HONG KONG INSTITUTE FOR MONETARY RESEARCH THE GREAT RECESSION: A SELF-FULFILLING GLOBAL ANIC hilippe Bahea ad Eri va Wioop HKIMR Workig aper No.09/03 Jue 03
Hog Kog Isiue for Moeary Researh (a ompay iorporaed wih limied liabiliy) All righs reserved. Reproduio for eduaioal ad o-ommerial purposes is permied provided ha he soure is akowledged.
The Grea Reessio: A Self-Fulfillig Global ai hilippe Bahea Uiversiy of Lausae Swiss Fiae Isiue Cere for Eoomi oliy Researh Hog Kog Isiue for Moeary Researh ad Eri va Wioop Uiversiy of Virgiia Naioal Bureau of Eoomi Researh Hog Kog Isiue for Moeary Researh Jue 03 Absra While he 008-009 fiaial risis origiaed i he Uied Saes we wiessed seep delies i oupu osumpio ad ivesme of similar magiudes aroud he globe. This raises wo quesios. Firs give he observed srog home bias i goods ad fiaial markes wha a aou for he remarkable global busiess yle syhroiiy durig his period? Seod wha a explai he differee relaive o previous reessios where we wiessed far weaker o-moveme? To address hese quesios we develop a wo-oury model ha allows for self-fulfillig busiess yle pais. We show ha a busiess yle pai will eessarily be syhroized aross ouries as log as here is a miimum level of eoomi iegraio. Moreover we show ha several faors geeraed pariular vulerabiliy o suh a global pai i 008: igh redi he zero lower boud uresposive fisal poliy ad ireased eoomi iegraio. We would like o hak Mahias Thoeig ad various semiar pariipas. Fag Liu ad ierre-yves Deléamo provided able researh assisae. We graefully akowledge fiaial suppor from he Naioal Siee Foudaio (gra SES-064944) he Bakard Fud for oliial Eoomy he Hog Kog Isiue for Moeary Researh he Naioal Cere of Compeee i Researh "Fiaial Valuaio ad Risk Maageme" (NCCR FINRISK) ad he ERC Advaed Gra #69573. The views expressed i his paper are hose of he auhors ad do o eessarily refle hose of he Hog Kog Isiue for Moeary Researh is Couil of Advisers or he Board of Direors.
Hog Kog Isiue for Moeary Researh Workig aper No.09/03. Iroduio The 008-009 Grea Reessio learly had is origis i he Uied Saes where a hisori drop i house pries had a deep impa o fiaial isiuios ad markes. I is remarkable he as illusraed i Figure ha he seep delie i oupu osumpio ad ivesme durig he seod half of 008 ad begiig of 009 was abou he same i he res of he world as i he Uied Saes. This is surprisig boh i he oex of exisig heory ad hisorial experiee. Trasmissio haels i exisig models deped riially o rade ad fiaial likages ad o he ype of shoks. A ree lieraure has show ha i is possible o have oe-o-oe rasmissio of shoks if goods ad fiaial markes are perfely iegraed ad here are redi raher ha ehology shoks. Bu i realiy goods ad fiaial markes are far from perfely iegraed ad here is sigifia home bias i boh goods ad asse rade. As illusraed i va Wioop (03) a model wih redi shoks ha apures he observed fiaial home bias will have parial rasmissio a bes. Cosise wih his Rose ad Spiegel (00) ad Kami ad ouder (0) fid ha here is lile relaio bewee fiaial likages ha ouries have wih he U.S. ad he delie i heir GD growh ad asse pries durig 008-009. 3 The lose o-moveme of busiess yles illusraed i Figure is also uusual from a hisorial perspeive. Figure shows ha durig he Grea Depressio he delie i oupu i he res of he world was muh smaller he i he Uied Saes. erri ad Quadrii (0) show ha busiess yle o-moveme durig he 008-009 reessio sads ou sigifialy relaive o previous reessios sie 965. Hiraa Kose ad Orok (03) fid ha over he pas 5 years he global ompoe of busiess yles has aually delied relaive o loal ompoes (regio ad oury-speifi). This he leads o wo quesios ha we aim o address i his paper. Firs give he limied exe of goods ad fiaial iegraio how a we explai ha he sharp delie i busiess yles was similar i he res of he world as i he Uied Saes durig he Grea Reessio? Seod wha a explai he differee relaive o previous reessios? To aswer hese quesios we develop a wo-oury wo-period New Keyesia model ha explais he reessio as resulig from a self-fulfillig shok o expeaios as opposed o a exogeous shok o fudameals. The self-fulfillig beliefs are a resul of several ier-likages bewee he prese (period ) ad he fuure (period ). The fuure affes he prese as beliefs of lower ad riskier seod-period iome lead o higher firs period savig. As osumpio falls oupu ad firm Eve ouside of Europe whih had by far he larges foreig exposure o U.S. asse baked seuriies he busiess yle delie was of similar magiude. Examples are Devereux ad Suherlad (0) Kollma Eders ad Muller (0) ad erri ad Quadrii (0). I is well kow ha wih ehology shoks oupu eds o be egaively orrelaed aross ouries eve i models wih perfe goods ad fiaial marke iegraio. 3 Kalemli-Oza e al. (03) fid ha fiaial iegraio has a egaive effe o busiess yle syhroizaio ouside of risis imes ad a zero effe durig risis imes. They also fid ha he bulk of he irease i syhroizaio durig he 008-009 risis is assoiaed wih a udeermied ommo shok.
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 profis delie. 4 Bu he prese also affes he fuure as lower profis lead o a expeaio of lower fuure eoomi aiviy ad greaer sesiiviy of firms o fuure shoks. This lowers expeed fuure oupu ad ireases ueraiy abou fuure oupu. Figure 3 whih is based o survey daa shows ha here was ideed a large drop i expeed GD growh ad a irease i is pereived variae. Moreover hese hages i beliefs were of similar magiude i he res of he world as i he Uied Saes. 5 A key resul of he model is ha a busiess yle pai is eessarily syhroized aross he wo ouries as log as hey have some miimum level of rade ad fiaial iegraio. The drop i oupu osumpio ad ivesme will he be of equal magiude i he wo ouries. Whe rade ad fiaial likages are very weak i is possible o have a busiess yle pai ha is limied o jus oe oury. This is o loger possible whe here is suffiie eoomi iegraio. Iuiively eiher he oury ha pais drags he oher oury io a pai or he oury ha does o pai pulls he oher oury ou of he pai. Their ieroeedess makes i impossible for oe oury o have self-fulfillig egaive beliefs abou he fuure while he oher oury has favorable beliefs abou he fuure. Limied ieroeedess he implies ha heir fae will be ommo. A pai if i happes will eessarily be global. The hreshold level of eoomi iegraio does o eed o be high. I is herefore possible o sill have sigifia home bias i rade ad asse holdigs as see i he daa. The model also provides a explaaio for he differee relaive o previous reessios. Limied omoveme of busiess yles i ope eoomy models is usually he resul of parial rasmissio (hrough rade ad fiaial likages) of exogeous oury-speifi shoks. Tha may well be a good desripio for mos busiess yles. However i our model he o-moveme is o a resul of rasmissio bu raher of a oordiaed pai. A ombiaio of disi faors all feaured i he model made he 008 period pariularly vulerable o suh a global self-fulfillig pai. Firs redi was igh. We show ha whe redi odiios are easier self-fulfillig pais are o feasible i equilibrium. Tigh redi makes firms more susepible o defaul whe hi by a drop i demad ha lowers profis. This is a riial eleme i our model of self-fulfillig beliefs. Seod ieres raes were low lose o he zero-lower boud. This redues he poeial sabilizig role of moeary poliy sie i is easier o fall i a liquidiy rap. Third here were osrais o ouerylial fisal poliy espeially due o hisorially high deb levels. Fourh he world has experieed a sigifia irease i boh rade ad fiaial iegraio over he pas wo deades. The model he implies ha pais are more likely o be ommo aross ouries. The risis i U.S. fiaial markes plays a role i our heory of a global reessio bu oly as a rigger eve for he self-fulfillig shif i beliefs. This sads i oras o models i whih he likage 4 This relaes o he lassi aradox of Thrif where higher savig implies lower demad whih redues oupu ad may aually ed up lowerig savig. We will disuss he aradox of Thrif i he oex of our model i Seio 5. For ree oribuios see Eggersso ad Krugma (0) Eggersso (00) ad Chrisiao (004). 5 The daa omes from Cosesus Eoomis who survey abou 50 promie fiaial ad eoomi foreasers. Eah Jauary foreasers are asked o give probabiliies for GD growh rae iervals for he urre year. We ompue he average ad he variae for eah oury as explaied i more deail i Appedix A. For he o-us daa lie we use he average aross he 7 oher ouries i he sample.
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 bewee fiaial markes ad he real eoomy operaes hrough a redi shok or a delie i wealh. While redi was igh i is hard o argue ha here was a large global redi shok. Figure 4 shows BIS daa o oal redi o he privae seor for he U.S. ad o-u.s. G-7 ouries. Two pois sad ou. Firs he experiee of he o-u.s. G7 was quie differe from ha i he U.S. wih a oiued irease i privae redi durig ad afer he risis. Seod while i he U.S. here was a delie i privae redi sie 008 his delie was gradual ad oiued hrough 0. The mai soure of redi delie was he gradual deleveragig of U.S. households whih was o oeraed durig he period of he sharp oupu delie i lae 008 ad early 009. 6 I is also hard o argue ha a delie i wealh was resposible for he global reessio. Wih he exepio of some smaller Europea ouries (Irelad ad Spai) he sharp delie i housig wealh was a U.S. pheomeo raher ha a global pheomeo. 7 The paper is relaed o some oher ree work o self-fulfillig busiess yle pais. 8 The mos impora differee is ha hese are losed eoomy models ad herefore do o address he omoveme quesio. Farmer (0a b) aalyzes models where self-fulfillig beliefs are assoiaed wih wealh. A belief of a lower value of fiaial wealh leads o lower osumpio whih leads o lower firm profis whih jusifies he drop i wealh. Bu as jus poied ou he delie i wealh was muh smaller i he res of he world ha i he Uied Saes. Heahoe ad erri (0) also have a model where he delie i wealh is riial o self-fulfillig beliefs alhough hrough a differe mehaism. I heir model lower housig wealh makes i possible o have self-fulfillig beliefs of higher uemployme. If households fid i less likely ha hey have a job omorrow ad i is hard o borrow whe heir housig ollaeral is low hey will redue osumpio. This redues oupu whih ideed leads o more uemployme. Boh his paper ad he Farmer papers rely o labor marke rigidiies raher ha omial rigidiies o geerae a lik from demad o produio. Behabib Wag ad We (0) develop a model where busiess yles are affeed by marke seimes whe produio deisios eed o be made i advae of kowig demad ad ages reeive imperfe iformaio abou aggregae demad. I has i ommo wih he Farmer papers ha 6 Chari Chrisiao ad Kehoe (008) doume ha bak redi aually ireased i he U.S. durig he seod half of 008 (boh osumer ad idusrial bak redi). Adria Colla ad Shi (0) fid ha a delie i bak redi o firms i 009 was replaed by a equal irease i bod fiaig. Also osise wih he absee of a large redi shok Kahle ad Sulz (03) use firm level daa o show ha here was o relaioship bewee he drop i ivesme by firms ad heir bak depedee. Helblig Huidrom Kose ad Orok (0) esimae a global VAR o fid ha a global redi shok aous for oly 0% of he global drop i GD i 008-009. 7 While sok markes delied sigifialy everywhere hey ed o be less impora i mos ouries ha i he Uied Saes. 8 See Shmi-Grohé (997) for a review of earlier models. 3
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 he busiess yle he depeds o a marke seime variable ha a ake o a oiuum of values as opposed o models suh as ours where here is eiher a pai or o. 9 Fially erri ad Quadrii (0) irodue a mehaism leadig o self-fulfillig redi shoks. If he resale value of firms is expeed o be low redi will be igh. Bu igh redi makes i diffiul for osraied firms o purhase asses from defaulig firms whih ideed makes he resale value low. While hey have a wo-oury model wih perfe busiess yle o-moveme his is a resul of perfe fiaial ad goods marke iegraio. 0 To prese he basi mehaism we aalyze a behmark model wihou ivesme fiaial asse rade or ueraiy. I ha oex i is possible o derive heoreially he odiios uder whih global pais our. Our mai resul saed i roposiio is ha parial iegraio is suffiie o guaraee ha busiess yles are perfely syhroized durig a pai. We show umerially ha he exe of iegraio required is relaively small. A pai limied o oe oury is o possible wih suffiie iegraio. Whe we exed he model o ilude ivesme fiaial asse rade ad ueraiy he resuls are similar bu a oly be derived umerially. The remaider of he paper is orgaized as follows. Seio desribes he behmark model. Seio 3 aalyzes he equilibria ad deermies whe busiess yle pais are global. Seio 4 shows ha ouries are more vulerable o global pais wih igh redi low ieres raes or rigid fisal poliies. Seio 5 osiders various exesios ad Seio 6 oludes.. The Model I his seio we desribe he behmark model. There are wo ouries Home ad Foreig ad wo periods ad. The basi wo-period New Keyesia sruure is similar o losed eoomy models foud i he lieraure sarig wih Krugma (998). ries are pre-se while wages are flexible. There is parial iegraio of goods markes hrough rade. Couries are i fiaial auarky wih fiaial asses (laims o firms a bod ad moey) oly held domesially. Goods are oly used for osumpio absraig from ivesme. There are households firms a goverme ad a eral bak. There is o ueraiy bu i period here may be differe expeaios i ase of muliple equilibria. 9 Also relaed is Bahea Tille ad va Wioop (0) who fous o he sok marke raher ha busiess yles. Their model feaures self-fulfillig spikes i sok prie risk ad a assoiaed sharp delie i sok pries. Bahea ad va Wioop (03) exed his o a ope eoomy framework. 0 Dedola ad Lombardo (0) fid ha ha perfe o-moveme is possible eve wih porfolio home bias. Bu his relies o a seup ha preludes arbirage bewee risky ad riskfree asses as oly leveraged ages hold risky asses ad fae borrowig osrais. As show i va Wioop (03) allowig for o-leveraged ages ha a odu suh arbirage ad alibraig he relaive size of leveraged isiuios i fiaial markes rasmissio is limied. The 008 risis saw very large arbirage bewee risky ad low risk asses wih a large fligh o qualiy ha ireased pries of low risk Treasuries. See Makiw ad Weizierl (0) or Feradez-Villaverde e al. (0) for ree oribuios. Aghio Bahea ad Baerjee (000) aalyze a small ope eoomy. 4
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 I Seio 5 we examie several exesios o his behmark model. I pariular we examie he role of ivesme ueraiy ad fiaial iegraio.. Households Households make osumpio ad leisure deisios i boh periods. Households i he Home oury maximize γ γ + λl + β γ γ + λl () where l is he fraio of ime devoed o leisure i period ad is he period- osumpio idex of Home ad Foreig goods: ψ H = ψ F ψ ψ () where µ µ µ = H µ ( j) dj H 0 H (3) µ µ µ = F µ ( j) dj F 0 F (4) Here is he osumpio idex of Home goods ad H he osumpio idex of Foreig goods. F Cosumpio of respeively he Home ad Foreig good j is H ( j) ad F ( j). The umber of Home ad Foreig goods i period is ad whih are equal o he umber of Home ad H Foreig firms. The elasiiy of subsiuio amog goods of he same oury is µ > while he elasiiy of subsiuio bewee Home ad Foreig goods is (we examie o-uiary elasiiies i Seio 5). There is a preferee home bias owards domesi goods as we assume ψ > 0.5. The speifiaio is symmeri for he Foreig oury wih he overall osumpio idex deoed as F ad ( ) ( ) H j F j deoig he osumpio of idividual Home ad Foreig goods osumpio by Foreig households. 5
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 The parameer ψ apures he degree of goods marke iegraio wih he limi of ψ = 0.5 refleig perfe goods marke iegraio. As we will see ψ = 0.5 implies ha i equilibrium = so ha fiaial markes are omplee eve hough here is o asse rade. This is a feaure ha resuls speifially from he Cobb-Douglas speifiaio ad is familiar from Cole ad Obsfeld (99). We a he hik of ψ = 0.5 as perfe eoomi iegraio aross he wo ouries. I period Home households ear labor iome W ( l ) where W is he omial wage rae. C They also ear a divided Π ad reeive a rasfer of M i moey balaes from he eral bak. They use hese resoures o osume pay a ax T o he goverme buy Home omial bods wih ieres rae i ad hold moey balaes: H ) F H ( j) H ( j) dj + SF ( j) F ( j) dj + T + B + M = 0 0 W ( l + Π C + M (5) j j where H ( ) ad F ( ) are he prie of respeively Home ad Foreig good j i he Home ad Foreig urrey. S is he omial exhage rae i period (Home urrey per ui of Foreig urrey). I period Home households ear labor iome W ( l) ear a divided C Π reeive (+ i) B from bod holdigs arry over M i moey balaes from period ad reeive a addiioal moey rasfer of M M from he eral bak. These resoures are he used o osume pay a ax T o he goverme ad hold moey balaes M : 3 H F H ( j) H ( j) dj + SF ( j) F ( j) dj + T + M = 0 0 C W ( l) + Π + (+ i) B + M + ( M M) (6) We assume a ash-i-advae osrai wih he buyer's urrey beig used for payme: Fiaial marke ompleeess implies ha he raio of margial uiliies of osumpio aross he wo ouries is equal o he real exhage rae whih is whe ψ = 0.5. 3 As usual i fiie-ime models here is a implii assumpio o he fial use of moey e.g. ages eed o reur he moey sok o he eral bak. 6
7 Hog Kog Isiue for Moeary Researh Workig aper No.09/03 F F F H H H M dj j j S dj j j + ) ( ) ( ) ( ) ( 0 0 (7) The osrai will always bid i period. I will bid i period whe he omial ieres rae i is posiive. Whe 0 = i he osrai will geerally o bid i period. Households hoose osumpio ad leisure o maximize (). The firs-order odiios are γ γ β + ) ( = i (8) H H H H j j ) ( = ) ( µ (9) F F F F j j ) ( = ) ( µ (0) H H =ψ () F F S ) ( = ψ () γ λ W = (3) where µ µ 0 ) ( = dj j H H H µ µ 0 ) ( = dj j F F F ψ ψ ] [ = F H S
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 ad H are prie idies of Home ad Foreig goods ha are deomiaed i respeively F Home ad Foreig urreies. is he overall prie idex deomiaed i he Home urrey. Equaio (8) is a sadard ieremporal osumpio Euler equaio. (9)-(0) represe he opimal osumpio alloaio aross goods wihi eah oury. ()-() represe he opimal osumpio alloaio aross he wo ouries. (3) represes he osumpio-leisure rade-off. As usual he iverse of γ measures he ieremporal rae of subsiuio. However i equaio (3) γ also measures he wage elasiiy o osumpio. There is a aalogous se of firs-order odiios for Foreig households. Oher ha for Home ad Foreig pries ad prie idies we oly eed o add supersrips o he variables ad exhage ψ ad ψ. The Foreig prie idex is ψ ψ = ( H / S ) F.. The Goverme ad he Ceral Bak The goverme ad eral bak poliies are aalogous i he wo ouries. We herefore agai oly desribe he Home oury. The Home goverme oly buys Home goods. The oal goverme osumpio idex is aalogous o he CES idex for privae Home osumpio: g = µ µ µ H µ g ( j) dj 0 (4) I he behmark ase we will simply se g = 0. Bu we will also osider a posiive osa level of goverme spedig where g = g. Moreover i Seio 4 we osider he role of ouerylial fisal poliy where g g Θ( ) wih osumpio i he o-pai equilibrium of he model ad Θ 0. = Opimal alloaio of goverme spedig aross he differe goods implies g j) = H ( ) H j µ ( (5) g We have H H ( j) g ( j) dj = H 0 g. Sie he imig of axaio aross he wo periods does o maer due o Riardia equivalee we simply impose he balaed budge odiio 8
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 T H = g (6) The eral bak's behavior is modeled as i oher wo-period models (e.g. Krugma 998 or Makiw ad Weizierl 00). The eral bak redibly ses seod-period moey supply o sabilize seod-period pries. We assume ha he eral bak has a zero iflaio arge from period o period so ha =. Sie he ash-i-advae osrai is bidig i period we have M = supply. ad he seod-period prie level a be orolled hrough he seod period moey I he firs period he eral bak ses he omial ieres rae i. For ow we will assume ha he eral bak ses he ieres rae suh ha (+ i) β =. This orrespods o he ieres rae i he flexible prie equilibrium of he model. We will see ha he o-pai equilibrium of he model he orrespods o he flexible prie equilibrium. I Seio 4 we osider wha happes whe durig a pai he eral bak lowers he ieres rae o simulae demad. Suh a poliy will o aver a pai whe we are lose o he zero-lower boud. The eral bak he has limied abiliy o ouer a busiess yle delie ad he equilibrium will be similar o ha wihou ay ouerylial eral bak aio..3 Firms The umber of firms operaig i period is based o prior deisios ad herefore ake as give. We ormalize i a for boh ouries so =. A he ed of period firms deide H = F wheher o oiue o operae i period. We deoe he umber of period- firms by H = ad F =. We do o allow ew firms o eer. 4 We fous our desripio maily o Home firms. Resuls are aalogous for Foreig firms. Oupu of Home firm j i period is y ( j) = ( AL ( j)) α (7) where L ( j) is labor ipu A a osa labor produiviy parameer ad α is bewee 0 ad. Firms se pries a he sar of eah period. This Keyesia assumpio oly bies for period as o uexpeed shoks happe afer firms se pries a he sar of period. For period a drop i osumpio durig a pai lowers demad for goods ad herefore produio. Labor demad is he 4 We ould allow for ery uder a fixed os. If he fixed os is large eough we rever o our urre seup. Lower fixed oss ha leads o limied ery oly parially replaig exiig firms will oly affe resuls quaiaively o qualiaively. 9
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 adjused o saisfy he demad for goods. This Keyesia aspe is riial o he self-fulfillig busiess yle pai i he model. Sie pries i period are prese ad heir level does o maer for wha follows we simply assume ha all firms se he same prie of H so ha H ( j) = H. Similarly for he Foreig firms. I period Home firm j ses is prie ( ) F ( j) = H H o maximize profis j W /α Π ( j) = H ( j) y( j) y( j) (8) A subje o H ( j) S y ( j) = H ( j) + g( j) + H ( j) = ψ + g + ( ψ ) H H H µ (9) The opimal prie is a markup µ /( µ ) over he margial os: α µ W α ( j) = y( j) H (0) µ αa Seod-period profis are he / α Π ( j) = κ W y( j) () A κ = µ α α µ α where [ ( ) + ]/[( ) ]. Sie all firms fae he same demad ad he same wage hey se he same prie. From he defiiio of he Home prie idex we have /( µ ) H = H ( j). Bakrupy a our a he ed of period. The oly differee aross firms i period is a fixed os. A fraio of firms fae a addiioal real os z i period. This os apures busiess ~ oss oher ha wages. 5 Toal profis of Home firm j i period Π ( ) are equal o j ~ Π ( j) = Π z( j) = H y W L z( ) () j 5 We irodue firm heerogeeiy o avoid he exreme ase where eiher all or o firms go bakrup. We hoose o do so hrough a addiive erm i profis oly beause i simplifies he algebra. Resuls would o hage fudameally if 0
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 z for a fraio of firms ad z ( j) = z for a fraio where ( j) = 0 of firms. I is also useful o defie Π as period- profis before payig his os. Whe firm j is uable o fully pay he fixed os i is delared bakrup ad ao produe i period. We assume ha z ( j) does o affe aggregae resoures ad is paid o a agey. I ase of bakrupy he agey seizes Π. The agey operaes a o os ad rasfers is iome o households. Π he firms for whih ( j) Sie > 0 z is zero always have posiive profis i period ad herefore do o eed o borrow o oiue heir operaio io period. The oher firms may eed o borrow whe heir firs-period profis are egaive. Bu hey fae a maximum limi o heir borrowig apaiy. Le D ( j) be borrowig by firm j a he ed of period. The firm he owes (+ i) D( j) i period. I is assumed ha his a be o larger ha a fraio φ of seod period profis: (+ i) D( j) φ Π ( j) (3) This sadard borrowig osrai refles ha leders a seize a mos a fraio φ of seod period profis i ase of o-payme. Seod-period profis are posiive ad kow a he ed of period. The firms faig he os z are fragile i ha hey will go bakrup if heir deb limi is isuffiie o over egaive profis i period. This is he ase whe Π Π + φ < z (4) + i Aoher way o look a he bakrupy odiio is o defie he real quaiy of fuds π available o pay for he fixed os: π π + φ + i π (5) where π = Π/ ad = Π / π. From (4) he fragile firms will go bakrup whe π < z (6) isead we irodued differees i firm produiviy whih ieras mulipliaively wih W L. The biomial disribuio of he os is also assumed for aalyial oveiee.
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 Therefore he umber of firms i period is eiher or depedig o wheher π z or < z π. Le D deoe aggregae borrowig by firms. The oal divideds reeived by households ilude divideds from firms ad from he servie agey. Divideds reeived i periods ad are C Π Π + D = (7) = Π ( C + i) D Π (8).4 Marke Clearig For he Home oury he marke learig odiios are y ( j) = H ( j) + g ( j) + H ( j) = (9) L = l = H (30) M = M = (3) B = D (3) These represe respeively he goods markes learig odiios he labor marke learig odiio he moey marke learig odiio ad he bod marke learig odiio. There is a aalogous se of marke learig odiios for he Foreig oury. If we subsiue io he household budge osrais (5)-(6) he bod moey ad labor marke learig odiios alog wih he divided expressios (7)-(8) we ge H = H H + H g + SF F H ( j) y ( j) dj (33) 0 This says ha aioal osumpio is equal o GD. The rade balae is herefore zero. Ideed muliplyig he goods marke learig odiio (9) by H ( ) ad aggregaig ad subsiuig io he righ had side of (33) gives he balaed rade odiio j S F F H H = (34)
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 Usig he expressios for ad F his a also be wrie as H = S (35) The omial value of osumpio is equal aross he wo ouries. This does o imply ha real osumpio is equal as he real exhage rae S / is o eessarily equal o whe ψ > 0.5. Oly whe markes are perfely iegraed ( ψ = 0.5 ) is he real exhage rae equal o ad =. Togeher wih he defiiios of he prie idies (35) also gives a expressio for relaive pries ha we will use below: H = ψ ψ (36) The Foreig relaive pries are he reiproal: F / = / H..5 Equilibrium Appedix B provides a desripio of he mai equilibrium odiios. Assumig (+ i) β = ad g = 0 he equilibrium a be redued o a se of 6 equaios i π π ad : θ ( δ ) ζ δζ = ( ) (37) θ δζ ( δ )ζ = ( ) (38) π = / α λ γ + / α φβκλ γ + / α + ( ) A H A H / α µ ( µ ) α (39) π = / α / α µ λ γ α φβκλ + / γ + / α ( µ ) α ( ) ( ) + ( ) A F A F (40) 3
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 if π < z = (4) if π z = if if π < z π z (4) where λµ θ = ( µ ) αa α/( α + αγ ) α + µ ( α) ζ = ( µ )( α + αγ ) δ = ( ψ )/[( α + αγ )(ψ ) + ( ψ )] ad he relaive pries deped o / as i (36). Appedix B provides algebrai deails behid hese equaios. Equaios (37)-(38) are derived by ombiig he Home ad Foreig ouerpar of he opimal seod period prie seig equaio (0) γ /( µ ) he labor supply shedule W / H ( j)/ H ad he osumpio Euler equaios = λ = (ad he assumed moeary poliy). Equaio (39) is he expressio for available fuds γ λ π = π /( +φπ + i) usig W / = (35) ad he fa = from he osumpio Euler equaios. Equaio (40) is he Foreig ouerpar for available fuds. Afer subsiuig he expressio (36) for he relaive prie available fuds deped o follow from he desripio of defaul i Seio.3. ad. Fially (4)-(4) Before urig o he soluio of he model some brief ommes are i order abou he flexible prie equilibrium where firs-period pries are perfely flexible. We show i Appedix B ha he equilibrium is he uique. This resuls from he absee of a Keyesia demad effe. Idepede of parameers firs-period osumpio is = / θ while firs-period profis are π = π = [ µ ( α) + α]/( µθ) profis of all firms are posiive: =. We will assume ha i he flexible prie equilibrium firs-period < µ α + α µθ Assumpio z [ ( ) ]/( ) 4
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 The righ had side of he expressio i Assumpio is equal o equilibrium. We he also have π = π i he flexible prie z < π sie π > 0 so ha o firms go bakrup ( = = ). β i β Fially we fid ha he equilibrium ieres raes are give by (+ i ) = (+ ) =. As meioed above his orrespods o he poliy we assume i our behmark model. The global o-pai equilibrium i he behmark Keyesia model will he orrespod exaly o he flexible prie equilibrium. 3. Muliple Equilibria ad Global ais The model a geerae muliple equilibria wih eiher = (o bakrupies) or = (wih bakrupies). Whe boh equilibria exis we all he equilibrium wih bakrupies he pai equilibrium as i is simply geeraed by low expeaios. There are poeially four equilibria haraerized by he values of ad. We refer o equilibria where = as symmeri equilibria. The ase where = = is a global o-pai equilibrium. If i addiio here is a equilibrium where = = we refer o i as a global pai. Bu here may also be asymmeri equilibria where oly oe oury pais ad he oher does o. There are poeially wo asymmeri equilibria wih eiher = ad = or = ad =. = I his seio we firs fous o symmeri equilibria i whih. I ha ase firs-period osumpio oupu ad profis are also equal aross he wo ouries. The we look a equilibria whe ouries are i auarky where ψ =. Fially we osider all equilibria for ay value of ψ bewee 0.5 ad. We will show ha whe eoomies are i auarky ( = ) asymmeri equilibria always exis. However whe ouries are somewha iegraed i.e. ψ is below some uoff here are oly symmeri equilibria ad a pai is eessarily global. ψ 3. Symmeri Equilibria Cosiderig symmeri equilibria allows us o learly illusrae he mehaism behid a global pai. Moreover osiderig global pais firs is aural as we will see ha wihou a global pai equilibrium he model does o feaure ay ype of pai equilibrium iludig asymmeri pais. The moeary poliy rules + = + i = / β i imply ha = Euler equaios. Usig his i is immediae from he oher equaios ha π = π. From (37)-(4) he equilibria are haraerized by ( ) ad from he osumpio = π ha saisfy = implies = ad 5
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 ζ = θ (43) π = λ A µ ( α) µθ α γ + / α + ζ + φβ (44) if π < z = (45) if π z Subsiuig (43) io (44) we a wrie available fuds π as a fuio of oly. Le π () ad π () represe available fuds wihou ad wih bakrupies i he symmeri equilibrium. We will assume ha parameers are suh ha available fuds are higher wihou bakrupies: π π Assumpio () > ( ) This a be wrie i erms of a odiio o he various parameers i he model. 6 A suffiie bu o eessary odiio for his o hold is ha ζ whih implies αγ ( µ ). Togeher wih Assumpio whih implies ha z < π () he equilibria follow direly from (43)-(45) ad are summarized i he followig proposiio. roposiio Whe Assumpios ad hold here are oe or wo symmeri equilibria. They are haraerized by: π. ( ) = (/ θ ) if ( ) z ζ. ( ) = (/ θ ) or ) = ( / ) ( θ if π ( ) < z < π () For he ase where φ = 0 so ha π = π Figure 5 illusraes he muliple equilibria i roposiio. The hump-shaped urve represes he firs-period profis fuio (44). The verial lies represe (43) for he wo levels of ad he u-off poi is deermied by he level of z. Whe ζ > boh verial lies ross he profi shedule whe i is upward slopig. Whe z is i he iermediae rage ( ( ) < z < ) here are wo equilibria A ad B. Equilibrium A is a good oe whih we refer o π π () as he o-pai equilibrium. Firs-period osumpio ad profis are high ad o firms go bakrup 6 φβ κ ζ κ ζ The odiio is ( ) + ( ) + > 0. The odiio is o saisfied for a high γ as real wages he delie sigifialy durig a pai whih raises profis. We will reur o his issue i Seio 3.5. 6
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 ( = ). Equilibrium B is he bad oe whih we refer o as he pai equilibrium. Firs-period osumpio ad profis are low ad firms go bakrup. The presee of wo equilibria is a resul of he possibiliy of self-fulfillig busiess yle pais. This ours due o reiforig likages bewee periods ad. The lik from period o period is sadard as low expeed period iome leads o low period osumpio. The lik from period o period operaes hrough profis ad bakrupies. Low period osumpio leads o low period firm profis whih leads o bakrupies ad herefore a low umber of firms i period. This implies low period iome makig he belief of low period iome self-fulfillig. We should be lear ha his is by o meas he oly possible way o model he lik from he prese o he fuure. Oe a hik of may aleraives ha should deliver similar resuls. Low urre demad may affe fuure oupu hrough iveory buildup lower urre ivesme or produio hais. I addiio raher ha hrough bakrupy low urre profis may lower fuure oupu hrough os-uig measures suh as redued R&D less raiig of labor losig some deparmes or brahes or less ivesme. Fially lower oupu oday may redue fuure oupu whe a reduio i produive apaiy is ombied wih suk oss. Togeher wih he sadard lik from he fuure o he prese hrough expeed iome hese aleraive mehaisms for likig he prese o he fuure may also geerae self-fulfillig beliefs. 3. Auarky Whe ψ = he wo eoomies are i auarky. They oly osume heir ow goods so ha he relaive pries H / ad / F are equal o i boh periods. I he follows from (37)-(4) ha for eah oury he equilibria orrespod exaly o he symmeri equilibria desribed above. Bu i auarky he equilibrium i oe oury has o impa o he equilibrium of aoher oury. Whe π ( ) < z < π () here are he four possible ouomes. Eiher oury may be i he pai equilibrium B or he o-pai equilibrium A idepede of he oher oury. Therefore i is possible for boh ouries o experiee a pai ogeher bu i is also possible for jus oe of he wo ouries o experiee a pai (asymmeri equilibria). There is o a priori reaso why he wo ouries would pai simulaeously. There may be argumes ouside of he model why a pai would be global. For example if he rigger ha ses off he pai is pariularly frigheig he wo ouries may rea ogeher. Bu if his rigger eve akes plae i he Home oury 7 i would seem odd ha he Foreig oury would rea o i i he absee of ay iegraio bewee he wo ouries. 7 A example is he bakrupy of Lehma Brohers or more geerally eves surroudig U.S. fiaial markes i he Fall of 008. 7
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 3.3 Whe Are ais Global? I his seio we examie all equilibria for values of ψ bewee 0.5 ad. We have already desribed he symmeri equilibria where ( ) = () or ( ) = ( ) osider asymmeri equilibria as well where eiher ( ) = ( ). We ow eed o or ( ) = ( ). We are pariularly ieresed i irumsaes where oly he wo symmeri equilibria exis. Whe a pai ours i will he eessarily be global. π ( π We will assume ha symmeri muliple equilibria exis i.e. ) < z < () from roposiio. As disussed i Seio 3. his implies ha muliple equilibria also exis i idividual ouries i auarky. ψ This meas ha asymmeri equilibria exis whe =. However as we move away from auarky i.e. as we lower ψ he asymmeri equilibria will o loger exis so ha pais a oly be global. This is saed i he followig proposiio. π π () roposiio Assume ( ) < z < so ha here are muliple equilibria. There is a hreshold ψ (z) > 0.5 suh ha oly he symmeri equilibria exis whe < ψ ( z) ψ. roof. See Appedix C. Usig (37) Figure 6 illusraes roposiio by ploig all equilibrium Home osumpio levels as a fuio of ψ. Symmeri equilibria give perfely horizoal shedules as osumpio is = ζ / whih is uaffeed by he level of iegraio. This is o he ase i he asymmeri equilibria. For example a Foreig pai affes Home osumpio more he greaer he exe of iegraio (he lower ψ ). θ Whe ψ is below he hreshold ψ (z) oly he wo symmeri equilibria exis. I ha ase pais are eessarily global. I oher words whe he level of rade is suffiiely high or home bias suffiiely low a pai will be perfely oordiaed aross he wo ouries. However he wo ouries do o eed o be perfely iegraed. A pai will be eessarily global for all values of ψ larger ha 0.5 ad less ha ψ (z). A suffiie degree of iegraio o perfe iegraio is eeded o guaraee ha pais will be global. As we show i Seio 3.5 he uoff for ψ will geerally be far above 0.5 so ha we do o eed o be aywhere lose o full iegraio o assure ha pais will be perfely oordiaed aross ouries. Before we ur o he iuiio behid his key resul i is useful o firs draw ou some of he impliaios. Firs roposiio implies ha whe he wo ouries are suffiiely iegraed ψ ψ ( > ( z) ) a pai leads o a drop i osumpio ha is ommo aross ouries. Cosumpio i 8
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 boh ouries drops from / θ o ζ / θ. Seod oupu drops equally i boh ouries ad he same as osumpio. 8 Third fuure oupu is expeed o drop i boh ouries by he same amou as well. All hese piees of evidee are osise wih he busiess yle ad survey daa repored i Figures ad 3. Also osise wih he model we a observe a worldwide delie i profis. Figure 7 shows subsaial delies i profis boh for he U.S. ad oher G7 ouries. 9 3.4 Iuiio Behid Global ais Uless ouries are perfely iegraed busiess yles shoks are oly parially rasmied aross ouries i sadard models. As we will see his is he ase i our model as well i he sese ha a asymmeri pai i oe oury is oly parially rasmied o he oher oury. Bu he key o perfe busiess yle o-moveme here is ha uder suffiie iegraio we a rule ou asymmeri equilibria so ha a pai is eessarily global. While we will disuss he reaso for his i he oex of he speifis of our model he key poi is more geeral. Expeaio shoks i our model are self-fulfillig. Whe ouries are suffiiely iegraed i is hard o see how oe oury a have very egaive self-fulfillig expeaios abou fuure oupu ad iome while he oher oury has very favorable expeaios. If ages a o hose beliefs he weak oury would egaively impa he srog oury ad he oher way aroud ad more so he more iegraed hey are. Suh beliefs will he o be self-fulfillig as for example iome i he weak oury will be favorably impaed by srog demad from he oher oury (wih rade iegraio) or srog porfolio reurs i he oher oury (wih fiaial iegraio). Reurig o he speifis of our pariular model we will osider he feasibiliy of a asymmeri equilibrium where = ad =. Before we a deermie wheher suh a equilibrium may exis we firs osider he impa of he Home pai o firs-period osumpio oupu ad profis i boh ouries. Le y = y ( j) dj be aggregae Home oupu i period (real GD) ad y aggregae Foreig 0 oupu. We he have = θ ( δ )ζ (46) 8 The real value of Home oupu i period is / H from (33) while / H depeds o / from (36) ad herefore says equal o. The drop i Home real GD i period is herefore he same as he drop i Home osumpio. The same is he ase for he Foreig oury. 9 There is o ross-oury daabase o aggregae orporae profis ha we are aware of. The umbers i Figure 7 have bee derived by aggregaig profis from firms lised i he Worldsope daabase. We seleed oiuig firms over he ierval ad widsorized he op ad boom ails a pere. The resulig profi series are divided by he GD deflaor. 9
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 δζ = θ (47) ad θ (+ δα ( γ )) ζ y = (48) θ δα ( γ )) ζ y = (49) Firs osider oupu. Uder auarky where δ = 0 oly Home oupu is lower i ase of Home defauls. Whe ouries are iegraed Home oupu is always lower ha Foreig oupu. Whe γ > i is eve he ase ha Foreig oupu rises. So he rasmissio of he Home shok (lower ) o he Foreig oury is eiher posiive ad parial or egaive. Two faors play a role here. Firs lower Home seod-period iome due o a lower dereases Home osumpio whih dereases demad for Foreig goods. This leads o posiive bu parial rasmissio. Seod lower Home oupu leads o a irease i he relaive prie of Home goods. 0 This leads o a expediure swih o Foreig goods whih may aually raise Foreig oupu i period. Cosumpio is equal o = H y/ ad = F y. Two faors impa osumpio: he / hage i oupu disussed above ad he erms of rade. Similar o oupu uder auarky oly Home osumpio delies. Whe ouries are iegraed here is a addiioal posiive rasmissio hael hrough he erms of rade whih improves for he Home oury ad deerioraes for he Foreig oury. This raises Home osumpio ad lowers Foreig osumpio. The overall impa is ha boh Home ad Foreig osumpio delie. Bu Foreig osumpio delies less ( δ < 0.5 ) so ha rasmissio is posiive bu parial. We fially eed o osider profis whih are riial o udersadig wheher asymmeri equilibria exis. We a wrie Home ad Foreig firs period profis as π λ A / α γ + / α = (50) H 0 This is he ase for period as well as = ad = ogeher imply ha he erms of rade is he same i boh periods. 0
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 π λ A / α γ + / α = ( ) (5) H wih ad as i (46)-(47) ad = H ( α + αγ ) δζ (5) Uder auarky ( δ = 0 ) we have = ad oly Home profis are lower due o he delie i / H Home osumpio. Trade iegraio impas profis i several ways. There are hree haels hrough whih i raises Home profis ad lowers Foreig profis. Firs Home faes srog expor demad from Foreig ad Foreig faes weak expor demad from Home. Seod for a give quaiy of sales he irease i he relaive prie of Home goods raises Home real reveues ad lowers Foreig real reveues. Fially we have already see ha ireased iegraio raises Home osumpio ad lowers Foreig osumpio whih ireases demad for Home goods ad lowers demad for Foreig goods. There is oe rasmissio hael ha operaes he oher way. The higher relaive prie of Home goods leads o a expediure swih o Foreig goods whih lowers Home profis ad raises Foreig profis. We show i Appedix C ha he firs hree rasmissio haels domiae ad herefore ireased iegraio raises Home profis ad lowers Foreig profis. We also show ha for suffiie iegraio Home profis aually beome larger ha Foreig profis. To see why his is he ase osider ψ 0.5. Whe we ge lose o perfe iegraio i follows from (46)-(47) ha ad beome equal. This resul is familiar from Cole ad Obsfeld (99) who show ha wih Cobb-Douglas uiliy a relaive hage i oupu does o affe relaive osumpio due o he edogeous erms-of-rade adjusme. I he follows from (50)-(5) ha Home profis oly differs from Foreig profis as a resul of he erms of rade whih is apured by / H. We a see from (5) ha / H < refleig he drop i he relaive prie of Foreig goods. This implies from (50)-(5) ha Home profis are higher ha Foreig profis. More geerally we show i Appedix C ha Home profis is larger ha Foreig profis uder suffiie iegraio as measured by ψ < ψ for some uoff > 0.5 ψ. Based o hese resuls formalized i Appedix C Figure 8 graphs Home ad Foreig profis as a fuio of ψ. The graph apures hree key pois disussed above. Firs uder auarky ( ψ = ) Home profis are weaker ha Foreig profis as oly he Home oury is affeed by he Home defauls. Seod ireased iegraio (lower ψ ) raises Home profis ad lowers Foreig profis. Fially Home profis are higher ha Foreig profis whe ψ is below a uoff ψ.
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 We a oly have a asymmeri pai equilibrium where = ad = whe π < z π (53) I ha ase he fragile Home firms will ideed defaul ( defaul ( = = ). Assumpios ad imply ha his is saisfied whe ψ = ) while he fragile Foreig firms will o saisfied whe he wo ouries are suffiiely iegraed. I is learly o he ase whe i ha ase Home profis are higher ha Foreig profis.. Bu i is o loger ψ < ψ as More geerally (53) is o saisfied for ψ less ha a uoff ψ (z) ha lies somewhere bewee ψ ad. This is illusraed i Figure 8. Whe z = z he uoff for ψ is ψ. Whe ψ <ψ Foreig profis are below z so ha fragile Foreig firms will defaul ad ( ) = ( ) ao be a equilibrium. Similarly whe z = z3 he uoff for ψ is 3 ψ. Whe <ψ 3 ψ Home profis are above z so ha fragile Home firms will o defaul ad ( ) = ( ) ao be a equilibrium. The lowes possible uoff value for ψ ours whe z = z i whih ase he uoff is ψ = ψ where Home ad Foreig profis are equal. I follows ha for ψ < ψ ( z) he asymmeri equilibria do o exis. Wha is riial o roposiio is o he fidig ha Home profis beome larger ha Foreig profis whe ψ < ψ. Raher wha is key is ha Home profis rise ad Foreig profis delie whe ouries beome more iegraed whih is aural wih posiive rasmissio aross ouries. Eve if ψ were 0.5 so ha Home profis is always lower ha Foreig profis wih limied iegraio ψ (z) will sill be above 0.5. If ouries are suffiiely iegraed ad herefore he differee bewee Home ad Foreig profis beomes suffiiely small here will geerally o be a equilibrium where oly Home firms go bakrup. Therefore oly a limied amou of rade is suffiie o assure ha a pai will be global i aure ad herefore osumpio ad oupu move perfely ogeher aross ouries. A limied amou of rade is suffiie o eiher provide eough sabiliy o he Home oury avoidig a pai alogeher or o drag he Foreig oury dow io a pai as well. A self-fulfillig shok o expeaios ao jus our i oe oury if he ouries are suffiiely iegraed. The ouries eessarily suffer a ommo fae. This requires Assumpio. The oly exepio is he kife-edge ase where z = z.
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 3.5 Numerial Illusraio While he model is obviously highly sylized i is sill useful o provide a umerial illusraio for reasoable levels of parameers. We will se he elasiiy µ equal o 3. Broda ad Weisei (006) esimae his elasiiy usig 8-digi 5-digi ad 3-digi idusry levels. I all ases hey fid ha he media elasiiy aross idusries is jus below 3. We se α = 0.75. This delivers a labor share of α( µ )/ µ = 0.5 whih is osise wih 00 daa for he U.S. Japa ad he Euro zoe o he raio of employee ompesaio o GD. We ormalize privae osumpio i he o-pai sae o be by seig λ / A suh ha θ =. We re-irodue goverme spedig whih was oly suppressed i he previous subseios for aalyi raabiliy. We se g = g = 0.3 i boh periods implyig ha goverme osumpio as a fraio of GD is 0.3/.3=0.3. This is osise wih ree daa from idusrialized ouries for goverme spedig (osumpio plus ivesme) relaive o GD. For ow we se φ = 0 so ha he borrowig osrai is very igh: firms ao borrow a all. We will ivesigae he role of borrowig osrais furher i he ex seio. The oly parameer lef is γ. I is hard o alibrae as i plays hree roles i he model: rae of risk aversio iverse of ieremporal elasiiy of subsiuio ad real wage ylialiy. The real wage is γ λ. Based o esimaes of risk-aversio ad he ieremporal elasiiy of subsiuio γ should be larger ha. Bu his is iosise wih he evidee ha he average real wage rae is o very ylial. Moreover give realisi hoies for he oher parameers he model implies oueriuiively ha () < ( ) π π whe γ is se a or larger. The reaso is ha i he pai sae he real wage is muh lower whih raises firm profis. I order o avoid his srog ylialiy of he wage rae we osider resuls boh for he ase where γ is well below ad he exesio where omial or real wages are rigid (prese a he sar of eah period). This exesio is sraighforward ad desribed i Appedix D. Whe we se γ = 0. so ha he real wage rae is o very ylial we fid ψ = 0.9 idepede of he level of. The aual uoff ψ (z) he lies somewhere bewee 0.9 ad. Oly limied rade is he suffiie o guaraee a global pai. Whe 0% of privae osumpio goods are impored a pai is eessarily global ad herefore busiess yles will be perfely syhroized durig he pai. ψ will be oly slighly lower a 0.88 whe we se γ ifiiesimally lose o 0 so ha he real wage rae is o ylial a all. As disussed furher i Appedix D uder boh omial ad real wage rigidiy wages are se a he sar of eah period uder he assumpio ha here will be o pai. 3 Resuls will be very similar whe seig he probabiliy of a pai a a small posiive umber. This does o affe period as 3 Eve hough firms prese heir pries here is a differee bewee omial ad real wage rigidiy due o he exhage rae impa o he prie level. 3
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 here are o furher uexpeed shoks durig period. Whe he real wage is egoiaed a he sar of period i will he be se a is equilibrium o-pai level. Whe isead he omial wage rae is / agreed o i advae he real wage will be equal o he o-pai real wage rae imes where is he prie idex wihou a pai. We ow se γ a 3 whih is a sadard value whe measurig risk aversio or he iverse of he ieremporal elasiiy of subsiuio. Uder real wage rigidiy we fid ha ψ is 0.89. Noe ha his is o he same model as uder flexible real wages wih γ very small sie he seod period equilibrium does deped o γ. Noeheless he resul is virually ideial ad i agai does o deped o. Uder omial wage rigidiy ψ is a bi lower a 0.77 so ha ψ (z) is i he rage of 0.77 o. Bu i is sill he ase ha limied rade is eeded o guaraee perfe syhroizaio of pais aross ouries. I is suffiie ha 3% of privae osumpio goods are impored. This umber may be eve less depedig o he preise value of z. 4 We a also umerially evaluae he exe of radiioal busiess yle rasmissio assoiaed wih asymmeri shoks. Sie here are o exogeous asymmeri shoks i he model we osider rasmissio assoiaed wih a asymmeri pai. Take he example of real wage rigidiy where ψ = 0.89. Assume ha ψ (z) = ψ ad ha ψ 0.9 > ψ =. We are he i he regio where asymmeri pais are possible. Usig he parameer values disussed above he drop i log Foreig osumpio is he oly a fraio 0.05 of he drop i log Home osumpio. Trasmissio is posiive bu small. Sie γ > (49) implies ha Foreig oupu rises i his ase so ha rasmissio o Foreig oupu is egaive. Bu oly slighly more rade iegraio (ψ equal o 0.89 or less) guaraees ha pais are global allowig us o explai he perfe busiess yle syhroizaio while reaiig sigifia home bias as see i he daa. 4. Vulerabiliies We a ow osider faors ha make ouries vulerable o self-fulfillig pais. We fous o symmeri equilibria. If symmeri pais do o exis o ype of pai iludig asymmeri oes exis i he model. We osider a versio of he model ha is geeral eough o fous o he role of redi moeary poliy ad fisal poliy. These are apured by respeively φ i ad g. A he 4 The slighly lower uoff uder omial wage rigidiy a be explaied as follows. We have see ha whe a pai is limied o he Home oury Home profis rise ad Foreig profis delie as we lower ψ uil hey are equal a ψ = ψ. Bu he derease i he relaive prie of Foreig goods will lower he Home prie idex ad more so he higher he level of rade (he lower ψ ). Whe he omial wage rae is fixed his by iself raises he real wage rae ad lowers Home profis as we lower ψ. I will remai he ase as a resul of he oher haels ha we disussed ha Home ad Foreig profis are equal for a value ψ larger ha 0.5 bu his ouerweigig fore redues somewha he value of ψ. 4
Hog Kog Isiue for Moeary Researh Workig aper No.09/03 ζ = α same ime we will simplify by seig =. This leads o a leaer se of equilibrium equaios bu is o riial o he resuls. As show i Appedix B he shedules ha deermie he symmeri equilibrium are he = [ β ( i)] θ / γ + (54) λ γ φ g + + + + θ π = g ( g) (55) A (+ i) µθ if π < z = (56) if π z We osider differe versios of his se of equilibrium equaios depede o he vulerabiliy of ieres. We a hik of φ = 0 g = 0 ad ( i) β = parameer a a ime. + as a behmark ha we deviae from oe 4. Credi I order o osider he role of redi we fous o he impa of he parameer φ while seig β (+ i) = ad g = 0. Equilibrium is he haraerized by wo shedules: = θ wih = if π < z ad = if π z (57) λ π = A + γ + φβ µθ (58) These shedules are show i Figure 9 for wo values of φ. The verial lies represe he osumpio shedule while he humped shaped lie refles he available fud shedule. A higher φ raises he available fud shedule. Figure 9 shows ha whe φ is low so ha redi is igh here may be wo equilibria so ha self-fulfillig pais are possible. Bu whe redi is loose so ha φ is high oly he o-pai equilibrium exiss. The more firms are able o borrow he less fragile hey are. They are he beer able o wihsad a drop i demad ha lowers firs-period profis. This i ur a make a self-fulfillig pai impossible. While i remais he ase ha odiios i period affe osumpio i period he likage i he oher direio is broke uder loose redi odiios. Eve wih low osumpio i period leadig o low profis firms a avoid bakrupy by borrowig. 5