International Capital Flows and Debt Dynamics

Transcription

1 WP/12/175 Inernaional Capial Flows and Deb Dynamics Marin D. D. Evans

2 2012 Inernaional Moneary Fund WP/12/175 IMF Working Paper Research Inernaional Capial Flows and Deb Dynamics Prepared by Marin D. D. Evans 1 Auhorized for disribuion by July 2012 This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. Absrac This paper presens a new model for sudying inernaional capial ows and deb dynamics ha emphasizes he role played by expecaions concerning fuure rade ows and reurns. I use he model o esimae he drivers of he U.S. exernal posiion and capial ows beween 1973 and The esimaes show ha mos of he secular rise in U.S. inernaional indebedness is aribuable o growing opimism abou fuure reurns on U.S. holdings of foreign equiy and FDI asses. They also show ha he ransformaion of world savings ino risky asses by he U.S. had lile effec on is exernal posiion, bu he expeced fuure real depreciaion of he dollar allowed he U.S. o susain a higher level of inernaional deb afer he 1990s. JEL Classificaion Numbers:F31, F32, F34 Keywords: Capial Flows, Exernal Imbalances, Inernaional Deb, Inernaional Solvency, Exorbian Privilege Auhor s Address:mevans@imf.org 1 This paper is a revised and exended version of an earlier paper eniled Undersanding he Dynamics of he U.S. Exernal Posiion. I hank Albero Fueres for his assisance in updaing he daa used here.

3 -1- Conens 1 Inroducion 3 2 Inernaional Asses, Liabiliies, Reurns and Trade Flows The Balance of Paymens and Consolidaed Budge Consrain Trade Flows, Asse Pricing and Porfolio Choice A Model of Capial Flow Dynamics Approximaing he Consolidaed Budge Consrain Ne Posiions and Capial Flows Gross Posiions and Capial Flows Equilibrium Posiions and Capial Flows Daa and Esimaion Daa Adjusing Trade Flows Sample Saisics Esimaion Resuls Ne Posiion Dynamics Gross Posiion Dynamics Ne Capial Flows Gross Capial Flows U.S. Reurns and The Exorbian Privilege Porfolio Composiion The Role of he Dollar Conclusion 53

4 -2- Lis of Figures 1 Alernaive Measures of he U.S. Exernal Posiion Trends In U.S. Foreign Asses, Liabiliies and Real Trade Flows Approximaion Accuracy Changes in he Composiion of Asse and Liabiliy Porfolios Hisorical Behavior of he U.S. Ne Exernal Posiion and is Componens Hisorical Behavior of U.S. Gross Foreign Asse and Liabiliy Posiions and heir Componens Variance Conribuions of Trade and Reurns o U.S. Ne Capial Flows Variance Conribuions of Ne Capial Flows Hisorical Behavior of U.S. Gross Foreign Asse and Liabiliy Posiions and heir Componens Variance Conribuions o Gross Capial Flows Variance Conribuions of Gross Capial Flows Composiion Effecs and he size of he Valuaion Channel The U.S. Ne Exernal Posiion and he Role of he Dollar Lis of Tables 1 Summary Saisics Reurns and Porfolio Shares Granger Causaliy Tess Variance Decomposiions of xp Variance Decomposiions for and Porfolio Reurns and Their Componens Reurns and he Dollar Depreciaion Raes

5 -3-1 Inroducion The pas quarer cenury has winessed a dramaic change in world financial markes. The liberalizaion of capial accouns and globalizaion of financial ransacions has been accompanied by a rapid increase in he size of he gross foreign asse and liabiliy posiions of many counries. In he wo decades preceding he 2008 crisis, gross capial ows were ypically larger han curren accoun gaps in indusrialized counries, and grew a a ser rae han inernaional rade ows. The precrisis period also winessed a marked increase in curren accoun imbalances across he globe, wih numerous counries running persisen surpluses or deficis. Mos noably, he U.S. coninued o run large curren accoun deficis in he ce of a growing level of inernaional deb. These developmens provide a challenge o boh researchers and policymakers. Tradiional macro models focus on he behavior of he curren accoun driven by naional savings and invesmen decisions raher han he financial decisions ha govern he size and composiion of gross capial ows (see, e.g., Obsfeld and Rogoff, 1995). The limi on a counry s abiliy o run curren accoun deficis in such models is largely deermined by he prospecs for fuure surpluses whereas acual limis also depend on he prospecive fuure reurns on foreign asses relaive o liabiliies. As a resul, persisen curren accoun deficis may be more susainable han a radiional macro-based evaluaion would sugges. Conversely, a counry wihou a hisory of curren accoun deficis may find iself in an unsusainable posiion if he composiion of foreign asses and liabiliies make is ne foreign asse posiion vulnerable o unexpeced asse-price movemens. Exising models provide lile guidance on how o assess such balance shee consideraions. In his paper I develop a new model for sudying he dynamics of a counry s foreign asse and liabiliy posiions. The model provides an inegraed framework for examining he real and financial cors ha affec he evoluion of any counry s exernal posiion. In paricular, he empirical model I build on his framework allows me o esimae he cors driving variaions in U.S. foreign asse and liabiliy posiions, and heir associaed capial ows before he 2008 financial crisis. In so doing, I shed new ligh on he source and imporance of he so-called exorbian privilege enjoyed by he U.S. over he pas quarer cenury. The model is buil around he consolidaed budge consrain ha links he evoluion of a counry s foreign asses and liabiliies o expors, impors and reurns. This accouning ideniy is usually used o relae a counry s curren ne asse posiion o he hisory of curren accoun balances and he capial gains on pas asse and liabiliy holdings. Here I combined i wih a no-ponzi condiion o derive he inernaional solvency consrain ha places an upper limi on a counry s inernaional borrowing. This solvency consrain lies a he hear of he model. Specifically, I derive a se of presen value expressions ha link a counry s curren asse and liabiliy posiions o expecaions concerning he fuure course of expors, impors, he reurns on foreign asses and liabiliies. These expressions also deermine gross and ne capial ows. I combine he posiion and ow equaions

6 -4- wih esimaes of a Vecor Auogression (VAR) o empirically sudy he cors driving he U.S. exernal posiions and capial ows. The economic logic underlying he model is simple. Consider a siuaion where a counry wih a negaive ne foreign asse posiion wans o run a curren accoun defici o ciliae ineremporal consumpion smoohing. Clearly, his is only possible if he counry can finance he defici via he accumulaion of foreign liabiliies or hrough he sale of foreign asses. Eiher way, in he absence of Ponzi schemes, he counry s crediors mus expec ha he addiional ne deb will ulimaely be repaid using he proceeds from fuure ne expors and/or he reurn differenial beween foreign asses and liabiliies. Any variaion in a counry s ne foreign asse posiion mus herefore be accompanied by a revision in expecaions concerning fuure rade ows and/or reurns. Similarly, changes in gross asse or liabiliy posiions mus reec revisions in he expeced fuure reurns on he underlying securiies or he dividend ows hey produce financed by rade ows. These links beween expecaions and posiions lie a he hear of he model and are he focus of he empirical analysis. The rapid rise in he gross foreign asse and liabiliy posiions of many counries in recen decades presens a challenge for anyone developing a model of inernaional asse posiions. In he case of he U.S., gross asses and liabiliies have grown much ser han expors, impors, GDP or esimaes of U.S. wealh. Gourinchas and Rey (2007b) accommodae his feaure by focusing on he process of inernaional adjusmen around slow-moving rends in he raios of asses, liabiliies, expors and impors o wealh (under he assumpion ha he rends represen srucural changes relaed o rade and financial globalizaion). I adop a fundamenally differen approach. Insead of derending he daa, I adjus expors and impors by he addiion of a common rend ha mainains he inegriy of he consolidaed budge consrain. These adjusmens allow me o derive equaions for oal foreign asse and liabiliy posiions from an accurae log-approximaion o he consolidaed budge consrain. As a consequence, my model accommodaes he prominen rends observed in inernaional daa. My empirical analysis of he U.S. daa produces hree ses of resuls. The firs se concerns he evoluion of he U.S. foreign asse and liabiliy posiions. I find ha he expecaions of fuure rade ows and reurns idenified by he model esimaes accoun for approximaely 97 percen of he quarerly variaions in he U.S. ne exernal posiion beween 1973:I and 2007:IV. Furhermore, he esimaes imply ha revisions in he expeced fuure reurn differenial beween foreign asses and liabiliies are he dominan driver of he U.S. exernal posiion, conribuing more han 75 percen o he sample variance in he baseline version of he model. These esimaes of he valuaion componen are roughly wice he size of hose repored by Gourinchas and Rey (2007b). They reec he c ha he low-frequency swings in he U.S. exernal posiion are more closely relaed o changes in expeced reurn differenials han o changes in expeced fuure rade ows. I also find ha expecaions concerning fuure rade ows and reurns had asymmeric affecs on he dynamics of gross foreign asse and liabiliy posiions. A rise in expeced fuure expor growh

7 -5- induced he accumulaion of liabiliies, while a rise in expeced fuure impor growh produced a ll in foreign asse holdings. Changes in expeced fuure reurns had similarly asymmeric effecs: higher expeced reurns on asses increased asse holdings, while higher expeced reurns on liabiliies lowered liabiliy holdings. My second se of resuls concerns capial ows. I find ha changes in expeced fuure reurn differenials beween foreign asse and liabiliy porfolios are an empirically imporan driver of U.S. ne capial ows; indeed hey are a good deal more imporan han changes in expeced fuure rade ows. A he same ime, ne capial ows have played a raher minor role as he driver of changes in he U.S. exernal posiion; making a variance conribuion of jus 10 percen over a en year horizon. In conras, gross capial ows are primarily driven by a common componen ha reecs inernaional capial deepening driven by he expeced growh in average ne income from asse and liabiliies relaive o reurns. Flows are also an imporan driver of gross posiion changes, accouning for approximaely 50 percen of heir variance over a en year horizon. I also use he model esimaes o evaluae he idea ha he U.S. has enjoyed an exorbianprivilege from issuing a reserve currency and ransforming world savings ino risky capial. I find ha while he asymmeric composiion of U.S. foreign asse and liabiliy porfolios affeced he behavior of realized reurn differenials, i did no maerially affec he long-horizon forecass of fuure reurns ha deermine he valuaion componen. As a consequence, my resuls indicae ha he U.S. did no benefi significanly from he concenraion of is asse holdings in equiy and FDI and is liabiliies in deb. On he oher hand, he U.S. did benefi from he reurn differenials on equiy and FDI. Persisen and predicable variaions in hese differenials are he main drivers of he valuaion componen. I also find ha he hisorical variaions in he valuaion componen embedded significan expecaions concerning he fuure real depreciaion of he dollar. In paricular, much of he marked deerioraion in he U.S. exernal posiion beween 1998 and 2003 appears o be aribuable o expecaions of a fuure real dollar depreciaion ha was associaed wih higher expeced fuure reurn differenials on equiy and FDI. This paper is closely relaed o Gourinchas and Rey (2007b) in is focus on he link beween a counry s exernal posiion and forecass of fuure rade ows and reurns. However, I go beyond heir analysis in hree key respecs: Firs, he model I develop accommodaes he rends in gross asse and liabiliy posiions so I can examine he dynamics of oal posiions raher han heir cyclical componens. Second, I examine he dynamics of boh gross and ne posiions and heir associaed capial ows. Third, I use he model o quanify how composiion effecs and variaions in he inernaional value of dollar conribue o he U.S. exorbian privilege via heir implicaions for he inernaional solvency consrain. My resuls are also relaed o a larger lieraure on inernaional reurns. Early papers in his lieraure (Obsfeld and Rogoff, 2005; Lane and Milesi-Ferrei, 2005; Meissner and Taylor, 2006 and Gourinchas and Rey, 2007a) esimaed ha he reurn on U.S. foreign asses was on average

8 -6- approximaely 3 percen per year higher han he reurn on foreign liabiliies. Subsequen papers by Curcuru, Dvorak, and Warnock (2007) and Lane and Milesi-Ferrei (2009) argued ha hese esimaes were biased upward because of inaccuracies in daa. The daa on reurns I use avoids his bias and has similar sample properies o he reurns used in Curcuru, Dvorak, and Warnock (2007) and Forbes (2009). More imporanly, I show ha persisen variaions in expeced fuure reurn differenials played a dominan role in he evoluion of he U.S. exernal posiion even hough average reurn differenials are very small. In oher words, he economic relevance of reurn differenials for a counry s exernal posiion depends on he behavior expeced fuure differenials condiioned on real-ime informaion, raher han on he size of uncondiional expeced reurn differenials. Finally, my analysis concerning he drivers of capial ows relaes o he large lieraure sudying he effecs of capial conrols (see, Magud, Reinhar, and Rogoff, 2011, for a recen survey). The disincive feaure of he paper wih respec o his lieraure is ha I sudy he deerminans of capial ows in a dynamic, ineremporal seing. The remainder of he paper is srucured as follows: Secion 2 describes he links beween he balance of paymens accouns and he consolidaed budge consrain ha lies a he hear of he model. Secion 3 presens he model. I describe he daa and model esimaes in Secion 4. Secion 5 uses he model esimaes o sudy he evoluion of U.S. exernal posiions and capial ows. The source of he U.S. exorbian privilege is sudied in Secion 6. Secion 7 concludes. 2 Inernaional Asses, Liabiliies, Reurns and Trade Flows I begin by esablishing he links beween he balance of paymens accouns and he consolidaed budge consrain ha governs he evoluion of a counry s foreign asse and liabiliy posiions. I hen examine he role of expecaions, capial gains and porfolio choices in he deerminaion of ne foreign asse posiions and capial ows. This analysis ses he sage for he developmen of he model in Secion The Balance of Paymens and Consolidaed Budge Consrain Consider he accouning ideniy ha links he change in foreign asse and liabiliy holdings o he balance of he paymens. Le A j, and L i, denoe domesic agens holdings of foreign asse j and liabiliy i a he end of period, respecively. Changes in he aggregae asse and liabiliy holdings during period are relaed o he balance of paymens accouns by X X Pj, a A j, Pi, l L i, = CA + KA + EO, (1) j i where is he firs-difference operaor (i.e., Z = Z Z ), and he relaive prices of asse j and liabiliy i, measured relaive o he domesic price level, are Pj, a and P i, l, respecively. The erm

9 -7- on he lef-hand-side idenifies he period ne real capial ow. This ow is equal o he curren accoun balance, CA, plus capial accoun ransfers, KA, and he errors and omissions erm, EO, from he balance of paymens a he end of period, all measured in real erms. The righ-hand-side of (1) may be furher decomposed by wriing he curren accoun in erms of is main componens: CA = X M + UT a UT l + IY a IY l, (2) where X M denoes he difference beween he real ows of expors X and impors M (i.e. real ne expors) during period ; UT a and UT l denoe he real value of unilaeral ransfers (including compensaion of employees) ha add o asse and liabiliy holdings; while IY a and IY l he real invesmen income from asses and liabiliies held a he end of period 1. idenify We can derive an equaion for he evoluion of he counry s exernal posiion from (1) and (2) in hree seps. Firs, le FA = P j P j, a A j, and FL = P i P i, l L i, define he real value of foreign asse and liabiliy holdings a he end of period. Changes in he value of hese holdings are given by FA = X j P a j, A j, + X j P a j,a j, 1 = X j X Pj, a A j, + FA 1 j, a 1apple a j,, (3a) j FL = X i P l i, L i, + X i P l i,l i, 1 = X i P l X i, L i, + FL 1 i, l 1apple l i,, (3b) i where j, a = P j, a A j,/f A and i, l = P i, l L i,/f A are he shares of asses j and liabiliies i in he porfolios of asses and liabiliies, wih P j j, =1and P i i, =1. apple a j, and applel i, are he period real capial grain on asse j and loss on liabiliy i, equal o Pj, a /P j, a 1 and P j, l /P j, l 1, respecively. Thus he change in real value of asses comprises he gross capial ow, P j P a j, A j,, and FA 1 imes he weighed average of capial gains on individual asses, P j j, 1apple a j,. The gross ow in liabiliies, P i P i, l L i, and FL 1 imes he weighed average of capial losses on individual liabiliies, P i i,, similarly deermine he change in he real value of foreign liabiliies. 1apple l i, Nex, we link he invesmen income, ransfers and capial adjusmens o asses and liabiliies in he form of dividends. In paricular, he dividend raes, D j, and D i, for asse j and liabiliy i idenify he porion of hese ows accruing o he holders of exising asse and liabiliies such ha IY a + UT a + KA a = X j X Dj,A a a j, 1 = FA 1 j, 1 j,, and (4a) j IY l + UT l + KA l = X i X Di,L l l i, 1 = FL 1 j, 1 j,, (4b) j wih a j, = Da j, /P a j, 1 and l i, = Dl i, /P l i, 1. Here KAa and KA l denoe he asse and liabiliy ransfers in he capial accoun: i.e., KA = KA a KA l.

10 -8- In he absence of ransfers and adjusmens, D j, and D i, would be deermined by he cash ow associaed wih each asse or liabiliy. For example, in he case of a domesic coupon-paying bond liabiliy, D i, would be deermined by he coupon rae. Similarly, if a long-erm foreign bond is held as a foreign asse, D j, would be deermined by he bond s coupon rae and he prevailing spo exchange rae ha ranslaes coupon paymens ino domesic currency. Here he dividend raes are also deermined by how ransfers and adjusmens are accrued o individual asses and liabiliies. The final sep combines equaions (1) - (4) o give FA FL = X M + X j a j, 1 X a j, + apple a j, FA 1 i l i, l i, + apple l i, FL 1 + EO, or, more compacly, FA FL = X M + R FA 1 R FL 1 + EO. (5) This is he counry s consolidaed budge consrain. R a he porfolios of foreign asses and liabiliies defined by and R l denoe he gross real reurns on R = X j a j, 1R j, wih R a j, = 1+ a j, + apple a j, =(P a j, + D a j,)/p a j, 1 and (6a) R = X i l i, 1R i, wih R l i, = 1+ l i, + apple l i, =(P l i, + D l i,)/p l i, 1. (6b) Equaion (5) shows ha he evoluion of a counry s foreign asse and liabiliy posiion reecs four ses of cors. Firs, decisions concerning inernaional rade in goods and services add o he value of ne foreign asses, NFA = FA FL, insor as hey aler ne expors, X M. Second, decisions concerning he composiion of he asse and liabiliies porfolios made in period 1 (i.e., j, a 1 and l i, 1 ), affec NFA via heir impac on he reurns on asses and liabiliies realized in period. Third, variaions in he dividends and prices of asses (liabiliies) expressed in local currency affec he reurns on individual asses (liabiliies) by changing dividend/price and capial gains componens, a j, and apple a j, ( l i, and applel i, ). Finally, variaions in exchange raes may affec NFA via heir impac on ne expors, foreign-currency denominaed dividends and securiies prices. 2.2 Trade Flows, Asse Pricing and Porfolio Choice The consolidaed budge consrain in (5) combines he effecs of rade ows, asse-pricing and porfolio choice ino a single equaion ha governs he evoluion of a counry s exernal posiion. To appreciae he role of hese cors, i proves informaive o consider he link beween a counry s

11 -9- ne foreign asse posiion and he hisory of is curren accoun balances. For his purpose, I combine (2) wih (4) o wrie CA + KA = X M + X j X j, a 1 a l j,fa 1 i, 1 i, FL 1. Subsiuing his expression ino (5) and simplifying he resul wih (6) produces NFA = X CA s + s=0 X (apple a s apple l s) FA s 1 + where = KA + EO, apple a = P j a j, 1 applea j, and applel = P i l i, 1 applel i,. s=1 i X apple l snfa s 1 + s=1 X s, (7) Equaion (7) shows ha a counry s curren ne foreign asse posiion reecs he hisory of pas (real) curren accoun balances, he cumulaive effecs of capial ransfers, errors and omissions, and he effecs of pas real capial gains and losses via apple a and apple a (he weighed averages of he capial gains and losses on individual asses and liabiliies, respecively). Noice ha capial gains and losses will conribue lile o he curren exernal posiion in counries wih a hisory of small ne foreign asse posiions and porfolio choices ha make apple a s apple l s close o zero for s apple. If he cumulaive effecs of capial ransfers, errors and omissions are also small (as is ofen he case), he curren accoun can be righly viewed as he dominan deerminan of he exernal posiion in hese counries. For oher counries, he capial gains erms appear o have made a significan hisorical conribuion o he ne foreign asse posiion. For example, in he U.S. case, NFA has llen much less han he cumulaion of pas curren accoun balances implying ha he capial gains on foreign asses have r ouweighed he capial loss on foreign liabiliies. As Figure 1 shows, hese effecs have been paricular significan since he early 1980 s. The figure plos he raios of NFA and P s=0 CA s relaive o GDP beween 1973:I and 2007:IV, so he verical disance beween he plos represens he cumulaive conribuion of ne capial gains relaive o GDP. These plos show he deerioraion in he U.S. exernal posiion beween 1980 and 2002 was significanly cushioned by he cumulaive effecs of capial gains, bu since hen he effecs have become much larger. Indeed, all of he recen improvemen in he U.S. exernal posiion is aribuable o capial gain effecs, accouning for as much as 41 per cen of GDP by he end of While capial gains can be an hisorically imporan conribuor o a counry s exernal posiion, heir presence does no imply ha a counry can run persisen curren accoun deficis wih im- 1 This discussion ignores inaccuracies in he daa, which are poenially quie imporan. For example, direc esimaes of he capial gains erms, apple a s and apple l s,areunableoreconcileallhedifferencebeweennfa and P s=0 CAs, see, e.g., Curcuru, Dvorak, and Warnock (2007), Lane and Milesi-Ferrei (2009), and Gohrband and Howell (2010). This backward-looking perspecive on he ne foreign asse posiion depends on how reurns are spli beween capial gains and yields. Below I ake a forward-looking perspecive on he deerminaion of he ne foreign asse posiion ha depends on expeced fuure reurns. Also, in a similar vein, Hausmann e al. (2006) argue ha he posiive income balance on U.S. ne asse holdings is indicaive of mis-measuremen in he U.S. ne asse posiion. s=0

12 -10- Figure 1: Alernaive Measures of he U.S. Exernal Posiion NFA /GDP -solidblack, P s=0 CA s/gdp -dashedred. puniy. Ulimaely, he requiremens of inernaional solvency place limis on he conribuions capial gains and rade ows can make o he evoluion of a counry s exernal posiion. To idenify hese limis, I re-arranging equaion (5) and ierae forward o give NFA = 1X D 1 +i [X +i M +i +(R +i R +i)fa +i 1 ] lim i!1 D 1 +i (FL +i FA +i ), (8) where D +i = i j=1 R +j is he discoun rae. The firs erm on he righ-hand-side of (8) is he presen value of ne expors and he excess reurns on foreign asses. The second erm idenifies he presen value of he fuure inernaional indebedness as he horizon rises wihou limi. This erm mus be equal o zero when inernaional invesors are unwilling o engage in Ponzi-schemes. For example, if lim i!1 D+i 1 (FL +i FA +i ) > 0, curren indebedness exceeds he value of he resources available for domesic residens o pay off heir inernaional deb in he fuure so he counry would have o borrow ever larger amouns o avoid deuling. Clearly, foreign invesors would never consen o such a Ponzi scheme because i amouns o providing domesic residens wih free resources. Alernaively, if lim i!1 D+i 1 (FL +i FA +i ) < 0 domesic invesors would be consening o an analogous Ponzi-scheme. Imposing he no-ponzi condiion and aking expecaions condiional on period- informaion, ha includes he value of NFA, (8) becomes NFA = E 1 X D 1 +i [X +i M +i +(R +i R +i)fa +i 1 ]. (9)

13 -11- Thus, in a world wihou inernaional Ponzi-schemes, a counry s curren exernal posiion is limied by expecaions abou he fuure pahs of expors, impors, and he reurns of foreign asses and liabiliies. More specifically, (9) implies ha any ll in a counry s ne foreign asse posiion mus be accompanied by expecaions of higher fuure ne expors, higher excess reurns and/or a lower discoun raes D +i. Equaions (7) and (9) provide complimenary perspecives on he evoluion of a counry s exernal posiion. (9) shows how he value of foreign asses and liabiliies a a poin in ime embed expecaions abou fuure rade ows and reurns. As hese expecaions change hrough ime he corresponding changes in NFA are apporioned beween capial gains and loss and he ne real capial ows recorded in he balance of paymens accouns. Equaion (7) simply cumulaes he resuling accouning enries ogeher wih he gains and losses. For example, he rise in NFA for he U.S. afer 2004 shown in Figure 1 mus have been accompanied by some combinaion of greaer pessimism regarding fuure ne expors, lower excess reurns, and/or higher discoun raes ha accrued in he form of significan ne capial gains on exising asse and liabiliy posiions. Capial gains and losses also conribue o capial ows. Equaion (3) implies ha he change in he ne foreign asse posiion can be wrien as NFA = FLW + apple a FA 1 apple l FL 1, where FLW = P j P j, a A j, Pi P i, l L i,. Combing his expression wih (9) produces he following equaion for ne capial ows during period : FLW = NFA {(1 + apple a )FA 1 (1 + apple l )FL 1 }. (10) Here capial ows are deermined by he difference beween he desired value for NFA consisen wih curren expecaions, and he ne value of pre-exising foreign asse and liabiliy posiions (incorporaing capial gains and losses). As a maer of accouning, equaion (1) implies ha FLW = CA + KA + EO, so for mos counries ne capial ows simply mirror he curren accoun balance (because KA + EO = 0). In conras, (10) links capial ows o expeced fuure rade ows, reurns, and porfolio choices. To illusrae he usefulness of his perspecive, suppose he economy is hi by a shock ha leads o a downward revision in forecass of fuure ne expors, bu has no effec on fuure reurns. Under hese circumsances, equaion (9) implies ha here mus be a rise in NFA, bu he effec on he ne capial ow could be in eiher direcion. If, for example, he shock produces no capial gains or losses on prior asse and liabiliy holdings, apple a = apple l =0so FLW = NFA and he shock will induce a posiive ne capial ow. In his case, capial ows move in a manner consisen wih ineremporal smoohing (i.e., he curren accoun moves ino surplus as agens anicipae fuure deficis). Alernaively, he shock may induce sizable gains and/or loss on exising asse

14 -12- and liabiliy posiions so ha apple a FA 1 >apple l FL 1. Under hese circumsances he ne capial ow could be negaive, a resul inconsisen wih ineremporal smoohing. Equaion (10) also allows us o idenify he effecs of inernaional porfolio allocaions on capial ows. For example, suppose he economy is hi by a shock ha raises he expeced fuure excess reurn on a paricular securiy, say he equiy on firms in one secor of he economy. If foreign invesors have access o he domesic equiy marke and are expeced o hold some of hese securiies in he fuure, he expeced fuure reurn on foreign liabiliies R+i will rise; and, ceeris paribus, so oo will NFA. Once again, he effec on ne capial ows depends on foreign invesors exising posiions and he response of curren equiy prices. If he news induces a ll in curren equiy prices (as one would expec), bu foreign invesors currenly hold none of he equiies, apple l FL 1 (and apple a FA 1 ) are zero so here are no offseing capial gains or losses on foreign asses and liabiliies. In his case he rise in NFA produces a capial inow. Alernaively, if foreign invesors already hold large posiions in he equiies, he capial loss hey suffer represens a gain o domesic agens because i lowers he value of exising foreign liabiliies. In his case apple l FL 1 is negaive, so here will only be a capial inow if he rise in NFA dominaes (i.e., if NFA + apple l FL 1 > 0). Thus, he response of capial ows o news concerning fuure reurns depends on expeced fuure holdings, reurns and realized capial gains/losses on exising holdings. To summarize, equaions (9) and (10) provide perspecives on he deerminaion of a counry s exernal posiion and ne capial ows ha emphasize he role of expecaions and porfolio choices. These perspecives form he basis for he model of capial ows developed in he nex secion. 3 A Model of Capial Flow Dynamics This secion presens a model of inernaional posiions and capial ows ha incorporaes rade ows, porfolio choice and he capial gains and losses on foreign asses and liabiliy posiions. The model is developed from a log-linear approximaion of he counry s consolidaed budge consrain in equaion (5) and a no-ponzi condiion. I produces presen value expressions for he counry s asse and liabiliy posiions, like equaion (9), bu wihou he nonlineariies involving fuure reurns, ne expors and foreign asses. I combine hese expressions wih forecass from a VAR o model he dynamics of exernal posiions and capial ows. 3.1 Approximaing he Consolidaed Budge Consrain I approximae he counry s consolidaed budge consrain in equaion (5) in several seps: Firs, noice ha (5) can also be wrien as FA FL = X M R FL 1 + R FA 1, (11)

15 -13- wih X = X + T and M = M + T, where T denoes a common rend. 2 Clearly, adding a common rend o expors and impors has no effec on he consolidaed budge consrain because expors and impors only ener as ne expors, X M. I does, however, allow me o use raios involving adjused expors and impors, X and M, as approximaion poins in he seps below. 3 The nex sep is o rewrie (11) as = r + 1 +ln(1 exp(m r 1 )+< ), (12) where < =(FL + X R FL 1 ) /R FA 1. Here lowercase leers denoe naural logs of heir uppercase counerpars, e.g., =lnfa. I now ake a firs-order Taylor approximaion o he las erm erm on he righ-hand-side of (12) around he poin where < =0and 1 2 (0, 1). This produces where k ln ()+ 1 (M /R FA 1 )= = r (m r 1 )+ 1 < + k, (13) ln(1 ). In he second sep I approximae he dynamics of foreign liabiliies. For his purpose, I rewrie he definiion of < as exp ( and ake logs: r 1 )=(1 exp(x r 1 )) exp (r r )+<, r 1 =ln{(1 exp(x r 1 )) exp (r r )+< }. I hen ake anoher firs-order Taylor approximaion o he erm on he righ-hand-side around he poin where 1 (X /R FL 1 ) =, < = 0 and R FA 1 /R FL 1 = 1. Afer some simplificaion, his produces = r (x r 1 )+ 1 < + k. (14) In he final sep I combine (13) and (14) o eliminae <. For his purpose, i is useful o inroduce wo new variables: n =, and r n = r r. Recall ha FA and FL denoe he real value of foreign asses and liabiliies a he he end of period, while R and R are he reurns on he asse and liabiliy porfolios beween he sar of periods 1 and. Thus, n denoes he log raio of foreign asses o liabiliies a he a he end of period, and r n denoes he log excess reurn on asses over liabiliies beween sar of periods 1 and. Combining (13) and (14) 2 Iwillignorehe errorsandomissions ermeo for he sake of clariy. Non-zero values for EO in acual daa will conribue o he approximaion error, see Figure 3 below. 3 Hereafer I drop he erm adjused when i is clear ha I m referring o X and M raher han X and M.

16 -14- o eliminae < produces n = 1 (rn + n 1 )+ 1 (x m ). (15) Equaion (15) approximaes he join dynamics of foreign asses, liabiliies, reurns and adjused expors and impors consisen wih he consolidaed budge consrain in (11) around he poin where M /R FA 1 = X /R FL 1 =1, < =0and R FA 1 = R FL 1. I is easy o check ha his poin is where he counry is in exernally balanced posiion wih ne expors equal o zero and he value of foreign asses is equal o he value of foreign liabiliies. Equaion (15) differs in an imporan way from he approximaion derived by Gourinchas and Rey (2007b). They sar from he consolidaed budge consrain in (5) bu assume ha asse and liabiliy holdings, reurns, expors and impors all comprise cyclical and rend componens. They hen derive an approximaion o he dynamics in (5) around a deerminisic rend pah where solvency is saisfied. More specifically, le a, l, x and m denoe he log deviaions of asses, liabiliies, expors and impors from rend, respecively. Gourinchas and Rey s approximaion can be wrien as n c = 1 (n c 1 + r c 1)+ 1 nx c, (16) wih 2 (0, 1), where nx c = µ x x µ m m and n c = µ a a 1 µ l l 1 for posiive consans µi. Here r+1 c is proporional o he log deviaion of reurns on ne foreign asses; i increases wih he reurn on foreign asses and decreases wih he reurn on foreign liabiliies. Clearly, approximaion in (16) has a similar form o (15), bu i applies o he cyclical componens of expors, impors and he foreign asse and liabiliy posiions raher han he rade ows and posiions hemselves. This disincion is of lile imporance when he rends in he rade ows and posiions are small, bu if he variaions are large and persisen, de-rending may remove much of he variaion in he daa. In such cases, focusing on (esimaes of) he cyclical componens can only provide an incomplee picure of he cors affecing a counry s exernal posiion and capial ows. In conras, (15) can be used o analyze he complee exernal posiion and capial ows for any counry once we add a common rend o expors and impors. As we shall see, hese adjusmens are sraighforward in he U.S. case. 3.2 Ne Posiions and Capial Flows I now combine he approximaion in (15) wih a no-ponzi condiion o derive equaions for a counry s ne exernal posiion and capial ows. For his purpose, i proves useful o define some new variables. Le 1 = r + 1 and 1 = r + 1 denoe he value of asse and liabiliies a he beginning of period. 4 Furher, le nx = x m and xp = nx 4 Iusehe 1 subscrip o indicae ha hese are posiions chosen in period 1 valued a period prices.

17 -15- so ha (15) can be rewrien as xp = r n + nx + 1 xp 1. (17) Iusexp as my measure of a counry s curren ne exernal posiion. I combines he log raio of U.S. asses o liabiliies a he beginning of period, wih raio of expors o impors during he period. The exernal posiion deerioraes when here is a ll in he log raio of expors o impors, or a ll in he value of foreign asses relaive o liabiliies, or some combinaion of he wo. Hereafer, I will refer o nx as simply ne expors. I now use (17) o derive a simple presen value equaion for he exernal posiion. Firs, I rewrie he equaion as xp = r+1 n nx +1 + xp +1. Recall ha he linearizaion parameer,, akes a value beween zero and one. Nex, I ierae forward and ake expecaions condiioned on agens period informaion, which includes he value of xp. This produces xp = 1X i E [r n +i + nx +i]+ lim i!1 E i xp +i, where E denoes expecaions condiioned on agens period informaion. Noice ha lim i!1 E i xp +i < 0 if he counry is expeced o simply issue more liabiliies in he fuure o avoid deuling on is exising inernaional obligaions. Similarly, lim i!1 E i xp +i > 0 when he counry s rading parners are expeced o run an analogous Ponzi scheme. I impose he no-ponzi condiion lim i!1 E i xp +i =0o obain wih xp r = E 1X xp = xp r + xp val, (18) 1X i r+i n. i E nx +i and xp val = E Equaion (18) relaes a counry s curren exernal posiion o expecaions concerning he fuure reurns on foreign asses, foreign liabiliies and he fuure growh in ne expors. Imporanly i embeds he cenral feaure of he forward-looking equaion for NFA in (9) wihou he nonlineariies involving reurns, discoun raes and fuure foreign asse holdings. I will refer o xp r he rade and valuaion componens of he exernal posiion. and xp val By definiion, he ne capial ow during period is equal o he difference beween he ne value of foreign asse holdings a he end of period and heir ne value a he sar of he period: FLW = P j P j, a A j, Pi P i, l L i,. To idenify he capial ows consisen wih (18), I work wih an analogous definiion based on log raios. Specifically, I define he gross log asse (liabiliy) ow during period as he log raio of he end-of-period value of asse (liabiliy) holdings o he as

18 -16- value of beginning-of-period holdings: w = 1 and w = 1. Noice ha posiive values for w and w indicae he accumulaion of asses and liabiliies, respecively. Furher, I idenify he period ne log capial ow as he growh differenial beween foreign asses and liabiliies, w = w So subsiuing for xp from (18) gives w. Combining his definiion wih (15) produces w = 1 (rn + n 1 )+ 1 nx = 1 xp. w = (1 ) 1X i 1 E [r n +i + nx +i]. (19) Equaion (19) idenifies he period ne capial ow necessary o keep he value of foreign asses and liabiliies a he levels consisen wih inernaional solvency. For inuiion, suppose ha a counry enjoys a posiive exernal posiion because ne expors are expeced o ll in he fuure nx +i < 0 (see equaion 18). Under hese circumsances, w mus also be posiive because he E counry needs o accumulae foreign asses more quickly han foreign liabiliies in anicipaion of he ime when hey mus be sold o finance fuure rade deficis. Alernaively, if xp > 0 because expeced fuure reurn on foreign asses are less han hose on liabiliies (i.e., E r+i n < 0), he counry needs o accumulae foreign asses more quickly in anicipaion of lower asse and higher liabiliy prices ha would oherwise erode he relaive value of is fuure asse and liabiliy posiions o he poin of insolvency. 3.3 Gross Posiions and Capial Flows Equaion (15) can also be used o derive expressions for he value of gross foreign asse and liabiliy posiions and heir associaed capial ows. Firs, I use he definiion in (6a) o wrie he reurn on foreign asses as R =(FA + Y )/F A 1, where Y = P j (A j 1Dj a P j A j, ). Recall ha Dj a is he dividend rae for asse j, soa j 1Dj a P j A j, idenifies he difference beween he dividend sream and he cos of acquiring a larger posiion in asse j. Y herefore represens he ne income from all foreign asses during period. To relae ne income o he log reurn on foreign asses, I ake a firs-order log approximaion o he reurn around he poin where Y = M. This produces r = 1 +(1 )y k, (20) where k =ln()+ 1 ln(1 ).

19 -17- Nex, le = 1 x denoe he log raio of he value of foreign liabiliies a he sar of period o expors during period. Combining his definiion wih (15) and (20) produces = +1 + x +1 r +1 +(1 )(y m ) k. Ulimaely, in he absence of Ponzi schemes, here mus be an upper limi on he value of a counry s foreign liabiliies relaive o is expors, so lim i!1 E i +1+i =0. Ieraing forward and applying his no-ponzi condiion gives = E 1X i [ x +i r +i]+(1 )E 1X i=0 i (y +i m +i) k 1. (21) Equaion (21) shows how he counry s consolidaed budge consrain relaes he value of foreign liabiliies a he sar of period o curren expors, expecaions of fuure expor growh, liabiliy reurns, and he ne asse income o impor raio, y+i m +i. For inuiion, is useful o hink of expors as a dividend paymens made o he holders of he counry s foreign liabiliies. Under his inerpreaion, he lef-hand-side of (21) is simply he log price-o-dividend raio for foreign liabiliies. As in sandard asse-pricing, his raio depends posiively on expeced fuure dividend growh and negaively on expeced fuure reurns, as shown by he firs erm on he righ-hand-side (see, e.g., Campbell and Shiller, 1987). The las erm on he righ-hand-side accouns of he effecs of foreign asse accumulaion. Specifically, if E (y+i m +i ) > 0, expeced fuure asse income will be available o pay for impors and reduce foreign liabiliies. Ceeris paribus, his improves he counry s fuure exernal posiion, so he curren value of foreign liabiliies rises relaive o expors consisen wih he inernaional solvency consrain in (18). The gross asse posiion is idenify analogously. Le foreign asses o impors. By definiion, xp = l = 1 m denoe he log raio of so (18) and (21) imply ha = E 1X i [ m +i r +i]+(1 )E 1X i=0 i [y +i x +i] k 1, (22) where y = y + x m is he ne income paid o foreign crediors. The inuiion behind (22) is analogous o ha of equaion (21) excep ha impors now play he role of dividends for foreign asses. Finally, I idenify gross capial ows from he gross posiions and ne income ows. Specifically, combining (15) and (21) wih he definiions of w, w, and produces w = 1 ( )+ 1 (x y ), (23a) w = 1 ( )+ 1 (m y ), (23b)

20 -18- where and are he seady sae values of and (equal o k/(1 )), respecively. These equaions have he inuiive implicaion ha a couny accumulaes a larger asse and liabiliy posiion in response o an increase in he (desired) price-o-dividend raios. Gross asse ows also reec excess expor earnings represened by x, while gross liabiliy ows respond o excess impor coss represened by m y. Of course, hese wo expressions also imply ha he dynamics of ne ows w = w w are consisen wih (19). y 3.4 Equilibrium Posiions and Capial Flows The equaions for he ne and gross posiions and capial ows derived above represen he implicaions of a counry s consolidaed budge consrain and no-ponzi condiions. As such, hey idenify he proximae deerminans of he exernal posiion and capial ows in he form of expecaions concerning fuure rade ows and reurns, raher han a full-blown model where hese expecaions are hemselves deermined as par of he equilibrium. In his paper I use a VAR o idenify he expecaions ha are he proximae drivers of he exernal posiion and capial ows. This approach, inspired by he work of Campbell and Shiller (1987), avoids he complexiy of developing a model ha adequaely represens he complex array of financial insrumens used as foreign asses and liabiliies by many counries. 5 Le denoe a subse of agens informaion a ha comprises he hisory of reurns on asses and liabiliies, expor and impor growh and he exernal posiions available o he researcher: i.e. = {r i,r i, x i, m i, i, i } i 0. By he law of ieraed expecaions, E[E nx +i ]= E[ nx +i ] and E[E r+i n ]=E[r+i n ] for all i>0. Thus, aking expecaions condiional on on boh sides of (18) produces E[xp ]= 1X i E[r n +i + nx +i ]. Since xp = expression above becomes 2, he expecaion on he lef-hand-side is simply equal o xp, so he xp = 1X i E[r n +i + nx +i ]. (24) Unlike (18), his equaion relaes he exernal posiion o forecass for fuure reurns and ne expor growh ha are condiioned on a subse of agens informaion,. I may seem srange ha any addiional informaion available o agens a he ime has no effec on xp. Surely hey have 5 Recall ha r and r are he log reurns on porfolio of foreign asses and liabiliies, so a full-blown DSGE model would need o idenify he porfolio choices embedded in hese reurns. While recen papers by Evans and Hnakovska (2005 & 2007), Hnakovska (2010), Tille and Wincoop (2010), Devereux and Suherland (2010) and ohers begin he developmen of such DSGE models, hey have no reached he poin where hey can be par of an esimable srucural model for exernal posiions and capial ows.

21 -19- informaion ha is useful for forecasing fuure changes in reurns ha is no available o he researcher. However, is no jus any subse of agens informaion. Because conains he elemens ha comprise curren and pas values of xp as well as he hisory of reurns and he growh in ne expors, i effecively conains all he informaion agens are using o calculae E [r n nx +i +i + ] for i>0. For example, if agens have informaion ha leads hem o forecas higher growh in ne expors weny quarers ahead han hey would based on heir observaions of { nx i, r n i } i 0, his informaion will be reeced in a lower value for xp. Any informaion se conaining { i, i, nx i,rn i } i 0 will herefore capure his exra informaion affecing E [r+i n + nx +i ]. In shor, we are using equaion (24) o consruc a paricular subse of agens informaion for which he implicaions of he presen value model for he exernal posiion remain valid. Following Campbell and Shiller (1987), we can use (24) o derive resricions on he join dynamics of he exernal posiion, ne expors, and he reurn differenial. Firs, I compue E[r+i n nx +i ] for i>0 from a VAR. Le he vecor z =[ r r x m ] 0 follow a k 0 h. order VAR: z = a 1 z 1 + a 2 z a k z k + u, where a i are marices of coefficiens from each of he VAR equaions, and u is a vecor of mean-zero shocks. To compue E[r n +i z.. z k+1 nx +i ], he VAR is wrien in companion form: a 1 a k I = I 0 z 1 z.. k u , or, more compacly, Z = AZ 1 + U. (25) Muli-period forecass are easily compued from (25) as E[Z +i Z ]=A i Z, where A i denoes i muliplicaions of he A marix. Nex, consider he implicaions of equaion (24) for he dynamics of Z. Le he vecors ı r =[ ], ı nx =[ ] and ı xp =[ ] selec r n, nx and xp from Z. I can now compue he muli-period forecass of ne expor growh and he reurn differenial as E[r+i n ]=ı r A i Z and E[ nx +i ]=ı nx A i Z for all i>0. Subsiuing hese forecass ino (24) produces 6 ı xp Z = xp = (ı r + ı nx ) 1X i A i Z = (ı r + ı nx )A(I A) 1 Z. 6 In deriving he equaion I have implicily assumed ha he eigenvalues of A are less han one in absolue value. Since 1 >>0, his condiion is saisfied if z follows a covariance saionary ime series process.

22 -20- This equaion mus hold for all possible values of he Z vecor, so he companion marix A from he VAR mus saisfy ı xp = (ı r + ı nx )A(I A) 1. (26) Equaion (26) conains a se of resricions on he VAR coefficiens in (25) ha represen consrains on he join dynamics of r n, nx, and xp. They can be empirically examined for paricular values of by compuing a nonlinear Wald es from esimaes of he A marix compued from OLS esimaes of he VAR equaions. This is really a es of a join null hypohesis. In addiion o he presen value relaion in (24) we are also esing he assumpion ha forecass of fuure reurns and ne expor growh can be compued from he VAR as (ı r + ı nx )A i Z. This is no an innocuous assumpion. Even if he dynamics of z can be represened by a k 0 h. order VAR, hese forecass only represen he bes forecass of r n ha can be compued using linear +i + nx +i combinaions of he variables in Z. I is possible ha forecass based on boh linear and nonlinear combinaion of he variables in Z have a lower mean squared forecas error. If his is he case, E[r+i n + nx +i ] 6= (ı r + ı nx )A i Z and he resricions in (26) will no hold rue even if he presen value relaion in (24) is valid. The VAR can also be used o sudy gross foreign asse and liabiliy posiions. In paricular since is an elemen in, we can rewrie (21) as 1X = i E[ x +i r +i ]+(1 )E 1X i=0 i E[y +i m +i ] 1 k. (27) Noice ha he firs erm on he righ-hand-side can be compued from he VAR, so we can examine he exen o which variaions in he gross liabiliy posiion reec changes in expors and he presen value of fuure expor growh and reurns. The one cach here is ha agens forecass for x +i r+i x +i r+i ] even hough 2. The reason is ha may conain agens privae informaion concerning y+i m +i as well as x +i r+i so he hisory of is no necessarily sufficien for capuring all heir privae informaion in E [ x +i r+i ]. For his reason, I examine he robusness of he esimaes for E[ x +i r+i ] o alernaive VAR specificaions. Finally, recall ha he period ne capial ow is relaed o he exernal posiion by w = 1 xp, so aking condiional expecaions on boh sides of (19) produces w = (1 ) 1X i 1 E[r n +i + nx +i ]. (28) This equaion provides he basis for sudying he drivers of ne capial ows using he VAR esimaes. The drivers of gross asse and liabiliy ows can also be examined wih he VAR using (23) wih (27) and (28).

23 -21-4 Daa and Esimaion I use he model o sudy he U.S. exernal posiion and capial ows in quarerly daa beween 1973:I and 2007:IV. I exclude daa from 2008 onwards o avoid confounding he effecs of he world financial crisis wih normal condiions in world rade and financial markes. This secion firs describes he daa and discusses how I esimae he common rend in expors and impors ha is used in my approximaion of he consolidaed budge consrain. I hen presen summary saisics and he VAR esimaes. 4.1 Daa I use an exended version of he daa used by Gourinchas and Rey (2007b). They compued he marke values for four caegories of U.S. foreign asse and liabiliies: equiy, foreign direc invesmen (FDI), deb and oher, by combining daa on inernaional posiions wih informaion on he capial gains and losses. I exend heir daa o 2007:IV following he deailed procedures described in Gourinchas and Rey (2005). In brief, he posiions of asse j and liabiliy i are updaed according o FA j, = FA j, 1 + Flow j, + Dis j,, and FL i, = FL i, 1 + Flow i, + Dis i,, where: FA j, and FL i, denoe he posiions a he end of period ; Flow j, and Flow i, denoe he period- ows ha ener he balance of paymens; while Dis j, and Dis i, are he disconinuiies reecing a marke valuaion adjusmen beween he end of periods 1 and. When daa on he disconinuiies is no direcly available, hey are compued from he capial gains on he individual securiies ha comprise he foreign asse or liabiliy caegory. In he final quarer of each year Dis j, and Dis i, are adjused so ha FA j, and FL i, map ino he Inernaional Invesmen Posiion (IIP) daa repored by he Bureau of Economic Analysis (BEA). Below I use ime series of he U.S. aggregae foreign asse and liabiliy posiions, FA = P j FA j, and FL = P i FL i,, as well as he four caegories of asses and liabiliies. The reurns on he asse and liabiliy caegories, Rj, and R i,, are compued from he porfolio weighed average of he reurns on he individual asses ha comprise each caegory. The porfolio shares for he underlying securiies come from U.S.Treasury repors on U.S. holdings of foreign securiies and foreign porfolio holdings of U.S. securiies. These shares are also used o compue he capial gains on foreign asse and liabiliy caegories when needed. The reurns on he aggregae foreign asse and liabiliy posiions are calculaed as R a = P j a j, 1 RFa j, and R l = P i l i, 1 R i, where j, a = FA j,/f A and i, l = FL i,/f L. All posiions and reurns are compued in consan U.S. dollars. 7 7 I is worh emphasizing ha his mehod for compuing reurns differs from he one used by early papers in he