International Financial Adjustment

Transcription

1 Inernaional Financial Adjusmen Pierre-Olivier Gourinchas Berkeley, CEPR and NBER Hélène Rey Princeon, CEPR and NBER Working Paper Version This Draf: April 3, 2006 Absrac The paper explores he implicaions of a counry s exernal budge consrain o sudy he dynamics of ne foreign asses and exchange rae movemens. We show ha deerioraions in a counry s ne expors or ne foreign asse posiion relaive o heir rend have o be mached eiher by fuure ne expor growh (he rade channel) or by fuure increases in he reurns of he ne foreign asse porfolio, a hihero unexplored valuaion channel. Using a newly consruced daa se on US gross foreign posiions, we find ha sabilizing valuaion effecs conribue as much as 27% of he cyclical exernal adjusmen. Our approach also has asse pricing implicaions. Our measure of exernal imbalance predics ne foreign asse porfolio reurns one quarer o wo years ahead and ne expors a longer horizons. The exchange rae affecs he rade balance and he valuaion of ne foreign asses. I is forecasable in and ou of sample a one quarer and beyond. A one sandard deviaion increase in exernal imbalances predics an annualized 4% depreciaion of he exchange rae over he nex quarer. JEL Codes: E0, F3, F4, G1 Keywords: exernal adjusmen, curren accoun deficis, ne asse posiions, exchange raes, predicabiliy. Alejandro Jusiniano provided excellen research assisance. We hank Agnès Bénassy-Quéré, John Cochrane, Mick Devereux, Darrell Duffie, Charles Engel, Gene Grossman, Dale Henderson, Philip Lane, Barosz Mackowiak, Gian Maria Milesi-Ferrei, Maury Obsfeld, Anna Pavlova, Richard Pores, Chris Sims, Alan Sockman, Lars Svensson, Mark Wason, Mike Woodford, numerous seminar paricipans as well as wo anonymous referees and our edior for deailed commens. This paper is par of a research nework on The Analysis of Inernaional Capial Markes: Undersanding Europe s Role in he Global Economy, funded by he European Commission under he Research Training Nework Program (Conrac No. HPRNŒCTŒ 1999Œ00067). We hank also he NSF for financial suppor (grans SES and SES ). Deparmen of Economics, Universiy of California a Berkeley, Berkeley, CA, USA. Telephone: (1) [email protected]. Web page: socraes.berkeley.edu/ pog Deparmen of Economics and Woodrow Wilson School, Princeon Universiy, Princeon, NJ, USA. Telephone: (1) [email protected]. Web page: hrey

2 1 Inroducion Undersanding he dynamic process of adjusmen of a counry s exernal balance is one of he mos imporan quesions for inernaional economiss. To wha exen should surplus counries expand; o wha exen should defici counries conrac? asked Mundell (1968). These quesions remain as imporan oday as hen. The modern heory focusing on hose issues is he ineremporal approach o he curren accoun (see Sachs (1982) and Obsfeld and Rogoff (1995)). I views he curren accoun balance as he resul of forward-looking ineremporal saving decisions by households and invesmen decisions by firms. As Obsfeld (2001)[p11] remarks, i provides a concepual framework appropriae for hinking abou he imporan and inerrelaed policy issues of exernal balance, exernal susainabiliy, and equilibrium real exchange raes. This approach has yielded major insighs ino he curren accoun paerns ha followed he wo oil price shocks of he sevenies and he large U.S. fiscal deficis of he early eighies. Ye in many insances, is key empirical predicions are rejeced by he daa. Our paper suggess ha his approach falls shor of explaining he dynamics of he curren accoun because i fails o incorporae capial gains and losses on he ne foreign asse posiion. 1 The recen wave of financial globalizaion has come wih a sharp increase in gross cross-holdings of foreign asses and liabiliies. Such leveraged counry porfolios open he door o poenially large wealh ransfers across counries as asse and currency prices flucuae. These valuaion effecs are absen no only from he heory bu also from official saisics. The Naional Income and Produc Accouns (NIPA) and he Balance of Paymens repor he curren accoun a hisorical cos. Hence hey give a very approximae and poenially misleading reflecion of he change of a counry s ne foreign asse posiion. These consideraions are essenial o discuss he susainabiliy of he unprecedenly high US curren accoun deficis. According o our calculaions, he US experienced a srong deerioraion of is ne foreign asse posiion, from a sizeable credior posiion in 1952 (15% of GDP) o a large debor posiion by he end of 2003 (-24% of GDP) (see Figure 1). Moreover, he US foreign liabiliy o GDP raio has more han quadrupled since he beginning of he 1980s o reach 99% of GDP in 2003, while is foreign asse o GDP increased o 75% of GDP. The ineremporal approach o 1 Some papers have inroduced ime-varying ineres raes (e.g. Bergin and Sheffrin (2000)). Bu mos of hese models eiher assume away predicable reurns and wealh effecs or reproduce complee markes which reduces he curren accoun o an accouning device. Kehoe and Perri (2002) is an ineresing excepion ha inroduces specific forms of endogenous marke incompleeness. See also Kraay and Venura (2000) and Mercereau (2003) for models ha allow invesmen in risky asses wih ineresing empirical predicions. 1

3 he curren accoun suggess ha he US will need o run rade surpluses o reduce his imbalance. We argue insead ha par of he adjusmen can ake place hrough a change in he reurns on US asses held by foreigners relaive o he reurn on foreign asses held by he US residens. Imporanly, his wealh ransfer may occur via a depreciaion of he dollar. Since almos all of US foreign liabiliies are in dollars and approximaely 70% of US foreign asses are in foreign currencies, a back of he envelope calculaion indicaes ha a 10% depreciaion of he dollar represens, ceeris paribus, a ransfer of 5.3% of US GDP from he res of he world o he US. For comparison, he US rade defici on goods and services was only 4.5% of GDP in [Figure 1 abou here] Our approach emphasizes his inernaional financial adjusmen mechanism. We sar from a counry s ineremporal budge consrain and derive wo implicaions. The firs is he link beween a curren shorfall in ne savings and fuure rade surpluses. If oal reurns on ne foreign asses are expeced o be consan, oday s curren accoun deficis mus be compensaed by fuure rade surpluses. This is he radiional rade channel. The second (new) implicaion is a he cener of our analysis. In he presence of sochasic asse reurns which differ across asse classes, expeced capial gains and losses on gross exernal posiions consiue a hihero unexplored valuaion channel. An expeced increase in he reurn on US equiies relaive o he res of he world, for example, ighens he exernal consrain of he Unied Saes by raising he oal value of he claims he foreigners have on he US. We esimae he respecive conribuions of he rade and valuaion channels o he exernal adjusmen process using a newly consruced daa se on US gross foreign posiions. We firs conrol for slow moving rends in expors, impors, exernal asses and liabiliies ha we aribue o he gradual process of rade and financial inegraion. We consruc a measure of exernal imbalances in deviaion from hese rends. I incorporaes informaion boh from he rade balance (he flow) and he foreign asse posiion (he sock). In he daa, we find ha, hisorically, abou 27% of he cyclical inernaional adjusmen of he US is realized hrough valuaion effecs. Our se up has also asse-pricing implicaions. The budge consrain implies ha oday s curren exernal imbalances mus predic eiher fuure expor growh or fuure movemens in reurns of he ne foreign asse porfolio, or boh. We show in secion 3 ha our measure of exernal imbalances conains significan informaion abou fuure reurns on he US ne foreign porfolio 2

4 from a quarer up o wo years ou. A one sandard deviaion increase in exernal imbalances predics an annualized excess reurn on foreign asses relaive o US asses of 17% over he nex quarer. A long horizons, i also helps predic ne expor growh. Hence, a shor o medium horizons, he brun of he (predicable) adjusmen goes hrough asse reurns, while a longer horizons i occurs via he rade balance. The valuaion channel operaes in paricular hrough expeced exchange rae changes. The dynamics of he exchange rae plays a major role since i has he dual role of changing he differenial in raes of reurn beween asses and liabiliies denominaed in differen currencies and also of affecing fuure ne expors. We find in secion 3 ha our measure of oday s imbalances forecass exchange rae movemens a shor, medium and long horizons boh in and ou-of-sample. In paricular, we overurn he classic Meese and Rogoff (1983) resul for he dollar mulilaeral exchange rae. A one sandard deviaion increase in our measure of exernal imbalances predics an annualized 4% depreciaion of he exchange rae over he nex quarer. Our mehodology builds on he seminal works of Campbell and Shiller (1988) and, more recenly, of Leau and Ludvigson (2001) on he implicaion of he consumpion wealh raio for predicing fuure equiy reurns. In conras wih hese papers, however, we also allow for slow-moving srucural changes in he daa capuring increasing rade and financial inegraion. Few papers have hough of he imporance of valuaion effecs in he process of inernaional adjusmen. Lane and Milesi-Ferrei (2002) poin ou ha he correlaion beween he change in he ne foreign asse posiion a marke value and he curren accoun is low or even negaive. They also noe ha raes of reurn on he ne foreign asse posiion and he rade balance end o comove negaively, suggesing ha wealh ransfers affec ne expors. More recenly, Tille (2003) discusses he effec of he currency composiion of US asses on he dynamics of is exernal deb, Corsei and Konsaninou (2004) provide an empirical analysis of he responses of US ne foreign deb o permanen and ransiory shocks, while Lane and Milesi-Ferrei (2004) documen exchange rae effecs on raes of reurn of foreign asses and liabiliies for a cross-secion of counries. None of hese papers, however, provides a quaniaive assessmen of he imporance of he financial and rade channels in he process of inernaional adjusmen nor explores he asse pricing implicaions of he heory. The remainder of he paper is srucured as follows. Secion 2 presens he heoreical framework ha guides our analysis. Empirical resuls are presened in secion 3. We firs quanify he 3

5 imporance of he valuaion and rade channels in he process of exernal adjusmen. We hen explore he asse pricing implicaions of our heory. Secion 4 concludes. 2 Inernaional financial adjusmen. This secion explores he implicaions of a counry s exernal budge consrain and long run sabiliy condiions for he dynamics of exernal adjusmen. We define a measure of exernal imbalances and show ha curren imbalances mus be offse by fuure improvemens in rade surpluses, or excess reurns on he ne foreign porfolio, or boh. We sar wih he accumulaion ideniy for ne foreign asses beween period and + 1 : NA +1 R +1 (NA + NX ) (1) NX represens ne expors, defined as he difference beween expors X and impors M of goods and services. NA represens ne foreign asses, defined as he difference beween gross exernal asses A and gross exernal liabiliies L measured in he domesic currency, while R +1 denoes he (gross) reurn on he ne foreign asse porfolio, a combinaion of he (gross) reurn on asses R+1 a and he (gross) reurn on liabiliies Rl +1.2 Equaion (1) saes ha he ne foreign posiion improves wih posiive ne expors and wih he reurn on he ne foreign asse porfolio. 3 To explore furher he implicaions of equaion (1), a naural sraegy consiss in observing ha, along a balanced-growh pah, he raios of expors, impors, exernal asses and liabiliies o wealh are all saisically saionary. 4 In ha case, one could follow he mehodology of Campbell and Shiller (1988) and Leau and Ludvigson (2001) and log-linearize equaion (1) around he seady sae mean raios o obain an approximae exernal consrain. 5 For he U.S., however, we face he immediae problem ha he raios of expors, impors, exernal asses and liabiliies o wealh are no saionary over he poswar period. As figure 2 indicaes, he variables Z /W, where 2 In equaion (1), ne foreign asses are measured a he beginning of he period. This iming assumpion is innocuous. One could insead define NA as he sock of ne foreign asses a he end of period, i.e. NA +1 = R +1NA. The accumulaion equaion becomes: NA +1 = R +1 NA + NX In pracice, ne foreign asses could also change because of unilaeral ransfers, capial accoun ransacions or errors and omissions. Transfers and capial accoun ransacions are ypically small for he US, while errors and omissions are excluded from he financial accoun in he BEA s esimaes of he US Inernaional Invesmen Posiion. We absrac from hese addiional erms. See Gourinchas and Rey (forhcoming 2006) for deails. 4 For insance, in a Meron-ype porfolio allocaion model, he porfolio shares A /W and L /W are saionary as long as gross asses and liabiliies are no perfec subsiues. 5 See Appendix A for a deailed derivaion along hese lines. 4

6 Z {X, M, A, L } and W denoes domesic wealh, exhibi a srong upward rend. 6 Where are hese rends coming from? A naural explanaion is ha hey represen srucural changes in he world economy, such as financial and rade globalizaion. Inernaional financial inerdependence has grown remendously among indusrial counries. In he pas weny years, for example, gross asses and liabiliies have ripled as a share of GDP. 7 This increased financial inegraion has been brough abou in paricular by he phasing ou of he Breon-Woods-inheried resricions on inernaional capial mobiliy and by fas progress in elecommunicaion and rading echnologies. In parallel, rade flows have also sizably increased, spurred by declines in uni ranspor coss, and he developmen of mulinaional companies. 8 Indeed, looking a inernaional financial inegraion from a hisorical perspecive (see for example Obsfeld and Taylor (2004)), capial mobiliy increased beween 1880 and 1914; decreased beween he Firs World War and he end of he Second World War; and has been increasing since hen. [Figure 2 abou here] The approach we develop in his paper has nohing o say abou hese srucural changes. Henceforh, we sudy he process of inernaional adjusmen around hese slow-moving rends. Formally, we make he assumpion ha he ineremporal budge consrain holds along hese rends. This is a naural assumpion since here are no reason o hink ha long-run srucural shifs in goods and financial marke inegraion lead he U.S. o violae is budge consrain in he absence of shocks. Under ha assumpion, we show ha we can purge he daa from he rend componen in Z /W and concenrae on he flucuaions of he ne asse and ne expor variables in deviaion from hese rends Log-linearizaion of he exernal consrain Formally, using lower-case variables o denoe he logarihm of upper-case variables (z ln Z), and o denoe firs differences ( z +1 z +1 z ), we make he following assumpions: 6 Formal ess confirm he visual impression. Simple ADF-ess of he non-saionariy of ln Z /W fail o rejec he null of uni roo for all four variables while he Kwiakowski, Phillips, Schmid and Shin (1992) s es of saionariy rejecs mean saionariy a he 1% level. 7 For he US, gross exernal asses (resp. liabiliies) increased from 30% (resp. 22%) of GDP in 1982, o 75% (resp. 99%) in For he US, he raio of expors (resp. impors) over GDP increased from 5.3% (resp. 4.3%) in 1952, o 9.8% (resp. 14.1%) in An analogy migh help: our enerprise is parallel o he business cycle lieraure which separaes rend growh from medium frequency flucuaions and focuses exclusively on he laer. I differs in ha he rends we consider have considerably lower frequency. Secion 3 discusses our approach o derending in more deail. 5

7 Assumpion 1 Le z {x, m, a, l } and w be sochasic processes. (a) The variables z w admi he following decomposiion: z w = lnµ zw + ǫ z (2) where lnµ zw represens he rend and ǫ z he saionary componens of z w. (b) The rend componens µ zw converge asympoically o a consan value: lim µzw = µ zw Assumpion 2 The growh rae of domesic wealh w +1 is saionary wih seady sae mean value lnγ. Assumpion 3 The reurn on gross asses R+1 a, gross liabiliies Rl +1 and he ne foreign asse porfolio R +1 are saionary wih a common seady sae mean value R ha saisfies R > Γ. Assumpion 4 The exernal consrain (1) holds along he rend, i.e.: ( ) ( +1 µ lw +1 = R/Γ µ lw + µ xw ) µ mw (3) Assumpion 1-(a) decomposes he variables of ineres ino a rend and a saionary componen. Assumpion 1-(b) allows differen variables o have differen rends in he sample, as observed on Figure 2 (he figure repors our esimaes of he rends µ zw as well as he deviaions ǫ z ). Togeher wih assumpion 2, i imposes ha all variables evenually grow a he same rae Γ along a balancedgrowh pah. We view hese resricions as very mild: hey simply rule ou he implausible siuaion where, e.g., he rae of growh of exernal asses would permanenly exceed he rae of growh of he economy. On he oher hand, hey allow for a permanen increase in he raio of gross asses o wealh, as observed in he daa. The assumpion ha he long-erm growh rae of he economy is lower han seady-sae raes of reurn (assumpion 3) is a common equilibrium condiion in many growh models. In our conex, i has an inuiive inerpreaion: manipulaing equaion (1), one can show ha if assumpion 3 holds, he seady sae mean raio of ne expors o ne foreign asses NX/NA saisfies NX/NA = ρ 1 < 0 (4) where ρ Γ/R < 1. In words, counries wih long run credior posiions (NA > 0) should run rade deficis (N X < 0) while counries wih seady sae debor posiions (N A < 0) should run rade surpluses (N X > 0). 6

8 Assumpion 4 is quie naural: i implies ha, absen any shocks, he U.S. would sill face is exernal consrain, bu now evaluaed a he mean growh-adjused reurn R/Γ. 10 We discuss is empirical validiy in deails in secion 3. The following lemma esablishes ha under he above assumpions we can derive a simple and inuiive log-linear approximaion of he exernal budge consrain. Lemma 1 Define nx µ x ǫ x µ m ǫ m, na µ a ǫ a µ l ǫ l and ˆr +1 µ a +1 ra +1 µl +1 rl +1. Under assumpions 1-4, a firs-order approximaion of he exernal consrain (1) saisfies: where na +1 1 ( ) 1 na + (ˆr +1 w +1 ) 1 nx (5) ρ ρ. µ x = µ a = µ xw µ xw µ mw µ lw ρ 1 + µxw ; µ m = µ x 1; ; µ l = µ a 1; µ mw µ lw. Proof. See appendix A. The weighs µ z are no consan bu converge asympoically o a consan µ z. Similarly, he growh-adjused discoun facor ρ is also ime varying and converges asympoically o ρ. µ x represens he (rend) share of expors in he rade balance. Similarly, µ a denoes he (rend) share of asses in he ne foreign asses. 11 The variable nx is a linear combinaion of he saionary componens of (log) expors and impors o wealh raios ha we shall call, wih some abuse of language, ne expors. In he same fashion, na is a linear combinaion of he saionary componens (log) asses and liabiliies o wealh raios, ha we call, also wih some abuse of language, ne foreign asses. Finally, ˆr +1, is an approximaion of he ne porfolio reurn, i.e. a linear combinaion of he (log) reurn on asses r a +1 lnra +1 and he (log) reurn on liabiliies r+1 l lnrl +1. Equaion (5) carries he same inerpreaion as equaion (1) wih a few differences. Firs, i involves only he saionary componen ǫ z of he raios lnz /W ; second, hese saionary componens are muliplied by ime-varying weighs µ z ha reflec he rends in he daa; finally, 10 The assumpion of consan reurns along he rends simplifies he derivaion and can be relaxed if we assume differen mean reurns on asses and liabiliies. In Appendix A, we show ha his does no aler our analysis subsanially. Gourinchas and Rey (forhcoming 2006) show ha he reurn on US exernal asses consisenly exceeds he reurn on gross liabiliies. 11 These rend-weighs are well-defined since µ lw and µ xw µ mw almos everywhere in our sample. 7

9 everyhing is normalized by wealh, hence he rae of reurn ˆr +1 is adjused for he growh rae of wealh ( w +1 ). 2.2 A measure of exernal imbalances Equaion (5) simplifies drasically in he special case where he rend componens µ zw have a common -possibly ime-varying- growh rae. In ha case, he weighs µ z are consan, equal o heir asympoic value µ z and ρ is consan and equal o ρ. This is an imporan case for wo reasons. Firs, from assumpion 1, his is he relevan case asympoically. Second, and more imporanly, we show in secion 3 ha assuming consan weighs provides a robus and accurae approximaion of he general case. 12 Hence we make he following assumpion: Assumpion 5 The rend componens admi a common, possibly ime varying, growh rae: for z {x, m, a, l }, µ zw = µ zw µ. We obain he following resul: Lemma 2 Under assumpions 1-5, a firs-order approximaion of he exernal consrain (1) saisfies: where: nxa +1 1 ρ nxa + r +1 + nx +1 (6) nxa µ a ǫ a µ l ǫ l + µ x ǫ x µ m ǫ m (7) nx +1 µ x ǫ x +1 µ m ǫ m +1 w +1 (8) r +1 µ a r a +1 µ l r l +1 (9) Proof. See appendix A. nxa combines linearly he saionary componens of expors, impors, asses and liabiliies. I is a well-defined measure of cyclical exernal imbalances. Unlike he curren accoun, i incorporaes informaion boh from he rade balance (he flow) and he foreign asse posiion (he sock). Since i is defined using he absolue values of he weighs µ z, nxa always increases wih asses and expors and decreases wih impors and liabiliies. nx +1 represens ne expor growh beween and +1, while he reurn r +1 is defined so as o increase wih reurn on foreign asses and decrease wih he reurn on foreign liabiliies. 13 Jus 12 I is imporan o realize ha he assumpion ha he weighs are consan does no imply ha z w is saionary. I only imposes a common -and ime-varying- rend growh rae for X, M, A and L. 13 The erm in w +1 eners he definiion of nx +1 because ǫ x (resp. ǫ m ) measure he saionary componen of he raio of expors (resp. impors) o wealh. 8

10 like (1) and (5), equaion (6) shows ha a counry can improve is ne foreign asse posiion eiher hrough a rade surplus ( nx +1 > 0) or hrough a high reurn on is ne foreign asse porfolio (r +1 > 0). We can solve equaion (6) forward under he no-ponzi condiion ha nxa canno grow faser han he seady sae growh adjused ineres rae: Assumpion 6 nxa saisfies he no-ponzi condiion We obain: lim j ρj nxa +j = 0 wih probabiliy one Proposiion 1 Lemma 2 and assumpion 6, imply ha he ineremporal exernal consrain saisfies approximaely: Proof. See appendix A. + nxa ρ j [r +j + nx +j ] (10) j=1 Finally, since equaion (10) mus hold along every sample pah, i mus also hold in expecaions: Corollary 1 Under he condiions for proposiion 1 he ineremporal exernal consrain saisfies approximaely: + nxa ρ j E [r +j + nx +j ] (11) j=1 Equaion (11) is cenral o our analysis. I shows ha movemens in he rade balance and he ne foreign asse posiion mus forecas eiher fuure porfolio reurns, or fuure ne expor growh, or boh. Consider he case of a counry wih a negaive value for nxa, eiher because of a defici in he cyclical componen of he rade balance, or a cyclical ne deb posiion, or boh. Suppose firs ha reurns on ne foreign asses are expeced o be consan: E r +j = r. In ha case, equaion (11) posis ha any adjusmen mus come hrough fuure increases in ne expors: E nx +j > 0. This is he sandard implicaion of he ineremporal approach o he curren accoun. 14 We call his channel he rade channel. We emphasize insead ha he adjusmen may also come from high expeced ne foreign porfolio reurns: E r +j > We call his channel he valuaion channel. Imporanly such 14 See Obsfeld and Rogoff (forhcoming 2006) for an analysis along hese lines. 15 I is of course possible ha some of oday s adjusmen comes from an unexpeced change in asse prices or expors. These unexpeced changes would be refleced simulaneously in he lef and righ hand side of equaion (11). We do no focus on such surprises. 9

11 predicable reurns can occur via a depreciaion of he domesic currency. While such depreciaion cerainly also helps o improve fuure ne expors, he imporan poin is ha i operaes hrough an enirely differen channel: a predicable wealh ransfer from foreigners o domesic residens. While he empirical asse pricing lieraure has produced a number of financial and macro variables wih forecasing power for sock reurns and excess sock reurns in he U.S, o our knowledge, our approach is he firs o produce a predicor of he reurn on domesic asses relaive o foreign asses. The role of he exchange rae can be illusraed by considering he case -relevan for he USwhere foreign liabiliies are denominaed in domesic currency while foreign asses are denominaed in foreign currency. We can hen rewrie r +1 as: r +1 = µ a ( r a +1 + e +1 ) µ l r l +1 π +1 (12) where r a +1 represen he (log) nominal reurns in foreign currency, e +1 is he rae of depreciaion of he nominal exchange rae (measured as he domesic price of he foreign currency) and π +1 is he realized domesic inflaion rae beween periods and + 1. Holding local currency reurns consan, a currency depreciaion increases he domesic reurn on foreign asses, an effec ha can be magnified by he degree of leverage of he ne foreign asse porfolio when µ a > 1. I is imporan o emphasize ha since equaion (10) holds in expecaions bu also along every sample pah, one canno hope o es i. 16 Ye i presens several advanages ha guide our empirical sraegy. Firs, his ideniy conains useful informaion: a combinaion of expors, impors, gross asses and liabiliies -properly measured- can move only if i forecass eiher fuure reurns on ne foreign asses or fuure ne expor growh. The remainder of he paper evaluaes empirically he relaive imporance of hese wo facors in he dynamics of adjusmen and invesigaes a wha horizons hey operae. Second, our modeling relies only on he ineremporal budge consrain and some long run sabiliy condiions. Hence, i is consisen wih mos models. We see his as a srengh of our approach, since i ness any model ha incorporaes an ineremporal budge consrain. More specific heoreical mechanisms can be inroduced and esed as resricions wihin our se up. They will have o be consisen wih our empirical findings regarding he quaniaive imporance of he wo mechanisms of adjusmen and he horizons a which hey operae. Thus our findings provide useful informaion o guide more specific heories. 16 Technically, only equaion (1) is an ideniy. Equaion (11) holds up o he log-linearizaion approximaions if (a) assumpions 1-6 hold and (b) expecaions are formed raionally. 10

12 3 Empirical resuls. 3.1 Measuring Exernal Imbalances In secion 2 we used he ineremporal budge consrain o consruc a measure of exernal imbalances, nxa, defined as a linear combinaion of derended (log) expors (ǫ x ), impors (ǫ m ), gross foreign asses (ǫ a ) and liabiliies (ǫ l ) relaive o wealh. In his secion, we esimae nxa and quanify he share of he adjusmen coming from ne expors and from valuaion effecs using a vecor auoregression (VAR). We hen invesigae he forecasing properies of our measure of exernal imbalance. To implemen empirically our mehodology we use newly consruced quarerly esimaes of he US ne and gross foreign asse posiions a marke value beween 1952:1 and 2004:1, as well as esimaes of he capial gains and oal reurns on hese global counry porfolios. Figure 1 repors ne foreign asses and ne expors, relaive o GDP. A brief descripion of he daa is relegaed o appendix D. 17 We decompose he variables z w ino a low-frequency rend lnµ zw and a saionary componen ǫ z according o equaion (2). µ zw reflecs low frequency srucural changes in he world economy due o rade and financial inegraion. If he wenieh cenury has been characerized by one wave of decreasing globalizaion (from 1913 o 1945), followed by one -unfinished- period of increased globalizaion, i seems appropriae o define he rend componen as a low-pass filer wih a relaively low frequency cu-off. In pracice, we choose o implemen his wih a Hodrick-Presco filer se o filer ou cycles of more han fify years. 18 We noe hree imporan feaures of our filering procedure. Firs, by consrucion, he HP filer removes uni roos from he daa (see King and Rebelo (1993)). Second, since we eliminae only very low frequencies, he variables ǫ z sill conain mos frequency componens. In oher words, our approach enables us o render he daa saionary while keeping mos of he informaion from he ime series. Third, filering ou only very low frequencies miigaes end poin problems common wih wo-sided filers. 19 We per- 17 See Gourinchas and Rey (forhcoming 2006) for a deailed descripion of he daa. 18 To selec he smoohing parameer of he HP filer we impose ha he frequency gain of he filer be equal o 70% a he frequency corresponding o a fify-year cycle. In sandard business cycle applicaions wih quarerly daa, he gain is 70% a 32 quarers (8 years). 19 Sock and Wason (1999) argue for a one-sided HP filer. We obained similar resuls using heir one-sided filer. In finie sample, however, a one-sided filer is problemaic since i acs as a filer wih varying frequency cu-off a differen poins in he sample. A he beginning of he sample, i keeps inside he rend more high frequency componens since i has few observaions o work wih (hink abou compuing a rend wih only wo observaions: necessarily everyhing is kep inside he rend; he HP filer needs a leas four observaions, bu he basic poin remains). As more observaions are added, he frequency cu-off effecively drops, so ha he rend conains less and less high frequency componens for laer observaions in he sample. We dislike he one-sided filer for anoher reason: from he poin of view of in-sample regressions, dropping observaions leads o a less accurae esimae of he rend componen (even if he frequency cu-off was appropriaely mainained). 11

13 formed numerous robusness checks by considering shorer cycles (30 and 40 years), longer cycles (100 years) and he exreme case of linear rends. The exac filer used does no maer provided i akes ou only slow moving rends 20. Figure 2 repors he consruced values for he rend and cycle componens while Figure 3 repors he compued nxa for various filers (30, 40 and 100 years as well as a linear rend). I is immediae ha all esimaes are very close. 21 I is worh pausing here o discuss in more deails how our derending procedure migh affec our empirical resuls. By assuming ha he US exernal consrain holds along he rend (assumpion 4), we purposely absrac from he mechanisms ha ensure ha his rend exernal consrain holds. Our inerpreaion is ha hey are irrelevan for he process of adjusmen which we do sudy in his paper, i.e. he cyclical adjusmen. Clearly, in he sample some significan imbalances are building along hese rends (see figure 2). This raises a number of imporan quesions. Shouldn he exchange rae or oher asse reurns play a role in he rebalancing of hese rend imbalances? If so isn a rend esimaed on he enire sample period already capuring par of he impac of exchange raes on ne foreign asse posiions? These are imporan poins o address. Indeed, US rend-imbalances will need o sabilize a some poin in he fuure. Does his imply ha we are hrowing away relevan informaion wih our derending procedure? There are wo reasons why his issue is no a concern for our empirical work. Firs, suppose ha here is indeed a link beween rend imbalances and fuure exchange rae or asse price movemens. For insance, suppose ha given he large curren US rend imbalances he US dollar does need o depreciae in he fuure. If anyhing, his should reduce he predicive power of our variable nxa, since i is consruced from derended variables. This is especially so given ha we predic he acual (no derended in any way) depreciaion rae of he currency and he acual reurns on he ne porfolio, equiies, ec... (see equaion (11)). Therefore if here is any informaion in he rends ha is relevan for any of hese variables, by aking he rends ou, we are biasing he exercise owards finding no predicabiliy. 22 Second, we only ake ou very slow moving rends (wih cycle of 50 years and more in our 20 Since he differen esimaes of nxa are essenially idenical, his indicaes ha sampling uncerainy is no a relevan issue when using nxa as a regressor. 21 We also experimened wih Chrisiano and Fizgerald (2003) s asymmeric filer and using GDP insead of household wealh in he denominaor. All our resuls are very robus o hese changes and are repored in an appendix available upon reques. 22 Anoher possibiliy is ha our predicabiliy resuls are spurious. For his o be he case, i would have o be ha he predicive power in our regressions does no come from our variable nxa, as we hink i does, bu insead ha nxa is correlaed wih hese rends. Ye we find no correlaion beween he rend and cyclical imbalances: rend imbalances have been increasing more or less monoonically hroughou he sample. By conras nxa is large and negaive in , hen large and posiive in (see figure 4). 12

14 benchmark esimaes). This could sill be a problem o he exen ha real exchange raes oo may exhibi low frequency rends. Bu heories of long run rends in real exchange raes, such as Balassa Samuelson, emphasize he role of produciviy differenials. These models do no have any paricular implicaion for long-run rade balances. The key insigh is ha Balassa Samuelson effecs come from he supply side, independenly from he demand srucure. In urn, he demand srucure conrols wha happens o he rade balance. Hence i is possible o have rending real exchange raes due o produciviy differenials and worsening, improving or unchanged long run rade imbalances, depending upon he specificaion of preferences. A real world example of his is he appreciaion of he Japanese real exchange rae beween he 1950s and he 1990s, which has no been mached by any secular rend in he bilaeral Japan US rade. While, as jus argued, rends in real exchange raes may have no effec on rade balances, hey may, in heory, sill conribue o he valuaion channel by changing he relaive value of gross asses and gross liabiliies. This would have wo implicaions for our analysis. Firs, i would imply ha our derending procedure ils he resuls in favor of he rade channel of adjusmen and agains he valuaion channel: removing he rend par of A and L, we also eliminae heir poenial conribuions o explaining he rend exchange rae. Again, his would bias he exercise agains finding predicabiliy in reurns. To he exen ha we wan o esablish he imporance of he valuaion channel, our resuls should hen be inerpreed as lower bounds on he conribuion of ha channel. Second, a rend valuaion channel would require ha predicable excess reurns persis over very long horizons (basically, a he horizon a which we are derending: 50 years and above). We find his hard o believe. If, as seems more reasonable, predicable excess reurns disappear a hese very long horizons, hen he logical implicaion is ha valuaion effecs canno be playing a role in he rend rebalancing, and he rend in real or nominal exchange raes does no play any role in he valuaion channel eiher. Eiher way, we feel our resuls are quie robus o rends in he exchange rae. To summarize, he null we mainain is one where we remain agnosic abou he role of he exchange rae in eliminaing US rend imbalances. The alernaive where exchange raes would have a role in he rend adjusmen a he horizons we invesigae would bias our exercise again finding forecasabiliy since by derending, we would be hrowing away relevan informaion. To consruc he ne foreign asses na and ne expors nx (see lemma 1) we need esimaes of he ime-varying weighs µ z. Doing so raises wo imporan empirical issues. Firs, since he U.S. goes from being a ne credior/ne exporer o being a ne debor/ne imporer, hese weighs 13

15 exhibi large non-linear variaions, especially in he neighborhood of = µ lw and µ xw = µ mw. Clearly, hese flucuaions dominae he movemens in na and nx bu have lile o do wih he adjusmen process. Second, our variables (especially A, L and W, less so X and M) are measured imprecisely. These measuremen errors ge magnified by he non-lineariy in he weighs. In order o ge around hese issues, we replace he ime varying weighs by heir sample average. Wih consan weighs, corollary 1 applies and we can consruc an approximae measure of exernal imbalances as nxa = µ a ǫ a µ l ǫ l + µ x ǫ x µ m ǫ m (see equaion 7). The benefis of doing so are hreefold. Firs, by fixing he weighs, we reduce he impac of measuremen errors. This makes our empirical exercise much more robus. Second, consan weighs are consisen wih our approach, which focuses on he adjusmen in he deviaions from rend (ǫ z ) as opposed o he inernal dynamics impared by he rends hemselves (µ zw ). Third, our consruced nxa is robus o he changes in sign of he ne foreign asses and ne expors variables. The drawback is ha we are losing some informaion. We diagnose how serious his loss is in hree seps. Firs, we direcly check he accuracy of equaion (6) and find a small and saionary approximaion error (see below). Second, using our VAR esimaes, we show ha his approximaion error is condiionally uncorrelaed wih he variables of ineres (see secion 3.2). Third, we show ha, even wih consan weighs, our measure of exernal imbalances performs very well and predic fuure reurns and exchange raes in and ou of sample (secions ). Hence, i seems ha lile relevan informaion is omied by seing he weighs o heir sample average. 23 Using quarerly daa from he firs quarer of 1952 o he firs quarer of 2004, we obain he following esimaes: µ a = 8.49 ; µ l = 7.49 ; µ x = 9.98 ; µ m = 10.98; ρ = 0.95 and consruc nxa using equaion (7) o obain: 24 nxa = 0.85 ǫ a 0.75 ǫ l + ǫ x 1.1 ǫ m We observe ha nxa pus similar weighs on gross asses, gross liabiliies, gross expors and gross impors. The resuling nxa is repored on Figure 5(a). Several feaures are noeworhy. Firs, 23 As a robusness check, we also compued differen weighs for he firs par of he sample (beween 1952 and 1973) and he second par of he sample (pos Breon Woods). The resuls are very similar and available from he auhors upon reques. 24 In his expression, we normalize nxa so ha he weigh on expors is uniy. This is a naural normalizaion since i implies ha nxa is expressed in he same unis as expors : i measures approximaely he percenage increase in expors necessary o resore exernal balance. 14

16 we observe a paern of growing cyclical imbalances, saring in , hen and 2001 o he presen. Second, he cyclical imbalance of 2003 was in fac slighly smaller han he one of he mid-80s despie burgeoning rade deficis since he end of he 90s, indicaing ha mos of he addiional imbalances are rend imbalances. According o he figure, he cyclical exernal imbalance represened abou 25.0% of expors in 1985:4. By conras, he exernal imbalance represened only 18.1% of expors in 2003:1 and has since shrunk by more han half o 7.6% as of 2004:1. [Figure 3 abou here] [Figure 4 abou here] Table 1 repors some summary saisics on nxa, as well as some asse reurns and he rae of depreciaion of he relevan financially weighed exchange rae, consruced using FDI counry weighs (see appendix D). All he reurns are oal quarerly reurns, including capial gains and losses. Table 1 indicaes ha nxa and he reurn on he porfolio on ne foreign asses are quie volaile. The sandard deviaion of expor and impor growh (4.28 and 3.81) is much smaller han he sandard deviaion of he ne porfolio reurn (13.16). The reurn on gross asses is equivalen o he reurn on gross liabiliies (each abou 0.78% per quarer), and also o he reurn on he ne foreign posiion (0.72% per quarer). Looking a he subcomponens, domesic and foreign dollar equiy and foreign direc invesmen average reurns r le, r ae r lf and r af exceed average bond reurns r ad and r ld, in urn larger han reurns on shor erm asses r ao and r lo. As is well-known, he volailiies saisfy he same ranking. The exchange rae exhibis a smaller volailiy han equiy reurns, comparable o he volailiy of bond reurns. Finally, mos reurns, expors and impors growh and he exchange rae exhibi lile auocorrelaion. By conras, nxa exhibis subsanial serial correlaion (0.92). [Table 1 abou here] Le us now revisi he validiy of equaion (6) as an approximaion o he exernal consrain (1). We provide direc evidence ha he assumpions behind lemma 2 do no do much violence o he daa by looking a he approximaion error from equaion (6). Since he saionary componens ǫ z are consruced separaely for each variable z, here is no reason, a priori, o expec equaion (6) o hold exacly unless i represens an accurae characerizaion of he exernal dynamics around 15

17 he rends. Figure 4 repors his approximaion erm ε = nxa 1 ρ nxa 1 r nx defined as he difference beween he lef and righ hand side of (6) (panel c), ogeher wih nxa (panel a) and he flow erm r + nx (panel b). As can be seen immediaely from he figure, his error erm is quie small relaive o boh nxa and he flow componen, for mos of he sample period. 25 We emphasize ha nohing in our empirical approach ensures ha his erm remains small. Tha i is so validaes our empirical procedure. A second check on he validiy of our assumpions relies on he VAR esimaes presened in he nex subsecion. There, we es direcly he resricion ha he error erm is condiionally uncorrelaed wih he variables of ineres: E 1 [ε ] = The financial and rade channels of exernal adjusmen nxa is a heoreically well-defined measure of cyclical exernal imbalances. By decomposing i ino a reurn and a ne expor componen and observing heir variaion over ime, we can gain clear insighs regarding he relaive imporance of he rade and financial adjusmen channels. We rewrie equaion (11) as: nxa + = ρ j E r +j j=1 nxa r + nxa nx + j=1 ρ j E nx +j (13) nxa r is he componen of nxa ha forecass fuure reurns, while nxa nx is he componen ha forecass fuure ne expors growh. We follow Campbell and Shiller (1988) and consruc empirical esimaes of nxa r and nxa nx using a VAR formulaion. Specifically consider a VAR(p) represenaion for he vecor y = (r, nx, nxa ). Appropriaely sacked, his VAR has a firsorder companion represenaion: ȳ +1 = A ȳ +ǫ Equaion (13) implies ha we can consruc nxa r and nxa nx as: nxa r nxa nx = ρe ra (I ρa) 1 ȳ = ρe nxa (I ρa) 1 ȳ where e r (resp. e nx ) is a dummy vecor ha selecs r (resp. nx ) and I is he ideniy marix. We represen he ime pahs of nxa r and nxa nx in figure 5-(a) Wih a zero mean and a sandard deviaion of 1.67%, i is 7 imes less volaile han nxa and 2.5 imes less volaile han r + nx (s.d. 4.20%). The correlaion beween he error erm and he flow erm r + nx is also very small (0.05). 26 where ȳ = (y,y 1,...,y p+1). See Appendix B for a deailed derivaion. 27 We use p = 1, according o sandard lag selecion crieria. 16

18 Several feaures are noeworhy. Firs, nxa r and nxa nx are posiively correlaed: he valuaion and rade effecs are muually reinforcing, underlining he sabilizing role of capial gains in he exernal adjusmen of he US. 28 Given our normalizaion of nxa, valuaion effecs represen he equivalen of a 7.04% conemporaneous increase in expors in 1986:3 (ou of 25.89%) and 4.85% in 2003:1 (ou of 18.17%). Second, he esable resricion e nxai + (e r + e nx e nxa)ρa = 0 should be saisfied. 29 This resricion is equivalen o a es ha he error erm ε +1 is condiionally uncorrelaed wih he variables of ineres: E [ε +1 ] = 0. As discussed above, his provides our second es of he validiy of our assumpions and he qualiy of he approximaion (6). We use a Wald es and find a χ 2 equal o Wih hree resricions, he p-value is 0.986, so we canno rejec he ineremporal equaion (13). 30 This, and he fac ha nxa (predic) nxa r + nxa nx Figure 5-(a)) show he excellen overall qualiy of our approximaion. is very close o nxa (see Finally, following he same mehodology, figure 5-(b) decomposes nxa r ino a gross asse and gross liabiliy reurn componens (nxa ra and nxa rl ). The figure illusraes ha financial adjusmen comes mosly from excess reurns on gross asses; he conribuion of expeced reurns on gross liabiliies -while posiive- is always much smaller. [Figure 5 abou here] We are also ineresed in he long run properies of nxa. Following Cochrane (1992), we use equaion (13) o decompose he variance of nxa ino componens reflecing news abou fuure porfolio reurns and news abou fuure ne expor growh. Given ha nxa r and nxa nx correlaed, here will no be a unique decomposiion of he variance of nxa ino he variance of nxa r and he variance of nxa nx. Ye, an informaive way of decomposing he variance is o spli he covariance erm, giving half o nxa r and half o nxa nx, as follows: 1 = cov (nxa, nxa) var (nxa) β r + β nx = cov (nxar, nxa) var (nxa) + cov ( nxa nx, nxa ) var (nxa) 28 This feaure may be specific o he US. In he case of emerging markes, valuaion and rade effecs would likely be negaively relaed since gross liabiliies are dollarized. 29 This resricion is obained by lef-muliplying nxa = nxa r + nxa nx by (I ρa). 30 The prediced coefficiens for e nxa = [1, 0, 0] are [0.906, 0.012, 0.004]. are (14) 17

19 This decomposiion is equivalen o looking a he coefficiens from regressing independenly nxa r and nxa nx on nxa. The resuling regression coefficiens, β r and β nx represen he share of he uncondiional variance of nxa explained by fuure reurns or fuure ne expor growh. 31 Table 2 repors he decomposiion for differen values of ρ beween 0.94 and For our benchmark value ρ = 0.95, we ge a breakdown of 64% (ne expors) and 27% (porfolio reurns) accouning for 91% of he variance in nxa. The resuls are sensiive o he assumed discoun facor. Lower (higher) values of ρ increase (decrease) he conribuion of porfolio reurns. 32 For ρ = 0.94, we find ha porfolio reurns accoun for 29% of he oal variance while for ρ = 0.96 heir conribuion decreases o 24%. The general flavor of our resuls is no alered by hose robusness checks. These findings have imporan implicaions. Firs, financial adjusmen accouns for approximaely 27% of cyclical exernal adjusmen, even a long horizons, while 64% comes from movemens in fuure ne expors. Thus, our findings indicae ha valuaion effecs do no replace he need for an ulimae adjusmen in ne expors via expendiure swiching or expendiure reducing mechanisms, a poin developed in deail in Obsfeld and Rogoff (forhcoming 2006). Wha our esimaes indicae, however, is ha valuaion effecs profoundly ransform he naure of he exernal adjusmen process. By absorbing 25-30% of he cyclical exernal imbalances, valuaion effecs subsanially relax he exernal budge consrain of he US. Using he same mehodology, lines 3 and 4 of Table 2 furher decompose he variance of nxa r ino he conribuions of reurns on gross asses and liabiliies. For he sandard specificaion, we obain a breakdown of roughly 21% (β ra ) and 6% (β rl ) making up he 27% oal conribuion of he reurns o he cyclical exernal adjusmen. These findings confirm Figure 5-(b): gross asse reurns accoun for he bulk of he variance, while reurns on gross liabiliies, which are all in dollars, are much less responsive. 33 [Table 2 abou here] 31 This is no an orhogonal decomposiion, so erms less han 0 or greaer han 1 are possible. Empirically, he sum of β r and β nx can differ from 1 if he approximaion nxa = nxa r + nxa nx is no saisfied. As we argued above, he qualiy of he approximaion is very good. 32 Whenever we perform comparaive saics on he discoun rae ρ we adjuse µ a accordingly. The corresponding values are presened in line 6 of Table 2. Noe ha ρ conrols also he seady sae raio of ne expors o ne foreign asse (equaion (4)). 33 If we allow for differen mean reurns on asses and liabiliies along he rends, as described in AppendixA, he resuls remain qualiaively similar: in he long run, ne expors accoun for 58% of he process of inernaional adjusmen while valuaion effecs accoun for 26%. 18

20 3.3 Forecasing quarerly reurns: he role of valuaion effecs Equaion (11) indicaes ha nxa should help predic eiher fuure reurns on he ne foreign asse porfolio r +j, or fuure ne expor growh nx +j, or boh. This secion looks specifically a he predicive power of nxa for fuure reurns on he ne foreign asse porfolio r +j a he quarerly horizon. Table 3 repors a series of resuls using nxa as a predicive variable. Each column of he able repors a regression of he form: y +1 = α + β nxa + δ z + ǫ +1 where y +1 denoes a quarerly reurn beween + 1 and, z denoes addiional conrols shown elsewhere in he lieraure o conain predicive power for asse reurns or exchange raes and ǫ +1 is a residual. Looking firs a Panel A of Table 3, we see ha nxa has significan forecasing power for he ne porfolio reurn r +1 one quarer ahead (column 1). The R 2 of he regressions is 0.10 and he negaive and significan coefficien indicaes ha a posiive deviaion from rend predics a decline in ne porfolio reurn ha is qualiaively consisen wih equaion (11). We observe also ha here is essenially no forecasing power from eiher lagged values of he ne porfolio reurn (column 2), he difference beween domesic and foreign dividend-price raios (column 3), or he deviaion from rend of ne expors, xm, defined as ǫ x ǫ m (column 4). We emphasize ha he predicive power of he regression is economically large: he coefficien of 0.36, coupled wih a sandard deviaion of nxa of 11.94% indicaes ha a one-sandard deviaion increase in nxa predics a decline in he ne porfolio reurn of abou 430 basis poins over he nex quarer, equivalen o abou percen a an annual rae. Panel A of Table 3 also repors he resuls of similar regressions for he excess equiy oal reurn, defined as he quarerly dollar oal reurn on foreign equiy r ae (a subcomponen of US asses) minus he quarerly oal reurn on US equiy r le (a subcomponen of US liabiliies). Since r a is very correlaed wih r ae and r l is very correlaed wih r le, i is naural o invesigae he predicive abiliy of our variables on his measure of relaive sock marke performance. 34 To he exen ha he average weighs µ a and µ l are imperfecly measured, he degree of leverage of he ne foreign asse porfolio could also be mismeasured, which could influence our resuls on oal ne porfolio reurns. We are able o confirm our resuls wih his more parial bu also arguably 34 The correlaions are and respecively. 19

21 less noisy measure of ne foreign asse porfolio reurns. There is significan one-quarer ahead predicabiliy of he excess reurn of foreign socks over domesic socks (column 5). The R 2 of he regression is equal o 0.07 and he sign of he saisically significan coefficien is negaive, as expeced. Again, alernae regressors such as lagged reurns (column 6), dividend price raios (column 7), or deviaions of he rade balance from rend (column 8) do no ener significaively. The predicive impac of nxa on r ae +1 rle +1 is smaller han on r +1, ye i is sill highly economically significan. Wih a coefficien of -0.13, a one-sandard deviaion increase in nxa predics a decline in excess reurns of 155 basis poins over he nex quarer, or 6.21 percen annualized. I is imporan o emphasize ha hese regressions indicae significan predicabiliy for he one-quarer ahead relaive sock marke performance! [Table 3 abou here] We also invesigae separaely he predicabiliy paern for he dollar and foreign currency reurn on gross asses and he dollar reurn on gross liabiliies. As shown in Table 4 (panel B), we find no evidence of predicabiliy for he reurn on gross liabiliies, and limied evidence of predicabiliy for he reurn on gross asses in local currencies (bu no in dollars) 35. In Panel C of Table 4, we find very weak evidence of predicabiliy of reurns on foreign equiies in dollars (bu no in local currencies). These mixed resuls indicae ha he correlaion srucure beween reurns on gross asses and gross liabiliies plays an imporan role for undersanding he adjusmen of ne foreign asse reurns. [Table 4 abou here] 3.4 Exchange rae predicabiliy one quarer ahead The resuls from Panel A raise an obvious and analizing quesion: could i be ha he predicabiliy of he dollar reurn on ne asses arises from predicabiliy in he exchange rae? Afer all, a depreciaion of he exchange rae increases he reurn on gross asses relaive o he reurn on gross liabiliies. Panel B of Table 3 presens esimaes using boh our FDI-weighed effecive exchange rae ( e +1 ) and he Federal Reserve rade-weighed rade-weighed mulilaeral exchange rae for major currencies ( e T +1 ). The sample covers he pos Breon Woods period, from 1973:1 o 2004:1. 35 We define he reurn in local currencies as he dollar reurn minus he financially weighed exchange rae. 20

22 We observe firs ha nxa conains srong predicive power for boh exchange rae series (columns 1 and 5). The coefficien is negaive (around for boh series) and significan, implying ha a negaive nxa predics a subsequen depreciaion of he dollar agains major currencies. The R 2 are high (0.09 and 0.11 respecively) and he effecs are also economically large: a onesandard deviaion decrease in nxa predics a 4.30% (annualized) increase in he expeced rae of depreciaion of he mulilaeral exchange rae over he subsequen quarer. Our resuls are robus o he inclusion of he hree-monh ineres rae differenial i 1 i 1 where we consruc i using 1997 weighs from he benchmark US Treasury survey (column 4 and 8)). As before, we also find ha he predicive power of xm on he exchange rae does no survive he inclusion in he regression of our variable nxa (columns 3 and 7). Finally, Table 5 ess he quarer-ahead predicive power of nxa 1 for bilaeral nominal raes of depreciaion of he dollar agains he Serling, he Japanese yen, he Canadian dollar he German D-Mark (Euro afer 1999) and he Swiss Franc. We find a modes predicive power for all currencies excep he Canadian dollar, wih R 2 ranging from 0.02 o The larges significan effec is on he DM/Euro and Swiss Franc, and he weakes on he Japanese yen. [Table 5 abou here] Overall, hese resuls are sriking. Tradiional models of exchange rae deerminaion fare paricularly badly a he quarerly-yearly frequencies. Our approach, which emphasizes a more complex se of fundamenal variables, finds predicabiliy a hese horizons Long horizon forecass: he imporance of ne expor growh and of he exchange rae A naural quesion is wheher he predicive power of our measure of exernal imbalances increases wih he forecasing horizon. According o equaion (11), nxa could forecas any combinaion of r and nx a long horizons. We invesigae his quesion by regressing k horizon reurns 36 There is one poenial cavea o our resuls: ess of he predicabiliy of reurns may be invalid when he predicing variable exhibis subsanial serial correlaion. The preesing procedure of Campbell and Yogo (2006, forhcoming) indicaes no problem in our case for any of he forecasing regressions of his secion, excep for he ne reurns. In all cases, he correlaion beween he innovaion in nxa and he residual from he predicabiliy regression is smaller han in absolue value, indicaing lile size disorion (i.e. a 5% nominal -es has a rue size of 7.5% a mos). For ne reurns, he coefficien is 0.167, suggesing a poenially larger size disorion. Bu performing Campbell and Yogo s es leads us o rejec he hypohesis of no predicabiliy a he 5% level. Therefore all our predicabiliy regressions are robus. 21

23 y,k ( k i=1 y +i) /k beween and + k on nxa. Table 6 repors he resuls for forecasing horizons ranging beween one and weny-four quarers. When he forecasing horizon exceeds 1, he quarerly sampling frequency induces (k 1) h order serial correlaion in he error erm. Accordingly, we repor Newey-Wes robus sandard errors wih a Barle window of k 1 quarers. For each horizon we repor wo regressions. The firs one uses nxa 1 as he regressor, as before. Is explanaory power is summarized by R 2 (1). In he second one, we used direcly ǫ z as regressors (nxa is a linear combinaion of he ǫ z s), o allow for he fac ha he seady sae weighs of expors, impors, asses and liabiliies may be measured wih errors. We repor only one summary saisic for his second regression, R 2 (2). Table 6 indicaes ha he in-sample predicabiliy increases up o an impressive 0.26 (0.34 wih separae regressors) for ne foreign porfolio reurns a a four-quarer horizon, hen declines o 0.02 or 0.16 a weny four quarers. A similar paern is observed for oal excess equiy reurn. These resuls sugges ha he financial adjusmen channel operaes a shor o medium horizons, beween one quarer and wo years. I hen declines significanly and disappears in he long run. As shown in secion (3.2), is overall conribuion o exernal adjusmen amouns o roughly 27%. [Table 6 abou here] The picure is very differen when we look a ne expor growh. We find ha nxa 1 predics a subsanial fracion of fuure ne expor growh in he long run: he R 2 is 0.58 a 24 quarers (0.79 wih hree regressors!). This resul is consisen wih a long run adjusmen via he rade balance. A large posiive exernal imbalance predics low fuure ne expor growh, which resores equilibrium. The classic channel of rade adjusmen is herefore also a work, especially a longer horizons (8 quarers and more). Looking a exchange raes, we find a similarly srong long run predicive power on he rae of depreciaion of he dollar. The R 2 increases up o 0.41 (0.55 wih hree regressors!) a 12 quarers. There is significan predicive power a shor, medium and long horizons. 37 Taken ogeher, hese findings indicae ha wo dynamics are a play. A horizons smaller han wo years, he dynamics of he porfolio reurns seem o dominae, and exchange rae adjusmens 37 Again, he persisence of nxa in he predicive regressions is no an issue. Performing he pre-es of Campbell and Yogo (2006, forhcoming), we find ha here is no problem for he exchange rae nor for he oal excess equiy reurns. In he case of ne expors and ne reurns here is some size disorsion. When we perform Cambpell and Yogo s es however we can rejec he hypohesis of no predicabiliy a he 5% level. Once again, his implies ha our predicabiliy regressions are robus. 22

24 creae valuaion effecs ha have an immediae impac on exernal imbalances. A horizons longer han wo years, here is lile predicabiliy of asse reurns. Bu here is sill subsanial exchange rae predicabiliy, which goes hand in hand wih a correcive adjusmen in fuure ne expors. 38 Hence, because he exchange rae plays key roles boh in he financial adjusmen channel and in he rade adjusmen channel i is predicable a shor, medium and long horizons. The sign of he exchange rae effec is similar a all horizons since an exchange rae depreciaion increases he value of foreign asses held by he US and affecs ne expors posiively. The evenual adjusmen of ne expors is consisen wih he predicions arising from expendiure swiching models. Because hese adjusmens ake place over a longer horizon, heir influence on he shor erm dynamics is raher limied. To furher es he robusness of our approach, and see wheher our variable nxa 1 improves on he predicive power of he lagged exchange rae, we invesigae he forecasing abiliy of he following regression: e,k = c + αe 1 + β e 1 + δnxa 1 + u,k (15) where e,k = (e +k 1 e 1 ) /k is he k period rae of depreciaion (quarerlized). Table 7 repors he R 2 as well as he coefficiens α, β and γ from hese regressions. As is immediae from he able, he lagged level of he exchange rae conains subsanial informaion abou fuure raes of depreciaions. However, when nxa 1 is included in he regressions, e 1 becomes insignifican a shor horizons and he fi of he regression improves markedly. I is only a 24 quarers ha we find ha nxa 1 drops ou from he regression. Our inerpreaion is ha a longer horizons, oher deerminans of exchange raes are likely o become imporan as well (see for example Mark (1995)). [Table 7 abou here] Figure 6 repors he FDI-weighed nominal effecive depreciaion rae from 1 o 12 quarers ahead agains is fied values wih nxa and independenly wih our hree regressors. The improvemen in fi is sriking as he horizon increases. Our prediced variable does well a picking he general endencies in fuure raes of depreciaion as well as he urning poins, even one o four quarers ahead. 38 Oher facors can also influence he nominal exchange rae a longer horizons. For insance, Mark (1995) demonsraes ha he fi of he moneary model improves dramaically beyond 8 quarers. We do no include hese deerminans in our analysis. 23

25 [Figure 6 abou here] 3.6 Ou-of-sample forecas Since he classic paper of Meese and Rogoff (1983), he random walk has been considered he appropriae benchmark o gauge he forecasing abiliy of exchange rae models. These auhors showed ha none of he exising exchange rae models could ouperform he random walk a shor o medium horizons in ou-of-sample forecass, even when he realized values of he fundamenal variables were used in he predicions. More han weny years laer, his very srong resul sill sands. 39 We perform ou-of-sample forecass by esimaing our model using rolling regressions and comparing is performance o he random walk. We sar by spliing our sample in wo. We refer o he firs half, from 1952:1 o 1978:1, as he in-sample. We hen consruc ou-of-sample forecass in hree seps. Firs, we re-esimae our variable nxa following he mehodology of secion 2 over he in-sample. 40 This guaranees ha our consruced nxa does no incorporae any fuure informaion. 41 Second, sill over he in-sample, we esimae he forecasing relaionship beween fuure reurns and lagged nxa. Finally, we use his esimaed relaion o form a forecas of he firs non-overlapping reurn or depreciaion rae enirely ouside he esimaion sample. We hen roll over he sample by one observaion and repea he process. This provides us wih up o 104 ou-of-sample observaions. 42 We emphasize ha, since we are esimaing he rend componens and he weighs using only daa available a he ime of predicion, we canno fall vicim o any look-ahead bias. 43 This exercise is very sringen: given he reduced size of he sample, nxa canno be as precisely esimaed as if we used he whole sample each ime. We compare he mean-squared errors (MSE) of a model feauring only nxa and a consan o 39 See Chinn, Cheung and Garcia (2005). A very shor horizons however (beween one and weny rading days), Evans and Lyons (2005) show ha a model of exchange rae based on disaggregaed order flow ouperforms he random walk. 40 We also consruc he sample weighs µ z using daa from he in-sample only and he resricion ha he discoun facor be consan and equal o is seady sae value, as in secion 3. We use our benchmark value of ρ = 0.95 in hose calculaions. 41 Noe ha we consruc nxa using daa saring in 1952 bu forecas he exchange rae ou-of-sample from 1978 onward only. Since our ou-of-sample forecass sar well ino he floaing period, he goodness of fi canno be ascribed o he fac ha we forecas he consan exchange raes of he Breon Woods era! 42 See Appendix C for deails. Changes in he cu-off poin o do no seem o make any difference for our resuls, provided he number of observaions used o perform he esimaion is sufficien. 43 Furhermore, for his exercise we use non-seasonally adjused expors and impors daa. We undersand from conversaion wih BEA saffers ha he BEA s seasonal adjusmen procedure makes use of some fuure daa. 24

26 he M SE of a drifless random walk. We consruc he forecass involving nxa as described above, using only daa available up o he dae of he forecas. 44 To assess he saisical significance of our resuls we use he M SE-adjused saisic described in Clark and Wes (2006, forhcoming). This saisic is appropriae o compare he mean squared predicion errors of wo nesed models esimaed over rolling samples. I adjuss for he difference in mean-squared predicion errors semming purely from spurious small sample fi. The es compares he MSE from he random walk (MSE r ) o he MSE for he unresriced model (MSE u ), where he laer is adjused for a noise erm ha pushes i upwards in small sample (MSE u adj). The difference beween he wo M SE is asympoically normally disribued. We use a Newey- Wes esimaor for he variance of he difference in MSE in order o ake ino accoun he serial correlaion induced by overlapping observaions when he forecas horizon exceeds one quarer. Table 8 presens he resuls. A posiive M SE-Adjused saisic indicaes ha our model ouperforms he random walk in predicing exchange rae depreciaions. For he FDI-weighed exchange rae, our model ouperforms significanly he random walk, including one quarer ahead. The p values are always very small excep a 16 quarers. Resuls for he rade-weighed exchange rae are very similar. The able also repors he raio of he (unadjused) MSE. This raio is smaller han one a all horizons and for boh exchange raes. The curse of he random walk seems herefore o be broken for he dollar exchange rae. [Table 8 abou here] More ou-of-sample ess Besides he classic Meese-Rogoff exercise, we also assess he predicive power of our variable nxa by comparing he mean-squared forecasing error of several oher nesed models. We use a regression ha includes jus lagged reurns (resp. depreciaion rae) as a predicive variable (resriced model) and compare i wih a regression ha includes boh he lagged reurn (resp. depreciaion rae) and nxa 1 (unresriced model) a various horizons. We compue he raio of he mean-squared errors of he unresriced model o he resriced model MSE u /MSE r and es wheher i is significanly smaller han one using he modified Harvey, Leybourne, and Newbold es saisic (Clark and McCracken (2001)); 45 he null hypohesis is ha of equaliy of he MSEfor he resriced and he 44 Our es is more sringen han Meese and Rogoff (1983) who fed realized fundamenal variables o form heir forecas. 45 This saisic is correc only for one-sep ahead forecass. We perform rolling regressions and use accordingly he criical values presened in Table 4 of Clark and McCracken (2000). The resuls are similar if we use recursive esimaes insead. 25

27 unresriced model. The alernaive is ha MSE r > MSE u. Panels A and B of Table 9 repor resuls for he oal reurn on he ne asse porfolio r,k = ) /k as well as for he excess equiy reurn r,k ae rle,k are defined ( k 1 i=0 r +i where rae,k and rle,k analogously. We find ha nxa 1 improves he ou-of-sample forecasabiliy of ne foreign reurns and excess equiy reurn a all horizons from one o sixeen quarers. 46 The improvemen in fi is significan. We repea he exercise augmening he model wih dividend price raios, known o predic equiy reurns in conjuncion wih he lagged variable. In all cases he resuls are similar and suppor he imporance of our imbalance variable for ou-of-sample forecass. Panel C of Table 9 repors our resuls for he rae of depreciaion of he exchange rae. The improvemen in fi when using our nxa variable is imporan a all horizons, even a he shor end. Augmening he equaion wih ineres rae differenials does no affec our resuls. 47 [Table 9 abou here] 4 Conclusion This paper presens a general framework o analyze inernaional adjusmen, in deviaion from slow moving rends due o very long srucural changes such as financial and rade inegraion. We model joinly he dynamic process of ne expors, foreign asse holdings and he reurn on he porfolio of ne foreign asses. For he ineremporal budge consrain o hold, oday s curren exernal imbalances mus predic eiher fuure ne expor growh or fuure movemens in reurns of he ne foreign asse porfolio, or boh. Using a newly consruced quarerly daase on US foreign gross asse and liabiliy posiions a marke value, we consruc a well-defined measure of cyclical exernal imbalances. Hisorically, we find a subsanial par of cyclical exernal imbalances (27%) are eliminaed via predicable changes in asse reurns. These valuaion effecs occur a shor o medium horizons 46 We canno invesigae he ou-of-sample predicabiliy for longer horizons because we do no have enough observaions. For he excess equiy reurns, here is no improvemen for he sixeen quarers horizon. 47 We also looked a he ou-of sample resuls based on regression (15). We es wheher he unresriced model (he ADF specificaion and our nxa 1 variable) ouperforms he resriced model (he ADF specificaion). We find ha he raio of MSE (MSEu/MSEr) is smaller han one beween 1 and 8 quarers. These horizons are he ones for which no exchange rae model could ouperform he random walk in Meese and Rogoff (1983). Beyond 8 quarers, we do no find a significan saisical improvemen of our model compared o he ADF-ype specificaion (resuls available from he auhors upon reques). 26

28 while adjusmens of he rade balance come ino play a longer horizons (mosly afer wo years). The exchange rae has an imporan dual role in our analysis. In he shor run, a dollar depreciaion raises he value of foreign asses held by he US relaive o he liabiliies, hence conribuing o he process of inernaional adjusmen via he valuaion channel. In he longer run, a depreciaed dollar favors rade surpluses, hence conribuing o he adjusmen via he rade channel. The counerpar of he effec of exchange rae movemens as an adjusmen ool is ha oday s exernal imbalance conains significan informaion on fuure exchange rae changes. We are able o predic in sample 9% of he variance of he exchange rae one quarer ahead, 31% a year ahead and 41% hree years ahead. Our model has also significan ou-of-sample forecasing power, so ha we are able o bea he random walk a all horizons beween one and sixeen quarers. Our approach implies a very differen channel hrough which exchange raes affec he dynamic process of exernal adjusmen. In radiional frameworks, fiscal and moneary policies are seen as affecing relaive prices on he goods markes (compeiive devaluaions are an example) or as affecing saving and invesmen decisions. Bu, fiscal and moneary policies should also be hough of as mechanisms affecing he relaive price of asses and liabiliies, in paricular hrough ineres rae and exchange rae changes. This means ha moneary and fiscal policies may affec he economy differenly han in he sandard New Open Economy Macro models à la Obsfeld and Rogoff. 48 We used accouning ideniies and a minimal se of assumpions o derive our resuls. Any ineremporal general equilibrium model can herefore be nesed in our framework. More specific heoreical mechanisms can be inroduced and esed as resricions wihin our se-up. They will have o be compaible wih our empirical findings regarding he quaniaive imporance of he wo adjusmen mechanism and he horizons a which hey operae. Thus our resuls provide useful informaion o guide more specific heories. The challenge consiss in consrucing models wih fully-fledged opimizing behavior compaible wih he paerns we have uncovered in he daa. A naural quesion arises as o why he res of he world would finance he US curren accoun defici and hold US asses, knowing ha hose asses will underperform. In he absence of such model, one should be cauious abou any policy seeking o exploi he valuaion channel since o operae, i requires ha foreigners be willing o accumulae furher holdings of (depreciaing) dollar denominaed asses. 48 See Tille (2004) for a recen new open economy model allowing for valuaion effecs. His model, however, does no pin down he pah of foreign asses and liabiliies. 27

29 Several economic mechanisms could a priori be consisen wih our empirical resuls. Firs and foremos, he porfolio balance heory, which emphasizes marke incompleeness and imperfec subsiuabiliy of asses, seems well-suied o formalize our findings. In a world where home bias in asse holdings is prevalen, shocks may have very asymmeric impacs on asse demands, leading o large relaive price adjusmens on asse markes. Suppose for example ha he world demand for US goods falls, hereby increasing he curren accoun defici of he Unied Saes. The wealh of he US goes down relaive o is rading parners. Bu since he res of he world invess mosly a home, he dollar has o fall o clear asse markes. Hence a negaive shock o he curren accoun leads o an exchange rae depreciaion a shor horizons. Sandard porfolio rebalancing requires a subsequen expeced depreciaion o resore long run equilibrium. 49 This depreciaion increases he reurn of he ne foreign asse porfolio of he US and hereby conribues o close he gap due o he shorfall in ne expors. 50 Anoher ineresing avenue o explore are models generaing ime-varying risk premia such as Campbell and Cochrane (1999). A deeper heoreical undersanding of he valuaion channel seems unavoidable, in order o fully grasp exernal adjusmen dynamics. 49 See Kouri (1982), Henderson and Rogoff (1982) and Blanchard, Giavazzi and Sa (2005). 50 Obsfeld (2004) provides an illuminaing discussion of hose heoreical mechanisms. 28

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31 of Economics Dynamics and Conrol, 1993, 17, Kouri, Peni, Balance of Paymen and he Foreign Exchange Marke: A Dynamic Parial Equilibrium Model, in Jagdeep Bhandari and Bluford Punam, eds., Economic Inerdependance and Flexible Exchange Raes, MIT Press, 1982, pp Kraay, Aar and Jaume Venura, Curren Accouns in Debor and Credior Counries, Quarerly Journal of Economics, November 2000, 115 (4), Kwiakowski, Denis, Peer C. B. Phillips, Peer Schmid, and Yongcheol Shin, Tesing he null hypohesis of saionariy agains he alernaive of a uni roo., Journal of Economerics, 1992, 54 (1-3), Lane, Philip R. and Gian Maria Milesi-Ferrei, Exernal Wealh, he Trade Balance and he Real Exchange Rae, European Economic Review, june and, Financial Globalizaion and Exchange Raes, mimeo, Inernaional Moneary Fund Leau, Marin and Sydney Ludvigson, Consumpion, Aggregae Wealh and Expeced Sock Reurns, Journal of Finance, 2001, 56 (3), Mark, Nelson, Exchange Raes and Fundamenals: Evidence on Long Horizon Predicabiliy, American Economic Review, March 1995, 85, Meese, Richard and Kenneh Rogoff, Empirical Exchange Rae Models of he Sevenies: Do hey Fi Ou-of-sample?, Journal of Inernaional Economics, 1983, 14, Mercereau, Benoi, How o Tes (and no o Tes) a Presen Value Model in he Presence of Persisence, mimeo, Yale Economics Deparmen, November 2001., The Role of Sock Markes in Curren Accoun Dynamics: a Time Series Approach, Topics in Macroeconomics, 2003, 3 (1). Aricle 6. Mundell, Rober A., Inernaional Economics, New York: Macmillan Company, Obsfeld, Maurice, Inernaional Macroeconomics: Beyond he Mundell-Fleming Model, IMF Saff Papers, 2001, 47 (special issue), 1 39., Exernal Adjusmen, Review of World Economics, December 2004, 140 (4), and Alan Taylor, Global Capial Markes: Inegraion, Crisis, and Growh, UK: Cambridge Universiy Press, and Kenneh Rogoff, The Ineremporal Approach o he Curren Accoun, in Gene M. Grossman and Kenneh Rogoff, eds., Handbook of Inernaional Economics, Norh-Holland Amserdam 1995, pp and, The Unsusainable US Curren Accoun Posiion Revisied, in Richard Clarida, ed., G-7 Curren Accoun Imbalances: Susainabiliy and Adjusmen, forhcoming Sachs, Jeffrey, The Curren Accoun in he Macroeconomic Adjusmen Process, Scandinavian Journal of Economics, 1982, 84 (2), Sock, James H. and Mark W. Wason, Forecasing inflaion, Journal of Moneary Economics, 1999, 44 (2), Tille, Cedric, The Impac of Exchange Rae Movemens on U.S. Foreign Deb, Curren Issues in Economics and Finance, 2003, 9 (1), 1 7., Financial Inegraion and he Wealh Effec of Exchange Rae Flucuaions., mimeo, Federal Reserve Bank of New York US Treasury, U.S. Holdings of Foreign Long-Term Securiies, Deparmen of he Treasury. Division of Inernaional Finance, Board of Governors of he Federal Reserve Sysem. 30

32 Appendix A Proofs The Saionary Case This appendix derives he approximae ineremporal exernal consrain when he economy is close o a balanced growh pah. We require he following assumpions. Assumpion 7 The raios Z /W where Z {X, M, A, L } are saisically saionary. Denoe by µ zw he seady sae mean value of hese raios. Assumpion 8 The growh rae of domesic wealh w +1 is saionary wih seady sae mean value lnγ. Assumpion 9 The reurn on gross asses R+1 a, gross liabiliies Rl +1 and he ne foreign asse porfolio R +1 are saionary and admi a common seady sae mean value R ha saisfies R > Γ. Define he weigh µ x (resp. µ m ) as he seady sae share of expors (resp. impors) in he rade balance: µ x µ xw = µ xw µ mw ; µ mw µm = µ xw µ mw (A.1) Similarly, he weigh µ a (resp. µ l ) is he seady sae share of gross asses (resp. liabiliies) in ne foreign asses: 51 µ a = µ lw ; µ lw µl = µ lw (A.2) We obain he following resul: Lemma 3 Under assumpions 7-9 he law of moion of exernal asses (1) can be approximaed as: na +1 1 ( ) 1 ρ na + r +1 + ρ 1 nx (A.3) where ρ = Γ/R < 1, and: na = µ a a µ l l nx r = µ x x µ m m = µ a r a µ l r l Proof. The law of asse accumulaion is given by: NA +1 = R +1 (NA + NX ) Divide hrough by household oal wealh W o obain: ( A+1 L ) ( +1 W+1 A = R +1 L + X M ) W +1 W +1 W W W W W (A.4) (A.5) 51 Implicily, we are assuming ha µ a µ l and µ x µ m. We do no view his assumpion as resricive: i will be verified in mos general open economy models excep under very specific assumpions resricing he ne foreign asse posiion and he rade balance o be zero in seady sae. 31

33 Under assumpion 7, wrie he following firs order approximaion: Z W µ zw (1 + ǫ z ) W +1 ) +1 W Γ ( 1 + ǫ w R +1 R (1 + r +1 ) where ǫ z = ln(z /W ) lnµ zw, ǫ w +1 = ln(w +1/W ) lnγ and r +1 = ln(r +1 ) lnr are (log) deviaions from seady sae. Subsiue ino he lef hand side and he righ hand side of (A.4) and re-arrange o obain: ( µ lw) Γ ( 1 + µaw ǫ a +1 µlw ǫ l +1 µ lw + ǫ w +1 ( R µ lw + µ xw µ mw) ( 1 + r +1 + µaw ǫ a µ lw ǫ l + µ xw ǫ x µ mw ǫ m µ lw + µ xw µ mw By definiion of he seady sae, we mus have: ( µ lw) Γ = R ( µ lw + µ xw µ mw) Re-arranging we obain ǫ a +1 µlw ǫ l +1 µ lw + ǫ w +1 = r +1 + µawǫa µ lwǫl + µ xwǫx µ mwǫmw µ lw + µ xw µ mw We now use he fac ha ǫ z = z w lnµ zw and ǫ w +1 = w +1 w lnγ, o obain (up o unimporan consans): a +1 µ lw l +1 µ lw = r +1 + µaw a µ lw l + µ xw x µ lw m µ lw + µ xw µ mw Finally, using he definiion of ρ, na and nx (consider separaely he cases µ a < 0, µ x > 0 and µ a > 0, µ x < 0) his collapses o: na +1 = r ( ) 1 ρ na + ρ 1 nx ) ) Define now he linear combinaion of ne expors and ne foreign asses nxa as nxa na + nx = µ a a µ l l + µ x x µ m m. Subsiuing ino (A.3), we obain: nxa +1 = 1 ρ nxa + r +1 + nx +1 (A.6) Assumpion 10 nxa saisfies he no-ponzi condiion lim j ρj nxa +j = 0 a.s. 32

34 If we impose he no-ponzi condiion ha nxa canno grow faser han he growh adjused ineres rae, equaion (A.6) can be solved forward, which leads o: Proposiion 2 Under assumpions 7-10, he exernal budge consrain (1) saisfies approximaely: + nxa ρ j [r +j + nx +j ] j=1 (A.7) Proof. Ierae forward and impose assumpion 10. Finally, since equaion (A.7) mus hold along every sample pah, i mus hold in expecaions: + nxa ρ j E [r +j + nx +j ] j=1 (A.8) Proofs for he rending case Proof of Lemma 1 Proof. The law of asse accumulaion is given by: NA +1 = R +1 (NA + NX ) Divide hrough by household oal wealh W o obain: ( A+1 L ) ( +1 W+1 A = R +1 L + X M ) W +1 W +1 W W W W W (A.9) (A.10) Under assumpions 1-3, wrie he following firs order approximaions: Z µ zw (1 + ǫ z W ) W +1 ) +1 Γ ( 1 + ǫ w W R+1 a R ( 1 + r+1 a ) ( ) R+1 l R 1 + r+1 l Subsiue ino he exernal budge consrain (A.10). The lef hand side of he consrain becomes approximaely (and up o a consan) ( ( ) +1 µ lw +1 Γ 1 + µaw +1 ǫa +1 ) µlw +1 ǫl ǫ w µlw +1 (A.11) +1 The erm beween brackes of he righ hand side of he budge consrain becomes approximaely (and up o a consan): [ ] µ lw + µ xw µ mw (A.12) (1 + µaw ǫ a µ lw ǫ l + µ xw ǫ x µ mw ǫ m ) µ lw + µ xw µ mw 33

35 We now loglinearize he oal reurn R +1. Since A and L are defined as he beginning of period asses and liabiliies, we have: A +1 L +1 R +1 = A +1 /R+1 a L +1/R+1 l Expand his expression (divide by W +1 ec...) o obain, given he definiions µ a = / ( and µ l = 1 µ a : ( ) R +1 R 1 + r+1 a + r+1 l ( ) ǫ a +1 µ lw ( ǫ a +1 + r+1 l ) ( R 1 + µ a +1r+1 a µ l +1r+1 l ( ) ǫ l ) ( +1 ) µ lw ǫ l +1 + r+1 a µ lw ) R (1 + ˆr +1 ) (A.13) Now reconsruc (A.10) puing ogeher (A.11), (A.12) and (A.13) and using assumpion 4 (he rend budge consrain): +1 ǫa +1 µlw +1 ǫl µlw +1 + ǫ w +1 = ˆr +1 + µaw ǫ a µ lw ǫ l + µ xw µ lw + µ xw ǫ x µ mw ǫ m µ mw Finally, define, as in he ex na = µ a ǫ a µ l ǫ l and nx = µ x ǫ x µ m ǫ m consrain (up o a consan) as: na +1 + w +1 ˆr ( ) 1 na 1 nx ρ ρ and rewrie he budge which is equaion (5) of he paper. Proof of Lemma 2 Proof. When he rends µ zw have a common growh rae, he weighs µ z are consan and equal o µ z and ρ = ρ. Assume ha µ a > 0 and µ x < 0 (he symmeric case is immediae) and observe ha nxa = na nx, nx +1 = nx nx +1 w +1 and r +1 ˆr +1. From 1, we can wrie: na +1 = r ( ) 1 na 1 nx w +1 ρ ρ nxa +1 = r ( ) 1 ρ (nxa + nx ) ρ 1 nx w +1 nx +1 = r ρ nxa + nx w +1 nx +1 which is equaion (6) of he paper. = r ρ nxa + nx +1 Proof of Proposiion 1 Proof. Ierae forward equaion (6) and impose assumpion 6 o ge equaion (10) of he paper. 34

36 Differen mean reurns on asses and liabiliies We generalize Lemma 1 o he case where he reurns on asses and liabiliies differ and become equal only asympoically. We build on he proof of Lemma 1. We adop he same noaions. We sar wih a modificaion of assumpion 3: Assumpion 3b: The reurn on asses R+1 a and he reurn on liabiliies Rl +1 admi he following decomposiion: R a +1 = R a +1e ra +1 R l +1 = R l +1e rl +1 where R +1 i is a rend componen and ri +1 is he deviaion componen. R +1 a and R +1 i saisfy: lim R +1 a = lim Rl +1 = R > Γ The erms R +1 a and R +1 l represen he (unobserved) reurns on gross asses and gross liabiliies along he rend. Since R+1 a and Rl +1 are saionary, hey oo, are saionary. Assumpion 3 obains as a special case of assumpion 3b where R +1 a = R +1 l = R. We modify assumpion 4 as follows: Assumpion 4b: The exernal consrain holds along he rend, i.e.: ( ) +1 µ lw +1 = R ( ) +1 /Γ µ lw + µ xw µ mw (A.14) where he rend reurn on ne foreign R +1 asses saisfies (see below; recall ha gross posiions are measured a he beginning of he period): 1 R +1 = µ a +1 1 R a +1 µ l +1 Observe ha he rend reurn R +1 is ime-varying as long as R +1 a R +1 l and hese reurns are hemselves ime-varying. In he special case where R +1 a = R +1 l = R, he rend reurn is consan and also equal o R since µ a +1 µl +1 = 1. Noe also ha in he case where R +1 a = R a and R +1 l = R l bu R a R l, he rend reurn is sill ime-varying, because of he ime-variaion in he weighs µ a and µ l : 1 = µ R a R a 1 µl +1 R l Under assumpions 3b and 4b (in place of assumpions 3 and 4 in he paper), we can derive an approximaion o he exernal consrain around he rend. Sar from he budge consrain normalized by wealh: ( A+1 W +1 L +1 W +1 ) W+1 W = R +1 1 R l +1 ( A W L W + X W M W ) (A.15) The lef handside and he erms beween brackes of he righ handside can be expanded exacly in he same way as above (proof of Lemma 1). Denoe by A and L he end of period holdings (before reurns, bu afer ne expors). They saisfy: A L = A L + NX and NA +1 = R a +1A R l +1L = A +1 L +1 35

37 so ha he oal reurn on NA, denoed by R +1, is R +1 = Ra +1 A R l +1 L A L A = R+1 a A L L R+1 l A L Now, subsiue using: A +1 = R a +1 A ; L +1 = R l +1 L o obain: R +1 = A +1 L +1 A +1 /R a +1 L +1/R l +1 Dividing by W +1 and expanding under assumpion 3b, we obain: R +1 = ( ) ( ) ǫ a +1 µ lw ǫ l / R ( ) +1 a 1 + ǫ a +1 r+1 a µ lw +1 / R ( ) +1 l 1 + ǫ l +1 r+1 l = +1 µlw / R +1 a µlw +1 / R l ( a +1 / R +1 a µlw +1 / R +1 l r+1 a + ( µ a / R +1 a +1 / R +1 a µlw +1 / R +1 l Now, recall ha R +1 is defined as: ) ǫ a +1 ( µ l +1 µ lw +1 / R l / R a +1 µlw µ lw +1 / R l / R a +1 µlw +1 / R l / R +1 l ) ǫ l +1) r l +1 R +1 = +1 µlw / R +1 a µlw +1 / R +1 l We obain R +1 = R +1 (1 + + ( µ a / R +1 a +1 / R +1 a µlw +1 / R +1 l r+1 a +1 / R +1 a +1 / R +1 a µlw +1 / R +1 l ) ǫ a +1 µ lw +1 / R l / R +1 a µlw +1 / R +1 l ( µ l +1 r l +1 µ lw +1 / R l / R a +1 µlw +1 / R l +1 Compared o he case in which R +1 a = R +1 l = R, here are wo differences: 1. he weigh on r+1 a is µra +1 = µaw +1 / R +1 a / ( +1 / R +1 a µlw +1 / R +1 l ) insead of µ a +1 = +1 / ( These weighs depend on rend asses, liabiliies and on he rend reurns on asses and liabiliies. We noe ha lim µ ra = lim µ a (and similarly for µ rl ) since lim Ra +1 = lim Rl +1 = R. 2. There are erms in ǫ a +1 and ǫl +1 wih weighs (for ǫa +1 ) equal o ) ǫ l +1) +1 +1) µlw. ψ a +1 = µ a +1 = +1 / R +1 a +1 / R +1 a µlw µ a +1 µl +1 ( µ a +1 / R a +1 µl +1 / R l +1) +1 / R l +1 ( 1/ R a +1 1/ R l +1 ) 36

38 and (for ǫ l +1 ) ψ l +1 = µ l +1 = µ lw +1 / R +1 l +1 / R +1 a µlw µ a +1 µl +1 ( µ a +1 / R a +1 µl +1 / R l +1) +1 / R l +1 ( 1/ R a +1 1/ R l +1 ) = ψ a +1 = ψ +1 In he special case where R a +1 = R l +1 = R, we verify direcly ha ψ +1 = 0. In he general case, we can rewrie: R +1 = R +1 ( 1 + µ ra +1r a +1 µ rl = R +1 ( 1 + ˆr +1 + ψ +1 (ǫ a +1 ǫ l +1 +1r+1 l + ψ +1 (ǫ a +1 ǫ l +1 )) )) (A.16) where we define ˆr +1 as: ˆr +1 = µ ra +1r a +1 µ rl +1r l +1 We can now proceed as above and reconsruc A.15 using A.16 and ǫ w +1 = w +1 lnγ. We obain (up o a consan): na +1 + w +1 = ˆr ) na (1 1ρ ( ) nx + ψ ρ +1 ǫ a +1 ǫ l +1 (A.17) where ρ is defined as before as ρ = 1 + ( (µ xw as in Lemma 1. µ mw )/ ( µ lw )) and nx and na are defined This expression is formally almos idenical o Lemma 1. I differs only by wo erms: 1. he definiion of he reurn ˆr, which is now consruced wih weighs incorporaing emporary rends in reurns on asses and liabiliies (which can differ). 2. he las erm in (A.17) ha reflecs a cyclical leverage effec : Suppose ha R a +1 > R l +1. Anoher way o ease he exernal adjusmen is o load up on asses (i.e. o increase leverage in order o ake advanage of he differenial in raes of reurns). We can quanify he imporance of his cyclical leverage effec in he process of inernaional adjusmen by performing a VAR decomposiion using equaion (A.17). In he same way and for he same reason we approximae he ime varying shares µ a and µ l by heir sample averages, we approximae ψ by is sample average. We find ψ = We hen perform a VAR decomposiion for he vecor ( nxa, ˆr, nx, ψ ( ǫ a +1 ǫl +1)). This is similar o Lemma 1 excep ha we have now one addiional variable, ψ ( ǫ a +1 ǫl +1). Figure 7 repors he decomposiion of nxa ino hree componens corresponding o nx, ˆr ψ ( ǫ a +1 ǫl +1). We find ha i) he cyclical leverage conribues o he process of inernaional adjusmen; ii) i is quaniaively less imporan han he rade or he valuaion channels; iii) inroducing i in our variance decomposiion slighly improves he fi of our approximaion. [Figure 7 abou here] [Table 10 abou here] 37

39 These resuls are confirmed if we perform he uncondiional variance decomposiion (see Table (10)). In he long run, ne expors accoun for 58% of he process of inernaional adjusmen, while valuaion effecs accoun for 26% and he cyclical leverage effec for 12%. Appendix B VAR decomposiion Consider a VAR(p) represenaion for he vecor y = (r, nx, nxa ). Appropriaely sacked, his VAR has a firs order companion represenaion: y +1 = Ā y + ǫ +1 (B.1) where y = ( y,..., y p+1) and ǫ = (ǫ, 0). Define he indicaor vecors e nx, e r and e nxa ha pick he corresponding elemens of y (i.e. e ry = r for insance). Equaion (11) implies he following resricion on he VAR represenaion: nxa e nxay + = ρ j Ē (r +j + nx +j ) j=1 = ( e r + e ) + nx ρ j Ē y +j j=1 (B.2) where Ē denoes expecaions according o he informaion conained in he VAR represenaion (B.1). 52 According o equaion (B.1), he condiional expecaions of y +j saisfy: Ē y +j = A j z. Subsiuing ino equaion (B.2) we obain: e nxay = ( e r + e ) + nx ρ j A j y j=1 = ( e r + e nx) ρa (I ρa) 1 y (B.3) = nxa r + nxa nx where nxa r = e rρa (I ρa) 1 y and nxa nx = e nx ρa (I ρa) 1 y. Moreover, since (B.3) needs o hold for all values of y, i implies he following resricion on he companion marix A : e nxa = ( e r + e ) nx ρa (I ρa) 1 (B.4) Equaion (B.4) consiues a presen value es (see Campbell and Shiller (1987)). Pos-muliplying by (I ρa), his is equivalen o: e nxai + ( e r + e nx e nxa) ρa = 0 Campbell and Shiller (1987) show ha his es is numerically idenical o he one-sep ahead es Ē (Q +1 ) = 0 where Q +1 = nxa +1 nxa /ρ (r +1 + nx +1 ). Mercereau (2001) argues ha he one-sep-ahead es is preferable when some of he variables are persisen, as is he case here wih nxa. 52 We do no impose ha economic agens form expecaions according o Ē. We only require ha he informaion conained in (B.1) is a subse of he informaion available o economic agens. See Campbell and Shiller (1988) for a discussion. 38

40 Following he same mehodology, we can also decompose he reurn effec ino a reurn on gross liabiliies and reurn on gross asses. They are defined as nxa ra nxa rl = µ a e raρa (I ρa) 1 y = µ l e rl ρa (I ρa) 1 y These differen componens are shown on Figure 5. Appendix C Ou-of-Sample esimaes We consruc he ou-of-sample forecass for a given horizon k by running: y,k = α k + β k nxa + γ k X + ε,k (C.1) where y,k represens he k quarer ahead reurn (resp. depreciaion rae) beween period and + k, X represens oher variables ha are known o predic y,k, including lagged reurns y k,k. We use he informaion available unil dae o o run equaion (C.1). The las observaion used is herefore ( y 0 k,k, nxa o, X ) o k o k. Our noaions indicae ha nxa o o k is he value a dae o k of our variable nxa esimaed using only daa available up o dae o. Once he coefficiens ˆα k ( o ), ˆβ k ( o ) and ˆγ k ( o ) have been esimaed, we use hem o predic he firs k-horizon forecas: ŷ 0,k= ˆα k +ˆβ k nxa o o +ˆγ k X o (C.2) We hen add one period o our sample. We include informaion of dae o in our esimaing equaion and produce a forecas for ŷ 0+1,k. The whole procedure is repeaed again in o + 1,... unil we reach observaion T, where T is he oal number of observaions in our sample. We se o = 1978 : 1 o spli he sample in half wih 105 observaions in sample and 104 observaions ou of sample. Appendix D US ne foreign asses, ne expors and exchange raes. We apply our heoreical framework o he exernal adjusmen problem of he Unied Saes. Our mehodology requires consrucing ne and gross foreign asse posiions a marke value over relaively long ime series and compuing capial gains and reurns on global counry porfolios. In his secion, we describe briefly he consrucion of our daa se. A complee descripion of he daa is presened in Gourinchas and Rey (forhcoming 2006). D.1 Posiions. Daa on he ne and gross foreign asse posiions of he US are available from wo sources: he US Bureau of Economic Analysis (BEA) and he Federal Reserve Flows of Funds Accouns for he res of he world (FFA). 53 Following official classificaions, we spli US ne foreign porfolio ino four caegories: Deb (corporae and governmen bonds), Equiy, Foreign Direc Invesmen (FDI) and Oher. The oher caegory includes mosly bank loans and rade credis. I also conains gold reserves. 54 Our sraegy consiss in re-consrucing marke value esimaes of he gross exernal 53 See Hooker and Wilson (1989) for a deailed comparison of he FFA and BEA daa. 54 I is naural o include inernaional gold flows in our analysis since during Breon Woods (he only period where hey were quaniaively non-negligible) hey were designed o be perfec subsiues o dollar flows and cenral o he process of inernaional adjusmen. 39

41 asses and liabiliies of he US ha conform o he BEA definiions by using FFA flow and posiion daa and valuaion adjusmens. Denoe by X he end of period posiion for some asse X. We use he following updaing equaion: X = X 1 + FX + DX where FX denoes he flows corresponding o asse X ha ener he balance of paymens, and DX denoes a discrepancy reflecing a marke valuaion adjusmen or (less ofen) a change of coverage in he series beween periods 1 and. Using exising sources, we consruc an esimae of DX as r x X 1 where rx represens he esimaed dollar capial gain on asse X beween ime 1 and ime. This requires ha we specify marke reurns r x for each sub-caegory of he financial accoun. D.2 Capial gains, oal reurns and exchange raes. We consruc capial gains on he subcaegories of he financial accoun as follows. For equiy and FDI, we use he broades sock marke indices available in each counry. For long erm deb, we consruc quarerly holding reurns and subrac he curren yield, disribued as income, o compue he ne reurn. We assume no capial gain adjusmen for shor-erm deb and for oher asses and liabiliies, since hese are mosly rade credi or illiquid bank loans. 55 We consruc oal reurns for each class of financial asses as follows. For equiy and FDI, we use quarerly oal reurns on he broades sock marke indices available in each counry. The oal reurn on deb is a weighed average of he oal quarerly reurn on 10-year governmen bonds and he hree-monh ineres rae on governmen bills, wih weighs reflecing he mauriy srucure of deb asses and liabiliies. The oal reurn on oher asses and liabiliies is compued using hree-monh ineres raes. All reurns are adjused for US inflaion by subracing he quarerly change in he Personal Consumer Expendiure deflaor. In all cases, we use end of period exchange raes o conver local currency capial gains and oal reurns ino dollars. Gourinchas and Rey (forhcoming 2006) gives a precise descripion of he currency weighs and mauriy srucure (for deb) and of he counry weighs (for equiy and FDI asses) ha we use in our calculaions. We consruc oal reurns on he ne foreign asse porfolio as follows. Firs, we use he definiion of r = µ a r a µ l r l. Second, by analogy, r a and r l are weighed averages of he reurns on he four differen subcaegories of he financial accoun: equiy, foreign direc invesmen, deb and oher. For insance, we wrie he oal reurn on gross asses r a as: r a = w a er ae + w a f raf + w a d rad + w a or ao where r ai denoes he real (dollar) oal reurn on asse caegory i (equiy, FDI, deb or oher) and wi a denoes he average weigh of asse caegory i in gross asses. A similar equaion holds for he oal reurn on gross liabiliies r l (wih corresponding reurns r li on asse caegory i). I is difficul o consruc precise esimaes of he financially-weighed nominal effecive exchange rae, needed in paricular o compue ne porfolio reurns in equaion (12). There is lile available evidence on he currency and counry composiion of oal foreign asses. In pracice, he Treasury Survey (2000) repors counry and currency composiion for long-erm holdings of foreign securiies in benchmark years. Because few daa are available before 1994, he weighs are likely o be subsanially off-base a he beginning of our sample. Insead, we consruc a mulilaeral financial exchange rae using ime-varying FDI hisorical posiion counry weighs. This exchange rae proxies he rue financially weighed exchange rae ha affecs he dollar reurn on gross foreign asses. 56 We also make he realisic assumpion ha mos foreign asse posiions are no hedged for 55 Due o daa availabiliy, we assume away any spread beween corporae and governmen deb. 56 We checked he robusness of our resuls by using alernae definiions of he mulilaeral exchange rae, based on fixed equiy or deb weighs. The resuls are qualiaively unchanged. We noe also ha he correlaion beween he rae of depreciaion of our mulilaeral exchange rae and he rae of depreciaion of he Federal Reserve major 40

42 currency risk (see Hau and Rey (2006)). For he period , our esimaes are very close o he BEA Inernaional Invesmen Posiion a marke value (see Gourinchas and Rey (forhcoming 2006)). currencies rade weighed mulilaeral nominal rae is high a

43 Table 1: Descripive Saisics Summary Saisics x m a l r r a r l e nxa Mean (%) Sandard deviaion (%) Auocorrelaion r ae r le Mean (%) Sandard deviaion (%) Auocorrelaion Noe: Sample period is 1952:1-2004:1, excep for e, 1973:1-2004:1. r ad r ld r af r lf r ao r lo Table 2: Uncondiional Variance Decomposiion of nxa Discoun facor ρ # percen β nx β r of which: 3 β ra β rl Toal (lines 1+2) 6 µ a Noe: The sum of coefficiens β ra + β rl is no exacly equal o β r due o numerical rounding in he VAR esimaion. Sample: 1952:1 o 2004:1. 42

44 Table 3: Forecasing Quarerly Reurns Column: Panel A: Reurns Toal real reurn (r +1 ) Real Equiy Differenial ( r+1) e d z : r p d p xm r e d p d p xm ˆβ (s.e.) (0.07) (0.07) (0.08) (0.16) (0.03) (0.03) (0.03) (-0.06) ˆδ (s.e.) (0.07) (1.60) (0.19) (0.07) (0.61) (0.07) R # obs Panel B: Depreciaion Raes FDI-weighed ( e +1 ) Trade-weighed ( e T +1) z : e xm i i e T xm 1 i i ˆβ (s.e.) (0.02) (0.02) (0.04) (0.02) (0.02) (0.02) (0.03) (0.02) ˆδ (s.e.) (0.07) (0.05) (0.32) (0.07) (0.05) (0.34) R #obs Noe: Regressions of he form: y +1 = α + βnxa + δz + ǫ +1 where y +1 is he oal real reurn (r +1 ); he equiy reurn differenial ( r+1 e = r+1 ae r+1) le (panel A); he FDI-weighed depreciaion rae ( e +1 ) or he rade weighed depreciaion rae ( e T +1) (panel B). d p d p is he relaive dividend price raio (available since 1970:1); i i is he shor erm ineres rae differenial; xm is he saionary componen from he rade balance, defined as ǫ x ǫ m. Sample: 1952:1 o 2004:1 for oal reurns and 1973:1 o 2004:1 for depreciaion raes. Robus sandard errors in parenhesis. 43

45 Table 4: Forecasing Quarerly Reurns (con ed) Column Panel A: Dollar reurn on US equiies and US gross liabiliies US equiy reurn (r+1) le US liabiliies reurn (r+1) l z : r le d /p cay r l d /p cay ˆβ (s.e.) (0.05) (0.08) (0.05) (0.05) (0.02) (0.02) (0.02) (0.02) ˆδ (s.e.) (0.06) (0.60) (0.45) (0.07) (0.19) (0.16) R # obs Panel B: US gross asses reurn (dollar and local currency) Dollar reurn (r+1) a Local currency reurn (r+1) a z : r a d /p xm r a d /p xm ˆβ (s.e.) (0.02) (0.02) (0.02) (0.04) (0.02) (0.02) (0.02) (0.04) ˆδ (s.e.) (0.09) (0.21) (0.05) 0.08 (0.22) 0.05 R # obs Panel C: Reurn on foreign equiies (dollar and local currency) Dollar reurn (r+1) ae Local currency reurn (r+1) ae z : r ae d /p xm r ae d /p xm ˆβ (s.e.) (0.04) (0.04) (0.07) (0.08) (0.05) (0.04) (0.06) (0.11) ˆδ (s.e.) (0.08) (0.59) (0.09) (0.08) (0.57) (0.13) R # obs Noe: Regressions of he form: y +1 = α + βnxa + δz + ǫ +1 where y +1 is he dollar reurn on US equiies (r+1), le he dollar reurn on US liabiliies (r+1) l (panel A); he dollar reurn on US asses (r+1), a he local currency reurn on US asses (r+1) a (panel B); he dollar reurn on foreign equiies (r+1), ae he local currency reurn on foreign equiies (r+1) ae (Panel C). d d p (resp. p ) is he domesic (resp. foreign) dividend price raio (available since 1970:1); cay is he Leau and Ludvigson (2001) s deviaion of he consumpion-wealh raio from rend; xm is he saionary componen from he rade balance, defined as ǫ x ǫ m. Sample: 1952:1 o 2004:1. Robus sandard errors in parenhesis. Table 5: Forecasing Bilaeral Quarerly Raes of Depreciaion Currency nxa 1 R2 #obs UK pound (0.06) Canadian dollar (0.01) Swiss franc (0.03) Japanese yen (0.03) Deuschmark (Euro) (0.02) Noe: Sample: 1973:1 o 2004:1. Robus sandard errors in parenhesis. 44

46 Table 6: Long Horizon Regressions Forecas Horizon (quarers) Real Toal Ne Porfolio Reurn r,k nxa (0.07) (0.05) (0.04) (0.04) (0.03) (0.03) (0.02) (0.02) R 2 (1) [0.11] [0.18] [0.24] [0.26] [0.21] [0.13] [0.09] [0.02] R 2 (2) [0.14] [0.25] [0.34] [0.38] [0.35] [0.24] [0.19] [0.16] Real Toal Excess Equiy Reurn r,k ae,k nxa (0.03) (0.02) (0.02) (0.02) (0.01) (0.01) (0.01) (0.01) R 2 (1) [0.07] [0.13] [0.17] [0.18] [0.10] [0.03] [0.01] [0.00] R 2 (2) [0.11] [0.20] [0.28] [0.31] [0.26] [0.15] [0.10] [0.17] Ne Expor growh nx,k nxa (0.02) (0.02) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) R 2 (1) [0.05] [0.10] [0.13] [0.17] [0.31] [0.44] [0.53] [0.58] R 2 (2) [0.04] [0.08] [0.12] [0.17] [0.38] [0.55] [0.66] [0.79] FDI-weighed effecive nominal rae of depreciaion e,k nxa (0.02) (0.02) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) R 2 (1) [0.09] [0.16] [0.28] [0.31] [0.41] [0.41] [0.33] [0.12] R 2 (2) [0.10] [0.21] [0.35] [0.40] [0.52] [0.55] [0.55] [0.38] Noe: Regressions of he form: y,k = α+βnxa +ǫ +k where y,k is he k-period real oal ne porfolio reurn (r,k ); oal excess equiy reurn (r,k ae rle,k ); ne expor growh ( nx,k) or he FDI-weighed depreciaion rae ( e,k ). Newey-Wes robus sandard errors in parenhesis wih k 1 Barle window. Adjused R 2 in brackes. R(1) repors he adjused R-squared of he regression on nxa ; R(2) repors he adjused R-squared of he regression on ǫ x, ǫ m, ǫ a and ǫ l. Sample: 1952:1 o 2004:1 (1973:1 o 2004:1 for exchange rae). 45

47 Table 7: Forecasing Exchange Raes. Sample 1973:2004. ADF-like Regressions Forecas Horizon (quarers) FDI-weighed effecive nominal rae of depreciaion e,k e (s.e.) (0.027) (0.020) (0.015) (0.013) (0.10) (0.008) (0.006) (0.004) e (s.e.) (0.090) (0.065) (0.049) (0.043) (0.032) (0.025) (0.020) (0.012) R 2 [0.01] [0.04] [0.08] [0.15] [0.28] [0.39] [0.48] [0.65] e (s.e.) (0.028) (0.019) (0.014) (0.012) (0.008) (0.006) (0.005) (0.004) e (s.e.) (0.091) (0.062) (0.045) (0.039) (0.026) (0.019) (0.016) (0.013) nxa (s.e.) (0.025) (0.017) (0.012) (0.011) (0.007) (0.005) (0.004) (0.003) R 2 [0.08] [0.20] [0.30] [0.37] [0.57] [0.68] [0.70] [0.68] IFS nominal effecive rae of depreciaion e IFS,k e IFS (s.e.) (0.027) (0.020) (0.016) (0.014) (0.010) (0.008) (0.006) (0.004) e IFS (s.e.) (0.090) (0.068) (0.054) (0.048) (0.035) (0.027) (0.021) (0.015) (i) R 2 [0.03] [0.03] [0.10] [0.14] [0.25] [0.35] [0.43] [0.55] e IFS (s.e.) (0.029) (0.021) (0.016) (0.015) (0.010) (0.008) (0.007) (0.005) e IFS (s.e.) (0.096) (0.068) (0.053) (0.047) (0.034) (0.027) (0.022) (0.017) nxa (s.e.) (0.029) (0.020) (0.016) (0.014) (0.010) (0.008) (0.007) (0.005) (ii) R 2 [0.10] [0.20 [0.27] [0.30] [0.42] [0.47] [0.51] [0.55] Noe: Runs regressions of he form e,k = αe 1 + β e 1 + γnxa 1 + c + ǫ,k. Sample 1973:2004. Table 8: Ou of Sample Tess for Exchange Rae Depreciaion agains he Maringale Hypohesis Horizon: (quarers) FDI-weighed depreciaion rae MSE u /MSE r MSE-adjused (MSE r MSE u -adj) (s.e.) (0.68) (0.60) (0.57) (0.53) (0.37) (0.24) (0.23) p-val [0.01] [0.01] [<0.01] [<0.01] [<0.01] [<0.01] [0.06] Trade-weighed depreciaion rae MSE u /MSE r MSE-adjused (MSE r MSE u -adj) (s.e.) (1.03) (1.03) (1.02) (0.98) (0.69) (0.38) (0.24) p-val [<0.01] [<0.01] [<0.01] [<0.01] [<0.01] [0.03] [0.11] Noe: M SP E adjused is he Clark-Wes (2004) es-saisic based on he difference beween he ou of sample MSE of he drifless random-walk model and he ou-of-sample MSE of a model ha regresses he rae of depreciaion e + 1 agains nxa. Rolling regressions are used wih a sample size of saisic in parenhesis. p-value of he one-sided es using criical values from a sandard normal disribuion in brackes. Under he null, he random-walk encompasses he unresriced model. Sample: 1952:1-2004:1. Cu-off: 1978:1. 46

48 Table 9: Ou of Sample Tess for various nesed models. ENC-NEW MSE u /MSE r Horizon: (quarers) Panel A: Real Toal Ne Porfolio Reurn r,k nxa vs AR(1) nxa vs AR(1), d d p and p Panel B: Real Toal Excess Equiy Reurn r,k ae,k nxa vs AR(1) nxa vs AR(1), d d p and p Panel C: FDI-weighed depreciaion rae e,k nxa vs AR(1) nxa vs AR(1), i i Noe: MSE u is he mean-squared forecasing error for an unresriced model ha includes he lagged dependen variable and lagged nxa (model 1); lagged d/p, d /p and lagged nxa (model 2). MSE r is he mean-squared error for he resriced models which include he same variables as above bu do no include lagged nxa. d/p (resp. d /p ) is he US (resp. res of he world) dividend price raio. Each model is firs esimaed using he sample 1952:1 1978:1. ENC-NEW is he modified Harvey, Leybourne and Newbold (1998) saisic, as proposed by Clark and McCracken (2001). Under he null, he resriced model encompasses he unresriced one. Sample: 1952:1-2004:1. (resp. ) significan a he five (resp. one) percen level. Table 10: Uncondiional Variance Decomposiion for nxa, when mean reurns on asses and liabiliies differ. Variance Decomposiion: # percen 1 β nx 58 2 β r 26 3 β cl 12 5 Toal 96 Noe: Sample: 1952:1 o 2004:1. 47

49 Figure 1: US Ne Expors and Ne Foreign Asses (% of GDP, ) 2% 1% 0% -1% -2% -3% -4% -5% -6% (a) Ne Expors/GDP 20% 15% 10% 5% 0% -5% -10% -15% -20% -25% -30% (b) Ne Foreign Asses/GDP Noe: The op panel shows he raio of US ne expors o US GDP. The boom panel shows he raio of US ne foreign asses o US GDP. Sample: 1952:1-2004:1. Source: Bureau of Economic Analysis, Flow of Funds and Auhors calculaions. 48

50 Figure 2: Cycle and Trend Componens for A/W, L/W, X/W and M/W. Noe: Top wo panels for US gross exernal asses A/W (lef) and US gross exernal liabiliies L/W (righ); Boom wo panels for US expors X/W (lef) and US impors M/W (righ). Each panel repors he series Z/W (raio o household wealh), he rend componen µ zw, labelled HP-rend, (righ-axis) and he cyclical componen ǫ zw (lef-axis). Sample: 1952:1-2004:1. 49

51 Figure 3: Various nxa Noe: nxa, consruced from various cu-offs (30, 40, 50, 100 years and linear filer). Sample: 1952:1-2004:1 50

52 Figure 4: nxa, flow r + nx and residual erm ε from equaion (6) (a) nxa (b) flow r + nx (c) residual ε 51

53 Figure 5: Decomposiion of nxa ino rade and valuaion componens. (a) reurn nxa(reurn) and ne expors nxa(expors) componens.!!!""!!##! $%&'() $%&'(&) $%&'(*) (b) asse reurn nxa(ra) and liabiliy reurn nxa(rl) componens. Noe: The op panel repors he decomposiion of nxa ino is reurn (nxa(reurn)) and ne expors (nxa(expors)) componens. The boom panel repors he decomposiion of he reurn componen (nxa(reurn)) ino an asse reurn (nxa(ra)) and a liabiliy reurn (nxa(rl)) componens. 52

54 Figure 6: Prediced One o 12-quarer ahead depreciaion raes quarer ahead 4-quarer ahead acual fied sep. reg. fied quarer ahead 12-quarer ahead Noe: Each graph repors (a) he realized depreciaion rae a 1 o 12 quarer horizon; (b) he fied depreciaion rae using nxa (fied); (c) he fied depreciaion rae using ǫ xw, ǫ mw, ǫ aw and ǫ lw as separae regressors (fied sep. reg.). 53

55 Figure 7: Decomposiion of nxa ino rade, valuaion and cyclical componens nxa nxa(reurn) nxa(expors) nxa(cyclical) nxa(predic) Noe: The figure repors he decomposiion of nxa ino a reurn (nxa(reurn)), a ne expors (nxa(expors)) and a cyclical (nxa(cyclical)) componens. 54