International Portfolio Equilibrium and the Current Account

Transcription

1 Inernaonal Porfolo Equlbrum and he Curren Accoun Rober Kollmann (*) ECARE Free Unversy of Brussels Unversy of Pars XII Cenre for Economc Polcy Research UK Ocober 006 Ths paper analyzes he deermnans of nernaonal asse porfolos usng a neoclasscal dynamc general equlbrum model wh home bas n consumpon. For plausble parameer values he model explans he fac ha ypcal nvesors hold mos of her wealh n domesc asses (porfolo home bas). In he model he curren accoun balance (change n ne foregn asses) s manly drven by flucuaons n equy prces; he curren accoun s predced o be hghly volale and o exhb low seral correlaon; changes n a counry's foregn equy asses and lables are predced o be hghly posvely correlaed. The paper consrucs curren accoun seres ha nclude exernal capal gans/losses for 7 OECD economes. The behavor of he emprcal seres confrms he heorecal predcons. JEL classfcaon: F F3 G. Keywords: Inernaonal porfolo holdngs; Curren Accoun; Consumpon and porfolo home bas (*) ECARE Unversé Lbre de Bruxelles; 50 Av. Frankln Roosevel ; B-050 Brussels; Belgum; [email protected]; hp:// Frs verson of hs paper: Aprl 005. Thanks for useful dscussons and suggesons are due o Jaewoo Lee Alan uherland Gabrel Felbermayer Fabrzo Perr and Mck Devereux as well as o Marn Bodensen Ncolas Coeurdacer John Coleman Harrs Dellas Bernard Dumas Marn Evans éphane Gubaud Jean-Olver Haraul Jonahan Heahcoe Vkora Hnakovska Tm Kehoe unghyun Km Jame Marquez Phlppe Marn Ako Masumoo Benoî Mercereau Gan Mara Mles- Ferre Alessandro Rebucc Hélène Rey Robero Rgobon Alan uherland Chrsoph Thoenssen Cédrc Tlle Marín Urbe Phlppe Wel. I also benefed from commens receved durng presenaons a ED and Royal Economc ocey conferences CEPR/IMF conference on he Macroeconomcs of Global Inerdependence CEPR European ummer ymposum n Inernaonal Macroeconomcs CEfo-Delph conference on Global Economc Imbalances Venna ymposum on Asse Managemen NBER "Economc Flucuaons and Growh (EFG)" workshop UBC conference New Issues n Inernaonal Fnancal Markes IMF Federal Reserve Board wedsh Rksbank Bank of Canada. Andrews Unversy Pars I Pars XII Duke Georgeown U Berne U Lausanne U Zurch. I also hank Aar Kraay for makng avalable nernaonal porfolo daa.

2 . Inroducon The lberalzaon of nernaonal fnancal markes n he 980s has been accompaned by a rse n foregn capal flows and n curren accoun mbalances. However ypcal nvesors connue o hold mos of her wealh n domesc asses and mos of he capal sock n a gven counry s owned by local nvesors--despe he fac ha nernaonal dversfcaon reduces rsk. E.g. among OECD counres he rao of foregn equy lables o he domesc physcal capal sock ranged beween 5% (Germany) and 4% (UK) n 997 (see Table ). Tha "porfolo home bas" s one of he key puzzles n nernaonal fnance. Ths paper shows ha a smple neoclasscal model wh free capal flows can explan porfolo home bas provded consumpon home bas s ncorporaed.e. he fac ha he bulk of prvae consumpon consss of locally produced goods. The model s also broadly conssen wh key feaures of he behavor of emprcal curren accoun measures ha nclude exernal capal gans/losses. The model assumes wo counres and wo freely raded non-sorable goods. Each counry s nhabed by a represenave household and receves an endowmen of a sngle good. Each household consumes boh goods bu has a preference for he local good and hus devoes mos of s spendng o ha good. The followng asses can be raded: a bond and wo socks each of whch s a clam o one of he endowmens. The asse marke s effecvely complee. Equlbrum porfolos hnge on he coeffcen of relave rsk averson and on he elascy of subsuon beween domesc and mpored goods. Esmaes of hese parameers sugges ha domesc and mpored goods are subsues (.e. ha he cross-paral dervave of he uly funcon wh respec o hese goods s negave) and ha he subsuon elascy beween goods does no markedly exceed uny. Consder he effec of a posve shock o he endowmen of one of he counres called "Home". Inernaonal rsk sharng requres ha he fracon of he Home endowmen consumed by he Home household falls n response o he shock f here s consumpon home bas and f domesc and mpored goods are subsues. If n addon he elascy of subsuon does no (oo much) exceed uny he prce of he Home good drops so srongly ha he value of he Home endowmen falls (relave o he value of he foregn endowmen)--and hus s opmal for Home o consume a smaller fracon of he local good n saes of he world n whch he (relave) value of he dvdend of Home equy (=Home endowmen) s lower. For plausble parameer values local equy hence provdes a hedge for varaons n he effcen locally consumed fracons of endowmens--he effcen allocaon can be mplemened f each counry holds a share of he local sock ha exceeds he locally consumed endowmen fracon. Ths enables he model o generae a realsc degree of porfolo home bas. Concepually a counry's curren accoun balance s he change of s ne foregn asses durng a perod. In he model he curren accoun s largely drven by flucuaons n equy prces. The curren accoun s predced o be hghly volale and o have low seral correlaon. When endowmens follow random walks a counry's ne asse poson a dae s solely a funcon of endowmens a and he curren accoun s hus approxmaely..d. The curren accoun seres publshed by sascal agences do no capure capal gans/losses on exernal asses and lables--hose offcal seres only measure he ne flow of exernal asses acqured by a counry. To evaluae he predcons descrbed n he precedng paragraph he paper consrucs curren accoun seres ha nclude capal gans/losses for 7 OECD economes by akng frs dfferences of new measures of ne foregn asses (compled by BEA and IMF) ha reflec marke prces of foregn asses and lables; hose curren accoun measures are hghly volale and her auocorrelaons are ypcally close o zero whch confrms he model predcons. The new curren accoun measure normalzed by domesc oupu s less volale for he U han for oher OECD counres. Calbraed versons of he model here capure hs fndng and sugges ha s due o he fac ha he U has less

3 volale oupu han he remanng OECD economes and ha s rade share s lower. Emprcally here s a hgh posve correlaon beween changes n a counry's foregn equy asses and changes n s exernal lables. Ths fac oo s capured by he model as he laer predcs ha equy prces and reurns are hghly posvely correlaed across counres as a counry's erms of rade are posvely correlaed wh he foregn endowmen. Ths paper brdges wo mporan srands n nernaonal macroeconomcs and fnance: he leraure on nernaonal porfolo choce and he leraure on curren accouns. Lucas' (98) classc paper analyzed porfolo choce n a wo-counry world wh radable goods and preferences ha are dencal across counres; n equlbrum all households hold dencal equy porfolos as hs perms full rsk sharng. In order o generae cross-counry dfferences n porfolos Dellas and ockman (989) develop a wocounry model n whch some consumpon goods are non-raded (an exreme form of consumpon home bas); however no home bas s assumed for raded goods: preferences for radables are posulaed o be dencal across counres; he model predcs ha eques of non-raded good frms are held locally whle holdngs of raded good eques are fully dversfed nernaonally whch s counerfacual. 3 In realy here are few goods (a a broad aggregaon level) ha are no raded. The model here assumes ha all goods are radable and are subjec o home bas. Obsfeld and Rogoff (000) oo consder a world n whch all goods are raded; n her model preferences are dencal across counres; consumpon home bas arses because of ranspor coss for goods (by conras n paper here: consumpon bas n preferences). These auhors compue porfolos for he specal case (whch perms a closed form soluon) n whch relave rsk averson equals he nverse of he subsuon elascy beween local and foregn goods; realsc porfolo home bas only arses when he elascy of subsuon s large and he rsk averson coeffcen s mplausbly low (0. or less). 4 everal auhors have argued ha equy home bas s due o he non-raded naure of human capal 5 and/or greaer coss of nvesng abroad han locally (greaer nformaonal barrers or agency problems). 6 In order o focus sharply on he effecs of consumpon home bas I assume a frconless world n whch all asses are raded. I remans o be seen wheher he human capal/nvesmen cos sores can explan he curren accoun facs descrbed above. everal recen emprcal sudes have shown ha capal gans/losses grealy affec ne foregn asse posons (NFA) and noed ha he new curren accoun measures (changes n NFA) can dffer sgnfcanly from convenonal measures. 7 However none of hose prevous For surveys of hese leraures see e.g. Dumas (994) and Obsfeld and Rogoff (996) respecvely. Emprcally here s home bas for manufacurng equy (manufacured goods: raded); see e.g. Kang and ulz (995) who documen home bas n Japanese manufacurng; see also Kollmann (006). 3 For a closely relaed analyss of porfolo choce wh non-radable goods see Baxer Jermann and Kng (998). 4 Uppal's (993) one-good model wh ranspor coss oo requres mplausbly low rsk averson o generae equy home bas. Coeurdacer (005) solves a ranspor cos model wh unresrced rsk aversons and subsuon elasces; equy home bas can arse f frcons n fnancal markes are assumed. 5 When wage ncome s negavely correlaed wh profs hen domesc equy may be a beer hedge agans local wage flucuaons han foregn equy. everal sudes argue ha emprcally hs condon s me; see e.g. Boazz e al. (996) Heahcoe and Perr (003) Jullard (004) Engel and Masumoo (005); for a dvergen vew see Baxer and Jermann (997). 6 ee e.g. Van Neuwerburgh and Veldkamp (005) Ahearne e al. (004) Trole (003) ulz (005). 7 ee.a. Kraay e al. (005) Lane and Mles-Ferre (00 005) and Gournchas and Rey (005); hose 4 papers also presen ndependen esmaes of exernal posons. For descrpons and analyses of he effec of asse prce changes on ne foregn asse posons see also Km (00) Tlle ( ) Hau and Rey (004) Devereux and ao (005) Ghron e al. (005) and Backus e al. (005). Canor and Mark (988) provded an early heorecal dscusson of he role of equy prce changes for curren accouns based on a one-good model wh rade n eques (her model predcs full porfolo dversfcaon). 3

4 papers has documened and analyzed quanavely he cyclcal behavor (volaly seral correlaon correlaon wh oupu) of he new curren accoun measures. Pror research has ofen vewed as a sylzed fac ha curren accouns are perssen and counercyclcal and sough o develop models conssen wh hose feaures (see e.g. Bergn (004) Obsfeld and Rogoff (996) and he references heren). The curren accoun measures ha nclude capal gans/losses show lle perssence (as menoned above) and are less srongly negavely correlaed wh domesc GDP han convenonal curren accoun measures. Exsng curren accoun models ypcally assume ha nernaonal fnancal markes are resrced o bonds and hus ncomplee; 8 by conras asse markes are (effecvely) complee n he model here. For racably prevous macroeconomc analyses of porfolo home bas have ofen used models wh resrcve assumpons regardng preferences (see above) and/or wo-perod models. Ths paper uses numercal soluon echnques ha allow o dspense wh hese feaures. econ descrbes he porfolo and curren accoun daa. ec. 3 presens he model and he soluon mehod. econs 4 and 5 dscuss model predcons. econ 6 concludes.. Emprcal evdence: equy and consumpon home bas; curren accouns.. Home bas Foregn equy holdngs have grown durng he pas 30 years bu equy home bas remans szable. Table documens hs for a sample of 8 OECD economes. Based on he Kraay e al. (005) daase (ha repors capal socks and exernal asses for ) Col. repors raos of counres' foregn equy lables FEL (defned as foregn drec nvesmen (FDI) lables plus porfolo equy lables) o he physcal capal socks n he respecve counres n 997. Tha rao ranged beween 5% (Germany Ialy) and 4% (wzerland UK) wh a medan value of 7%. The correspondng medan rao was % n 973. Cols. -5 repor raos of counres' FEL and foregn equy asses FEA o GDP n 997 and 003 usng FEL and FEA daa aken from he IMF's IIP (Inernaonal Invesmen Posons) daabase. (FEA: sum of FDI and porfolo equy asses.) The medan FEL/GDP rao was 0.3 [0.56] n 997 [003]. Wh wo excepons (wzerland Neherlands) he FEL/GDP and FEA/GDP raos are below uny. The physcal capal sock/gdp rao s n he range of 3 n OECD economes. Ths suggess ha n almos all counres foregn equy lables represen markedly less han one hrd of he domesc physcal capal sock. "Consumpon home bas" refers o he fac ha consumpon ncorporaes a larger share of domesc npus han of mpored npus. The rao of oal mpors (M) o (prvae) consumpon (C) ranged beween 9% (U) and 3% (Neherlands) n 003 (medan rao: 55%). However he M/ C rao oversaes he mpored componen of consumpon as M ncludes foregn goods ha are ncorporaed no physcal nvesmen (I) governmen consumpon (G) or expors (X). Under he assumpon ha he mpored conen of C s smlar o he mpored conen of I+ G+ X he rao M/[ C+ I+ G+ X] s an esmae of he mpored componen of C. Col. 6 n Table shows ha M/[ C+ I+ G+ X] ranged beween % (U) and 35% (Neherlands) n 003 wh a medan value of %... Curren accouns nernaonal busness cycles Table shows descrpve sascs for he U curren accoun oupu and real exchange rae; he curren accoun seres s based on porfolo daa from BEA (005). Table 3 shows curren accoun sascs for 7 OECD counres based on IIP daa; for mos counres 8 A noable excepon s Mercereau ( ) who develops a model of a small open economy wh rade n socks; emprcally ha model performs beer han a bonds-only srucure. 4

5 he IIP sample begns n he 980s and ends n 003. (Table 3 also shows resuls for he U; he IIP U sample (980-03) s shorer han he BEA sample; resuls are comparable across he BEA and IIP seres.) The BEA and IIP daabases valuae exernal asses and lables a marke prces. All daa are annual. Concepually a counry's curren accoun balance s he change of s ne foregn asse holdngs (NFA) durng a perod (Obsfeld and Rogoff (996 p.5)). The curren accoun seres publshed by sascal agences do no conform o hs noon: hose seres only measure he ne flow of asses acqured by a counry and do no ake no accoun exernal capal gans/losses (on asses acqured n he pas). Ths paper sudes a curren accoun measure ha ncludes exernal capal gans/losses: he frs dfference of he BEA and IIP NFA seres. Le NFA + NB + FEA + and FEL + be a counry's NFA ne foregn bond holdngs foregn equy asses and foregn equy lables respecvely a he end of year wh NFA FEA FEL + NB The curren accoun measure consdered here s: CA NFA + ECA BCA = + where ECA FEA+ FEL+ BCA NB + () wh x x x for any varable x. ECA (he change n ne foregn equy holdngs) and + + BCA (change n ne bond holdngs) are he equy and bond componens of he curren accoun respecvely. Tables and 3 also consder he convenonal curren accoun measure (aken from he IMF's Inernaonal Fnancal ascs IF) ha does no nclude exernal capal gans/losses denoed CA. 9 The model here absracs from nvesmen and governmen purchases; unless saed oherwse my emprcal "oupu" measure ( Y ) s GDP ne of nvesmen and governmen purchases ( Y GDP I G). For each counry I consruc a measure of "foregn" oupu ha equals oal oupu n 0 oher OECD economes (see Appendx). The daa sources provde asses and lables n curren U dollars. In Table he U curren accoun and s componens are expressed n uns of U oupu and normalzed by a fed geomerc rend of U oupu. In Table 3 counry 's curren accoun s expressed n uns of foregn oupu and normalzed by a geomerc rend fed o 's oupu (n uns of foregn oupu); he use of foregn oupu as numérare n Table 3 s movaed by he model calbraons below. 0 (The emprcal sascs n Table 3 are robus o usng counry oupu or U oupu as numérares). Oupu and real exchange raes are logged. Unless saed oherwse all sascs are based on HP-flered seres (smoohng parameer: 400). ee he Appendx for more dealed daa defnons. U: BEA daa (Table ) For he U he sandard devaon of he (HP flered) curren accoun measure CA (3.48%) s larger han ha of oupu GDP I G (.57%); he auocorrelaon of CA (0.04) and he correlaons of CA wh domesc oupu (0.0) and wh foregn oupu (0.00) are close o zero and sascally nsgnfcan; see Cols. -4 Panel (a) of Table. mlar resuls oban when GDP s used as he oupu measure (Cols. 5-7) and when he curren accoun s no HP 9 The superscrp sands for "bookvalue": CA s he frs dfference of an NFA + measure ha valuaes asses acqured before a bookvalues. 0 Below a wo-counry model wh counres of unequal sze s consdered. Ineres focuses on model predcons for he smaller counry; oupu of he foregn (larger) counry s used as numérare. A counry's real exchange rae RER s defned as a weghed average of consumpon based blaeral exchange raes vs-à-vs he oher OECD counres. A rse n a counry's RER represens a real deprecaon of s currency. 5

6 flered (Panel (b)). The sandard devaon of he U real exchange rae (9.99%) s larger han ha of CA ; oupu and he real exchange rae are perssen (auocorrelaons: respecvely). The behavor of he convenonal curren accoun measure CA dffers markedly from ha of CA : s sandard devaon (.47%) s less han half of ha of CA ; n conras o CA flucuaons of CA are perssen (auocorrelaon: 0.78). The correlaon of CA wh domescgdp I G s close o zero and sascally nsgnfcan (a a 0% level) bu s correlaon wh domesc GDP (-0.4) s szable and hghly sgnfcan Flucuaons n he U CA seres are manly drven by s equy componen ECA : he sandard devaon of ECA (3.0%) s larger han ha of he bond componen BCA (.77%). Changes n U foregn equy asses and lables ( FEA FEL) are more volale han ECA and hghly posvely correlaed wh each oher (sandard devaons of FEA and of FEL and cross-correlaon: 6.5% 5.3% 0.88 respecvely). ECA FEA FEL are bascally uncorrelaed wh oupu and her auocorrelaons are low. 7 OECD economes: IIP daa (Table 3) The resuls for he oher OECD counres show many smlares o he U resuls. For all counres CA s more volale han oupu (see Cols. -3 op par of Panel (a) Table 3). For mos counres he auocorrelaon of CA (and of s componens) does no sgnfcanly dffer from zero; he medan (and mean) auocorrelaon of CA s Also changes n a counry's foregn equy asses are posvely correlaed wh changes n s lables (Col. lower par of Panel (a)). Correlaons of he curren accoun and s componens wh domesc and foregn GDP I G vary wdely across counres; he medan and mean correlaons are close o zero. E.g. he correlaons beween CA and domesc GDP I G range beween and 0.69 wh a medan value of Correlaons of CA wh domesc GDP are mosly negave (medan correlaon: -0.) bu only abou half of he negave correlaons are sascally sgnfcan (Col. (3) Panel (b)). For almos all counres he convenonal curren accoun CA s markedly less volale han CA and hghly perssen (medan sandard devaons of CA and CA : 6.94%.46%). CA s ypcally posvely correlaed wh domesc GDP I G. The correlaons of CA wh domesc GDP are all negave (medan correlaon: -0.38) hghly sgnfcan (wh few excepons) and larger n absolue values han he correlaons beween CA and GDP (Col. (8) Panel (b) Table 3). 3 Pror research has ofen vewed as a sylzed fac ha curren accouns are perssen and counercyclcal (see e.g. Bergn (004) Obsfeld and Rogoff (996) and he references heren). The precedng dscusson shows ha curren accoun measures ha nclude capal gans/losses show lle perssence and are less srongly negavely correlaed wh domesc GDP (han convenonal curren accoun measures). When GDP s used as he oupu measure hen he CA seres s normalzed by rend GDP and he sandard devaon of (normalzed) CA s hus smaller han when he oupu measure GDP-I-G s used; by conras auocorrelaons are bascally unaffeced by he change n normalzaon (and are hus no repored n Cols. 5-7). 3 Faruquee and Lee (006) confrm some of he key fndngs here for a sample of 00 counres: n ha larger sample oo CA s markedly more volale and less perssen han convenonal curren accouns. 6

7 A srkng dfference beween he U and he oher OECD counres s ha curren accouns (and her componens) are ofen markedly more volale n non-u counres (medan sandard devaon of non-u CA : 7.0%; sandard devaon of U CA : 4.94% [IIP daa]). 3. The model 3.. Goods and preferences The economy sars a dae = 0 and lass unl T> 0. Tme s dscree. There are wo counres ndexed by = and wo freely raded non-sorable goods also ndexed by =. Counry receves an exogenous endowmen of good. Y > 0 denoes 's endowmen a. y ( Y Y )' follows he process ln( y) = ln( y ) + ε () where ε ( ε ε )' s a normally dsrbued (vecor) whe nose. Counry s nhabed by a represenave household whose preferences are descrbed by T E β UC ( ) wh UC ( ) = ( σ) [ C σ ] σ > 0 (3) 0 = 0 / φ ( φ )/ φ / φ ( φ )/ φ φ/( φ ) where UC ( ) s a uly funcon and α α j C s an ndex of 's consumpon a : C = [ ( c ) + ( ) ( c ) ] wh j and 0.5< < φ> 0. 4 (4) c j s s ' consumpon of good j. The parameer φ s he elascy of subsuon beween goods. Noe ha he local good has greaer wegh n he consumpon ndex han he mpored good--.e. here s "consumpon home bas". 3.. Markes budge consrans decson problems There s rade n goods n a one-perod rskless bond and n wo socks each of whch represens a share n one of he endowmen processes. Good s used as a numérare (he bond s denomnaed n he numérare). The counry household faces he budge consran P j j j j ( j j j ) ( ) j + + A+ + p c j j P p δ A r = = = for 0 T (5) j= where p j s he prce of good j (wh p ) and P j s he (ex-dvdend) prce of sock j n perod ; j + s he number of shares of sock j owned by counry a he end of perod (begnnng of + ) whle A + represens s ' bond holdngs a he end of ; r s he neres rae beween and. Counry 's nal sock and bond holdngs are exogenously gven by A ( + r). The supply of each ype of share s uny.e j = represens 00% ownershp of he "ree" ha generaes he good j endowmen. A he choce varables of households and are: D = ( A c c ) and α { } T D = ( A c c ) respecvely. Household selecs a process D = 0 ha maxmzes (3) subjec o (5) and o he (no-ponz) condon ha fnal wealh has o be zero: AT+ + P jt j T 0. j= + = (6) The followng equaons are frs-order condons of counres' decson problems: = E ( p Y + P )/ P for = ; j= ; 0 T. (7) ρ + j + j + j + j 4 α Model varans whσ = and φ = use UC ( ) = ln( C ) and ( / ) α C c ( c /( )) = α j α respecvely (hese expressons are he lms of (3) and (4) for σ and φ ). 7

8 ρ = ( + r ) Eρ for = ; 0 T. (8) + + / / p {[ /( )][ c / c ]} φ φ α α {[( α)/ α][ c / c ]} s + s β [ UC ( + s)/ c + s]/[ UC ( )/ c ] (for0 s T) = = for 0 T. (9) beween consumpon of good a and a + s. + s 's margnal rae of subsuon 3.3. Equlbrum Gven nal values 0 0 A0( + r0 ) 0 = 0 0 = 0 A0 = A0 a compeve equlbrum s a process { c } T c c c p r P P + + A+ + + A+ = 0 such ha: () (5)-(9) hold. () Markes clear: c + c = Y + = ; A + A = 0 for j= and 0 T. (0) ; j j j j + j Effcen allocaons Ths paper focuses on equlbra ha are Pareo effcen (.e. ha enal full rsk sharng)-- henceforh he erm "equlbrum" refers o an effcen equlbrum. An effcen allocaon s he soluon of he followng socal plannng problem: Max ( ) E T s U 0 ( C T s ) 0 s E U 0 ( C Λ β + Λ β ) s= s= 0 s w.r.. { c } T c c c = 0 s.. c + c = Y c + c = Y a 0 T () for some consan 0 Λ. 5 A key frs-order condon of hs problem s ha he margnal uly of each good s perfecly correlaed across counres ( Λ) UC ( )/ cj = Λ UC ( )/ cj for j= and 0 T. () ()() unquely pn down he effcen consumpons c c c c Decenralzng an effcen allocaon Le { c ( ) ( ) ( ) ( )} T Λ c Λ c Λ c Λ = 0 be an effcen allocaon for some Λ> 0. I now show how o T consruc a process { p ( Λ) r ( Λ) P ( Λ) P ( Λ ) A A } such ha = = 0 j A ( r ) { c ( Λ) c ( Λ) c ( Λ) c ( Λ) p ( Λ) r ( Λ) P ( Λ) P ( Λ ) A A } T s an equlbrum for approprae assgnmens of nal asse holdngs =; j=. All varables peranng o an effcen equlbrum are desgned by an asersk; equlbrum consumpons and prces are wren as funcons of Λ. p ( Λ) r+ ( Λ ) are found by subsung he effcen consumpons no he frs-order condons (8) (9): α / φ p ( Λ= ) { α [ c ( Λ)/ c ( Λ)]} ( + r+ ( Λ )) = /[ Eρ + ( Λ )] where ρ + s( Λ ) s he Arrow- Debreu prcng kernel: ρ + s( Λ ) ρ + s( Λ= ) ρ + s( Λ ). If agens can freely dspose of socks hen sock prces are zero a he ermnal dae: P jt = 0. Ierang (7) forward usng P jt = 0 gves: T Pj ( Λ= ) E ρ s( ) p ( ) s + Λ j s Y = + Λ j + s for j= 0 T. Le e ( Λ ) p j ( Λ) c ( ) j = j Λ denoe 's effcen consumpon spendng a. The * T porfolos { A A } have o sasfy he budge consran = 5 When Λ= 0 or Λ= he socal plannng problem s rval: one counry consumes he enre endowmens of boh goods; he subsequen dscusson assumes 0<Λ<. 8

9 j P j ( ) A e ( ) ( ) ( ( )) j j jp j A r + Λ + = + + Λ= Λ+ + Λ for = 0 T (3) = where T Pj ( Λ ) pj ( Λ ) Yj + Pj ( Λ ). Le W ( Λ) E ρ 0 s( ) e s( ) s= + Λ + Λ denoe he presen value T a dae of 's effcen consumpon spendng { e + s( Λ )} s= 0. (3) holds f and only f W ( Λ ) equals 's wealh a : W ( ) P j j ( ) A ( r Λ = Λ + + ( Λ)) for 0 T. (4a) j = A proof of he equvalence beween (3) and (4a) can be based on econ B of Kollmann (005b) (where a closely relaed model s solved) and on Campbell and Vcera (00 Ch. 5.). When { } T + + A+ = sasfes (4a) for = hen { } T + + A+ = wh j + = j + ( j= ) and A+ = A+ sasfes (4a) for = and vce versa. c ( Λ) p ( Λ ) and e ( Λ ) are me-nvaran funcons of he vecor of endowmens y : j ( ) ( ) j j p y r r y c Λ= c y Λ ( Λ= ) p( y Λ ) e ( Λ ) = e ( y Λ ). Thus r ( Λ ) s a me-nvaran funcon of ( Λ= ) ( Λ ) whle W ( Λ) and P j ( Λ ) are funcons of y and : W ( ) ( ) Λ= W y Λ ( ) P ( ). j Λ= Pj yλ (4a) can hus be wren as: ( ) ( ) ( W y ( )) Λ = j jpj y Λ + A + r y = Λ for 0 T. (4b) Any nal porfolo 0 0 A 0 ( + r 0 ) ha sasfes (4b) for =0 s suable for equlbrum: W ( y 0 Λ 0) = P j0 j( y 0 Λ 0) + A 0 ( + r 0). (4c) j = The porfolo A (for 0 < T) s chosen a.e. before y s known. In general here are no values of A such ha (4b) holds exacly for any realzaon of y. Here I solve for A ha ensure ha a frs-order Taylor expanson of (4b) (wh respec o y ) holds for arbrary y. Those A have o sasfy he followng equaons: ( ) W y Λ = j Pj ( y Λ ) + A ( + r ( y )) j= Λ (5a) DW ( ) k y j D j ( ) j k P Λ = y Λ for k= (5b) = where DW k ( y Λ ) and DP k j ( y Λ ) (for k= ) are he dervaves of W ( y Λ ) and P ( y Λ ) wh respec o Y evaluaed a he endowmen vecor y. In wha follows I use j k y. = y Usng a lnear approxmaon of (4b) o compue porfolos s approprae when endowmen shocks are small. The dscree me model here can be vewed as an approxmaon o a connuous me model; n connuous me he soluon for porfolos here would be exac. 6 As shown n he Appendx equlbrum bond holdngs are zero ( A = 0) when he uly funcon exhbs consan relave rsk averson (CRRA) as assumed n he presen model (see (3)). 7 6 In connuous-me complee-markes models porfolos are se n such a way ha he dffuson erm of agens' wealh equals he dffuson erm of he presen value of effcen consumpon spendng--hs ensures ha wealh suppors effcen spendng; see e.g. Campbell and Vcera (00 ec. 5.) and Kollmann (005b; 006 p.7). The logc behnd (5b) s analogous: up o a frs order approxmaon (5b) ensures ha he dae nnovaon o counry 's fnancal wealh equals he nnovaon o he presen value of 's effcen spendng. 7 Noe ha as markes are (effecvely) complee one can solve for prces and quanes before solvng for porfolos. Under ncomplee markes prces quanes and porfolos would have o deermned jonly; see e.g. 9

10 3.6. Characerzng effcen equlbra for exogenous nal asse holdngs The remanng analyss assumes ha nally bond holdngs are zero and each counry fully owns he local sock: A0 = 0 0= for =. I follows from (4c) ha an equlbrum exss relave o hose nal holdngs f here s a value of Λ for whch W ( Λ y00) = P ( Λ y00). Ths pns down Λ Equlbrum porfolos n a wo-perods economy (T=) Ths econ consders a wo-perod economy (T=) as analycal resuls can be derved for ha case. 4.. Analycal resuls Wh CRRA uly A = 0 holds and he budge consran (4b) of fnal perod T= becomes: c ( y Λ+ ) p( y Λ) c ( y Λ ) = Y+ p( y Λ ) Y for = (6) where j j. Le µ ( y ) c Λ ( y Λ )/ Y and v ( y Λ) Y /[ Y p( y Λ )] denoe respecvely he effcen locally consumed share of good and he rao of he counry endowmen dvded by he value of he counry endowmen. Dvdng (6) by p( y Λ ) Y gves: µ ( y Λ) v ( y Λ ) + [ µ ( y Λ )] = v ( y Λ ) +. (7) A lnear approxmaon of (7) around y= y gves: 0 * * µ µ + µ ν µ µ / ν = ν (8) where x ( xy ( ) x )/ x denoes he relave devaon of x( y ) from x xy ( ) for any quany x( y ) ha s a funcon of he vecor of dae endowmens y. Assume whou loss of generaly ha he effcen locally consumed fracon of counry 's endowmen a =0 equals he consumpon home bas parameer α (see (4)): α = µ ( y0 Λ ); n oher erms (nong ha µ µ ( y Λ ) = µ ( y0 Λ ) as y= y ) le 0 α = µ for =. 9 (9) (9) mples: [ µ ( y Λ)]/ µ ( y Λ= ) ( ( α)( α)/( αα )) µ ( y Λ)/[ µ ( y Λ )]; hence µ ( y Λ ) s nversely relaed o µ ( y Λ ). A lnear approxmaon yelds (usng (9)): µ = µ ( α )/( α ). (0) ubsuon of (0) no (8) (usng (9)) produces: µ [ α + ( α / ν )( α )/( α )] + αν = ν. () By assumpon nal foregn asse holdngs are zero (see ec. 3.6); hus he neremporal budge consran (4b) mples ha he presen value of ne expors s zero: Evans and Hnakoskva (005) and Hnakovska (005) who solve nernaonal fnance models wh ncomplee markes usng second order approxmaons. 8 Λ= holds when α = α and he dsrbuon of endowmens s symmerc across counres. 9 (9) s merely used o smplfy he presenaon. One can ensure ha (9) holds by usng suable ransformaons of uly funcons and normalzaons of physcal quanes; see Appendx. When α µ hen he key porfolo equaons (4a)-(5) below connue o hold excep ha α has o be replaced by µ n hose equaons. 0

11 NX ( y Λ+ ) E NX ( y Λ= ) 0 where ρ NX ( y Λ ) ( µ ( y Λ )) Y ( µ ( y Λ )) p ( y Λ ) Y s counry 's ne expor a. As (log) endowmens follow random walks (see ()) ne expor a =0 s zero up o a lnear approxmaon: NX ( y Λ ) = 0. Thus 0 ( αν ) ( α) = 0. 0 () () mples ha () can be expressed as: µ ( α + α ) + αν = ν. (3) Wh CRRA uly he funcons µ ( y Λ ) and ν ( y Λ ) are homogenous of degree 0 n y and hus µ ( y Λ ) and ν ( y Λ ) can be expressed as funcons of he rao of he endowmens a =: z Y / Y. A lnear approxmaon of he rsk sharng condon () gves (usng (9) (); see Appendx): * ( σφ)( α)( α α) µ =Γ µ z wh Γµ. (4a) ( σφ)( α α) + σφ α * * / φ The = prce of good s: p ( y Λ= ) { [(/ z )( µ ( y Λ))/ µ ( y Λ))]}. Lnearzaon of α ν ( y Λ= ) z / p ( y Λ ) gves: * ( α α) ν =Γ ν z wh Γ v [ φ Γ µ ]/ φ. (4b) ( α) The effcen allocaon canno be suppored by exsng asses when µγ 0 Γ= v 0.e. when he effcen locally consumed fracon of endowmens a = s affeced by endowmen shocks whle he rao of he values of he endowmens s unaffeced by hose shocks. Porfolos are ndeermnae when µγ =Γ v = 0. In all oher cases he unque soluon for he locally owned share of sock s (from (3)): = α + ( α + α ) Γ / Γ. (5) µ ν * α ν( α α) µ / ν A smlar reasonng shows ha = + + Γ Γ. When Γ= µ 0 he effcen allocaon s acheved (up o a lnear approxmaon) f counry holds a share α of s local sock a he begnnng of he fnal perod ( = α ) as ha porfolo ensures ha he dvdend ncome generaed by 's holdng of he local [foregn] sock equals 's purchases of he local [foregn] good. * * Noe ha α= ν( α). Thus exceeds α f and only f exceeds α. > α occurs f µγ / Γ> v 0 whle < α holds f µγ / Γ< v 0. Hence he locally owned equy * share s greaer [smaller] han he consumpon home bas parameer α f µ ( y Λ ) comoves posvely [negavely] wh he relave value of he counry endowmen a =. Inuvely: f s effcen for counry o consume a larger share of s endowmen a = n saes of he world n whch he relave value of he dvdend of he counry sock s hgh (.e. f µγ / Γ v > 0) hen he local sock provdes a hedge for flucuaons n he opmal local 0 () holds exacly when α α Y = 0 0 = Y and he dsrbuon of endowmens a = s symmerc across * counres. However even when () does no hold exacly ha erm ( α ) ν ( α ) s of second order ( can be made arbrarly small by seng he varance of endowmen shocks suffcenly close o zero) and equlbrum porfolos only dffer by a second order quany from he porfolos derved below.

12 consumpon share--he effcen allocaon can be mplemened f counry holds a local equy share ha exceeds α. 4.. Calbraon Whch of hese cases s emprcally mos relevan? Fgures and llusrae how he locally held equy share s relaed o σ and φ for wo model varans characerzed by dfferen * degrees of consumpon home bas and relave counry szes ( α α ν ). * In varan (Fg. ) counres are (nally) equal szed: z = ν = I nerpre he wo counres as he U and an aggregae of he remanng OECD economes respecvely and se α = α = 0.9 as he U rade share s abou 0% (see Col. 6 Table ). 0 ; In varan (Fg. ) counry s much smaller han counry. Counry s calbraed o he medan counry among he 5 smalles OECD economes ("G5") consdered n Table 3; counry represens he res of he OECD. The medan G5 economy (ranked by oupu) accouns for.38% of aggregae OECD oupu. In varan he rao of he wo counres' endowmens a =0 ( z Y / Y ) s se a z = /0.04; α s se a α = 0.8 as he G5 medan rade share s 0%. α s se a α =-(- α )/z = Ths enals ha n varan erms of 0 * rade are uny n he nal perod ( p 0 = ) and counry 's nal share of he world endowmen s.38%: p Y /[ Y + p Y ] = The downward [upward] slopng hck lne n he Fgures shows combnaons of φ σ for whch Γ= µ 0 [ νγ= 0] holds. () (4a) shows ha Γ= µ 0 holds when /σ = φ ; Γ µ < 0 when / σ < φ; Γ µ > 0 when / σ > φ. To undersand hs noe ha a lnear approxmaon of rsk sharng condon () gves: * * * * [( σφ)/ φ] C c / φ= [( σφφ )/ ] C c / φ for j=. (6) j j where he lef-hand [rgh-hand] sde s he margnal uly of good j n counry [counry ] a = (expressed as a relave devaon from margnal uly evaluaed a y ); see Appendx. When /σ = φ holds hen uly funcons are addvely separable n he wo goods; 3 (6) shows ha n ha case good j consumpon (for j=) s perfecly correlaed across counres c * = c * j j whch mples c * = Y for =. Consder he effec of an ncrease n he j j good endowmen a = Y ; when /σ = φ holds ha shock rases boh counres' effcen good consumpon by he same proporon and hence he effcen locally consumed fracon of good s consan.e. Γ µ = 0; hs ensures ha margnal ules of good are perfecly The G5 consss of he counres lsed n Table 3 less he wo "gans" U and Japan. The larges G5 counres are Germany (8% of OECD oupu) and he UK and France (6%). The denomnaor of (4a) s srcly posve as 0 < ( α α ) <. Thus sgn( Γ ) sgn( ). µ = σφ 3 / φ ( φ )/ φ / φ ( φ )/ φ UC ( ) = α ( c ) + ( α) ( cj ) ( j ) when / σ = φ.

13 correlaed across counres. Noe ha a shock o he good endowmen has no effec on good consumpons when / σ = φ. 4 When / σ < φ hen he wo goods are subsues n he sense ha UC ( )/ c c< 0. To undersand why Γ< µ 0 holds n ha case consder agan he effec of an ncrease n he good endowmen a = ( Y ); f boh counres ncreased her good consumpon a = by he same proporon as Y holdng good consumpons consan (as s opmal when / σ = φ see above) hen margnal ules of boh goods would fall more (n relave erms) n counry han n counry when / σ < φ. Ths s so because: () an equ-proporonal rse n boh counres' good consumpon rases aggregae counry consumpon C more srongly (n relave erms) han aggregae counry consumpon C because good has a greaer wegh n C due o consumpon home bas; () when / σ < φ he margnal uly of good j s a decreasng funcon of aggregae consumpon as can be seen from (6). To guaranee full rsk sharng counry consumpon of good has o rse less (n relave erms) han he good endowmen when / σ < φ.e. he fracon of he good endowmen consumed n counry has o fall (n response o he ncrease n he counry endowmen). Thus Γ µ < 0 when / σ< φ. mlar reasonng explans why Γ µ > 0 holds when / σ > φ. () (4a) and (4b) mply ha Γ= v 0 holds when σ= /[ φ+ ( φ)/( α α) ]. Γ< v 0 holds when an ncrease n Y lowers v ; hs occurs for ( σ φ ) pars locaed o he lef of he Γ v = 0 locus; for hose ( σ φ ) pars an ncrease n he counry endowmen rases he relave prce of good so much ha he relave value of he counry endowmen falls. The Γ= µ 0 and Γ= ν 0 loc cross a he pon σ = φ=. Thus porfolos are ndeermnae when σ = φ=. 6 The effcen allocaon canno be mplemened for parameers on he Γ= v 0 locus wh he excepon of he pon σ = φ=. The sgn of changes when he Γ= v 0 locus s crossed n ( σ φ ) space. By selecng pons suffcenly close o ha locus arbrary large absolue values of can be generaed. = α holds for parameers on he Γ µ = 0 locus. Γ< ν 0 Γ< µ 0 holds for ( σ φ ) pars ha are smulaneously above he Γ= µ 0 and Γ v = 0 loc; Γ> ν 0 Γ> µ 0 holds for pars ha are smulaneously below hose loc; for hose wo ses of ( σ φ ) pars he locally owned equy share exceeds he locally consumer fracon of he endowmen: > α. Porfolos are symmerc across counres ( = ) n model varan. In varan by conras porfolos are asymmerc : he larger counry (counry ) holds roughly 00% of he local sock excep when σ φ s close o he Γ = 0 locus.e. excep when he absolue ν 5 4 When/σ = φ he effcen equlbrum can be suppored exacly by socks no jus up o a lnear approxmaon. * * For/ σ= φ () mples ( ) /[ ( /( )) φ ( )] ( ) /[ (( )/ ) φ µ y Λ = α α + Λ Λ α µ y Λ = α α + Λ Λ ( α )]; as hese erms do no depend on y he effcen allocaon s mplemened exacly by * * * * =µ ( y Λ) = µ ( y Λ). 5 The denomnaor of ha expresson s zero for φ= φ /[ ( α α ) ]; φ< φ holds for emprcally plausble φ α. 6 Whenσ= φ= uly s logarhmc α U ln ( )ln ln( = α c+ α cj α ( α ) α ) j and he equlbrum s effcen even under fnancal auarky as shown by Cole and Obsfeld (99). 3

14 value of Γµ / Γ ν s large. For varan Fg. hus shows he locally held equy share n counry. The Γ= 0 ν loc are vrually dencal n varans and (as α + α s roughly dencal across he wo varans); he Γ µ = 0 loc are exacly dencal. Boh varans hus generae locally held equy shares ha exceed he degree of consumpon home bas for roughly he same values of σ and φ. Esmaes of σ n he range of (or greaer) are common for ndusralzed counres (e.g. Barronuevo (99)); φ corresponds o he prce elascy of a counry's (aggregae) mpor and expor demand funcons. 7 Hooper and Marquez (995) survey a large number of sudes ha esmaed (long run) prce elasces of aggregae rade flows for he U Japan Germany he UK and Canada; he medan esmaes (pos-breon Woods era) of φ for hose counres are and.0 respecvely (medan esmae across all 5 counres: 0.88); 80% of all esmaes are smaller han.. One of he mos comprehensve emprcal sudes on rade elasces s Bayoum (999) who uses daa on 40 blaeral rade flows beween ndusralzed counres; under he resrcon (no rejeced sascally) ha elasces are dencal for all couny pars he esmaed (long run) prce elascy ranges beween 0.38 and 0.89 (dependng on model specfcaon). 8 The emprcal evdence s hus conssen wh he vew ha domesc and mpored goods are subsues (/ σ < φ) and ha he subsuon elascy beween goods s no markedly above uny. For values of σ and φ n he range of he esmaes jus descrbed boh model varans generae szable equy home bas. For example assume σ =. Then model varan predcs locally held equy shares ( = ) of and.30 for φ= 0.6 φ= 0.9 and φ=. respecvely; n varan he correspondng values of are and.008 whle hose of are and.6 respecvely (for φ= 0.6 φ= 0.9 and φ=.). Noe ha for φ= 0.9 and φ=. more han 00% of he domesc sock s held locally (counres hold shor posons of foregn sock). 5. Infnely lved economy Ths econ consders an nfnely lved economy ( T ). To compue equlbra I use a nonlnear equaon solver o deermne effcen consumpons and erms of rade a dae as funcons of he vecor of endowmens y. Wh an nfne me horzon he presen value of counry 's effcen consumpon spendng process W and he sock prce (cum-dvdend) P are me nvaran funcons of he vecor of endowmens a : W ( Λ= ) W ( y Λ ) j 7 j Counry mpors are c ( α )( p / ) j P φ φ = C ( j ) where φ [ /( φ P ) α p ( ) ] + α p j s 's CPI. Thus he elascy of mpors wh respec o he mpor prce p j (holdng consan he domesc prce level P ) s φ. 8 Esmaed prce elasces a a dsaggregaed ndusry level are ypcally hgher (n he range of 5) han elasces of aggregae rade flows (Obsfeld and Rogoff (000 p.345)). Kollmann (00ab; 00; 004; 005a) presens models n whch he secoral prce elascy exceed he aggregae elascy; here he quanes c and j c n 's consumpon aggregaor (4) are ndces of dfferenaed domesc and mpored nermedae goods ( ψ )/ ψ ψ /( ψ ) respecvely: ck = { c 0 k () s ds} (k=j wh j) where c k () s s he quany of he ype s [0] nermedae good produced by counry k and consumed by. ψ s he own-prce demand elascy for ndvdual varees. If all frms locaed n he same counry receve dencal endowmen shocks hen he degree of equy home bas depends on he aggregae elascy φ (and no on ψ ). 4

15 ( ) PjΛ= Pj ( y ). Λ I compue hose funcons usng numercal negraon based on he nonlnear soluons for consumpons and erms of rade. I hen oban dervaves of W ( y Λ) and Pj ( y Λ ) a y y usng a fne dfference procedure; hose dervaves deermne counry * * 's sock holdngs a he end of perod (see (5b)). Noe ha a lnear approxmaon + + s solely used o compue porfolos; 9 he soluons for prces and quanes are globally accurae. ee he Appendx for furher dscussons of compuaonal aspecs. 5.. Calbraon I agan consder he wo model varans descrbed above: varan (calbraed o he U vs. an aggregae of he remanng OECD economes) assumes α = α = 0.9 Y 0 = Y 0 = whle varan (n whch counry represens he medan G5 counry) uses α = α = 0.8 Y = Y = In boh varans one perod represens one year n calendar me; as 0 0 s common n busness cycle models calbraed o annual daa β= 0.96 s assumed (whch mples ha he seady sae annual equy reurn s 4%). The rsk averson parameer s se a σ =. Three values of he elascy of subsuon φ are consdered: φ= 0.6 φ= 0.9 φ=.. The emprcal sandard devaons of he annual log growh raes of U and aggregae non-u oupu are.3% and.8% respecvely; he correlaon beween hese growh raes s 0.5 (sample perod: ). Varan hus uses sd ( ε) = sd ( ε) = 0.03 corr( ε ε ) = 0.5. For G5 counres he medan sandard devaons of he log growh raes of domesc and of foregn oupu are.% and.% respecvely (sample perod: ); hus domesc oupu s more volale han foregn oupu. The medan correlaon beween domesc and foregn oupu growh raes s 0.4. (The correlaon beween HP flered domesc and foregn log oupu s posve for almos all G5 counres; see Panel (a) Table 3.) Varan hence assumes sd( ε ) = 0.0; sd( ε ) = 0.0; corr( ε ε ) = ochasc smulaons Tables 4 and 5 show predced sascs for model varans and respecvely. For varan resuls for counry varables are repored; for varan resuls for he small counry (=) are shown. The model sascs for varan [varan ] are averages of sascs compued for 50 smulaon runs of 8 [] perods each (8: lengh of he BEA daa se for he U; : he medan number of daa years for G5 counres). In boh Tables Cols. -9 show predcons generaed for he baselne CRRA uly funcon (3); Cols. 0- show resuls for a model verson wh a consan absolue rsk averson (CARA) uly funcon. Cols 3-5 repor emprcal sascs; he emprcal sascs n Table 4 peran o he U (based on Table ) whle he emprcal sascs n Table 5 are medan sascs for he G5 counres (based on Table 3). 30 The heorecal curren accoun varables of counry are defned as: * * * * * j * * FEA+ = Pj j + Pj j * j * * FEL+ = P + P ECA= FEA FEL BCA= A + A CA = ECA + BCA wh j. I also defne a "convenonal" curren accoun measure for 9 The pon of lnearzaon y s me-varyng. A consan pon of lnearzaon would enal larger y approxmaon errors and would generae consan porfolos whereas he approach here capures me-varaon n porfolos. 30 The emprcal sasc for (locally held share of domesc equy) correspond o mnus he rao of foregn equy lables o physcal capal socks repored n Col. of Table. 5

16 CA. 3 counry based on book (hsorcal) values of asses/lables acqured n he pas: Theorecal sascs for counry 's curren accoun varables are based on smulaed seres normalzed by a fed (deermnsc) rend of counry 's oupu. 3 All seres are HP flered (smoohng parameer: 400). Oupu and he (consumpon based) real exchange rae (RER) seres are logged (before flerng). Model varan (equal szed counres) Table 4 Lke he wo-perod model ( T= ) he nfne horzon model can generae szable equy home bas. In fac share holdngs n he nfne horzon economy are very close o hose n he woperod economy. Under CRRA uly bond holdngs are zero and he varably of share holdngs ( ) s essenally zero: here are vrually no sock rades. Thus n he model flucuaons of he curren accoun measure CA (ha ncludes capal gans/losses) are almos fully due o changes n equy prces; he convenonal curren accoun CA s bascally consan (a zero). The predced sandard devaon of he real exchange rae s smaller han ha seen n he daa. The specfcaons of model varan n Table 4 predc a sandard devaon of CA ha represens beween 8% and 83% of he sandard devaon of he emprcal measure of CA for he U. The specfcaon wh φ= 0.6 maches bes he acual U equy home bas; ha specfcaon explans 49% of he emprcal sandard devaon of CA. The model capures he low emprcal auocorrelaon of he U curren accoun CA and s low correlaon wh domesc and foregn oupu. 33 In he model ne foregn asses a he end of perod ( NFA ) + are solely a funcon of endowmens a ; as log endowmens are assumed o follow random walks CA ( NFA ) s hus approxmaely..d; he predced + auocorrelaon of he HP flered CA seres s whch s no sgnfcanly dfferen (a a 0% level) from he emprcal auocorrelaon The predced correlaons beween CA and domesc oupu (0. when φ= 0.6; -0. when φ= 0.9 and φ=.) are lkewse no sgnfcanly dfferen from he emprcal correlaon for he U 0.0. In he model changes n foregn equy asses and lables ( FEA FEL) are more volale han CA and oupu whch s conssen wh he daa. The predced correlaon beween FEA and FEL abou 0.9 s close o he emprcal correlaon for he U (0.88); ha hgh predced correlaon s due o he fac ha he cross-counry correlaon of sock reurns s abou 0.9. A rse n he counry endowmen rases he counry sock prce (and reurn) and he relave prce of he counry good; herefore he prce of he counry sock (n uns of good ) rses oo (see dscusson of mpulse responses below). Thus he crosscounry correlaon of sock reurns exceeds ha of oupu * * * j* * CA Pj j + P + + A+ * * wh j. Noe: * j CA * CA = Pj j P. 3 The smulaed curren accoun seres are normalzed n he same manner as he emprcal seres. 33 In model varan he correlaon beween he curren accoun and foregn oupu s very close o he negave of he correlaon beween he curren accoun and domesc oupu. Only he laer s repored ( ρ ). Y 34 An HP flered..d. seres has an auocorrelaon of 0. (when he smoohng parameer s se a 400). 35 Coeurdacer and Gubaud (005) and Pavlova and Rgobon (005) also dscuss models n whch endogenous erms of rade responses nduce szable cross-counry correlaons of sock reurns. 6

17 To generae asse rade I consder he CARA uly funcon UC ( ) = exp( σc) wh σ =. 36 Cols. 0- show resuls for a CARA specfcaon wh φ= 0.6; ha specfcaon generaes non-neglgble sock rades and szable flucuaons n he bond componen of he curren accoun BCA (predced sandard devaons of * and BCA : 0.7% and 3.% respecvely; emprcal sandard devaon of BCA for he U:.77%). Under CARA uly he curren accoun remans volale and (approxmaely)..d. Impulse responses Table 6 Panel (a) of Table 6 shows mpac effecs of one-sandard-devaon endowmen nnovaons for each of he specfcaons of model varan consdered n Table 4. As log endowmens follow random walks he responses of consumpon ne expor prces and asse holdngs n all perods afer he shock equal he mpac responses; by conras he responses of he curren accoun (and s componens) are zero afer he shock. A posve endowmen shock n counry rases fnal good consumpon n boh * * counres--bu C rses more srongly han C ( j ) due o consumpon home bas. The parameers consdered n Table 4 enal ha a posve counry endowmen shock lowers counry 's local consumpon share µ j and ha ncreases µ ( j ); hus he shock rases j counry 's expors c * and lowers 's mpors c j. I also lowers he relave prce of good. Counry ne expor falls (n response o he ncrease n 's endowmen) when φ= 0.6 (low elascy of subsuon beween goods); ne expor rses for φ= 0.9 and φ=.. Under CRRA uly sock holdngs ( + + ) show (vrually) zero responses o endowmen shocks. The neremporal budge consran (4b) mples ha 's ne foregn asses a he end of NFA + equal he negave of he presen value of 's ne expors a daes s> : j ρ s s. + = s= + + In equlbrum a shock ha permanenly lowers 's ne expors NFA E NX rggers hus a rse n 's ne foregn asses and on mpac ncreases 's curren accoun. hare holdngs are srucured n a manner ha delvers ha response of ne foregn asses. Consder he case of a one-sandard-devaon counry endowmen shock under CRRA uly and φ= 0.6 (Row I Panel (a) of Table 6); he shock lowers he ne expor and rases he curren accoun of counry by 0.07% and.90% of pre-shock oupu respecvely. Each counry holds 7% of he foregn sock. The prces of socks and rse by.3% and.4% respecvely. (The relave prce of good rses srongly: +.45%; hs explans why he sock prce expressed n uns of good rses more srongly n counry han n counry.) Thus counry ne foregn asses ncrease. Wh CARA uly he responses of consumpon prces ne expor and he curren accoun are almos he same as n he CRRA case; however he equy vs. bond composon of he curren accoun adjusmen dffers noceably: e.g. n he CARA case wh φ= 0.6 a posve shock o counry producvy rggers a rse n 's bond holdngs by an amoun ha represens 3.6% of pre-shock oupu; see Panel (a4) Table 6 (he bond componen of he curren accoun s zero under CRRA preferences). 36 In model varan boh counres' aggregae consumpon equals uny n he nal perod; under CARA uly he coeffcen of relave rsk averson n he nal perod ( σ C ) hus equals wo he value assumed n 0 he baselne CRRA specfcaon. 7

18 Model varan (counry smaller han counry ) Table 5 In model varan he predced sandard devaons of he small counry (=) curren accoun (normalzed by small counry rend oupu) are 5.%.9% and 8.7% respecvely when φ= 0.6 φ= 0.9 and φ=. are assumed (CRRA uly). (Medan emprcal sandard devaon of G5 curren accouns: 7.4%.) For a gven value of φ he sandard devaon of he small counry's curren accoun (normalzed by s rend oupu) n model varan s abou 3 mes larger han he sandard devaon of he counry ("U") curren accoun n model varan (see Table 4). The model capures hus he fac ha he (normalzed) curren accouns of G5 economes are more volale han he U curren accoun. Noe ha he small counry (n varan ) has more volale endowmen shocks and ha s rade share s larger (compared o counry n varan ); hus s erms of rade and s ne expor (normalzed by domesc oupu) are predced o be more volale--hence s curren accoun s more volale as well. 37 Predced correlaons of he curren accoun wh domesc oupu are larger (n absolue value) n varan han n varan bu le n he range of emprcal correlaons observed for G5 counres. 38 As n model varan here s (almos) no rade n socks when CRRA uly s assumed and agan he sock holdngs generaed by he nfne horzon CRRA model are very smlar o hose predced by he wo-perod model. The small counry holds 86% % and 6% of he domesc sock when φ= 0.6 φ= 0.9 and φ=. respecvely. The large counry (=) holds close o 00% of s local sock. The CARA specfcaon agan generaes szable flucuaons n he bonds componen of he curren accoun; e.g. when φ= 0.6 he sandard devaon of he (normalzed) bond componen of he curren accoun s 0.04%. 39 Panel (b) n Table 6 repors mpac responses for model varan. The responses are qualavely smlar o hose generaed by varan. 6. Concluson Ths paper has analyzed nernaonal asse porfolos usng a neoclasscal dynamc general equlbrum model wh home bas n consumpon. For plausble parameer values he model explans he fac ha ypcal nvesors hold mos of her wealh n domesc asses (porfolo home bas). The model also capures key aspecs of curren accoun measures ha nclude capal gans/losses on exernal asses: hose curren accoun measures are volale and have low seral correlaons; changes n a counry's foregn equy asses and lables are hghly posvely correlaed and changes n ne foregn equy holdngs are an mporan source of curren accoun flucuaons. 37 The elasces of he erms of rade and of expors and mpors wh respec o endowmens are roughly dencal across model varans and. Holdng consan he sandard devaon of endowmens he sandard devaon of ne expors (normalzed by domesc oupu) s roughly proporonal o he rade share--whch helps o undersand he greaer volaly of he small counry's ne expors (and curren accoun). 38 For example when φ = 0.6 he correlaons of he counry curren accoun wh domesc and foregn oupu are 0.39 and respecvely (correlaons wh foregn oupu no shown n Table 5). In he neghborhood of he nal endowmen vecor CA s approxmaely a lnear funcon of he dfference beween he wo counres' oupu nnovaons; he curren accoun s more closely correlaed wh counry oupu as ha oupu s more volale (han counry oupu). 39 The CARA specfcaon for varan assumes ha n boh counres he coeffcen or relave rsk averson s wo n he nal perod. Ths s acheved by usng hese uly funcons for counres and respecvely: exp( C ) and exp( C / 0.04). (Consumpons n he nal perod are: C = C = 0.04.) 0 0 8

19 Appendx A.. Daa sources defnons of varables (Tables and 3) Le G denoe he se of 7 OECD counres lsed n Table 3 plus Belgum Ireland Mexco and Norway (no curren accoun seres for hese counres are consruced because of gaps n porfolo daa). The porfolo daa (for U) used n Table are from BEA (005). The porfolo daa used n Table 3 (7 OECD economes) are from he IMF's IIP daabase. All oher daa are from Inernaonal Fnancal ascs (IMF). Emprcal sascs (sandard devaons ec.) for real exchange raes peran o CPI based real exchange raes. Counry 's CPI based real exchange rae RER s a geomerc weghed average of blaeral CPI based real exchange raes beween and he oher G counres (weghs: mean oupu shares ): RER ( ) j. G / / / / j j j RER RER e CPI j j j j CPI s he real exchange rae beween counres and j; e s he currency prce of one un of / j currency j; CPI j s j's CPI. The Ω j> 0 weghs sum o uny. A rse n RER represens a real deprecaon of currency (vs-à-vs he res of he G). "Foregn" oupu from counry 's vewpon s aggregaed usng real exchange raes based on GDP deflaors; GD GD RER and RER / j denoe he blaeral real exchange rae beween counres and j and he real exchange rae beween and he res of he G based on GDP deflaors. 40 In Tables and 3 counry 's oupu measure GDP-I-G s defned as 's nomnal GDP-I-G nom nom nom GD nom nom nom GD ( GDP I G ) dvded by 's GDP deflaor P : Y ( GDP )/ I G P. Noe ha GDP-I -G s deflaed usng he GDP deflaor as no specfc deflaor alored o GDP-I-G s avalable. 4 Foregn oupu from counry 's perspecve Y *. s oal oupu n he res of he G aggregaed a real exchange raes (based on GDP deflaors) n a reference year T : 0 * nom nom nom GD GD. G j j j j / Y [( )/ ]. j j GDP I G P RER jt0 Table sest 0 = 990 whle Table 3 uses T = 993 (medan years n respecve samples). 0 Ω In Tables -3 a counry's foregn equy asses FEA represen he sum of s FDI asses and exernal porfolo equy asses; foregn equy lables FEL are he sum of FDI lables and exernal porfolo equy lables. A counry's ne foregn bond holdngs NB are consruced as NB NFA-FEA-FEL from daa on FEA FEL and ne foregn asses NFA. Table U Curren accoun In Table he U curren accoun and s componens are expressed n uns of U oupu. eps n compuaon: () U asses and lables NFA FEA FEL NB a he end of year (provded n U dollars by he BEA) are deflaed usng he U GDP deflaor; () he deflaed seres are frs-dfferenced as n equaon () o consruc CA FEA + FEL + ECA and BCA ; () he frs-dfferenced seres are normalzed by a fed geomerc rend of U oupu. 40 Defnons are analogous o hose of RER and RER / j (CPI's n formulae are replaced by GDP deflaors). 4 In Cols. 5-7 of Table and n Panel (b) of Table 3 he oupu measure s real GDP (here nom nom nom nom GDP I G n he formulae for domesc and foregn oupu s replaced by GDP ). 9

20 A U dollar seres on he convenonal curren accoun CA (ha does no nclude capal gans/losses) s aken from Inernaonal Fnancal ascs (IF) publshed by he IMF. In Table he IF seres s deflaed usng he U GDP deflaor and normalzed by he fed geomerc rend of U oupu. Table 3 (7 OECD economes): In Table 3 he sascs on he counry curren accoun (and s componens) peran o seres ha are expressed n uns of foregn oupu. eps n compuaon: () Counry asses and lables a he end of year (provded n U dollars by IIP) are expressed n counry currency usng he blaeral nomnal (end-of-year) exchange rae beween and he ( e ) deflaed by 's GDP deflaor and hen dvded by he real exchange rae beween U U / GD and he res of he G a RER (hs expresses he socks asses and lables n uns of foregn oupu). () The resulng seres are frs-dfferenced as n () o consruc CA FEA FEL ECA BCA for counry ; () he frs dfferences are normalzed by a + + GG fed geomerc rend of oupu expressed n uns of foregn oupu ( Y / RER ). A U dollar seres on counry 's convenonal curren accoun measure CA s aken from IF. In Table 3 he measure s expressed n uns of foregn oupu. pecfcally he IF seres for counry s expressed n counry currency usng he blaeral nomnal exchange rae beween and he U deflaed by 's GDP deflaor and hen dvded by he real exchange rae GD beween and he res of he G ( RER ) and normalzed by he fed geomerc rend of GD counry oupu expressed n uns of foregn oupu ( Y / RER ). A.. Proof ha bond holdngs are zero under CRRA uly Under CRRA uly he effcen consumpons cj ( y Λ ) are homogeneous of degree (HD) n he vecor of endowmen y ( Y Y ); see ec. A.5. below. The equlbrum prce of good p (y Λ ) s homogenous of degree 0 (HD0) n y as ha prce s a funcon of he rao of counry 's good consumpon dvded by 's good consumpon (see (9)). Therefore e (y Λ ) and p (y Λ )Y are HD n y. The equlbrum sock and bond holdngs for perods 0< T are found by solvng (5a) T s (5b). From ec. 3.5 W ( y Λ ) E βω( y )/ ( ) ( ) s 0 + sλ ω yλ e y = + sλ where ω ( y s Λ ) + s he margnal uly of good a + s. When he uly funcon s CRRA (see (3)) hen * ( )/ * / ( y s ) ( C ) σφ φ ω ( c / α) φ + Λ= whch mples ha ω ( y + s Λ ) s homogenous of degree σ n y + s ( C + s s HD n ( c c ) and hus HD n y + s + s + s). () mples ha y+ s= yε + s for s> where exp( s ). ε + s ε j= + j Thus ω ( y+ s Λ)/ ω ( y Λ ) = ω ( yε + s Λ)/ ω ( y Λ ) and e ( y+ s Λ ) = e ( yε + s Λ ) whch shows ha ω ( y+ s Λ)/ ω ( y Λ ) and e ( y+ s Λ ) are HD0 and HD n y respecvely. Thus W ( y Λ ) s HD n y. mlar reasonng shows ha Pj ( y Λ ) s HD n y. Euler's heorem hus mples: W ( y Λ ) = DW ( y Λ ) Y + DW ( y Λ ) Y ( ) ( ) P y Λ = D P y Λ Y + D P ( y Λ ) Y j j j 0

21 where (as n ec. 3.5) DW ( y Λ ) and DP ( y Λ ) (for k= ) are he dervaves of k W ( y Λ ) and P j ( y Λ ) wh respec o Yk evaluaed a y ( Y Y )'. ubsue hese * expressons no (5a). The resulng expresson and (5b) mply ha A = 0. A.3. Transformaons/normalzaons ha ensure ha (9) holds. Assume ha he locally consumed fracon of he counry endowmen n he nal perod * * = 0 µ µ ( y Λ ) dffers from 's preference parameer α. 0 The uly funcon (3) and he consumpon aggregaor (4) can be wren as: k j /( φ) σ U = ( σ ) [( Z ) ( C ) ] for = wh / φ / φ ( φ )/ φ / φ / φ ( φ )/ φ C α Z k c / k α Z kj cj / kj ( φ )/ φ ( φ )/ φ φ/( φ ) = [ ( ) + ( ) ( ) ] for j where Z Z k k are arbrary posve consans. Le's pck hese consans n such a way ha φ * α Z k ) = µ * ( ) Zk ( φ α = ( µ ) ( ) Zk ( φ α ) * = ( µ ) α Z * k = µ. /( φ ) (Ths requres ha k / k = {[ µ / α ][( α )/( µ )]} and Z / Z = [ µ / α ][( α )/( µ )] hold.) Under hese condons 's consumpon aggregaor can be wren as / φ ( φ )/ φ / φ ( φ )/ φ φ/( φ ) C [( α) ( c ) + ( α) ( c ) ] j wh α µ * j where c c / ( ) q q= s 's consumpon of good q normalzed by he consan k. q q q k (9) holds for he reformulaed consumpon aggregaor: he consumpon home bas parameer of ha aggregaor equals he consumpon share µ *. (In he normalzed economy he resource consran s replaced by c + c = Y c + c = Y where Y Y / k.) A.4. Dervaon of equaon (4a) Counry 's margnal uly of good j consumpon s κ j s a consan ( κ= α κ = α rsk sharng equaon () gves: ( σφ) / φ / φ UC ( )/ cj = ( C) ( cj / κ j) where κ = α κ = α ubsuon of hs expresson no he ). ( Λ)( C ( y Λ)) ( c ( y Λ )/ κ ) =Λ( C ( y Λ)) ( c ( y Λ )/ κ ) for j=. (A.) * ( σφ ) / φ * / φ * ( σφ ) / φ * / φ j j j j Consder he wo-perod model (T=) and lnearze he precedng equaon for he fnal perod T=. Ths gves equaon (6) n he ex: * * * * [( σφ)/ φ] C c / φ= [( σφφ )/ ] C c / φ for j=. (6) j j (Recall from ec. 4. ha x ( xy ( ) x )/ x denoes he relave devaon of x( y ) from x xy ( ) for any quany x( y ) ha s a funcon of y he vecor of endowmen n perod =; he pon of lnearzaon s he vecor of endowmens a =0: y ( Y Y )' = y.) 0 (4) mples ha * * * * * * * C = λc + ( λ) c where λ c /( c + p c ) s he share of good n counry consumpon expendures a he endowmen vecor y. Ne expor s zero a he * * * pon of lnearzaon; see (). Thus: c = p c where he lef- and rgh-hand sdes are * * * * counry 's expors and mpors respecvely n uns of good. Thus λ = c /( c + c ) = c / Y. By assumpon he fracon of he good endowmen consumed n counry s α a he pon * of lnearzaon (see (9)); hus c = α Y whch mples ha λ = α. Hence * * * C = α c + ( α) c. mlarly * * * C = ( α ) c + α c. ubsung hese expressons no (6) gves:

22 * * * * * * [( σφ)/ φ]{ αc + ( α) c } c / φ= [( σφφ )/ ]{( α) c + αc } c / φ for j=. (A.) j j * * * * Noe ha c ( y ) ( ) Λ= µ y Λ Y c ( y ) ( ( )) Λ = µ y Λ Y * * * * c ( y ) ( ( )) Λ= µ y Λ Y c ( y ) ( ). Λ = µ y Λ Y (A.3) Lnearzaon of hese expressons (usng (9)) gves: * * c = µ + Y * * c = ( α /( α )) µ + Y * * c = ( α /( α )) µ + Y * * c = µ + Y. (A.4) ubsuon of (A.4) no (A.) for good ( j=) gves: * * ( σφ) { α µ α [( α ) /( α )] µ } = * * * ( σφ) { α [( α ) /( α )] µ + α µ } + (/( α )) µ + ( σφ)( α α )z (A.5) where z Y Y ubsuon of µ = µ ( α )/( α ) (see (0)) no (A.5) gves (4a).. A.5. Infne horzon model: non-lnear soluon mehod ubsung (4) and (A.3) no rsk sharng condon () (or no (A.)) gves for good (j=): / φ * ( φ )/ φ / * ( )/ ( ) / ( )/( ) / * / y φ φ φ φ φ σφ φ φ φ µ + α µ y z α µ y / φ * ( φ )/ φ / φ * ( φ )/ φ ( φ)/ φ ( σφ )/( φ ) / φ * / φ ) µ ( y ) α µ ( y ) z ( α) µ ( y ) ( Λ) [ α ( ( Λ ) ( ) ( ( Λ ) ] ( ( Λ ) = Λ[( α ( Λ) + ( Λ) ] ( Λ) (A.6) * * * * where z Y / Y. (9) mples ha (( α )/ α)( c ( y )/ ( )) ( /( ))( ( )/ ( )); Λ c y Λ = α α c y Λ c y Λ * usng (A.3) hs can be used o express µ ( y Λ ) as a decreasng funcon of µ * ( y Λ ): µ ( y Λ= ) / { + ( ( α)( α)/( αα )) µ ( y Λ)/[ µ ( y Λ)] }. (A.7) ubsuon of hs expresson no (A.6) gves an equaon n µ * ( y Λ ) and z. As no analycal soluon exss I solve ha equaon numercally (bsecon mehod) o deermne µ * ( y Λ ) for gven values of y ( Y Y )'. Once µ * ( y ) Λ s known µ * ( y Λ ) and he consumpons can be compued usng (A.7) and (A.3). Noe: Wh CRRA uly funcons he equaon ha pns down µ * ( y Λ ) depends on he rao of endowmens z (and no on Y and Y per se); hus µ * ( y Λ ) s homogenous of degree 0 n y and (A.3) mples ha dae consumpons are lkewse homogenous of degree n y. (Ths fac s used n econ A.. above.) The funcon W ( y Λ ) (requred o compue porfolo a end of perod -) s defned by: s W ( y Λ ) E βω( y )/ ( ) ( ) s 0 + sλω yλe y = + sλ (A.8) * ( σφ) / φ * / φ where ω ( y+ s Λ ) ( C ( y+ s Λ)) ( c ( y+ s Λ )/ α) s counry 's margnal uly of good a + s (see econs 3.5 and A.). The mehod descrbed above allows o compue ω ( y s Λ + ) and e ( ) y+ sλ for an arbrary endowmen vecor y. + I compue he expeced value s E[ ω ( y s ) e + Λ ( y+ s Λ )] by numercal negraon (monomal formulae descrbed n Judd (998 p.75)) usng he fac ha he condonal dsrbuon of lny + s (gven dae nformaon) s normal wh mean Elny+ s= lny and covarance marx s V ε where V = Eε ε ε '. I runcae he seres (A.8) by only usng erms 0 s 350 (usng a larger number of erms does no affec he resuls). The compuaon of he sock prce (cum-dvdend) Pj( y Λ ) proceeds smlarly.

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25 Trole J Ineffcen Foregn Borrowng: A Dual- and Common-Agency Perspecve Amercan Economc Revew Uppal R A General Equlbrum Model of Inernaonal Porfolo Choce Journal of Fnance Van Neuwerburgh. Veldkamp L Informaon Immobly and he Home Bas Puzzle Workng Paper New York Unversy. 5

26 Table. Daa: exernal equy holdngs and rade shares (Foregn equy lables)/ (Foregn equy (Foregn equy Impors/ (capal sock) asses)/gdp lables)/gdp (C+I+G+X) () () (3) (4) (5) (6) Ausrala Ausra Canada wzerland Germany Denmark pan Fnland France UK Ialy Japan Neherlands Norway New Zealand Porugal weden U Medan Mean Noes: "Capal sock" (Col.): physcal capal sock; Foregn equy asses (lables): sum of FDI asses (lables) and porfolo equy asses (lables); C: prvae consumpon; G: governmen purchases; I: physcal nvesmen; X: expors. Daa sources: Col. () based on daa from Kraay e al. (005); porfolo daa for Cols. ()-(5) are from he Inernaonal Invesmen Posons (IIP) daa base (IMF). GDP C G I X daa are from IF. 6

27 Table. Properes of BEA daa on U nernaonal nvesmen poson (a) HP flered seres Oupu measure: GDP-I-G Oupu measure: GDP d (%) ρ (. Y ) ρ(.y ) ρ - d (%) ρ (. Y ) ρ(.y ) () () (3) (4) (5) (6) (7) Y.57 (.8).00 (.00) 0.5 (.0) 0.67 (.0).08 (.4).00 (.00) 0.54 (.0) RER 9.99 (.56) -0.5 (.4) (.) 0.76 (.04) 9.99 (.56) -0. (.0) (.3) CA 3.48 (.53) 0.0 (.5) 0.00 (.7) 0.04 (.08).6 (.35) -0. (.3) -0.5 (.6) FEA 6.5 (.83) (.) (.7) 0.9 (.5) 4.9 (.) 0.0 (.08) -0.7 (.) FEL 5.34 (.57) -0.0 (.07) (.5) 0.7 (.7) 3.5 (.04) 0.0 (.06) -0. (.09) ECA 3.0 (.53) -0.6 (.5) (.0) 0.6 (.).0 (.35) -0.5 (.8) (.09) BCA.77 (.5) 0.30 (.) 0.08 (.0) 0.5 (.). (.5) 0.03 (.9) 0.36 (.) CA.47 (.9) 0.08 (.) 0.4 (.) 0.78 (.05) 0.94 (.) -0.4 (.09) 0.40 (.0) ρ( FEA FEL) 0.88 (.05) 0.88 (.05)... (b) Unflered balance of paymens varables Oupu measure: GDP-I-G d (%) ρ ( ) ρ(.y ) ρ d (%) ( ). Y Oupu measure: GDP ρ. Y ρ(.y ) - () () (3) (4) (5) (6) (7) CA 3.79 (.57) 0.0 (.6) 0.0 (.5) 0.9 (.).46 (.38) -0.0 (.5) -0.3 (.4) FEA 6.8 (.57) (.4) -0.0 (.9) 0.4 (.5) 4.49 (.09) 0.0 (.) -0.4 (.) FEL 5.64 (.46) 0.0 (.0) 0.0 (.5) 0.34 (.9) 3.7 (.0) 0.09 (.08) (.0) ECA 3.8 (.5) -0.7 (.7) (.) 0.3 (.5).5 (.36) -0.4 (.8) (.09) BCA.67 (.5) 0.3 (.0) 0.08 (.) 0.66 (.06).73 (.34) 0.0 (.) 0.5 (.) CA.5 (.7) 0.04 (.6) 0.9 (.5) 0.89 (.04).47 (.8) -0.7 (.7) 0.3 (.) ρ( FEA FEL) 0.88 (.04) 0.88 (.04).. Noes: Columns labeled d% ρ( Y) ρ( Y ) ρ- denoe: sandard devaon (n %) correlaon wh domesc oupu correlaon wh foregn oupu auocorrelaon. ρ( x y): correlaon beween x and y. All daa are annual. Y: oupu; RER: real exchange rae (consumpon based). CA : curren accoun (ncludes capal gans/losses); FEA : change n foregn equy asses; FEL : change n foregn equy lables; ECA FEA FEL [ BCA ]: equy [bond] componen of curren accoun; CA : convenonal curren accoun. ample perods--curren accoun: ; oupu real exchange rae: ascs for CA FEA FEL ECA BCA CA peran o seres ha were expressed n uns of U oupu and normalzed by a fed geomerc rend of U oupu. Fgures n parenheses are sandard errors (GMM based assumng 5-h order seral correlaon n resduals). Underlned correlaons are sascally sgnfcan a 0% level (wo-sded es). Panel (a) [Panel (b)] uses curren accoun varables ha were HP flered [no flered]; n boh Panels Y and RER were logged and HP flered. 7

28 Table 3. Properes of IIP daa for 7 OECD economes (HP flered seres) andard devaons (%) Y CA FEA FEL ECA BCA (a) Oupu measure: GDP-I-G 8 Auocorrelaons CA Y CA FEA FEL ECA BCA () () (3) (4) (5) (6) (7) (8) (9) (0) () () (3) (4) (5) AU AT CA CH DE DK E FI FR UK IT JA NL NZ PT W U Medan Mean Corr ( FEA Corrs. wh domesc oupu Correlaons wh foregn oupu FEL) CA FEA FEL ECA BCA CA Y CA FEA FEL ECA BCA CA () () (3) (4) (5) (6) (7) (8) (9) (0) () () (3) (4) AU AT CA CH DE DK E FI FR UK IT JA NL NZ PT W U Medan Mean CA

29 Table 3 cd.--- (b) Oupu measure: GDP Oupu: Corrs. wh domesc oupu Correlaons wh foregn oupu %d Auocor. CA FEA FEL ECA BCA CA Y CA FEA FEL ECA BCA CA () () (3) (4) (5) (6) (7) (8) (9) (0) () () (3) (4) (5) AU AT CA CH DE DK E FI FR UK IT JA NL NZ PT W U Medan Mean Noes: All daa are annual. The sample perod for curren accouns dffers across counres: he Col. () (labeled "") n Panel (a) denoes he frs year; he sample ends n 003 excep for DK ('0) and W ('0). ample perod for CA : (for DK: ). ascs ha jus nvolve oupu are based on daa. ee Appendx and Table for defnons of CA FEA FEL ECA BCA CA ; for counry hese varables are expressed n uns of foregn oupu and normalzed by a fed deermnsc geomerc rend of counry oupu (also expressed n uns of foregn oupu). Column labeled Corr( FEA FEL ) shows correlaons beween FEA and FEL. All seres were HP flered (oupu: logged). Underlned correlaons are sascally sgnfcan a a 0% level (wo-sded es GMM based assumng 5-h order seral correlaon n resduals). AU: Ausrala; AT: Ausra; CA: Canada; CH: wzerland; DE: Germany; DK: Denmark; E: pan; FI: Fnland; FR: France; UK: Uned Kngdom; IT: Ialy; JA: Japan; NL: Neherlands; NZ: New Zealand; PT: Porugal; W: weden. 9

30 Table 4. Predcons of model varan : wo equal szed counres (nfne horzon) CRRA uly CARA uly φ =0.6 φ = 0.9 φ =. φ= 0.6 DATA (U) () andard devaons correlaons wh domesc oupu auocorrelaons d% ρ Y ρ - d% ρ Y ρ - d% ρ Y ρ - d% ρ Y ρ - d% ρ Y ρ - () () (3) (4) (5) (6) (7) (8) (9) (0) () () (3) (4) (5) Y RER CA FEA FEL ECA BCA CA r () Mean values (T=) () Correlaons ρ( FEA FEL ) ρ ( r r ) Noes: The Table shows predcons for counry varables. d%: sandard devaons (n %); ρ Y : correlaon wh counry oupu; ρ - : auocorrelaon. φ : elascy of subsuon beween domesc and mpored goods. Y : counry oupu RER : real exchange rae; CA: 's curren accoun; FEA : change n 's foregn equy asses; FEL : change n 's equy lables; ECA FEA FEL : equy componen of 's curren accoun; BCA : j change n 's ne foregn bond holdngs; CA : 's convenonal curren accoun measure (bookvalues); : j fracon of sock ssued by counry ha s held by j; (T=): sock holdng n wo-perod model verson; r : reurn on counry sock. The curren accoun and s componens are normalzed by fed geomerc rend of counry oupu. Cols. -: smulaed sascs; Cols. 3-5: emprcal sascs for U (from Tables and ). Underlned sascs are sascally sgnfcan a a 0% level. All sascs peran o seres ha have been HP flered. Oupu and he real exchange rae were logged before flerng. 30

31 Table 5. Predcons of model varan : counry smaller han counry (nfne horzon) CRRA uly CARA uly φ =0.6 φ = 0.9 φ =. φ= 0.6 DATA (G5) () andard devaons correlaons wh domesc oupu auocorrelaons d% ρ Y ρ - d% ρ Y ρ - d% ρ Y ρ - d% ρ Y ρ - d% ρ Y ρ - () () (3) (4) (5) (6) (7) (8) (9) (0) () () (3) (4) (5) Y RER CA FEA FEL ECA BCA CA ock r () Mean values (T=) (T=) () Correlaons ρ( FEA FEL ) ρ ( r r ) Noes: The Table shows predcons for counry varables. (Varables are expressed n uns of he counry good.) d%: sandard devaons (n %); ρ Y : correlaon wh counry oupu; ρ - : auocorrelaon. φ : elascy of subsuon beween domesc and mpored goods. ee Table 4 for defnons of varables. The curren accoun and s componens are normalzed by fed geomerc rend of counry oupu. Cols. -: smulaed sascs; Cols. 3-5: medan emprcal sascs for G5 economes (see Tables and 3). All sascs peran o seres ha have been HP flered. Oupu and he real exchange rae were logged before flerng. 3

32 Table 6. % Impac responses o one-sandard-devaon endowmen nnovaons (a) Model varan : equal szed counres C C c c NX p P P CA FEA FEL ECA BCA Y Y (a) CRRA uly φ = 0.6 I) II) (a) CRRA uly φ = 0.9 I) II) (a3) CRRA uly φ =. I) II) (a4) CARA uly φ = 0.6 I) II) (b) Model varan : counry smaller han counry C C c c NX p P P CA FEA FEL ECA BCA Y Y (b) CRRA uly φ = 0.6 I) II) (b) CRRA uly φ = 0.9 I) II) (b3) CRRA uly φ =. I) II) (b4) CARA uly φ= 0.6 I) II) Noes: Rows labeled I): mpac responses o one-sandard-devaon nnovaon o counry endowmen; Rows labeled II): mpac responses o one-sandard-devaon nnovaon o counry endowmen. The Columns labeled C C... show responses of correspondng varables. j c : counry consumpon of good j. NX : counry ne expor (n uns of good ); p : prce of good ( p ); P : prce of sock. ee Table 4 for defnons of oher varables. Responses of C C c c p P P Y Y are expressed as relave devaons from "unshocked" pah. Responses of : dfferences form "unshocked" pah. Responses of counry ne expor and curren accoun (componens) NX CA FEA FEL ECA BCA : expressed as dfferences from "unshocked" pah normalzed by counry preshock oupu. Panels (a) (a) (a3) (a4) [(b) (b) (b3) (b4)] peran o he followng specfcaons of model varan [varan ]: CRRA uly φ= 0.6; CRRA uly φ= 0.9; CRRA uly φ=.; CARA uly φ= 0.6. (Panels (a)- (a4) shows responses of counry ne expor and curren accoun varables whle Panels (b-(b4) show responses of counry ne expor and curren accoun.) All responses have been mulpled by 00.e. expressed n percenage erms. 3

33 K < fl= A r ^3! I < Q'.r & 7.\d:\-' + I I \r o<s a \ \ \ \ \r.._.._.._{ *<s<4 I Fgure. Local sock holdng j (:) for dfferen combnaons of d (elascy of subsuon beween domesc and mpored goods) and o (rsk averson coeffcen) wo-perod model wh equal szed counres (model varan I'. o-'ar=o.9). Downward slopng hck lns - fo=0; upward slopng hck lns -: Il =0; --- : l=l;...: /=0.5; -.-. : =0.

34 <sy lr. ls [-o *<*o^ { <o o]rlr\ -.\ *9 \L r\ \ \\\\ \ \ \ CZ v? - {4 gs /n^ )-\)_ ^/O' - l- Fgure. Counry local sock holdng l for dfferen combnaons of O (elascy of subsuon beween domesc and mpored goods) and o (rsk averson coeffcen) wo-perod model wh counry smaller han counry (model varan '.6r.0= a=0.997d=0.8). Downward slopng hck lns -: =0 ; upward slopng hck lns -: [ -0; ---: r=;...: =0.5; -.-. : r=0.