eSA,l Dri

hatausdey. Wexbraalidsht cat in

accounts may move in opposite directions. 2009 Elsevier B.V. All rights reserved.

er equincomen equiafter tha signiwidef correcebate o

Journal of International Economics 80 (2010) 144156

Contents lists available at ScienceDirect

Journal of Internat

j ourna l homepage: www.for a signicant correction. However, income from the capital gains couldhave been nancing consumption in the US, and so the imbalances couldhave been sustainable.3 After the 2008 nancial crisis some of the originalarguments will require certain revision, but one central conclusion isundisputed: the growth of gross asset holdings during the last couple ofdecadesmust change signicantly our understanding of howmeasures ofsustainability have to be dened, and how the adjustment process needsto take place.

To evaluate the stochastic properties of the external measures ofsustainability, we calibrate ourmodel to reect the current state of theUS economy. In particular, through our parameter selection, weattempt to match the magnitudes of the trade balance and currentaccount decits in the US, home bias in asset holdings, net foreigndebt of the US, and average cross-country correlations of consumptionexpenditures. We choose the parameters assuming that the currentsituation is one of equilibrium (as in our economy). In this Corresponding author. Tel.: +44 20 7000 8218.E-mail addresses: apavlova@london.edu (A. Pavlova), r

1 Tel.: +1 617 258 8374.2 As documented in e.g., Gourinchas and Rey (200

(2001, 2007), and Tille (2003, 2008).3 See, e.g., Caballero et al. (2008), Hausmann an

Gourinchas and Rey (2007b).

0022-1996/$ see front matter 2009 Elsevier B.V. Adoi:10.1016/j.jinteco.2009.09.003n the sustainability of thenally-measured) currenteled, indicating the need

because asset prices and portfolio holdings are all endogenous, it ispossible to study the interconnections between external sustainabilityand portfolio decisions.US current account decit. The (conventioaccount decits in the US have been unparall1. Introduction

An unprecedented rise in cross-bordtwo decades2 has generated a source ofthe national accounts: capital gains opractice incorporates capital gains onlylack ofmarking tomarketmay result inthe extent of external imbalances worldof Europe, and Japan. The importance ogains has been at the heart of a recent dity holdings over the pastpreviously disregarded inty holdings. The currentey are redeemed, and thiscantmisrepresentation ofespecially in the US, mosttly accounting for capital

In this paper we respond to the critique of the conventionaldenition of the current account and dene a capital-gains adjustedcurrent account a measure that explicitly accounts for capital gainson net foreign asset positions of a country. We investigate theproperties of this measure in the context of a two-country macro-nance model of Pavlova and Rigobon (2008a) and compare it toother measures of external accounts. The model is solved in closed-form, which allows us to examine several analytical properties thatlink the external accounts and nancial asset holdings. Moreover,environment, wmissing from theunexpected capitproperty, offsetttraditional curresimilar effect occcapital gains, hodynamic proper

igobon@mit.edu (R. Rigobon).

7a), Lane and Milesi-Ferretti

d Sturzenegger (2006), and

ll rights reserved.An asset-pricing view of external adjustm

Anna Pavlova a,, Roberto Rigobon b,1

a London Business School and CEPR, London Business School, Regents Park, London NW1 4b Sloan School of Management, MIT and NBER, Sloan School of Management, 50 Memoria

a b s t r a c ta r t i c l e i n f o

Article history:Received 24 July 2008Received in revised form 21 September 2009Accepted 21 September 2009

Keywords:Current accountPortfolio choiceIncomplete marketsInternational nanceAsset pricingValuation effects

Recent literature has argued taccount aremisleadingbecthe current account to incluadjustment and sustainabilitRigobon (2008a) that allowsaccounts' dynamics. We caliwhich have already been vadjusted current account andaccount. Second, we nd thaFinally, we demonstrate thant

United Kingdomve, Room E52-442, Cambridge, MA 02142-1347, USA

conventionalmeasures of external sustainability the trade balance and currente theyomit capital gains onnet foreign asset positions.Weadjust thedenitionofthe capital gains and discuss how this may affect our thinking about externale do so in the context of a two-country macro-nance model of Pavlova and

ploration of the interconnections between equilibrium portfolios and externalte the model and nd that it generates several testable implications, some ofated empirically. First, we establish dynamic properties of the capital-gainsow that they are fundamentally different from those of the conventional currentpital gains have a stabilizing effect on the trade balance and the current account.response to a shock, the conventional and the capital-gains adjusted current

ional Economics

e lsev ie r.com/ locate / j i ee rst analyze separately the two elements that areconventional current account: the expected and the

al gains. We show that the former have a stabilizinging the uctuations in the trade balance and thent account. Gourinchas and Rey (2007b) document aurring in their dataset. It is the unexpected part of thewever, that is key to the dramatic differences in theties of the traditional and the capital-gains adjusted

current account in our model. The traditional current account followsa persistent process, while the capital-gains adjusted current accountis highly volatile and serially uncorrelated. This is consistent with theevidence presented in Kollmann (2006) and Lane and Shambaugh(2007). In other words, the capital-gains adjusted current account

145A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156behaves much like asset returns, whose short-term dynamics are alsodominated by unexpected capital gains.

In order to understand the role of capital gains (valuation effects)in the external adjustment mechanism, we study impulse responsesof our economy. The standardmodel of external adjustment is the onebased on the canonical intertemporal approach to the currentaccount. In that model, when a shock occurs, we rst study itsimplications for output and consumption, and given those implica-tions, we can trace their impact on the trade balance, the currentaccount, the savings decisions, and ultimately on internationalpositions. Our view in this paper is different. It starts by recognizingthat agents already have wealth invested internationally. Therefore,the starting point even before the shock shows up is to determinethe distribution of wealth and how it is invested (i.e., the compositionof international portfolios). When a shock takes place, the rst step isto track its impact on production and asset prices. Once these impactsare understood, we can track how the net foreign asset positions aregoing to be affected by the shock. That in turnwill allow us to computea new wealth distribution in the world economy. Agents' wealth willdetermine their consumption patterns, and given output, we can trackthe implications for the external accounts. Guided by this view ofexternal adjustment, we do not nd it surprising that our impulseresponses show that following a shock, the conventional currentaccount and the capital-gains adjusted current account may move inopposite directions.

Our work is related to the growing theoretical macro-nanceliterature that incorporates portfolio choice and asset pricing intomodels of open economy macroeconomics. Similarly to our approachhere, Devereux and Sutherland (2008), Evans and Hnatkovska (2007),Ghironi et al. (2006), Kollmann (2006), and Tille and van Wincoop(2007) all base their analyses of external accounts on stochasticportfolio models with incomplete markets.4 These papers employvarious approximation techniques to study the behavior of theirmodels around their steady states. By contrast, we base our analysison an exact closed-form characterization of our equilibrium. More-over, the steady state in our economy is stochastic.

The rest of the paper is organized as follows. Section 2 brieydescribes the model. Section 3 denes the capital-gains adjustedcurrent account and explores some links between externalaccounts and nancial asset holdings. Section 4 studies dynamicproperties of the capital-gains adjusted current account, contrastingthem to those of the conventional current account. Section 5 dis-cusses the external adjustment mechanism in our model. Section 6offers some concluding remarks and directions for future research.The online appendix gives further theoretical background for ourexpressions.

2. The model

2.1. The economic setting

For the purposes of our investigation, we adopt the model fromPavlovaandRigobon(2008a).Webriey review it here for completeness.

We work with a pure-exchange nite-horizon continuous-timeeconomy populated by two countries: Home and Foreign. The Home

4 Also related, but, unlike ours, cast in the context of production economies, areelegant analyses of Devereux and Saito (2006), and Kraay and Ventura (2000).Coeurdacier et al. (2008) primarily focus on equity home bias, but do also reportimplications for NFA dynamics similar to ours. Other important contributions to thisliterature, but with a different focus than ours, include Engel and Matsumoto (2006)

and Mendoza et al. (2007).country represents a large industrialized country, while Foreign standsfor the rest of the world. Each country is endowed with a Lucas treeproducing a strictly positive amount of a country-specic perishablegood:

dYt = Y tYtdt + Y tYtdwt Home; 1

dY*t = Y* tY*tdt + Y* tY*tdw*t Foreign; 2

where w and w are the (independent) Brownian motions represent-ing Home and Foreign output shocks, respectively, and Y, Y, Y>0,and Y>0 are the mean growth rates and volatilities of output. Theprices of the Home and Foreign goods are denoted by p and p,respectively. We x the world numeraire basket to contain a(0,1)units of the Home good and (1a) units of the Foreign good, andnormalize the price of this basket to be equal to unity. The terms oftrade, q, are dened as the price of the Home good relative to that ofthe Foreign good: qp/p. Our modeling of nancial markets isstandard. The Home and Foreign stocks S and S, are claims to theHome and Foreign trees, respectively. They are available for trade byall investors and are in xed supply of one share each. There is also theworld bond B in zero net supply, which is a money market accountlocally riskless in units of the numeraire.

The Home country's representative consumer starts with anendowment of s Hs shares of the Home stock, s Hs shares of the Foreignstock and a (negative) position in the bond. The Foreign consumer ownsthe remaining shares of the stocks and an offsetting (positive) positionin the bond, denoted by b . Later in this paper we calibrate themodel sothat Home represents theUS economy,whose net bondposition is largeand negative. This is the rationale for giving the countries initialbondholdings. The initial wealth of the Home resident is thusWH(0)=sHs S(0)+s Hs

* S(0)b and that of the Foreign resident isWF(0)=S(0)+S(0)WH(0). A representative consumer in each country i, i{H,F},chooses nonnegative consumption of each good (Ci(t), Ci(t)) and aportfolio of the available securities si(t)(siS(t), siS*(t)), where sij thenumber of shares of asset j held by consumer i. The dynamic budgetconstraint of each consumer has the standard form

dWit = sBi tdBt + sSi tdSt + ptYtdt + sS*i tdS*t

+ p*tY*tdtptCitdtp*tC*i tdt;3

where Wi(T)0, i{H, F}. Preferences of consumer i, are representedby a time-additive utility function dened over consumption of bothgoods:

E T0etuiCit;C*i tdt

h i; >0; ifH; Fg; 4

where

uHCHt;C*Ht= Ht logCHt + Ht logC*Ht;

uFCFt;C*F t = F logCFt + F logC*F t:

Stochastic processes H and H in the utility of the Home countryrepresent preference shifts toward the Home and Foreign good,respectively. For generality, the innovations to H and H are given bya combination of supply shocks w and w as well as two independentstandard Brownianmotionsw andw. Without the last two Brownianmotions, nancial markets are complete. But if the preference shiftersdisplay nontrivial dependence on w and w, the existing investmentopportunity cannot span the uncertainty in the model, and hence thepossibilities of hedging against the preference shifts is impaired and risksharing in the world economy becomes imperfect. The main focus of

this paper is on the Home country, which is why we assume away any

preference shifts at Foreign and concentrate on the effects of domesticpreference shifts at Home.5

The preference shifts or demand shocks are important ingredients ofour model, for two reasons. First, in the absence of the demand shocks,free trade in goodsmakes stock prices perfectly correlated and nancialmarkets irrelevant (Helpman and Razin (1978), Cole and Obstfeld(1991), Zapatero (1995)). Second, empirical evidence indicates thatdemand shocks are important for reproducing the real-world dynamics;supply shocks alone are typically not sufcient. For example, Stockmanand Tesar (1995) calibrate preference shocks to be roughly 85% of the

The equilibrium terms of trade and stock prices are given by:

qt = Ht + tFHt + tF

Y*tYt 8

and

eig an b pres d as e Ap

WtF

S WF F + + F

S

146 A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156size of supply shocks. Pavlova and Rigobon (2007) estimate a modelmore similar to ours and conclude that demand shocks haveapproximately the same volatility as supply shocks.

2.2. Characterization of equilibrium

An equilibrium in this economy is dened in a standard way: it is acollection of goods and asset prices (p, p, S, S, B) and consumptioninvestment policies (Ci(t), Ci(t), xiS(t), xiS

*(t)), i{H, F} such that (i) eachconsumerinvestor maximizes his utility (Eq. (4)) subject to the budgetconstraint (Eq. (3)) and (ii) goods, stock, and bond markets clear.

In this incomplete markets economy, the usual construction of arepresentative agent's (planner's) utility as a weighted sum, withconstant weights, of individual utility functions is not possible.However, as we explain in Pavlova and Rigobon (2008a), one can stillsolve for the equilibrium allocations in this economy using an analogueof the central planning approach in which the weights in the ctitiousworld representative agent utility are stochastic.6 This ctitious repre-sentative agentmaximizes his utility subject to the resource constraints:

maxfCH ;CH*;CF ;CF*g

E T0etuHCHt;C*Ht + tuFCFt;C*F tdt

h i5

s:t: CHt + CFt = Yt; 6

C*Ht + C*F t = Y*t; 7

where we have normalized the weight on the Home consumer to beequal to one and assigned the weight to the Foreign consumer. Thepossibly stochastic weighting process is to be determined as part ofthe equilibrium. The consumption allocations and the goods and assetprices supporting these allocations are the same as those in adecentralized competitive equilibrium. In the decentralized equilib-rium, is simply the ratio of themarginal utilities of either good of thetwo countries. When markets are complete, this ratio is constant(constant ). When markets are incomplete, the marginal utilities areno longer proportional, and so becomes stochastic. It enters as anadditional (endogenous) state variable, which reects the relativeweight the planner puts on the Foreign country's utility.

We do not reproduce the full equilibrium characterization here andjust report the expressions that are relevant for our discussion in thispaper. We refer the reader to Pavlova and Rigobon for a completecharacterization and to the supplementary appendix to this paper for anintuitive derivation of the expressions below.

5 Solving a model with stochastic preference shifts at Foreign involves an additionaltechnical difculty, which has to do with the derivation of the expressions forequilibrium stock prices. While we believe that the model with stochastic preferenceshifts in all countries is still analytically tractable, we leave this extension for futureresearch.

6 The approach of solving for competitive equilibrium via solving for weights in therepresentative agent was pioneered by Negishi (1960). It was extended forcontinuous-time economies by Cuoco and He (1994) and afterwards used extensivelyin dynamic asset pricing models with nancial market frictions (see, among manyothers, Basak and Cuoco (1998), Detemple and Serrat (2003), and Pavlova andRigobon (2008b)). A related approach is the extra-state-variable methodology of

Kehoe and Perri (2002) and Marcet and Marimon (1999).and hence

t = WFtWHt

Ht + HtF + F

: 12

Adrop in is then akin to awealth transfer fromForeign toHome. Todevelop the intuition for the effect of thewealth transfer on the terms oftrade it is useful to recall the classic Transfer Problem.7 A wealth(income) transfer to Home raises Home's demand for both goods. But inthe presence of home bias in consumption, demand for the Home goodgoes up by more. Hence the relative price of the Home good increases,

7 The original Transfer Problem was the outcome of a debate between Bertil Ohlinand John Maynard Keynes regarding the true value of the burden of reparationspayments demanded of Germany after World War I. Keynes argued that the paymentswould result in a reduction of the demand for German goods and cause a deteriorationof the German terms of trade, making the burden on Germany much higher than theactual value of the payments. See Krugman and Obstfeld (2003) for an elaboration and

reHt = Ht + tferences.t; t =

Ht tt; 11Ht + H t Fealth of Home and F n c e re ente (se pendix A)w orSt = 1eTt

qt

aqt + 1a Yt; 9

S*t = 1eTt

1

aqt + 1a Y*t: 10

To convey the economic mechanisms behind the formulas, wepresent the following simple table that summarizes the signs of thedirections of responses to movements in the underlying state variables.

Effects of Y Y H H a drop in a

On the terms of trade q + + +On the Home stock S + + + +On the Foreign stock S + + + a The shocks to the rst four variables are positive, while the shock to the Foreign's

weight is negative (for ease of interpretation). Obtaining unambiguous signs of theeffect of (reported in the Table) requires an additional assumption of home bias inconsumption (i>i).

A positive output shock at Home (an increase in Y) raises thedividend on the Home stock and so Home's stock price increases. Atthe same time, it increases the supply of the Home good in theworld. Asthe good becomes less scarce, its price falls relative to that of the Foreigngood. Hence Home's terms of trade deteriorate and Foreign's terms oftrade improve. The improvement of Foreign terms of trade increases thevalue of Foreign's output and hence the Foreign stock goes up. Theresponse following a Foreign output shock is analogous.

A preference shift towards the Home good (an increase in H)creates an excess demand for the Home good. This pushes up its pricerelative to that of the Foreign good and therefore improves Home'sterms of trade. The value of Home's output (dividend) increases whilethat of Foreign's decreases. Hence Home's stock market goes up andForeign's stock market falls.

A negative shift in represents an increase of the weight of theHome country's utility in the representative agent. This weight can belinked formally to the wealth distribution in the economy. Indeed, the

147A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156i.e., Home's terms of trade improve, just as in the Transfer Problem. SinceHome's terms of trade improve, the value of its output (dividend) goesup, and hence Home's stock price increases. As Foreign's terms of tradedeteriorate, the value of that country's output goes down and the priceof its stock falls.

All equilibrium quantities can be pinned down as functions of thefour exogenous state variables (Y, Y, H, and H) and the endogenousstate variable . The dynamics of are derived as part of the equilibriumcharacterization.

3. The current account

Beforewe turn to investigating equilibriumbehavior of our economyand making a link between portfolio rebalancing and externaladjustment mechanisms, we highlight the model's implications forthe current account and its dynamics. We rst start with the textbookdenition of the current account and then consider the denition basedon changes in a country's net foreign asset position. In principle, the twodenitions should yield similar measures. However, once expected andrealized capital gains are accounted for, thedifferences between the twomeasures, andespecially their dynamic properties, canbe striking, aswedemonstrate below.

3.1. The conventional current account

Let us concentrate on the Home country. The conventional measureof the current account, employed in international nance textbooks andused in the national accounts, is

CA = Trade Balance + Net Dividend Payments

+ Net Interest Payments:

In our economy, the trade balance is given by

TBHt = ptYtCHtp*tC*Htdt;

and the current account by

CAHt = TBHt +sS*H tp*tY*tsSFtptYt + sBHtBtrtdt:13

The secondand the third terms in Eq. (13) are dividend receipts fromforeign assets minus dividend payments to Foreign, and the last term isnet interest payments. Recall that each of the above quantities in ourmodel is dened as a rate (e.g., the export rate, the dividend rate, etc.)and hence need to be scaled by a time increment.

3.2. The capital-gains adjusted current account

Dening the current account as the change in the net foreign asset(NFA) position of a country, we have

CGCAHt = dsS*H tS*tsSFtSt + sBHtBt; 14where the rst two terms in the square brackets are Home'sinvestment in the Foreign stock minus Foreign' investment in theHome stock, and the last term is Home's balance on the bond account.The label CGCA stands for capital-gains adjusted current account,the rationale for whichwill become clear shortly. Note that, by marketclearing, sFS(t)=1sHS (t) and that, by denition, Home's wealthequals its portfolio value, WH(t)=sHS (t)S(t)+sHS

*(t)S(t)+ sHB(t)B(t).Hence, we can rewrite Eq. (14) as

CGCA t = dW tdSt: 15H HTo simplify the exposition below, let us introduce some newnotation. Let us summarize all the Brownian motions driving theeconomy in the vector w(w,w,w,w) and represent the dynamicsof the bond and the stocks as follows

dBt = Btrtdt; 16

dSt + ptYtdt = StStdt + Stdwt; 17

dS*t + p*tY*tdt = S*tS* tdt + S* tdwt; 18

where the interest rate r, the stocks expected returns S and S andtheir volatilities S and S are determined in equilibrium (e.g., fromEqs. (9)(10)). Armed with this notation, we can rewrite the budgetconstraint of Home (Eq. (3)) as follows:

dWHt = sBHtBtrt + sSHtStSt + sS*H tS*tS* tdt+ sSHtStSt + sS*H tS*tS* tdwt+ TBHtptYtdt:

Substituting it into Eq. (15) and then using Eq. (17) and the stockmarket clearing, we arrive at the following expression:

CGCAHt=TBHt+sS*H tS*tS* tsSFtStSt+sBHtBtrtdt+ sS*H tS*tS* tsSFtStStdwt:

19

The rst difference between the conventional and the capital-gains adjusted current account revealed by Eq. (19) is the presence ofthe diffusion (dw) component in Eq. (19) and its absence in Eq. (13).This component is the unexpected part of the realized capital gains onHome's net foreign assets. A shock dw typically has a differentialimpact on the stock portfolios of Home and Foreign. The capital-gainsadjusted current account of Home improves if its return on foreignasset holdings exceeds the return the Foreign country makes on itsholdings of Home's assets. Eq. (19) assumes that all capital gains aremarked to market. This aspect makes CGCA different from book-value based measures of current account such as the one in Eq. (13),commonly employed in practice.

It is important to note that the twomeasures of the current accounthave fundamentally different dynamic properties. The conventionalcurrent account is a persistent process, in line with the results in theexisting literature. In contrast, the capital-gains adjusted currentaccount features additionally an increment of a randomwalk (dw) pro-cess, and therefore it bears a closer resemblance to the dynamics of astock market rather than a persistent macroeconomic series such asdividends or the conventional current account. It is amply documentedby the proponents of the efcient markets hypothesis in nance thatstocks' capital gains are large, volatile, and serially uncorrelated. And soshould be the uctuations in a NFA position of a country, captured hereby CGCA.

The second difference between the two measures of the currentaccount stems from the differences in the expected (dt) component.Comparing Eqs. (13) and (19), we nd two elements that arecommon to the conventional and the capital-gains adjusted currentaccount measures: the trade balance and net interest payments on

the (locally) riskless bond. The remaining terms, due to holdings of

the risky stocks, are different. To better highlight the differences, notefrom Eqs. (17)(18) that

In our choice of parameter values we have tried to match severalimportant statistics of the US economy. Where directly observable, weset the parameters equal to their average values in the data. Where notobservable (e.g., the preference shifters),we calibrate the parameters sothat themodel implies that theHomecountry (i) runs a trade decit anda (conventional) current account decit of the sizes roughly matchingthose of the US economy, and (ii) so that the countries have positive

9

Table 1

148 A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156StStdt = Et dSt + ptYtdt and

S*tS*tdt = Et dS*t + p*tY*tdt;

where Et[] is the expectation conditional on the information at timet. The rst term on the right-hand side of these expressions is theexpected capital gains and the second one is the dividends per share.Denoting the expected capital gains on holding a share of stocks S andS by ECGS and ECGS, respectively, we can express the differencebetween the expected capital-gains adjusted current account and theconventional one as

Et CGCAHtCAHt = sSFtECGSt + sS*H tECGS*t: 20

This simple formula describes what Hausmann and Sturzenegger(2006) label themissing dark matter in themeasurement the currentaccount. This dark matter accumulates due to the fact that thecountries hold risky assets which are issued at home as well as abroad,and these risky assets have different expected capital gains. Theexpected capital gain on an asset, of course, reects its risk and returntradeoff. If domestic assets are safer and have lower expected returnsthan foreign, a country earns a higher expected return on its assets thanit owes on its liabilities. In this scenario, the difference between thecapital-gains adjusted and the conventional current account is expectedto be positive. We expect such pattern to be occurring in the US whosegains on domestic assets have been lower than gains on assets abroad(Gourinchas and Rey (2007b)).

The sum of net expected capital gains and net unexpected capitalgains is what has been typically labeled as valuation effects in thecurrent account adjustment literature. Empirically, it is very hard todisentangle the two individual components. However, as we will pointout below, their stochastic properties are very distinct.

One may wonder why the terms of trade were mentioned nowherein this discussion. After all, the original arguments highlightingvaluation effects stress primarily the fact that the values of a country'sasset and liabilities change in response to uctuations in the exchangerate (or the terms of trade), and these uctuations need to be taken intoaccount when evaluating the NFA position of a country. This argumentdenitely applies in ourmodel in fact, all intuitions for the behavior ofstock prices that we have given above (Section 2), are based on themovements in the terms of trade. The terms of trade are thus embeddedin the prices of stocks and their dynamics.

It is worth mentioning that in our derivations in this section we didnot need to specialize consumer preferences to be loglinear. Theexpressions for both the current account in Eq. (13) and the capital-gains adjusted current account in Eq. (19) are valid for a general utilityfunction. The loglinear form of the preferences is needed only forobtaining a closed-form characterization of the inputs into the formulas,namely the stock prices and the countries' portfolios.

3.3. The links between financial asset holdings and external accounts

With the analytical structure we have established above, we canderive several properties linking external accounts and nancial assetholdings in the context of our model. Of most relevance for ourdiscussion in subsequent sections are the following two properties.8

8 These properties are, of course, model-specic. For a proof of the properties see

Pavlova and Rigobon (2008a).Property 1. The relationship between the Home country's net debtposition and its current account is as follows:

CAHt = rt

1eTt

sBHtBtdt: 21

Property 2. The relationship between the Home country's net foreignasset position and its trade balance is given by

TBHt =

1eTtNFAHtdt: 22

Property 1 may appear counter-intuitive: if the term in theparentheses is positive, a debtor country could be running a currentaccount decit forever! Note, however, that ours is not a bond-onlyeconomy and bondholdings constitute only a part of the country's netexternal wealth. The country's net external wealth also includes netequity holdings, and is captured by NFA. Countries with negative NFApositions (debtor countries) must run a trade surplus; they clearlycannot have a decit forever, according to Property 2. This result(Property 2) is very intuitive and in fact is quite similar to therelationship derived in Obstfeld and Rogoff (1996), Chapter 2, with themain difference being that we consider a general equilibrium modelwith trade in equities. Moreover, having a negative debt position inequilibrium implies that a country (say, Home) is holding a leveragedportfolio. That portfolio is riskier than that of the Foreign country. TheHome country is compensated for taking a greater share ofworld risk bycollecting risk premia on its risky asset holdings. These risk premia canbe used to nance current account decits.9 In a recent paperGourinchasandRey (2007a)argue that theUS,whoseexternal liabilitiesare mainly Treasury bills and bonds (with relatively low expectedreturns)while its external assets are riskier instruments (with relativelyhigh expected returns), collects additional income from positive riskpremia on its NFA positions. Our model allows for a calibration thatcaptures this possibility.

4. Dynamic implications

In this section, we calibrate our model to match several key aspectsof the data. The Home country in our calibration represents the USeconomy and the Foreign country the rest of the world. This exerciseallows us to contrast different measures of external accounts and toquantify the extent of discrepancies across themeasures. It also enablesus to examine valuation effects entailed by our model.

4.1. Calibration

Parameter choices.

Parameter Value Parameter Value Parameter Value

Y(0) 1 H(0) 0.7 Y 0.01Y (0) 2 F 0.7 Y 0.01Y 0.02 Y(0) 0.3 H (z1, 0, z2, 0)Y 0.02 F 0.3 H (0, z1, 0, z2), z1 [0, 0.0061], 0.05 (0) 0.9 z2[0.002, 0.0136]a 0.5We thank Mick Devereux for suggesting this intuition to us.

cap

149A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156cross-holdings and their portfolios exhibit a home bias of a reasonablemagnitude. Table 1 lists the ensuing parameter values.

According to this parametrization, the countries' output processesare geometric Brownian motions (since both the drift and diffusion areconstant). This is a specication most commonly assumed in theliterature. We chose the mean growth rate of 2% and the volatility of 1%for realism, but the results do not change much as we vary them. Theliterature provides little guidance for the form of preference shifts, andso we simply assume that they are also geometric Brownian motions.Furthermore, motivated by the estimated dynamics of demand shocksin Pavlova and Rigobon (2007), we posit that H loads positively on theHome output shock w and H loads positively on the Foreign outputshockw*. The diffusion coefcients of H and H are denoted byH andH, respectively, and their exact form is specied in Table 1. Thepresence of demand shocks allows us to attain realistic values for theconsumption (expenditure) correlations across countries and for ahome bias in portfolios. Otherwise, as has beenwell-documented in theliterature, the cross-country correlation of consumption is too high, anddenitely higher than the output correlation. Moreover, with nodemandshocks, the countries' portfolios in ourmodel are indeterminate

Fig. 1. Simulated sample paths of the trade balance, conventional current account, andsample path corresponds to one simulated history.(for the same reason as in Cole and Obstfeld (1991)), and hence nomeaningfulmatchingof international portfolio compositions is possible.As a sensitivity exercise, we vary the relative sizes of the demand andsupply shocks (from 0.05 to 1.85) by varying the volatility of thedemand shocks and keeping that of the supply shocks xed, as well asvary the instantaneous correlation between the demand and supplyshocks (from0 to 45%).10 The ensuing ranges ofH andH are speciedin Table 1. The implied cross-country consumption (expenditure)correlations are mainly sensitive to the parameter controlling therelative sizes of the supply and demand shocks, while the portfoliocompositions also to the parameter controlling the correlation of theshocks. The initial value of the Foreign country's weight reects theallocation of initial endowments of shares of stock and the bond. Thisallocation is necessarily asymmetric since we are trying to match the

10 The former is formally dened asH 2

p= Y and the latter as Y i1H =

YH 2

p , where i1=(1, 0, 0, 0). Here, the supply shock is represented by the Homeoutput shock and the demand shock by a preference shift towards the Home good. Theanalogous quantities corresponding to the Foreign good, namely

H 2

q=

Y* andY*i1

H = Y*

H 2

q, vary symmetrically (and simultaneously), within the same range.

We bound the volatility of the demand shocks from below because values close to zeroproduce a lot of variation in the countries' portfolios,with portfolios becoming indeterminatein the limit of zero volatility (Cole and Obstfeld).external assetliability structure of the US, and hence (0) is differentfrom one. This (0) is, of course, endogenous, but we can set the modelprimitives initial portfolios supporting this choice of (0), forexample, equal to those reported in Fig. 4.

Our economy is always ina (stochastic) steady state.We solve for theinitial steady state as determined by our calibrated parameters andreport the values of key variables in that steady state in Fig. 4. Unlessstated otherwise, all variables are for the Home country. We plot thenumber of shares of the Home stock held by the Home residents (panel(a)), the number of shares of the Foreign stock held by Home residents(panel (b)), the value of their bondholdings (panel (c)), the annualizedtrade balance and conventional current account measured as fractionsof GDP (panels (d) and (e)), and the capital-gains adjusted currentaccount as a fraction of GDP (panel (f)). In all gures, the x-axismeasures the instantaneous correlation between the demand andsupply shocks and the y-axis the relative size of the demand and supplyshocks, as captured by the ratio of their volatilities.

Our choice of parameters implies a home bias in portfolios,whereby Home holds more than 89% of the supply of Home shares,and between 10 and 20% of that of Foreign shares. When demand and

ital-gains adjusted current account (these series have not been scaled by GDP). Eachsupply shocks are uncorrelated, bond holdings are exactly zero. Whenthe correlation increases, Home's bondholdings become negative.11

Home demands more of both the Home and Foreign stock, ending upowning more shares of the Foreign stock than foreigners own abroad,and nances these stock purchases not by selling domestic shares(rebalancing), but by borrowing. The selling of the bond by Homeimplies a current account decit, as shown in panel (e) and implied byProperty 1. In our steady state, the current account decit varies fromzero up to 11% of GDP, while the trade decit is constant at 3% of GDP(panel (d)). Note that CGCA comes out positive, at around 3% of GDP(panel (f)). It is worth mentioning that the initial NFA position ofHome is also positive. In recent US data, we observe both trade decitsand negative NFA positions. In our model, such a situation cannot beconsistent with equilibrium according to Property 2, which says thatcountries running trade decits must have positive NFA. Sointerpreted within our model, recent external imbalances in the USwould be deemed unsustainable.

11 It is important to highlight that whether bondholdings are positive or negativedepends on the sign of the correlation between the demand shocks and the supply shocks.In our case, home supply shocks are positively correlatedwith the agents' demand for theHome good, and therefore, the Home stock is a good hedge against that correlation.

4.2. Unconditional responses

In this simulation we generate 500 histories, 100 years each, byrandomly drawing all four shocks. We start by examining the serialcorrelation of the conventional current account and the serial corre-lation of the capital-gains adjusted current account.

To provide an illustration, Fig. 1 depicts a constellation of samplepaths of the conventional and the capital-gains adjusted currentaccounts emerging from the Monte-Carlo simulations.

The difference in the dynamic behavior of the two series is striking.The conventional current account and the trade balance (not reportedhere for brevity) are highly persistent series, while the capital-gainsadjusted current account is not. The main reason why the latter doesnot exhibit much persistence is the fact that much of its variation isexplained by the unexpected capital gains, which are not seriallycorrelated. The series in panel (b) looks much like a return on anancial asset: very volatile and largely unpredictable. Table 2validates these observations and reports the serial correlations ofeach of the threemeasures of external accounts. We estimate a simpleAR(1) and average the coefcients across all simulations, for theentire parameter space.

One can see that irrespectively of the parameters chosen for asimulation, the current account is highly serially correlated. CGCA,

Table 2AR(1) serial correlation of the simulated conventional current account and capital-gains adjusted current account (in fractions of GDP).

AR(1) serial correlation Standard error

Average Max Min

CAH 97.52% 97.53% 97.51% 0.00%CGCAH 0.87% 1.97% 0.58% 0.35%

The average is computed as the simple average of the estimates across our parameterspace, and the standard error is for that average.

Fig. 2. Correlation of expected capital gains (panel (a)) and unexpected capital gains (panel (b)) with the trade balance (measured as a fraction of GDP). The x-axis measures theinstantaneous correlation between the demand and supply shocks Y i1H = Y

H 2

p, where i1=(1,0,0,0). The y-axis measures the ratio of the volatilities of the demand and

supply shocksH 2

p=Y (relative size of demand and supply shocks).

150 A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156Fig. 3. Correlation of expected capital gains (panel (a)) and unexpected capital gains (panel (x-axis measures the instantaneous correlation between the demand and supply shocks Y i1of the demand and supply shocks

H 2

p= Y (relative size of demand and supply shockb)) with the capital-gains adjusted current account (measured as a fraction of GDP). TheH = Y

H 2

p, where i1=(1,0,0,0). The y-axis measures the ratio of the volatilitiess).

however, does not exhibit much serial correlation.12 Its dynamicsclosely resemble those of asset returns.

4.3. Valuation effects: expected and unexpected capital gains

Capital gains (valuationeffects)havebeen at the sourceof thedebateon the current state of external imbalances in the US and worldwide.Capital gains can be split between expected and unexpected capitalgains, which contribute in rather different ways to the internationaladjustment process. The empirical literature faces a signicantchallenge of being able to disentangle the expected part of the capitalgains from theunexpectedpart.Webuild onour theoretical insights andstudy the properties of capital gains within our simulation.

Recall our decomposition of the current account:

S* S B

gains are almost perfectly positively correlated (Fig. 3b). The reason for

To relate our work to the international real business cycles (IRBC)literature, we report the standard statistics that this literature targets.We caution, however, that our model does not include many realisticfeatures highlighted in IRBC research, such as capital accumulation, timeto build, labor choice, etc. Table 3 reports the cross-country correlationsand volatilities of consumption expenditures and GDPs, volatilities ofthe terms of trade, of the trade balance and of the current account forfour scenarios. To generate the scenarios, we again vary the correlationbetween demand and supply shocks as well as their relative size.

With thecaveat thatourmodelhasnothing to sayabout investment the most important IRBC moment we proceed to describe ourndings.14 One long-standing puzzle in the literature is the consump-tion correlation puzzle: optimal risk sharing makes cross-countryconsumption (expenditures) highly correlated, and more so than thecountries' GDPs. We do not observe this pattern in the data. In ourmodel, there are two channels that reduce the cross-country consump-tion correlation: (i) the presence of demand shocks and (ii) imperfectrisk sharing due to market incompleteness. The rst channel isespecially important in our setup: in the simulations in which demandshocks are large (columns 2 and 4), we observe particularly low

Table 3IRBC statistics.

Correlation of supply and demand shocks 0.05 0.05 0.4 0.4

Relative size of supply and demand shocks 0.25 1.45 0.25 1.45

CorrelationsHome and Foreign GDPs 0.53 0.23 0.52 0.20

14 The IRBC moments computed in Table 3 have been estimated from 500simulations of 100 years each. It is important to mention that even though the modeland all the equations are developed in continuous time, in the estimation of IRBCmoments we sample the variables yearly. The sampling of all the variables is yearly tomake it comparable in terms of frequency with the standard sampling in the data. Asshown by At-Sahalia (2007), the choice of the sampling period is relevant for theestimation of instantaneous variancecovariances matrices. Hence, changing the

151A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156CAHt = TBHt + sH tp*tY*tsFtptYt|{z}Net Dividend Payments

+ sHtBtrt|{z}Net Interest Payments

dt

and

CGCAHt = CAHt + sS*H tECGS*tsSFtECGSt|{z}

Net Expected Capital Gains

dt

+ sS*H tS*tS*tsSFtStStdwt|{z}

Net Unexpected Capital Gains

:

Inwhat follows, we'll frequently drop theword netwhenwe referto capital gains, with the understanding that we are alluding to capitalgains on the NFA positions. Unless mentioned otherwise, all variablesthat we discuss below are for the Home country.

Recent empirical literature has produced an intriguing stylized fact:valuation effects the sumof expected andunexpected capital gains arenegatively correlated with the trade balance (see Gourinchas and Rey(2007b) andDevereux and Sutherland (2008)), or, in otherwords, capitalgains have a stabilizing effect on the trade balance. As one can see fromFig. 2a, indeed in all our simulations expected capital gains are highlynegatively correlated with the trade balance (around90%), providing astabilizing effect. This result is consistent with Gourinchas and Rey. Thecorrelation of the unexpected capital gains with the trade balance isconsistently negative as well (Fig. 2b), although the magnitudes of thecorrelations are much smaller (around 13%). Almost the samerelationship exists for the correlationswith the traditional current account(around90% for expected and11% for unexpected capital gains).13

Note that while the correlations of expected capital gains with thetrade balance and with the current account are very high, those ofunexpected capital gains aremuchsmaller. However,whenwecomparethe correlations with the change in the net foreign asset positions thecapital-gains adjusted current account the roles are reversed. Thecorrelation of expected capital gains with the change in the NFA

12 This is consistent with the evidence presented in Kollmann (2006) and Lane andShambaugh (2007).13 One possible explanation for the negative correlations between the currentaccount and expected capital gains is that expected returns and dividend payments aremechanically negatively correlated if the total asset returns are held constant and afraction of that return is randomly attributed to a capital gain and a fraction todividend. For example, assume that a country has a total expected return on netforeign assets (expected capital gains plus dividends) of, say, 5%. Assume this isconstant across all states of the world. If changes in the state variable imply highdividends, then, to keep the total expected return constant, an increase in thedividends has to imply a drop in the expected capital gain. If this is the case, therefore,because the current account has dividends in it but not capital gains, a negativecorrelation is just an outcome of accounting. We reject this possibility. First, expectedcapital gains are already negatively correlated with the trade balance. Second, whenwe compute the correlation between the expected capital gains and dividends, we ndthat they are perfectly positively correlated, and hence the negative relationshipbetween the current account and expected capital gains is coming from the tradebalance and interest payments terms. We thank Pierre-Olivier Gourinchas for

motivating us to explore this accounting explanation for the observed behavior.the change is that unexpected capital gains completely dominate theshare attributable to the current account and expected capital gains inthe variation of net foreign assets. This conclusion is very much in linewith the evidence reported in, among others, Devereux and Sutherland.

4.4. Standard macroeconomic (IRBC) statisticspositions is positive but not very high (Fig. 3a), but unexpected capital

Home and Foreign Consumption Expenditure 0.84 0.52 0.82 0.46Home Consumption Expenditure and Home GDP 0.91 0.76 0.90 0.75

Standard Deviations (%)Home Consumption Expenditure 6.29 6.90 6.34 7.09Foreign Consumption Expenditure 6.83 7.78 6.77 7.75Home Consumption of the Home Good 3.57 3.60 3.59 3.65Home GDP 5.95 6.47 6.03 6.66Foreign GDP 8.39 9.67 8.30 9.53Real Output (Home) (Y) 1.00 1.00 1.00 1.00Real Output (Foreign) (Y) 2.00 2.00 2.00 2.00Terms of Trade 21.96 30.45 18.27 23.86Trade Balance 3.18 7.84 3.21 7.94Current Account 0.09 0.50 0.64 3.84Capital-Gains Adjusted Current Account 23.40 58.06 23.97 59.34

All series are in log differences and detrended.The consumption expenditure of Home is dened as pCH+pCH and that of Foreign aspCF+pCF. Home consumption of the home good is CHH. GDP of Home is dened as pYand of Foreign as pY, and real output as Y and Y, respectively. All external accountsare for Home, and are measured in fractions of Home's GDP. The (instantaneous)correlation between the demand and supply shocks (row 1) is dened asY i1H = Y

H 2

p, where i1=(1,0,0,0) and the relative size of demand and

supply shocks (row 2) denotes the ratio of the volatilities of the demand and supplyshocks

H 2

p= Y .sampling period will change the moments reported in the table.

152 A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156correlations. These correlations are still higher than the cross-countryGDP correlations, and so we do not quite resolve the consumptioncorrelation puzzle, but we are making a step in the right direction. Thecorrelations of Home consumption and GDP are high, and higher thanthe correlations of Home and Foreign consumption, which is consistentwith the data.

We report volatilities of two types of variables: real variables, such asoutput and consumption (e.g., Y, CH) and nominal variables such as GDPand consumption expenditure (e.g., pY, pCH+pCH). The volatilities ofreal variables are either somewhat higher (because of demand shocks)or roughly in linewith those reported in the standard IRBCmodels15, butthose of nominal quantities are several times higher. This is becauseprices are volatile in ourmodel,which is necessary for obtaining realisticproperties of the nancial side of our economy. As one can see fromTable 3, we nd the terms of trade to be quite volatile, much more sothan GDP. This is due to the presence of incomplete markets anddemand shocks. In the data, the terms of trade are about three times asvolatile as GDP, contrary to predictions of the standard IRBC model, inwhich the terms of trade are too smooth. Finally, it is worth noting therelatively low volatilities of the trade balance and the conventionalcurrent account. The capital-gains adjusted current account is, of course,signicantly more volatile in our model (2360%). The numbers are

Fig. 4. Steady state values. The x-axis measures the instantaneous correlation between thmeasures the ratio of the volatilities of the demand and supply shocks

H 2

p= Y (relat

15 To save space, we just report the volatility of CH. The volatilities of CH* , CF, and CF*

are similar.high, but not exorbitant in light of the evidence presented in Kollmann(2006) and Lane and Shambaugh (2007).

5. External adjustment process

Properties 1 and 2 establish strong links between a country's assetpositions and its external accounts. For example, Property 2 says thatany gains and losses on nancial assets comprising the country'sportfolio must be compensated with an offsetting change to the tradebalance. As we have highlighted, part of these gains/losses isunexpected. The mechanism through which countries in our economyrespond in the event of experiencing a gain (loss) is to increase (reduce)their trade decits. So the trigger in this trade balance adjustmentmechanism is the uctuations in asset prices and the trade balancethen responds accordingly. This is the chain of reasoning we have inmind when we talk about an asset-pricing view of externaladjustment. In this section, we discuss how shocks are propagated inour model.

5.1. Impact responses

We focus our attention on the propagation of two types of shocks: apermanent shift in preferences toward the home good (a demandshock) and a permanent increase in productivity at Home (a supplyshock). Our model also allows for an investigation of the effects of apreference shift towards the Foreign good and a productivity shock at

e demand and supply shocks Y i1H = YH 2

p, where i1=(1,0,0,0). The y-axis

ive size of demand and supply shocks).

153A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156Foreign, but for brevitywe omit that discussion.We emphasize that theshocks that we study are permanent.16 That is, we have chosen to closeall the intrinsic dynamics and concentrate on the extrinsic dynamics ofthe model (see Obstfeld and Stockman (1985) for a discussion of thesetwo types of dynamics). Following a shock, our economymoves directly

16 Our focus on permanent shocks is motivated largely by the limitations of themodel: while productivity shocks can be modeled as transitory, preference shifts haveto be permanent (recall that, for tractability, we have assumed that H and H aremartingales). The analysis of transitory shocks is thus beyond the scope of this paper,and we leave it for future research.

Fig. 5. Impact responses to a shock dw (a shock to the utility weight H). The x-axiY i1H = Y

H 2

p , where i1=(1, 0, 0, 0). The y-axis measures the ratio of the volatilitishocks).into a new steady state. That is why it is sufcient to look at impactresponses to the shocks impulse responses (over many periods) donot contain any signicant information beyond that already capturedbythe impact responses.

For each shock we present a sequence of gures that capture theimpact responsesof the real sideof the economyandof thenancial sideof the economy and then highlight the resulting response of the currentaccount of the Home country. To compute the impact responses, westart from our steady state (illustrated in Fig. 4) and then introduce oneshock (of one standard deviation). Then, for each pertinent variable, wesubtract the steady-state series for this variable from the one with the

s measures the instantaneous correlation between the demand and supply shockses of the demand and supply shocks

H 2

p=Y (relative size of demand and supply

154 A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156shock, and report the impact of the shock the resulting change at thetime of the shock.

Fig. 5 presents impact responses to a shock dw. Recall that byconstruction, such a shock has no effect on the Home or Foreign output,and the only change in the primitives of our model that takes place inresponse to the stock is a preference shift atHome towards the domesticgood (H increases). The direction inwhich the terms of trade and stockprices move following the shock can be easily derived from Eqs. (8)(10). The economic intuition behind these responses is even simpler. Apure demand shock of the type we are considering here creates anexcess demand for the Home good. This pushes its price up andtherefore improves Home's terms of trade. This iswhy panel (a) of Fig. 5

Fig. 6. Impact responses to an output shock at Home dw. The x-axis measures the instantanei1 = 1; 0;0;0. The y-axis measures the ratio of the volatilities of the demand and supply sreports an increase in q for all parameter values. Output in bothcountries stays the same, but because of the movement in the terms oftrade, the value of the output increases at Home and decreases atForeign. Hence the increase in the stock market values at Home (panel(b)) and thedecrease at Foreign (panel (c)). It is noweasy tounderstandwhy the Home country suffers an net unexpected capital loss (panel(d)). Remember that our parameters imply positive steady stateholdings of both stocks by both countries. The increase in the stockprice atHome thus implies a capital gain for foreigners,while thedeclinein foreign stock prices implies a loss for Home agents. Both effects act inthe same direction, against theHome residents. The capital loss atHomeinduces the planner to reassign weights to the countries in its

ous correlation between the demand and supply shocks Y i1H = YH 2

p, where

hocksjjH jj2

p= Y (relative size of demand and supply shocks).

objective function in favor of Foreign (panel (e)). Such an outcome, inour case, is equivalent to an (unexpected)wealth transfer fromHome toForeign.17

As shown in panel (f), the trade balance improves for all parametervalues. This improvement of the trade balance is simply the ip side ofthe deterioration of the NFA position due to the unexpected net capital

155A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156loss (Property 2). According to ourmodel, the current trade balance hasto adjust to absorb the capital loss.

For all parameters, except the ones under which the demand andsupply shocks are uncorrelated,Homepurchases the bond. (For the caseof zero correlation, the gross holdings of the bond are zero). These bondpurchases decrease the decit in the current account according toProperty 1 and indeed an improvement in the current account isevident from panel (h). Finally, note that the movements in the netunexpected capital gains dominate the dynamics of the NFA position.The response of the capital-gains adjusted current account mimics thatof the net unexpected capital gains CGCA is negative for all parametervalues (panel (i)). Note that the direction of the response of theconventional current account is just the opposite (panel (h)).

In Fig. 6 we provide the impact responses to a shock to the Homeoutput dw. This case is more complex than the one above because apositive Home output shock also causes an increase in H through ourchoice of parametrization (see Table 1 and the surrounding discussion).Again, the direction in which the terms of trade and stock prices movefollowing the shock can be formally derived from (8)(10). Theintuition behind the responses is as follows. A positive shock to theHome output YH increases the value of its stock market (panel (b)). Atthe same time, the Home good becomes less scarce and hence its pricedrops relative to that the Foreign good or in other words, Home'sterms of trade deteriorate. The Foreign's terms of trade thereforeimprove, which increases the value of its output and benets its stockmarket (panel (c)). These responses are somewhat mitigated by theincrease in H that occurs contemporaneously. As we have seen in theprevious gure, a positive shock to H improves Home's terms of trade,boosts the stock market at Home, while decreasing the stock marketabroad. We can see that this confounding effect becomes morepronounced when the demand shocks have a high loading on thesupply shock dw i.e., when both the correlation between the demandand supply shocks and the relative variance of the demand and supplyshocks is high.

Furthermore, we nd that Home enjoys a net unexpected capitalgain in response to the supply shock (panel (d)). The intuition of thisresult is complicated because it depends on how prices and portfoliochoices interact. A capital gain at Home causes a wealth transfer fromForeign to Home, or, more accurately, the weight of Foreign in theplanner's problem falls, increasing the allocation to the Home country(panel (e)). Since the NFA position of Home has improved, it can affordto deteriorate its trade balance, which iswhatwe see in panel (f). Part ofthe nancing of the increased purchases of the two stocks comes fromselling the bond (panel (g)), which according to our Property 1 dete-riorates the conventional current account (panel (h)). The capital-gainsadjusted current account, however, moves in the opposite direction the same direction as the net unexpected capital gains, which arepositive here (panel (i)).

One question frequently asked in the literature is that about thedirections and magnitudes of responses of real and nancial variablesthat need to accompany a reduction of a current account decit. In ourcalibration, Home is the country running a current account decit, andso let us ask the question of how a reduction of this decit can be

17 We caution the reader that such a statement requires some qualication. This canbe seen from Eq. (12): t = WF tWH t

H t + H tF + F

. Indeed, a part of a change in therelative weight coincides with a change in the wealth distribution (a pure wealthtransfer), but the remaining part is due to imperfect demand risk sharing: undercomplete markets, does not move in response to any shock, but it does respond toshocks under incomplete markets because the shocks cannot be perfectly hedged. In

our case, the wealth transfer effect dominates, but this need not be the case in general.achieved. Figs. 5 and 6 illustrate two possible channels: (i) via a fall inHome output (a negative output shock, dw0). Both these channels have beenwell established in the literature. However, contrary to the conventionalwisdom, in our model the current account correction comes with animprovement of the terms of trade of Home. As we have highlightedabove, an improvement in the terms of trade brings about a capital losson Home's NFA position. In response to this capital loss, Home is forcedto curb its current account decit.

6. Concluding remarks

The swelling of international equity holdings in the last two decadeshas altered the way economists think of external sustainability: newmeasures of sustainability are being proposed, new channels of externaladjustment are being uncovered, and new frameworks are being andwill be developed. In this paper, we investigate properties of aneconomy which incorporates endogenous dynamics of internationalequity portfolios into a standard open economy macro model. Solvingsuch a model relies on several important simplications that futureresearch needs to relax. First, in order to be able to obtain closed-formsolutions and introduce asset pricing into our economy,we have chosento close all the intrinsic dynamics and concentrate on the extrinsicdynamics of themodel. In otherwords, all shocks are permanent and theeconomy is always in a (stochastic) steady state. Therefore, ourdenitions of sustainability and the relationship between the externalaccounts and the nancial holdings are all steady-state characteriza-tions. Extending the present framework to allow for intrinsic dynamicsis clearly an important next step. Second, we have made a number ofsimplifying assumptions about the fundamentals of the model:preferences are loglinear, demand shocks come only in the form ofexpenditure shifts, output is produced by Lucas trees (i.e., there is noinvestment), and soon.While themodel has beenable to replicate somekey stylized facts documented in the recent literature on net foreignasset dynamics, it is still a very crude depiction of reality. Clearly, ourassumptions will have to be relaxed in the future to tackle importantquestions that afict practitioners and policymakers.

Acknowledgments

We are grateful to Mick Devereux (the editor) and an anonymousreferee for their extensive comments and to Philippe Bacchetta,Bernard Dumas, Pierre-Olivier Gourinchas, Robert Kollmann, EnriqueMendoza, Stavros Panageas, Hlne Rey, and Carlos Vgh forstimulating discussions. We also thank seminar participants atBanque de France, Bank of England, Berkeley, British Columbia,Cornell, Dartmouth, LBS, Maryland, Michigan, PUC-Rio, San FranciscoFed, Yale and various conferences for their comments and FondationBanque de France for nancial support.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.jinteco.2009.09.003.

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156 A. Pavlova, R. Rigobon / Journal of International Economics 80 (2010) 144156

An asset-pricing view of external adjustment.....IntroductionThe modelThe economic settingCharacterization of equilibrium

The current accountThe conventional current accountThe capital-gains adjusted current accountThe links between financial asset holdings and external accounts

Dynamic implicationsCalibrationUnconditional responsesValuation effects: expected and unexpected capital gainsStandard macroeconomic (IRBC) statistics

External adjustment processImpact responses

Concluding remarksAcknowledgmentsSupplementary dataReferences