y a n d p r o p a g a t e e x o g e n o u s s h o c k st o t h e s y s t e m . F o r m o s t o f t h e a n a l y s i s w e a s s u m e t h a t th e r e i s a s i n g le t y p e o ff i rm ; h o w e v e r , w e e v e n t u a l ly e x t e n d t h e m o d e l t o a l l o w f o r h e t e ro g e n e o u s f i rm s w i t hd i f f e r en t i a l acces s t o c r ed it .

So lon g as b orrowers have finite horizons, net wo rth influences the term s of borrowing, eve n ai~erallowing for nm lti-period contracts. See, fo r exam ple, Gertter (1992).


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C h . 2 1 : T h e F i n a n c i a l A c c e l e r a t o r i n a Q u a n t i t a t i v e B u s i n e s s C y c l e F r a m e w o r k 1 3 4 9

3 . T h e d e m a n d f o r c a p i t a l a n d t h e r o le o f n e t w o r t hW e now s t udy t he cap i t a l i nves t m en t dec i s i on a t t he f i r m l eve l , t ak i ng a s g i ven t hep r i ce o f c ap i t a l goods and t he e xpec t ed re t u r n t o cap it a l. I n t he s ubs equen t s ec t i on weendo gen i ze cap i t a l p r i c e s and r e t u r ns a s pa r t o f a gene r a l equ i l i b r i um s o l u t i on .

At t i m e t , t he en t r ep r eneu r wh o m anages f i r m j pu r chas e s cap i ta l f o r u s e a t t + I .The quan t i t y o f c ap it a l pu r cha s ed i s de no t ed K/+ I, w i t h t he s ubs c r i p t deno t i ng t hepe r i od i n w h i ch t he cap i t a l i s a c t ua l ly u s ed , and t he s upe r s c r i p t j deno t i ng t he f i r m .The p r i ce pa i d pe r un i t o f c ap i ta l i n pe r i od t i s Q t . Cap i t a l i s hom ogeneous , and s oi t does no t m a t t e r whe t he r t he cap i t a l t he en t r ep r eneu r pu r chas e s i s newl y p r oducedwi t h i n t he pe r i od o r i s "o l d" , dep r ec i a t ed cap it a l. H av i ng t he en t r ep r eneu r pu r chas e( o r r epu r ch as e ) h i s en t i r e c ap i ta l s t ock each pe r i od i s a m ode l i ng d ev i ce t o ens u r e ,rea l i s t i ca l ly , tha t l everage res t r i c t ions or o ther f inanc ia l cons t ra in t s apply to the f i rmas a who l e , no t j u s t t o t he m ar g i na l i nves t m en t .

Th e r e t u r n t o cap i t a l is s ens i ti ve t o bo t h agg r ega t e and i d i o s ync r a t i c ri s k. T he ex pos tg r os s r e t u r n on cap i t a l f o r f i r m j i s t '~JPk w here coy i s an id iosyn cra t i c d i s turbance to* ' t + l ,f i r m j ' s r e t u r n and Rk+l i s the ex pos t aggrega te re turn to capi ta l ( i .e . , the gross re turnave r aged ac r os s f i r m s ) . The r andom va r i ab l e (.0 i s i . i .d , ac ross t ime and across f i rms ,wi t h a con t i nuo us a nd once - d i f f e r en t i ab l e c .d .f . , F ( ~o ) , ove r a non - nega t i ve s uppor t ,and E { { o J } = 1 . W e i m pos e t he f o l l owi ng r e s t r i c t ion on t he co r r e s po nd i ng haza r dra te h( (o) :

O(coh(o)))0 a ) > 0 , ( 3 . 1 )

dF(~o)wh ere h(co) _= ~ F(o~" This regula r i ty con di t ion i s a re la t iv e ly we ak res t r i c t ion tha t i ss a ti s fi ed by m o s t con ven t i ona l d i s tr i bu ti ons , i nc l ud i ng f o r exam pl e t he l og - no r m a l .

At t he end o f pe r i od t ( go i ng i n t o pe r i od t + 1 ) en t r ep r eneu r j ha s ava i l ab le ne twor t h , N / + 1 To f inance t he d i f f e r ence be t w een h i s exp end i t u r e s on cap i t a l goods andh is n e t w o r t h h e m u s t b o r r o w a n a m o u n t B J < , g i v e n b y

B t J l K j JQ, ,+, -N ,+ 1. (3.2)The en t r ep r eneu r bo r r ows f r om a f i nanc i a l i n t e r m ed i a r y t ha t ob t a i n s i t s f unds f r omhous eho l ds . T he f i nanc i a l i n t e r m ed i a r y f ace s an opp or t un i t y cos t o f f unds be t ween tand t + 1 equa l t o t he econo m y ' s r i s k l e ss g r os s r a t e o f r e t u r n , R t + l . The r i sk less ra te i st he r e levan t oppo r t un i t y cos t becaus e i n the equ i l ib r i um o f ou r m ode l , t he i n t e r m ed i a r yho l ds a p e r f ec t l y s a f e po r t f o l i o ( i t pe r f ec t l y d ive r s if i e s t he i d i o s ync r a t i c r i s k i nvo l vedi n lend i ng ) . B ecaus e en t r ep r eneu r s a r e r i sk - neu t r a l and hou s eho l ds a r e r i sk - ave r s e , thel oan con t r ac t t he i n t e r m ed i a r y s i gns ha s en t r ep r eneu r s abs o r b any agg r ega t e r i s k , a swe d i s cus s be l ow.To m o t i va t e a non t r i v i a l ro l e f o r f inanc i a l s tr uc t u re , w e f o l l ow a num ber o f p r ev i ouspape r s i n a s s um i ng a "cos t l y s ta t e ve r i fi c a t i on" ( CS V) p r ob l em o f the t ype f i rs t


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1 3 5 0 B . S. B e r n a n k e e t a l.

a n a l y z e d b y T o w n s e n d ( 1 9 7 9 ) , i n w h i c h l e n d e r s m u s t p a y a f i x e d " a u d i t i n g c o s t "i n o r d e r t o o b s e r v e a n i n d i v i d u a l b o r r o w e r ' s r e a l i z e d r e t u r n ( t h e b o r r o w e r o b s e r v e st h e r e t u r n f o r f r e e ) . A s T o w n s e n d s h o w e d , t h i s a s s u m p t i o n a l l o w s u s t o m o t i v a t ew h y u n c o l l a t e r a l i z e d e x t e r n a l f i n a n c e m a y b e m o r e e x p e n s i v e t h a n i n t e r n a l f i n a n c ew i t h o u t i m p o s i n g a r b i t ra r y r e s tr i c ti o n s o n t h e c o n t r a c t st r u ct u re . T h e r e a r e m a n y o t h e rs p e c i fi c a ti o n s o f th e i n c e n ti v e p r o b l e m b e t w e e n t h e e n t r e p r e n e u r a n d o u t s id e l e n d e rst h a t c a n g e n e r a t e q u a l it a ti v e l y s i m i l a r r e s ul ts . T h e v i r tu e s o f th e T o w n s e n d f o r m u l a t i o na r e i t s s imp l i c i t y and de s c r ip t i ve r ea l i s m .

F o l l o w i n g th e C S V a p p r o a c h , w e a s s u m e t h a t th e l e n d e r m u s t p a y a c o s t i f h e o rs he w i s hes t o obs e r ve t he bo r r ow er ' s r e a l i z ed r e tu r n on cap i t a l . Th i s aud i t i ng cos t i si n t e rp r e t a b l e a s th e c o s t o f b a n k r u p t c y ( i n c lu d i n g f o r e x a m p l e a u d i ti n g , a c c o u n t i n g ,and l ega l co s t s , a s w e l l a s l o s s e s a s s oc i a t ed w i th a s s e t l i qu ida t i on and i n t e r r up t i ono f b u s in e s s ) . T h e m o n i t o r i n g c o s t i s a s s u m e d t o e q u a l a p r o p o r t i o n / ~ o f th e r e a l i z ed

i k . igr os s pa yo f f t o t he f i r m ' s c ap i ta l , i .e . , th e m on i to r i n g cos t equa l s /~ ~ o R t + l Q t K i + I .A l t h o u g h o n e m i g h t e x p e c t th a t th e r e w o u l d b e e c o n o m i e s o f s c a le i n m o n i t o r in g , t h ep r o p o r t i o n a l i t y a s s u m p t i o n i s v e r y c o n v e n i e n t i n o u r c o n t e x t a n d d o e s n o t s e e m t o ou n r e a s o n a b l e .3 . 1 . C o n t r a c t t e r m s w h e n t h e r e i s n o a g g r e g a t e r i s kTo des c r ibe t he op t ima l con t r ac tua l a r r angemen t , i t i s u s e f u l t o f i r s t w or k t h r ough t hec a s e w h e r e t h e a g g r e g a t e r e t u r n t o c a p i t a l R t : ' + l i s know n in advance . I n t h i s i n s t ancethe on ly unce r t a in ty abou t t he p r o j ec t ' s r e tu r n i s i d io s ync r a t i c t o t he f i r m , a s i n t hec o n v e n t i o n a l v e r s i o n o f t h e C S V p r o b l e m .

A bs en t any agg r ega t e unce r t a in ty , t he op t ima l con t r ac t unde r cos t l y s t a t e ve r i f i c a t i onl o o k s v e r y m u c h l ik e s t a n d a rd r i s k y d e b t ( s e e A p p e n d i x A f o r a d e t a il e d a n a l y s i s o ft he con t r ac t i ng p r ob l em ) : I n pa r ti cu l a r , the e n t r ep r ene u r choo s e s t he va lue o f f i r mcapi ta l , Jt K i + t , and t he a s s o c i a t ed l eve l o f bo r r ow ing , B /+ L, p r i o r t o t he r ea l i z a t i ono f t he i d io s ync r a t i c s hock . G iv en / kt K i + l , B [ + I , and R t+ l , t he op t im a l co n t r ac t m ayb e c h a r a c t e r i z e d b y a g r o s s n o n - d e f a u l t l o a n r a t e , Z / ~ I , a n d a t h r e s h o ld v a l u e o f th eid io s ync r a t i c s hoc k ~ ) i, c a ll i t ~ sJ , s uch t ha t f o r va lue s o f t he i d io s ync r a t i c s hockg r e a t e r t h a n o r e q u a l t o ~ J , t h e e n t r e p r e n e u r i s a b le t o r e p a y t he l o a n a t th e c o n t r a c t u a ira te , Z j 1. Th a t i s , N. / i s d ef ined by

. . . . ~ - j . / . J~ R~+l t K i ~ 1 = Z t ~ l B t ~ 1 ( 3 . 3 )W hen ~ o/ ) c~ j, unde r t he op t ima l con t r ac t the en t r ep r eneu r r ep ays t he l ende r t he

r j j j /~ j ,- j jp r o m i s e d a m o u n t Z i + l B t + 1 and k eep s t he d i f f e r ence , equ a l t o c o R t + l Q t K i ~ . ~ - Z i + B : , 1 .I f coy < N : , t he en t r ep r eneu r c anno t pa y the con t r ac tua l r e tu r n and t hus dec l a r e sde f au l t , i n t h i s s i t ua t i on t he l end ing i n t e r med ia r y pays t he aud i t i ng cos t and ge t s t okeep w ha t i t f i nds . Tha t i s , t he i n t e r med ia r y ' s ne t r e ce ip t s a r e ( 1 - l ~ ) v ) R ~ + ~ Q ~ K / + 1 Ad e f a u l t in g e n t r e p r e n e u r r e c e i v e s n o t h i n g .


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C h . 2 1 : T h e t ,3 n a n c i a l A c c e l e r a t o r i n a Q u a n t i t a t iv e B u s i n e s s C y c l e F r a m e w o r k 1351T h e v a l u e s o f N J a n d Z /~ 1 u n d e r t h e o p t i m a l c o n t r a c t a r e d e t e r m i n e d b y t h e

r e q u i r e m e n t t h a t t h e f i n an c i a l i n t e r m e d i a r y r e c e i v e a n e x p e c t e d r e t u r n e q u a l t o t h eo p p o r t u n i t y c o s t o f it s f u n d s . B e c a u s e t h e l o a n r i s k i n t h is c a s e i s p e r f e c t l y d i v e rs i fi a b le ,t h e r e l e v a n t o p p o r t u n i t y c o s t t o t h e i n t e r m e d i a r y i s t h e r i s k l e s s r a t e , R t + l . A c c o r d i n g l y ,t h e l o a n c o n t r a c t m u s t s a t i s f y

~ o JP " " / ~ k j '[ 1 - F ( ~ S ) I Z / + I B / + , + ( 1 - ~ t ) ~ o R t + l Q t K i+ 1 d F ( ~ o ) = R , + ,S / + t, ( 3 .4 )

w h e r e t h e l e f t - h a n d s i d e o f E q u a t i o n ( 3 .4 ) is t h e e x p e c t e d g r o s s r e t u r n o n t h e l o a n t ot h e e n t r e p r e n e u r a n d t h e r i g h t s i d e is t h e i n t e r m e d i a r y ' s o p p o r t u n i t y c o s t o f l e n d i n g.N o t e t h a t F ( ~ j ) g i v e s t h e p r o b a b i l i t y o f d e fa u l t.

C o m b i n i n g E q u a t i o n s ( 3 .2 ) a n d ( 3 .3 ) w i t h E q u a t i o n ( 3 . 4 ) y i e l d s t h e f o l l o w i n ge x p r e s s i o n f o r ~ 5 i:

p[1 - F ( ~ J ) ] ~ j - + -( 1 -: -~ ) . /0 (o dF (co ) R ~ + I Q t K /+ , - - R t + I ( Q t K J 1 - N,{ 1). (3 .5)

B y u s i n g E q u a t i o n ( 3 . 4 ) t o e l i m i n a t e Z ~ I , w e a r e a b l e t o e x p r e s s t h e l e n d e r ' s e x p e c t e dr e t u r n s i m p l y a s a f u n c t i o n o f t h e c u t o f f v a l u e o f t h e f i r m ' s i d i o s y n c r a t i c p r o d u c t i v i t ys h o c k , k 5s . T h e r e a r e t w o e f f e c ts o f c h a n g i n g ~J on t h e e x p e c t e d r e t u r n , a n d t h e yw o r k i n o p p o s i t e d i r e c t io n s . A r i s e i n N J i n c r e a s e s t h e n o n - d e f a u l t p a y o f f ; o n t h eo t h e r h a n d , i t a l s o r a i s e s t h e d e f a u l t p r o b a b i l i t y , w h i c h l o w e r s t h e e x p e c t e d p a y o f f .T h e a s s u m e d r e s t r i c t i o n s o n t h e h a z a r d f u n c t i o n g i v e n b y E q u a t i o n ( 3 . 1 ) i m p l y t h a tt h e e x p e c t e d r e t u r n r e a c h e s a m a x i m u m a t a n u n i q u e i n t er i o r v a lu e o f N i : A s N Jr i s e s a b o v e t h i s v a l u e t h e e x p e c t e d r e t u r n d e c l i n e s d u e t o t h e i n c r e a s e d l i k e l i h o o do f d e f a u l t 6 . F o r v a l u e s o f ~O b e l o w t h e m a x i n m m , t h e f u n c t i o n i s i n c r e a s i n g a n dc o n c a v e 7 . I f th e l e n d e r ' s o p p o r t u n i t y c o s t i s s o l a rg e t h a t t h e r e d o e s n o t e x i s t a v a l u eo f N J t h a t g e n e r a t e s t h e r e q u i r e d e x p e c t e d r e t u r n , t h e n t h e b o r r o w e r i s " r a t i o n e d " f r o mt h e m a r k e t . A p p e n d i x A p r o v i d e s d e t a il s . F o r s im p l i c i t y , in w h a t f o l l o w s , w e c o n s i d e ro n l y e q u i l i b r i a w i t h o u t r a t i o n in g , i .e ., e q u i l i b r ia i n w h i c h t h e e q u i l i b r iu m v a l u e o f b 5a l w a y s l ie s b e l o w t h e m a x i m u m f e a s i b le v a l u e a . U n d e r t h e p a r a m e t r i z a t i o n s w e u s el a t e r , t h i s c o n d i t i o n i s i n f a c t s a t i s f i e d .

r' Flb see that the m aximm n m ust be in the interior of the support o f co, note th at as cO approaches itsupper bound, the default probability converges to u nity. Appe ndix A show s that the interior optimum isunique.J7 The ch ange in the expected payoff fl'om a unit increase m cO is {[ 1 -F(cOJ)] -#cO/dF(cOJ)}R~+IQtK i i 1The f irst term in the expression in brackets reflects the r ise in the non-default payoff. The secondterm ref lec ts the r ise in expected defau l t cos ts . Note that we can rewri te th is express ion as{1 - ~ S J h ( U S J ) } [ 1 - F(?O/)]RI+ QtK/+I, where h(a0 = dF(co)- ~ is the hazard rate. Given Equation (3.i) ,

the derivative o f this ex pression is negative for values of CO be low the m axinm m one feasible, implyingthat the ex pected payoff is con cave in this range.8 Note also that since w e are restricting attention to non-rationing equilibria, the lende r's expected returnis alw ays increasing in COJ.


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1352 B.S. Bernanke et al .3 . 2. C o n t r a c t t e r m s w h e n t h e r e i s a g g r e g a t e r i s kW i t h a g g r e g a t e u n c e r t a i n t y p r e s e n t , N J w i l l i n g e n e r a l d e p e n d o n th e e x p o s t r e a l i z a t i o no f R )+ ~. O u r a s s u m p t i o n t h a t t h e e n t r e p r e n e u r i s r i s k - n e u tr a l l e a d s t o a s i m p l e c o n t r a c ts t r u c tu r e , d e s p i t e th i s c o m p l i c a t i o n . B e c a u s e h e c a r e s o n l y a b o u t th e m e a n r e t u r n o n h i sw e a l t h , t h e e n t r e p r e n e u r i s w i l l i n g t o b e a r a l l t h e a g g r e g a t e r i s k 9 . T h u s h e i s w i l l i n g t og u a r a n t e e t h e l e n d e r a r e t u r n t h a t i s f r e e o f a n y s y s t e m a t i c r is k , i .e ., c o n d i t i o n a l o n t h ee x p o s t r e a l i z a t i o n o f R ~ + l , t h e b o r r o w e r o f f e r s a ( s t a t e - c o n ti n g e n t ) n o n - d e f a u l t p a y m e n tt h a t g u a r a n t e e s t h e l e n d e r a r e t u r n e q u a l i n e x p e c t e d v a l u e t o t h e r is k l e s s r a te . ( N o t et h a t t h e o n l y r e si d u a l r i s k t h e l e n d e r b e a r s a r i s e s f r o m t h e i d i o s y n c r a t i c s h o c k o )/+ 1, a n di s t h u s d i v e r s i f i a b l e .) P u t d i f f e r e n tl y , E q u a t i o n ( 3 . 5 ) n o w i m p l i e s a s e t o f r e s t r i c t i o n s ,

ko n e f o r e a c h r e a l i z a t i o n o f R t+ 1. T h e r e s u l t i s a s c h e d u l e f o r 75 , c o n t i n g e n t o n t h er e a l i z e d a g g r e g a t e s t a t e . A s w e a r e r e s t r i c t i n g a t t e n t i o n t o n o n - r a t i o n i n g e q u i l i b r i a ,w e c o n s i d e r o n l y p a r a m e t r i z a t i o n s w h e r e t h e r e i n fa c t e x is t s a v a l u e o f N / f o r e a c ha g g r e g a t e s ta t e t h a t s a t is f ie s E q u a t i o n ( 3 .5 ) . D i v e r s i f i c a t io n b y i n t e r m e d i a r i e s i m p l i e st h a t h o u s e h o l d s e a r n t h e r i s k l e s s r a t e o n t h e i r s a v i n g .

D e s c r i p t iv e l y , t h e e x i s t e n c e o f a g g r e g a t e u n c e r t a i n t y e f f e c t iv e l y t i es t h e r i s k yl o a n r a t e Z /+ ~to m a c r o e c o n o m i c c o n d i t i o n s . I n p a rt i c u la r , t h e l o a n r a t e a d j u s t sc o u n t e r c y c l i c a l ly . F o r e x a m p l e , a r e a li z a t i o n o f R~k+l t h a t i s lo w e r t h a n e x p e c t e d r a i s e sZi /~ ; t h a t is , t o c o m p e n s a t e f o r th e i n c r e a s e d d e f a u l t p r o b a b i l i t y d u e t o t h e l o w a v e r a g er e t u r n t o c a p it a l, t h e n o n - d e f a u l t p a y m e n t m u s t r i se . T h i s i n t u r n i m p l i e s a n i n c r e a s e i nt h e c u t o f f v a l u e o f t h e i d i o s y n c r a t i c p r o d u c t i v i t y s h o c k , ~5 . T h u s t h e m o d e l i m p l i e s ,r e a s o n a b l y , t h a t d e f a u l t p r o b a b i l i t i e s a n d d e f a u l t p r e m i a r i se w h e n t h e a g g r e g a t e r e t u r nt o c a p i t a l i s l o w e r t h a n e x p e c t e d ~0

3 .3 . N e t w o r t h a n d t h e o p t i m a l c h o i c e o f c a p it a l

T h u s f a r w e h a v e d e s c r i b e d h o w t h e s t a t e - c o n t i n g e n t v a l u e s o f N / a n d z iJ ~ a r ed e t e r m i n e d , g i v e n t h e e x p o s t r e a l i z a t i o n o f R~/'+l a n d t h e e x a n t e c h o i c e s o f Q : K i a n dB/~ I. W e n o w t u r n t o th e e n t r e p re n e u r 's g e n e r a l p r o b l e m o f d e t e rm i n i n g h i s d e m a n df o r c a p i t a l .

9 The entrepreneur's value function can be show n to be linear in wealth because (i) his utility is linear inconsum ption and (ii) the project he is investing in exhibits constant returns to scale. [See, e.g., Bernankeand G ertler (1989, 1990).]10 T hi s kin d of state-contingent financial arrangeme nt is a bit stylized, but may be thou ght o f ascorresponding to the follow ing scenario: Let the maturity o f the d ebt be sho rter than the m aturity of thefirm's project. The de bt is the n rolled over afte r the realization o f the ag gregate m~certainty. If there isbad aggregate news, then the new loan rate is higher than w ould be otherw ise. To implemen t the sort o frisk-sharing arrangement imp lied by the m odel, therefore, all tha t is necessary is that som e com ponento f the financing have a shorter maturity than that o f the project.


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C h . 2 1 . " T h e F i n a n c i a l A c c e le r a t o r i n a Q u a n t i ta t i v e B u s i n e s s C y c l e F r a m e w o r k 1353G i ve n t he s t a t e - con t i ngen t deb t f o rm o f the op t i ma l con t r ac t , the ex pec t ed r e t u rn t o

t h e e n t r e p r e n e u r m a y b e e x p r e s s e d as{ f i )jE o ) R t+ 1 Q t K i + 1 dF(c o) - (1 - F ( ~ J ) ) N J R ~ I Q t K /+ l ,/ (3.6)kw here expec t a t i ons a r e t aken w i t h r e spec t t o t he r andom va r i ab l e , R t + l , and i t i s

u n d e r s t o o d t h a t ~ / m ay be m ade con t i ngen t on t he r ea l i za t i on o f th i s va r iab l e .C ombi n i ng t h i s r e l a t i on w i t h Equa t i on (3 . 5 ) a l l ow s us t o s i mpl i fy t he en t r ep reneur ' so b j e c ti v e to m a x i m i z a t i o n o f

{ J o }9 )L 1 - - U ; + O , J ( 3 . 7 )k kw h e r e U [a ~I =_ R t + j / E { R t + 1} is t he r a t io o f t he r ea l i zed r e t u rn t o cap i ta l t o t he expe c t ed

re tu rn . G i v en t ha t t he i n t e rm ed i a ry mus t r ece i ve a com pe t i t i ve r e t u rn , the en t r ep rene uri n t e rna li zes t he ex pec t ed de f au l t cos ts , a s Eq ua t i on (3 . 7 ) sugges ts .

T h e f o r m a l i n v e s t m e n t a n d c o n t r a ct in g p r o b l e m t h e n r e d u c e s t o c h o o s i n g K /+ I an da schedu l e fo r N / ( a s a f unc t ion o f t he r ea l ized va l ues o f R )+I) to ma x i m i ze Equa-t ion (3 . 7 ) , sub j ec t t o t he s e t o f s t a t e - con t i ngen t cons t r a in t s i m pl i ed by E qua t i on (3 .5 ) .The d i s tr i bu t ions o f t he aggrega t e and i d i osync ra t i c r i sks t o t he r e t u rn t o cap i ta l , t hep r i ce o f cap i t al , and t he qu an t i ty o f ne t w or t h t ha t t he en t r ep reneu r b r i ngs t o t he t ab lea r e t aken a s g i ven i n t he max i mi za t i on .

L e t s t ~ E { R ~ + I / R t + I } be t he expe c t ed d i s coun t ed r e t u rn t o cap i t a l. Fo r en t r ep reneur sto pu rcha se cap i ta l in the c om pet i t ive equi l ibr ium i t mus t be the case tha t st ~> 1 . Giv ens : ~> 1 , the f i r s t -order necessary condi t ions y ie ld the fo l lowing re la t ion for opt imalcap i ta l pu rchases ( s ee A ppe nd i x A fo r de ta i ls ) :

Q a K / ~ , = * p ( s t ) N / + j , w i t h W ( 1 )== l, W :(') > O. (3 .8 )Equ a t i on (3 . 8 ) desc r i bes t he c r i t ica l l ink be t w een cap i t a l expe nd i t u r e s by t he f i rm andf i nanci a l cond i t i ons , a s measured b y t he w edge b e t w e en t he e xpec t ed the r e t u rn t ocapi ta l and the safe ra te , s t, and by ent repren eur ia l n e t w or th , Art/1 JL. Given the valueo f K / + l t ha t s a ti s fi e s Equa t i on (3 . 8 ) , t he s chedu l e fo r N J i s p i nn ed dow n un i que l y by t hes t a t e - con t ingen t cons t r a i n t on t he exp ec t ed r e t u rn t o deb t , de f i ned by E qua t i on (3 .5 ) .

Equa t i on (3 . 8 ) is a k ey r e l a t ionsh i p i n t he m ode l : I t show s t ha t cap i t al expend i t u r e sby each f i rm a r e p ropor t i ona l t o t he ne t w or t h o f t he ow ner / en t r ep reneur , w i t h ap ropor t i ona l i t y f ac t o r t ha t i s i nc r eas i ng i n t he expec t ed d i s coun t ed r e t u rn t o cap i t a l ,s t . Eve ry t h i ng e l s e equa l , a r i s e i n t he expec t ed d i s coun t ed r e t u rn t o cap i t a l r educest he expec t ed de f au l t p robab i li t y . A s a con sequence , t he en t r ep rene ur car l t ake on mo re

l J In the co stly enforcememmodel of Kiyotakiand M oore (1997 ), ~p(.) - 1, implying Q ,K , . t - N i+ .


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1354 B . S . B e r n a n k e e t a l .

E.2

c~o

Demand 0 ~ , i . , , / / / , , .,.'"

c5- - f l [ I i ~ - - T - -6 7 8 9 10 11 12

CapitalStockFig. 1. Effect of an increase in net worth.

d e b t a n d e x p a n d t h e s i z e o f h i s fi r m . H e i s c o n s t r a i n e d f r o m r a i s i n g t h e s i z e o f t h e f i r mi n d e f i n it e l y b y th e f a c t t h a t e x p e c t e d d e f a u l t c o s t s a l s o r i se a s t h e r a ti o o f b o r r o w i n gt o n e t w o r t h i n c r e a s e s .

A n e q u i v al e n t w a y o f e x p r e s si n g E q u a t i o n ( 3 .8 ) i s/ N j \E { R f , . l } = s [ ~ ',+1. | R ,~ , , s ' ( . ) < 0 . (3 .9 )\ o,K/+,]

F o r a n e n t r e p r e n e u r w h o i s n o t f u l l y s e l f - f i n a n c e d , i n e q u i l i b r i u m t h e r e t u r n t o c a p i t a lw i l l b e e q u a t e d t o th e m a r g i n a l c o s t o f e x t e rn a l f i n a n c e. T h u s E q u a t i o n ( 3 . 9 ) e x p r e s s e st h e e q u i l i b r i u m c o n d i t i o n t h a t t h e r a t io s o f t h e c o s t o f e x t e rn a l f i n a n c e t o t h e s a f er a t e - w h i c h w e h a v e c a l l e d t h e d i s c o u n t e d r e t u r n t o c a p i ta l b u t m a y b e e q u a l l y w e l li n t e r p r e t e d a s t h e e x t e rn a l f i n a n c e p r e m i u m - d e p e n d s i n v e r s e l y o n t h e s h a r e o f t h ef i n n ' s c a p i ta l i n v e s t m e n t t h a t i s f in a n c e d b y t h e e n t r e p r e n e u r ' s o w n n e t w o r t h .

F i g u r e 1 i l lu s t ra t e s t h i s re l a t i o n s h i p u s i n g t h e a c t u a l c o n t r a c t c a l i b r a t e d f o r m o d e la n a l y s i s i n t h e n e x t s e c t io n . F i r m j ' s d e m a n d f o r c a p i t a l is o n t h e h o r i z o n t a l a x i sa n d t h e c o s t o f f u n d s n o r m a l i z e d b y t h e s a f e r a te o f r e t u r n i s o n t h e v e r t ic a l a x i s .F o r c a p i ta l s t o c k s w h i c h c a n b e f i n a n c e d e n t i r e l y b y t h e e n t r e p r e n e u r ' s n e t w o r t h ,i n t h i s c a s e K < 4 . 6 , t h e f i r m f a c e s a c o s t o f f u n d s e q u a l t o t h e r i s k f r e e r a te . A sc a p i t a l a c q u i s i t i o n s r i s e i n t o t h e r a n g e w h e r e e x t e r n a l f i n a n c e i s n e c e s s a r y , t h e c o s t -o f - f u n d s c u r v e b e c o m e s u p w a r d s l o p i n g , r e f l e c t i n g t h e i n c r e a s e i n e x p e c t e d d e f a u l tc o s t s a s s o c i a t e d w i t h t h e h i g h e r r a t io o f d e b t t o n e t w o r t h . W h i l e t h e s u p p l y o ff u n d s c u r v e i s - u p w a r d s l o p i n g , o w i n g t o c o n s t a n t r e t u r n s t o s c a l e , t h e d e m a n d f o rc a p i t a l i s h o r i z o n t a l a t a n e x p e c t e d r e t u r n 2 p e r c e n t a g e p o i n t s a b o v e t h e r i s k f r e e r a t e .


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C h. 2 1 : T h e F i n a n c i a l A c c e l e r a t o r in a Q u a n t i t a ti v e B u s i n e s s C y c l e F r a m e w o r k 1355P o i n t E , w h e r e t h e f i r m ' s m a r g i n a l c o s t o f f u n d s e q u a l s t h e e x p e c t e d r e t u r n t o c a p i ta ly i e lds t he op t im a l cho ic e o f t he cap i t a l s t ock K = 9 .2 . Fo r t h i s con t r ac t, t he l eve ragera t i o i s 50%.

I t i s ea sy to i l l u s t r a t e how a sh i f t i n t he f i rm ' s f i nanc i a l pos i t i on a f f ec t s i t s demandfo r cap i t a l . A 15% inc rease i n ne t wor th , N i~ L fo r exam ple , ca uses t he r i gh tw ard sh i f ti n t he cos t -o f - funds cu rve dep ic t ed by the ha t ched l i ne i n F igu re 1 . A t t he o ld l eve lo f c a p i ta l d e m a n d , t h e p r e m i u m f o r e x t e rn a l f i n a n c e d e c li n e s: T h e r is e i n n e t w o r t hre l a t i ve t o t he cap i t a l s t ock r educes t he expec t ed de fau l t p robab i l i t y , eve ry th ing e l see q u al . A s a c o n s e q u e n c e , t h e f ir m i s a b le to e x p a n d c a p a c i t y t o p o i n t U . S i m i la r ly , ad e c l in e i n n e t w o r t h r e d u c e s t h e f i r m ' s e ff e c ti v e d e m a n d f o r c a p it a l.

I n t he nex t s ec t ion we inc o rpo ra t e t h i s fi rm- l eve l r e l a t i on in to a gene ra l equ i l i b r iumf r a m e w o r k . B e f o r e p r o c e e d i n g , h o w e v e r , w e n o t e t h a t , i n g e n e r a l , w h e n t h e f i r m ' sd e m a n d f o r c a p i t a l d e p e n d s o n i t s f in a n c i al p o s i ti o n , a g g r e g a t i o n b e c o m e s d i f fi cu l t. T h ereason i s t ha t , i n gene ra l , t he t o t a l demand fo r cap i t a l w i l l depend on the d i s t r i bu t iono f w e a l t h a c r o s s f i r m s . H e r e , h o w e v e r , t h e a s s u m p t i o n o f c o n s t a n t r e tu r n s t o s c a let h r o u g h o u t i n d u c e s a p r o p o r t i o n a l r e l a t i o n b e t w e e n n e t w o r t h a n d c a p i t a l d e m a n d a tt he f i rm l eve l ; f u r the r, t he f ac to r o f p rop or t i ona l i t y i s i ndep ende n t o f f irm-spe c i f i cf ac to r s . Thus i t i s s t r a igh t fo rward to aggrega t e Equa t ion (3 .8 ) t o de r ive a r e l a t i onsh ipb e t w e e n t h e t o t a l d e m a n d f o r c a p it a l a n d t h e t o ta l s t o c k o f e n t re p r e n e u r i al n e t w o r th .

4 . G e n e r a l e q u i l i b r i u mW e n o w e m b e d t h e p a r t i a l e q u i l i b r i u m c o n t r a c t i n g p r o b l e m b e t w e e n t h e l e n d e r a n dt h e e n t r e p r e n e u r w i t h i n a d y n a m i c g e n e r a l e q u i l i b r i u m m o d e l . A m o n g o t h e r t h i n g s ,t h i s w i l l pe rmi t u s t o endogen ize t he s a f e i n t e r e s t r a t e , t he r e tu rn t o cap i t a l , and there l a ti ve p r i ce o f cap i t a l , a l l o f wh ich w ere t aken a s g iven in t he pa r t i a l equ i l i b r ium .

W e p r o c e e d i n s e v e r a l s t e p s . F i r s t w e c h a r a c t e r i z e a g g r e g a t e b e h a v i o r f o r t h ee n t r e p re n e u r i a l s e c to r . F r o m t h i s e x e rc i s e w e o b t a i n a g g r e g a t e d e m a n d c u r v e s f o r l a b o ra n d c a p i ta l , g i v e n t h e r e a l w a g e a n d t h e r is k l e s s in t e r e s t ra t e . T h e m a r k e t d e m a n d f o rc a p i ta l i s a k e y c o m p o n e n t o f t h e m o d e l s in c e i t r e f le c t s t he i m p a c t o f fi n a n c ia l m a r k e ti m p e r f e c t i o n s . W e a l s o d e r i v e h o w t h e a g g r e g a t e s t o c k o f e n t r e p r e n e u r ia l n e t w o r t h ,a n i m p o r t a n t s t at e v a r ia b l e d e t e r m i n i n g t h e d e m a n d f o r c a p it a l, e v o l v e s o v e r ti m e .

W e n e x t p l a c e o u r " n o n - s t a n d a r d " e n t r e p r e n e u r i a l s e c t o r w i t h i n a c o n v e n t i o n a lD y n a m i c N e w K e y n e s i a n f r a m e w o r k . T o do s o , w e a d d t o th e m o d e l b o t h h o u se h o l d sand r e t a i l e rs , t he l a t t e r be ing inc luded on ly i n o rde r t o i n t roduce p r i ce i ne r t i a i n at~cac tabl e man ner . W e a l so add a gov e rnm en t s e c to r t ha t condu c t s f i sca l and m on e ta r ypo l i c i e s . S ince m uc h o f t he mod e l i s s t anda rd , w e s im ply wr i t e t he l og - l inea r i zedf r a m e w o r k u s e d f o r c o m p u t a t i o n s a n d d e f e r a m o r e d e t a i l e d d e r i v a t io n to A p p e n d i x B .E x p r e s s i n g t h e m o d e l i n a l o g - l i n e a r i z e d f o r m m a k e s t h e w a y i n w h i c h t h e f i n a n c i a la c c e l e r a t o r in f l u e n c es b u s i n e s s c y c l e d y n a m i c s r e a s o n a b l y t r a n s p ar e n t .


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1356 B.X Bernanke et al .4 . 1. T h e e n t r e p r e n e u r i a l s e c t o rR e c a l l t h a t e n t re p r e n e u r s p u r c h a s e c a p i t a l in e a c h p e r i o d f o r u s e i n t h e s u b s e q u e n tp e r i o d . C a p i t a l i s u s e d i n c o m b i n a t i o n w i t h h i r e d l a b o r t o p r o d u c e ( w h o l e s a l e ) o u t p u t .W e a s s u m e t h a t p r o d u c t i o n i s c o n s t a n t r e t u r n s t o s c a l e, w h i c h a l l o w s u s to w r i t e t h ep r o d u c t i o n f u n c t io n a s a n a g g r e g a t e r e la t io n s h ip . W e s p e c i f y th e a g g r e g a t e p r o d u c t i o nf u n c t i o n r e l e v a n t t o a n y g i v e n p e r i o d t a s

Y t = A t K a L ] - a , ( 4 . 1 )w h e r e Y t i s a g g r e g a t e o u t p u t o f w h o l e s a l e g o o d s , K t i s t h e a g g r e g a t e a m o u n t o f c a p i t a lp u r c h a s e d b y e n t r e p r e n e u r s i n p e r i o d t - 1 , L~ i s la b o r i n p u t , a n d A t is a n e x o g e n o u st e c h n o l o g y p a r a m e t e r.

L e t I t d e n o t e a g g r e g a t e i n v e s t m e n t e x p e n d i t u r e s . T h e a g g r e g a t e c a p i ta l s t o c k e v o l v e sa c c o r d i n g t o

K ,+ I = k ,K , j K t + ( 1 - 6 ) K t , ( 4 . 2 )

w h e r e /5 i s t h e d e p r e c i a t i o n r a te . W e a s s u m e t h a t t h e re a r e i n c r e a s i n g m a r g i n a la d j u s t m e n t c o s t s i n th e p r o d u c t i o n o f c a pi ta l , w h i c h w e c a p t ur e b y a s s u m i n g t h a ta g g r e g a t e i n v e s t m e n t e x p e n d i tu r e s o f L y i e l d a g r o s s o u t p u t o f n e w c a p i ta l g o o d s ( I ~ / K t ) K t , w h e r e q ~ (. ) i s i n c r e a s i n g a n d c o n c a v e a n d q ~ (0 ) = 0 . W e i n c l u d ea d j u s t m e n t c o s t s to p e r m i t a v a r i a b l e p r i c e o f ca p i ta l . A s i n K i y o t a k i a n d M o o r e ( 1 9 9 7 ) ,t h e i d e a i s t o h a v e a s s e t p r i c e v a r i a b i l i ty c o n t r i b u t e t o v o l a t il i t y i n e n t r e p r e n e u r ia l n e tw o r t h . I n e q u i l ib r i u m , g i v e n t h e a d j u s t m e n t c o s t f u n c t i o n , t h e p r ic e o f a u n i t o f c a p i ta li n t e r m s o f t h e n u m e r a i r e g o o d , Q t , i s g i v e n b y 12

= . (4 .3 )

W e n o r m a l i z e t h e a d j u s t m e n t c o s t f u n c t i o n s o t h a t t h e p r i c e o f ca p i t a l g o o d s i s u n i t yi n t h e s t e a d y s t a t e .

A s s u m e t h a t e n t r e p r e n e u r s s e ll t h e ir o u t p u t t o r e ta i le r s . L e t 1 /X ~ b e t h e r e l a t iv e p r i c eo f w h o l e s a l e g o o d s . E q u i v a l e n t l y , X t i s t h e g r o s s m a r k u p o f r e t ai l g o o d s o v e r w h o l e s a l e

~2 1b implement investment expenditures in the decentralized equilibrium, think of there beingcompetitive capital producing firms that purchase raw output as a materials input, I~ and combine itwith rented capital, K to produce new capital goods via the production function I,3(g~ K . Th ese capitalgoods are t he n sold at the pric e Qt. S ince the cap ital-producing technology assumes constant returns toscale, these capital-producing firms earn zero profits in equ ilibrium. Equation (4.3) is de rived from thefirst-order condition for investm ent for one of these firms.


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Ch. 21: The Financial Accelerator in a Quanti tat ive Business C ycle Fram ework 1357g o o d s . T h e n t h e C o b b - D o u g l a s p r o d u c t i o n t e c h n o l o g y i m p l i e s th a t t h e r e n t p a i d to au n i t o f c a p i t a l i n t + 1 (f o r p r o d u c t i o n o f w h o l e s a l e g o o d s ) i s 13

1 aY l+ lX t + l Kt+l

T h e e x p e c t e d g r o s s r e t u r n t o h o l d i n g a u n it o f c a p i t a l f r o m t t o t + 1 c a n b e w r i t t e n1 aYt+l }k x ,2 , x,+~ + Q t + l ( 1 - 6 )E { R z + 1} = E Ot ' ( 4 . 4 )

S u b s t i t u t io n o f E q u a t i o n s ( 4 .1 ) a n d ( 4 .3 ) i n t o E q u a t i o n ( 4 . 4 ) y i e l d s a r e a s o n a b l yc o n v e n t i o n a l d e m a n d c u r v e f o r n e w c a p it a l. A s u s u a l , t h e r e t u r n o n c a p i t a l d e p e n d si n v e r s e l y o n t h e l e v e l o f in v e s t m e n t , r e f l e c t i n g d i m i n i s h i n g r e t u r n s .

T h e s u p p l y c u r v e f o r i n v e s t m e n t f in a n c e i s o b t a i n e d b y a g g r e g a t i n g E q u a t i o n ( 3 . 8)o v e r f i r m s , a n d i n v e r t i n g t o o b t a i n :

l, I : N t + lE { R t + I } = s ( 4 . 5 )

A s i n E q u a t i o n ( 3 .9 ) , t h e f u n c t i o n s ( . ) is th e r a t i o o f t h e c o s t s o f e x t e r n a l a n d i n t e r n a lf i n a n c e ; i t i s d e c r e a s i n g i n N t + l / Q t K t + l f o r N t ~ l < Q t K t + l . T h e u n u s u a l f e a t u r e o ft h is s u p p l y c u r v e , o f c o u r s e , is t h e d e p e n d e n c e o f t h e c o s t o f f u n d s o n t h e a g g r e g a t ef i n a n c i a l c o n d i t i o n o f e n tr e p r e n e u r s , a s m e a s u r e d b y t h e r a t i o N t + l / Q t I ( t + l .

T h e d y n a m i c b e h a v i o r o f c a p i ta l d e m a n d a n d t h e r e t u r n t o c a p it a l d e p e n d o nt h e e v o l u t i o n o f e n t r e p r e n e u r i a l n e t w o r t h , N : + l. N :+ I r e f l e c t s t h e e q u i t y s t a k e t h a te n t r e p r e n e u r s h a v e i n t h e i r f i rm s , a n d a c c o r d i n g l y d e p e n d s o n f i r m s ' e a r n i n g s n e t o fi n t e r e s t p a y m e n t s t o l e n d e r s . A s a t e c h n i c a l m a t t e r, h o w e v e r , i t is n e c e s s a r y t o s t a r te n t r e p re n e u r s o f f w i t h s o m e n e t w o r t h i n o r d e r t o a l l o w t h e m t o b e g in o p e r a t i o n s .F o l l o w i n g B e r n a n k e a n d G e r t l e r ( 1 9 8 9 ) a n d C a r l s t r o m a n d F u e r s t ( 19 9 7 ), w e a s s u m e

t~ To be consistent with our assum ption that adjustment costs are external to the firm , we assum e thatentrepreneurs se ll their capital at the end of p eriod t + 1 to the investment sector at price Q~+ I. Thuscapital is then used to produce new investment goods and resold at the price Q ,j . The "rental rate"(Q , 1 - Qt+l) reflects the influence of capital accum ulation on adjustm ent costs. This rate is determhledby the zero -profit condition~2 / 1 \ I tQ, Q,)=o.

In s teady s ta te q~ ( ~ ) = 6 and ~ ' ( : t )~ = 1, implying that Q = Q = 1. Around tile steady state,the diffbrence between Q t~l and Qt is second o rder. We therefore om it the rental term and expressEquation (4.4) using Q:~ I rather than Qt+l-


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Ch. 21." The Financial Accelerator in a Qua ntitative Business Cycle Framew ork 1359U /p =-- f o ' o ) Q~_~Kt d F ( co ) - E t . i { ~ ' ~oQ t 1Kt dF(~o)} be t he une xpec t ed sh i f t in t hecond i t i ona l ( on t he aggrega t e s t a t e ) de f au l t cos t s . We can expres s Vt as

V, = [ U ~ k ( 1 - t t U / P ) ] Q t 1 K t + E , l{V~}. (4.9)N o w cons i de r t he i mp ac t o f a unex pec t ed i nc r ease i n t he ex pos t r e t u rn t o cap i ta l .

D i f f e r en t i a ti ng Equa t i on (4 . 9 ) y i e l ds an ex pres s i on fo r t he e l a s t i c i t y o f en t r ep reneur i a lequ i t y w i t h r e spec t t o an unan t i c i pa t ed movement i n t he r e t u rn t o cap i t a l :

o v t / E , l{v,} _ E t I { R ~ } Q t - I K to r ; k i n , 1 R ? } E , , { ) /> 1. (4. 10 )

A ccord i ng t o Equa t i on (4 . 10 ) , an unexpec t ed one pe r cen t change i n t he ex pos t r e t u rnt o cap i t a l l eads t o a pe r cen t age change i n en t r ep reneur i a l equ i t y equa l t o t he r a t i oo f g ros s ho l d i ngs o f cap it a l t o equ i ty . To the ex t en t t ha t en t r ep reneu r s a r e l eve raged ,t h i s r a t i o exceeds un i t y , i mpl y i ng a magn i f i ca t i on e f f ec t o f unexpec t ed a s se t r e t u rnson en t r ep reneur i a l equ i t y . The key po i n t he r e i s t ha t unexpec t ed movement s i n a s se tp r i ces , w h i ch a r e l i ke l y t he l a rges t source o f unexpec t ed movement s i n g ros s r e t u rns ,can have a subs tan t ia l e f fec t on f i rm s ' f inancia l pos i t ions .

In t he gene ra l equ i l ib r i um, fu r t he r, t he r e is a k i nd o f mul t i p l i e r e f fec t , a s w e sha lls ee . A n unan t i c i pa t ed r i s e i n a s se t p r i ces r a i s e s ne t w or t h more t han p ropor t i ona t e l y ,w h i ch s t imul a t e s i nves t m en t and , i n t u rn , ra i s e s a s se t p r i ces ev en fu r the r . A n d so on .T h i s p h e n o m e n o n w i l l b e c o m e e v i d e n t i n th e m o d e l s im u l a ti o n s.

W e n e x t o b t a i n d e m a n d c u r v e s f o r h o u s e h o l d a n d e n t r e p r e n e u r i a l l a b o r , f o u n d b yequa t i ng marg i na l p roduc t w i t h t he w age fo r each case :

(1 - a ) ~ = x , N ,(1 - a ) ( 1 - ~ ) ~ = x , w f ,

(4 .11)

(4 .12)

w here W~ i s t he r ea l w age fo r househo l d l abor and Wf i s t he r ea l w age fo rent repreneur ia l l abor .

C om bi n i ng Equ a t i ons (4 . 1 ), (4 . 7 ) , (4 . 8 ), and (4 . 12 ) and i m pos i ng t he cond i t i on t ha ten t r ep reneur i a l l abor i s f i xed at un i ty , y i e l ds a d i f f e r en ce equa t i on fo r Nt+l:

+ (1 - a)(1 O ) A t K ~ H ~ l - " ) o .(4 .13)

Equa t i on (4 . 13 ) and t he supp l y cu rve t b r i nves t men t f unds , Equa t i on (4 . 5 ) , a r e t het w o bas i c i ng red i en t s o f the f i nanc i a l acce le r a to r . The l a t te r equa t i on desc r i bes how


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1360 B.S. Bernanke et al.movement s i n ne t w or t h i n f l uence t he cos t o f cap i t a l . The fo rmer cha rac t e r i zes t heendogenous va r i a t i on i n ne t w or t h .Thus f a r w e have de t e rmi ned w ho l esa l e ou t pu t , i nves t men t and t he evo l u t i on o fcap i ta l , t he p r i ce o f cap i t al , and t he ev o l u t i on o f ne t w or t h , g i ven t he r i sk l e s s r ea lin teres t ra te R t + l , t he house ho l d r ea l w age Wt, and t he r e l a t ive p r ice o f w ho l esa l eg o o d s I / X , T o d e t e r m i n e t h e s e p r i c e s a n d c o m p l e t e t h e m o d e l , w e n e e d t o a d d t h ehouseho l d , r e t a i l , and gove rnmen t s ec t o r s .4 .2 . T h e c o m p l e t e l o g - l i n e a r i ze d m o d e lW e n o w p r e s e n t th e c o m p l e t e m a c r o e c o n o m i c f r a m e w o r k . M u c h o f th e d e r i v a ti o n i ss t anda rd and n o t cen t r a l to t he d eve l o pm ent o f t he f i nanc i a l acce le r a to r . W e t he r e fo r es i mpl y w r i t e t he com pl e t e l og - l i nea r i zed mo de l d i rec tl y , and de f e r mos t o f t he de t a i lst o A p p e n d i x B .

A s w e h a v e e m p h a s i z e d , t h e m o d e l i s a D N K f r a m e w o r k m o d i f i e d t o a l l o w f o ra f i nanc i a l acce l e r a t o r . I n t he background , a l ong w i t h t he en t r ep reneur s w e havedesc r i bed a r e househ o l ds and r e t a i le r s . H ou seho l d s a r e i n f i n i t e ly - l ived agen t s w hoc o n s u m e , s a v e , w o r k , a n d h o l d m o n e t a r y a n d n o n m o n e t a r y a s s e t s . W e a s s u m e t h a thou seho l d u t il i ty i s s epa rab l e ove r t i me an d o ve r consum pt i on , r ea l m on ey ba l ances ,and l e isu r e . Mo me nt a ry u t il it y , f u r the r , is l oga r i t hmi c i n each o f t hese a rgum ent s is .

A s i s s t anda rd i n t he l i t e r a t u r e , t o mot i va t e s t i cky p r i ces w e modi fy t he mode l t oa l l ow fo r monopo l i s t i c compe t i t i on and ( i mpl i c i t ) cos t s o f ad j us t i ng nomi na l p r i ces .I t i s inconve n i en t t o a s sume t ha t the en t r ep rene ur s w ho purchase cap i t a l and p ro duceou t pu t i n t h i s mode l a r e monopo l i s t i ca l l y compe t i t i ve , s i nce t ha t a s sumpt i on w ou l dcom pl i ca t e the ana l yses o f t he f i nanc i a l con t r ac t w i t h l ende r s and o f t he evo l u t i on o fne t w or t h . To avo i d t h is p rob l em, w e i ns t ead a s sume t ha t t he mo nopo l i s t i c com pe t i t i onoccu r s a t t he " r e t a i l " l eve l. Spec i f i ca l ly , w e a s sume t he r e ex i s t s a con t i nuum o f r e ta i le r s( o f m e a s u r e o n e ) . R e t a il e rs b u y o u t p u t f r o m e n t r e p r e n e u r - p r o d u c e r s i n a c o m p e t i ti v emarke t , t hen s l igh t l y d i f fe r en t i a t e t he o u t pu t t hey pu rchase ( say, by pa i n t i ng i t a un i queco l o r o r add i ng a b r and n ame ) a t no r e so urce cos t . B ecause t he p rod uc t is d i f f e r en t ia t ed ,each r e t a i l e r has a b i t o f ma rke t pow er . H ouse ho l ds and f i rms t hen purcha se C ESaggrega t e s o f t hese r e t a il goo ds . I t is t hese C ES aggrega t e s t ha t a re co nve r t ed i n t oconsu mp t i on and inves t men t goods , and w hose p r i ce i ndex de f ines t he aggrega t e p r i cel eve l. P ro f it s f r om r e t ai l ac t iv i t y a r e r eba t ed l um p- sum t o househ o l ds ( i. e ., hous eho l dsare the u l t imate o wn ers o f re ta i l out le t s . )

To i n t roduce p r i ce i ne r ti a , w e a s sum e t ha t a g i ven r e t a i le r i s f r ee t o cha nge h i s p r i cei n a g i ven pe r i od on l y w i t h p roba b i l i t y 1 - 0 . Th e expe c t ed dura ti on o f any p r i ce chang ei s 1@ 0- Th i s dev i ce , f o l l ow i ng C a l vo (1983) , p rov i des a s i mpl e w ay t o i nco rpora t es t agge red l ong- t e rm nomi na l p r i ce s e t t i ng . B ecause t he p robab i l i t y o f chang i ng p r i cei s i ndependen t o f h i s to ry , the aggreg a t i on p rob l em i s g r ea t l y s impl i f ied . O n e ex t r a

~5 In particular, househ old atility s given by {~ ;~ 0[ ~[ln(C~,k) + _~ n (M t. JP , .-/~ + ~ In{ 1 l[,+i,)] .


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Ch. 21 . " The Financ ia l Acce lerator in a Quant ita t ive Bus iness Cyc le Fra mew ork 1 3 6 1t w i s t , f o l l o w i n g B e r n a n k e a n d W o o d f o r d ( 1 9 9 7 ) , i s t h a t f i r m s s e t t i n g p r i c e s a t t a r ea s s u m e d t o d o s o p r i o r t o t h e r e a l iz a t i o n o f a n y a g g r e g a t e u n c e r t a i n t y a t t im e t.L e t l o w e r c a s e v a r i a b l e s d e n o t e p e r c e n t d e v i a t i o n s f r o m t h e s t e a d y s t a t e , a n d l e tr a t io s o f c a p it a l l e tt e r s w i t h o u t t i m e s u b s c r i p t d e n o t e s t h e s t e a d y s t at e v a l u e o f t h er e s p e c t i v e r at io . F u r t h e r , l e t ~ d e n o t e a c o l l e c t io n o f t e r m s o f s e c o n d - o r d e r i m p o r t a n c ei n t h e e q u a t i o n f o r a n y v a r i a b l e z , a n d l e t e [ b e a n i . i . d , d i s t u r b a n c e t o t h e e q u a t i o nf o r v a r i a b l e z . F i n a l l y , l e t G t d e n o t e g o v e r n m e n t c o n s u m p t i o n , : r t = - p ~ - p t - i t h e r a t eo f i n f l a t i o n f r o m t - 1 t o t , a n d r'/+ 1 ==- r ~+ ~ + E { p t + l - P t } b e t h e n o m i n a l i n t e r e s tr a te . I t i s t h e n c o n v e n i e n t t o e x p r e s s t h e c o m p l e t e l o g - l i n e a r i z e d m o d e l i n t e r m s o ff o u r b l o c k s o f e q u a t io n s : ( 1 ) a g g r e g a t e d e m a n d ; ( 2 ) a g g r e g a t e s u p p l y ; (3 ) e v o l u t i o no f t h e s t at e v a r ia b l e s ; a n d ( 4 ) m o n e t a r y p o l i c y r u l e a n d s h o c k p r o c e s s e s . A p p e n d i x Bp r o v i d e s d e t a i l s .(1 ) A g g r e g a t e d e m a n d

C 1 G C ey ~ = ] 7 c , + ~ i t + ~ g t + - -c ~ 'y + " + q ~, ( 4 . 1 4 )c t = - rt+L + E t {c t+ l } , (4 .1 5 )c ~ = n t , l + " " + 0 ~:~ , ( 4 . 1 6 )E t { r ~ I } - F z + I - " - u [ 1 t + l ( q t + k t l ) ] , ( 4 . 1 7 )r ) + t - ( 1 - - e ) @ t k l - k t - - i X t + l ) @ e q t ~ 1 q , ( 4 . 1 8 )q t = cp ( i t - k t ) . (4 .1 9 )

( 2 ) A g g r e g a t e S u p p l yy t = a, + a k t + ( 1 - a ) g 2 h , ( 4 . 2 0 )Y t - h t - x t - c t = ~ - I h t , ( 4 . 2 1 )YL) : E t l { l~ ( - X t ) + ~ 2T t+ l } . ( 4 . 2 2 )

( 3) E v o l u t i o n o f S ta t e V a r i a b le s

k t + l = 6 i t + ( 1 - 6 ) k , ( 4 . 2 3 )y R K t , ( 4 . 2 4 )


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1362 B . X B e r n a n k e e t a l .( 4 ) M o n e t a r y P o l i c y R u l e a n d S h o c k P r o c e s s e s

17 I t~r , - p r t 1 + g ac ~ I + e l " , (4 .25)& = p g g t - i + ~ , (4 .26)aL = p , , a t - i + g / , (4 .27)

wi th ( ; ) llo g Iz e ) d F ( ~ o ) R ~ Q t _ I K / D K ,P ? OD # j ) 6o dF(~o)R/ ',

O~'e = l o g ( 1 - C e + l / N i + ~ )i T c ~T; /N '

( R i ' l R - ( 1 - a ) ( 1 - [2)(Y/X)q~t = N 1 )K (r~"+ q ~ -i + k t ) + N Y t - x ~ ,l p ( R k / R ) 1 - b

~ ' ( R k / R ) ' (1 - cs) + a Y / ( X K ) '( ~ ( I / K ) 1 )t ( 1 ~ _ )

q ) ~ ( ( D ( I / K ) 1 ) , , ' K " ~ ( 1 - - 0 / ~ ) .

Equ a t i on (4 . 14 ) i s t he l og - l inea f i zed ve r s i on o f t he r e source cons t r a in t . T hepr i m ary de t e rm i nan t s o f t he va r i a t ion i n aggrega t e expend i t u r e s Y t a r e h o u s e h o l dconsumpt i on c t , i nves t men t i t , a n d g o v e r n m e n t c o n s u m p t i o n gL. O f l e s s e r i m p o r t a n c eis var ia t ion in e nt repren eur ia l con sum pt io n c~ 16. Final ly , var ia t ion in resou rces d evo tedmo ni t o r i ng cos t, em bed ded i n t he t e rm ~ , a l so ma t t e r s in p ri nc i p le . U nd er r easonab l epa rame t r i za t i ons , how ever , t h i s f ac t o r has no pe r cep t i b l e i mpac t on dynami cs .H o u s e h o l d c o n s u m p t i o n i s g o v e r n e d b y t h e c o n s u m p t i o n E u l e r r e l a t i o n , g i v e n b yEq ua t i on (4 .15 ) . The un i t coe f f i c i en t on t he r ea l i n t e re s t r a te ( i. e. , t he i n t e r t empora le las t ic i ty of subs t i tu t ion) ref lec t s the assumpt ion of logar i thmic u t i l i ty over con. -sumpt i on . B y en fo rc i ng t he s t anda rd consumpt i on Eu l e r equa t i on , w e a r e e f f ec t i ve l yas sum i ng t ha t fi nanc i a l ma rke t f r i c ti ons do no t i mped e house ho l d behav i o r. N um erousau t hor s have a rgued , how ever , t ha t c r ed i t cons t ra i n t s a t t he hou seho l d l eve l i n f l uencea non- t r iv i a l po r t i on o f aggrega t e co nsum pt i on spend i ng . A n i n t e re s t i ng ex t ens i on o f

16 N ote that each variable in the log-lmearized esou rce constraint is weighted by the variable's shareo f ou tput in the stea dy state. Under any reasonable parametrization o f the m odel, c~ has a relatively owweight.


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C h . 2 1." T h e F i n a n c i a l A c c e l e r a t o r i n a Q u a n t i ta t i e e B u s i n e s s C y c l e F r a m e w o r k 1363t h is mo de l w ou l d be t o i ncorpora t e househo l d bor row i ng an d a s soc i a t ed f ri c ti ons . W i t hsome s l igh t mo d i f i ca ti on , the f i nanc i a l acce l e r a to r w ou l d t hen a l so app l y t o househ o l dspending, s t rengthening the overa l l e f fec t .

S i nce en t r ep reneur i a l consum pt i on i s a ( sma l l) f i xed f r ac t i on o f aggrega t e ne t w o r t h( r eca l l t ha t en t r ep reneur s w ho r e t i r e s i mpl y consume t he i r a s se t s ) , i t s i mpl y va r i e sp ropo r t i ona t e l y w i t h ag grega t e ne t w or t h , a s Equ a t i on (4 . 16 ) i n

bernankegertlergilchrist.macrohandbook1999

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