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Journal of International Money and Finance 48 (2014) 271e290

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Journal of International Money and Finance

journal homepage: www.elsevier.com/locate/jimf

External balances, trade flows and financial conditions

Martin D.D. Evans Department of Economics, Georgetown University, Washington, DC 20057, USA

a r t i c l e i n f o

Article history: Available online 12 June 2014

Keywords: Global imbalances Foreign asset positions Current accounts Trade flows International asset pricing

JEL codes: F31 F32 F34

E-mail address: [email protected].

http://dx.doi.org/10.1016/j.jimonfin.2014.05.018 0261-5606/© 2014 Elsevier Ltd. All rights reserved

a b s t r a c t

This paper studies how changing expectations concerning future trade and financial conditions are reflected in international external positions. In the absence of Ponzi schemes and arbitrage opportunities, the net foreign asset position of any country must, as a matter of theory, equal the expected present discounted value of future trade deficits, discounted at the cumulated world sto- chastic discount factor (SDF) that prices all freely traded financial assets. I study the forecasting implications of this theoretical link in 12 countries (Australia, Canada, China, France, Germany, India, Italy, Japan, South Korea, Thailand, The United States and The United Kingdom) between 1970 and 2011. I find that variations in the external positions of most countries reflect changing expec- tations about trade conditions far into the future. I also find the changing forecasts for the future path of the world SDF are re- flected in the dynamics of the U.S. external position.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

This paper studies how changing expectations concerning future trade and financial conditions are reflected in international external positions. Economic theory links a country's net foreign asset (NFA) position to agents' expectations in a precise manner. In the absence of Ponzi schemes and arbitrage opportunities, the NFA position of any country must equal the expected present discounted value of future trade deficits, discounted at the cumulated world stochastic discount factor (SDF) that prices all freely traded financial assets. In practice this means that changes in observed external positions of countries across the world should reflect changing expectations about future trade flows and future financial conditions represented by the world SDF, or some combination of the two. The aim of this

.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290272

paper is to assess whether this is in fact the case. More specifically, the paper examines the extent to which changing expectations about future trade and financial conditions are reflected in the evolving external positions of 12 countries between 1970 and 2011.

To undertake this analysis, I present a new analytic framework that links each country's current NFA position to its current trade flows, expectations of future trade flows, and expectations concerning future returns on foreign assets and liabilities in an environment without arbitrage opportunities or Ponzi schemes. This framework incorporates several key features. First it accommodates the secular increase in international trade flows and national gross asset/liability positions that has taken place over the past 40 years. The secular growth in both trade flows and positions greatly exceeds the growth in GDP on a global and country-by-country basis. Between 1970 and 2011, the annual growth in trade and positions exceeds the growth in GDP by an average of 2.6 and 4.8 percent, respectively, across the countries studied.1

The second key feature concerns the identification of expected future returns. As a matter of logic, expected future returns on a country's asset and liability portfolios must affect the value of its current NFA position, so pinning down these expectations is unavoidable when studying the drivers of external positions. This is easily done in textbook models where the only internationally traded asset is a risk free bond, but in the real world countries' asset and liability portfolios comprise equity, FDI, bonds and other securities, with risky and volatile returns. Pinning down the expected future returns on these portfolios requires forecasts for the future returns on different securities and the composition of the portfolios. To avoid these complications, I use no-arbitrage conditions to identify the impact of ex- pected future returns on NFA positions via forecasts of a single variable, the world SDF. SDFs play a central role in modern finance theory (linking security prices and cash flows) and appear in theoretical examinations of the determinants of NFA positions (see, e.g., Obstfeld, 2012). A key step in my analysis is to show how the world SDF can be constructed from data on returns and then used to pin down how expectations concerning future financial conditions are reflected in external positions.

In the empirical analysis I study the external positions of 12 countries (Australia, Canada, China, France, Germany, India, Italy, Japan, South Korea, Thailand, The United States and The United Kingdom). I first show how the world SDF can be estimated from data on returns and discuss how the estimates can be tested for specification errors. Next I turn to the identification of expectations. In theory, external positions reflect expectations concerning the entire future paths of trade flows and the world SDF, so we need to forecast over a wide range of horizons. For this purpose I use VARs e a common approach in the literature following Campbell and Shiller (1987). I then compare the present values of future trade flows and the world SDF based on the VAR forecasts with external positions. If the actual expectations embedded in the external positions are well represented by the VAR forecasts, the present values computed from those forecasts should be strongly correlated with the external positions. This implication is borne out by my empirical findings using the VAR forecasts for trade flows. Forecasts of trade flows far into the future are strongly correlated with the external positions of 10 countries I study. Evidence on the role of expected future financial conditions is less clear cut. While VAR forecasts for the world SDF suggest that there have been persistent and sizable variations in the prospective future financial conditions that are relevant for the determination of external positions, the forecasts are only weakly correlated with the positions of many countries. One notable exception to this pattern is the U.S., whose external position is strongly correlated with the forecasts.

These findings add to a growing empirical and theoretical literature on international external adjustment. The analytic framework I present is most closely related to the work of Gourinchas and Rey (2007a). They derive an expression for a country's NFA position from a “de-trended” version of the consolidated budget constraint (that governs the evolution of a country's NFA position from trade flows and returns), that filters out the secular growth in trade flows and positions mentioned above. Thus their analysis focuses on the “cyclical” variations in NFA positions, rather than the “total” variations. Similarly, Corsetti and Konstantinou (2012) use the consolidated budget constraint to derive an approximation to the current account that includes deterministic trends in the log ratios of con- sumption, gross assets and gross liabilities to output to accommodate the long-term growth in trade

1 This feature of the data has proved to be a challenge for researchers studying the determinants of external positions, see e.g., Gourinchas and Rey (2007a) and Corsetti and Konstantinou (2012) discussed below.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290 273

flows and positions (relative to GDP).2 On the theoretical side, Pavlova and Rigobon (2008), Tille and van Wincoop (2010) and Devereux and Sutherland (2011) all study external adjustment in open economy models with incomplete markets. In these models changing NFA positions primarily reflect revisions in expected future trade flows and the world risk-free rate because the equilibrium risk premia on foreign assets and liabilities are (approximately) constant. In contrast, the framework I use allows for variations in the risk premia on assets and liabilities to also affect NFA positions.

My analysis also extends a related literature on international returns. Early papers in this literature (Obstfeld and Rogoff, 2005; Lane and Milesi-Ferretti, 2005; Meissner and Taylor, 2006; Gourinchas and Rey, 2007b) estimated that the return on U.S. foreign assets was on average approximately three percent per year higher than the return on foreign liabilities. Subsequent papers by Curcuru, Dvorak, and Warnock (2008) and Lane and Milesi-Ferretti (2009) argued that these estimates were biased upward because of inaccuracies in data. In their recent survey, Gourinchas and Rey (2013) show that alternative treatments of the data can produce average return differentials between U.S. foreign assets and liabilities that differ by as much as 1.1 and 1.8 percent, depending upon the sample period. My analysis shifts the focus away from average U.S. returns in two respects. First, I use the returns on the assets and liabilities of major economies to estimate the world SDF. Second I model how conditional expectations concerning the world SDF are related to external positions. Gourinchas and Rey (2007a) also consider the short-horizon (one quarter) forecasting power of the (cyclical) U.S. external position for returns on its NFA portfolio, and the return differential between equity assets and liabilities. Here I study forecasting power of external positions over longer horizons.

The remainder of the paper is structured as follows: Section 2 describes the data. I present the analytic framework in Section 3. Section 4 describes how I estimate the world SDF and compute long- horizon forecasts. I present the empirical results in Section 5. Section 6 concludes.

2. Data

I examine the external positions of 12 countries: the G7 (Canada, France, Germany, Italy, Japan, the U.S. and the U.K.) together with Australia, China, India, South Korea and Thailand. Data on each country's foreign asset and liability portfolios and the returns on the portfolios come from the data- based constructed by Lane and Milesi-Ferretti (2001), updated in Lane and Milesi-Ferretti (2009), available via the IMF's International Financial Statistics database. These data provide information on the market value of the foreign asset and liability portfolios at the end of each year together with the returns on the portfolios from the end of one year to the next. A detailed discussion of how these data series are constructed can be found in Lane and Milesi-Ferretti (2009). I also use data on exports, imports and GDP for each country and data on the one year U.S. T-bill rate, 10 year U.S. T-bond rate and U.S. inflation. All asset and liability positions, trade flows and GDP levels are transformed into constant 2005 U.S. dollars using the prevailing exchange rates and U.S. price deflator. All portfolio returns are similarly transformed into real U.S. returns. The Lane and Milesi-Ferretti position data is constructed on an annual basis, so my analysis below is conducted at an annual frequency.3 Although the span of individual data series differs from country to country, most of my analysis uses data spanning 1970e2011.

2 A related literature on external adjustment focuses attention on current account balances. For example, Lane and Milesi- Ferretti (2012) examine how changes in current account balances between 2008 and 2010 relate to pre-crisis current ac- count gaps estimated from a panel regression model. Similar empirical models of current account determination can be found in Chinn and Prasad (2003), Gruber and Kamin (2007), Lee et al. (2008), Gagnon (2011) and others. Current accounts also remain a focus in current multilateral surveillance frameworks used by the International Monetary Fund and the European Commission (see, e.g., IMF, 2012; EU, 2010).

3 Ideally, we would like to track international positions and returns at a higher (e.g. quarterly) frequency, but constructing the market value of foreign assets and liabilities for a large set of countries is a herculean task. For the U.S., Gourinchas and Rey (2005) compute quarterly market values for four categories of foreign asset and liabilities: equity, foreign direct investment, debt and other, by combining data on international positions with information on the capital gains and losses. In Evans (2012) I revise and update their data to 2012:IV. Corsetti and Konstantinou (2012) also work with quarterly U.S. position data which they impute from the annual Milesi-Ferretti data using quarterly capital flows. For a discussion of the different methods used to construct return data, see Gourinchas and Rey (2013).

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290274

The Web Appendix describes the characteristics of the data in detail. Here I simply note several prominent features. First, for many countries, variations in the ratios of net exports and NFA to GDP are highly persistent. Second, the cross-country dispersion in the ratios has widened in the last decade. Third, gross financial positions (i.e., the sum of foreign assets and liabilities) and trade (i.e., the sum of export and imports) have grown much faster than GDP. Averaging across all the countries, trade grew approximately 2.6 percent faster than GDP, while foreign asset and liability positions grew 4.8 percent faster. There have also been swings in global trade growth and position growth that are much larger than global business cycles. In light of these facts, the next section presents an analytic framework that links a country's current external position to prospective future trade and financial conditions while accommodating the growth in trade and positions.

3. Analytic framework

3.1. NFA positions

The framework I develop contains three elements: (i) the consolidated budget constraint that links a country's foreign asset and liability positions to exports, imports and returns; (ii) a no-arbitrage condition that restricts the behavior of returns; and (iii) a condition that rules out international Ponzi schemes.

I begin with country's n's consolidated budget constraint:

FAn;t � FLn;t ¼ Xn;t � Mn;t þ RFAn;tFAn;t�1 � RFLn;tFLn;t�1: (1)

Here FAn,t and FLn,t denote the value of foreign assets and liabilities of country n at the end of year t, while Xn,t and Mn,t represent the flow of exports and imports during year t, all measured in real terms (constant U.S. dollars). The gross real return on the foreign asset and liability portfolios of country n between the end of years t�1 and t are denoted by RFAn;t and RFLn;t, respectively. Equation (1) is no more than an accounting identity. It should hold true for any country provided the underlying data on po- sitions, trade flows and returns are accurate. Notice, also, that FAn,t and FLn,t represent the values of portfolios of assets and liabilities comprising equity, bond and FDI holdings, and that RFAn;t and R

FL n;t, are

the corresponding portfolio returns. These returns will generally differ across countries in the same year because of cross-country differences in the composition of asset and liability portfolios.

Next, I introduce the no-arbitrage condition. In a world where financial assets with the same payoffs have the same prices and there are no restrictions on the construction of portfolios (such as short sales constraints), there exists a positive random, Ktþ1; such that

1 ¼ Et h Ktþ1Ritþ1

i ; (2)

where Ritþ1 is the (gross real) return on any freely traded asset i. Here Et½:� denotes expectations conditioned on common period-t information. The variable Ktþ1 is known as the stochastic discount factor (SDF). This condition is very general. It does not rely on the preferences of investors, the ra- tionality of their expectations, or the completeness of financial markets.4 I assume that it applies to the returns on every security in a country's asset and liability portfolios, and so it also applies to the returns on the portfolios themselves; i.e.

1 ¼ Et h Ktþ1RFAn;tþ1

i and 1 ¼ Et

h Ktþ1RFLn;tþ1

i : (3)

Equations (1) and (3) enable me to derive a simple expression for a country's NFA position. First I multiply both sides of the budget constraint in (1) by the SDF and then take conditional expectations. Applying the restrictions in (3) to the resulting expression and simplifying gives

4 For a textbook discussion of SDFs, see Cochrane (2001); or in an international setting, Evans (2011).

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290 275

Et Ktþ1NFAn;tþ1 ¼ Et Ktþ1 Xn;tþ1 � Mn;tþ1 þ NFAn;t: (4)

� � � � ��

Rearranging this expression and solving forward using the Law of Iterated Expectations we obtain

NFAn;t ¼ Et X∞ i¼1

Dtþi � Mn;tþi � Xn;tþi

� þ Et lim

i/∞ DtþiNFAn;tþi; (5)

where Dtþi ¼ Qi

j¼1Ktþj. The last term on the right-hand-side on (5) identifies the expected present value of the country's

NFA position as the horizon rises without limit using a discount factor determined by the world's SDF. To rule out Ponzi-schemes, I assume that

Et lim i/∞

DtþiNFAn;tþi ¼ 0; (6)

for all countries n. For intuition, suppose a debtor country (i.e. a country with NFAn,t < 0) decides to simply roll over existing asset and liability positions while running zero future trade balances. Under these circumstances, the country's asset and liability portfolios evolve as FAn;tþi ¼ RFAn;tþiFAn;tþi�1 and FLn;tþi ¼ RFLn;tþiFLn;tþi�1 for all i>0. Since Et½Ktþ1Xtþ1� identifies the period �t value of any period tþ1 payoff Xtþ1, (4) implies that the value of claim to the country's net assets next period is just Et½Ktþ1NFAn;tþ1� ¼ Et½Ktþ1ðXn;tþ1 � Mn;tþ1Þ� þ NFAn;t ¼ NFAn;t. This same reasoning applies in all future periods, i.e., Etþi½Ktþiþ1NFAn;tþiþ1� ¼ NFAn;tþi for all i > 0, so the value of a claim to the foreign asset position t periods ahead is Et½DtþtNFAn;tþt� ¼ Et½Dtþt�1Et�1½KtþtNFAn;tþt�� ¼ :: ¼ NFAn;t: Taking the limit as t/∞ gives NFAn;t ¼ Etlimi/∞½DtþiNFAn;tþi� < 0: Thus, the country's current NFA position must be equal to the value of a claim on rolling the asset and liability positions forward indefinitely into the future. Clearly then, no country n can initiate a Ponzi scheme in period t when Etlimi/∞DtþiNFAn;tþi � 0. Moreover, since

P nNFAn;t ¼ 0 by market clearing, if

Etlimi/∞DtþiNFA~n;tþi > 0 for any one country, ~n, then at least one other must be involved in a Ponzi scheme. Thus, the restriction in (6) prevents any country from adopting a Ponzi scheme in period t.

We can now identify the determinants of a country's NFA position by combining (5) and the no- Ponzi restriction (6):

NFAn;t ¼ Et X∞ i¼1

Dtþi � Mn;tþi � Xn;tþi

� : (7)

This equation states that in the absence of Ponzi schemes and arbitrage opportunities, the NFA position of any country n must equal the expected present discounted value of future trade deficits, discounted at the cumulated world SDF. As such, it describes the link between a country's current external position and the prospects for future trade flows (i.e. exports and imports) and future financial conditions, represented by the future SDF's in Dtþi.

Several aspects of equation (7) deserve note. First, the equation is exact; i.e., it contains no approxi- mations.ItmustholdunderthestatedconditionsforaccurateNFAandtradedatagivenmarketexpectations and the world SDF. Second, (7) holds whatever the composition of the country's asset and liability portfolios (i.e. whatever the fractions held in equity, bonds, etc.), and however those fractions are determined (by optimal portfolio choice or some other method). Third, the equation applies simultaneously across all countries. If news about prospective future financial conditions anywhere change expectations concerning futureworldSDFs,itaffectstheNFApositionofallcountriesthatanticipaterunningfuturetradesurplusesor deficits. Equation (7) also takes explicit account of risk. It states that a country's NFA position is equal to the value of a claim to the future stream of trade deficits in a world where those deficits are uncertain.

Finally, it is worth emphasizing that the expected future trade flows and SDF on the right-hand-side of (7) represent the proximate determinants of the country's NFA position. More fundamental factors, such as demographic trends, fiscal policy or productivity growth, can only affect the NFA position insofar as they impact on these expectations. Moreover, since the same SDF applies to all countries, such fundamental factors can only account for cross-country differences in NFA positions insofar as they impact prospective future trade flows.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290276

3.2. Forecasting implications

Equation (7) implies that all variations in a country's NFA position reflect revisions in expectations concerning future trade deficits and the world SDF. Consequently, NFA positions should have fore- casting power for future trade flows and/or SDFs. To investigate this empirical implication, we must overcome two challenges: The first concerns the identification of the world SDF, Kt. Section 4 describes how I estimate Kt from data on returns. The second arises from fact that the present value expression in (7) includes forecasts for DtþiMn;tþi and DtþiXn;tþi with Dtþi ¼

Qi j¼1Ktþj for all i>0 rather than forecasts

for Mn,tþi, Xn,tþi and Ktþi separately. To meet this challenge, I use a standard approximation. To approximate the present value expression for each country's NFA position, I first rewrite (7) as

NFAn;t ¼ Mn;tEt X∞ i¼1

exp �Xi

j¼1Dmn;tþj þ ktþj � � Xn;tEt

X∞ i¼1

exp �Xi

j¼1Dxn;tþj þ ktþj � ; (8)

where kt ¼ ln Kt is the log SDF, and D is the first-difference operator. (Throughout I use lowercase letters to denote the natural log of a variable.) This transformation simply relates the NFA position to the current levels of imports and exports and their future growth rates, Dmn;tþi and Dxn;tþi, rather than the future levels of exports and imports shown in (7).

Next, I approximate the two terms involving expectations. If dt is a random variable with mean E½dt� ¼ d < 0; then a first-order approximation to dtþj around d produces

Et X∞ i¼1

exp �Xi

j¼1dtþj � ¼ Etexpðdtþ1Þ þ Etexpðdtþ1 þ dtþ2Þ þ …

x r

1 � r þ rEtðdtþ1 � dÞ þ r 2 Etðdtþ1 � dÞ þ r3Etðdtþ2 � dÞ þ …:

¼ r 1 � r þ

1 1 � r Et

X∞ i¼1

r iðdtþi � dÞ;

(9)

where r ¼ exp(d) < 1. To apply this approximation, I make two assumptions:

E � Dmn;t

� ¼ E

� Dxn;t

� ¼ g; and (A1)

g þ k ¼ d < 0; with E½kt� ¼ k; (A2) where E½:� denotes unconditional expectations. Under assumption A1 the mean growth rate for imports and exports are equal. This will be true of any economy on a balanced growth path and appears consistent with the empirical evidence for the G7 countries. To interpret assumption A2, note that in the steady state the log risk free rate r satisfies 1 ¼ E½expðktÞ�expðrÞ. Thus d ¼ g þ kx g � r � 12 V½kt�, where V½:� denotes the variance, so A2 will hold provided V½kt� > 2ðg � rÞ: The mean growth rate for trade across the countries in the dataset is approximately 6.5 percent, which is well above any reasonable estimate of the mean risk free rate of close to 1 percent. Clearly then, A2 will only hold if the variance of the log SDF exceeds roughly 0.11 ¼ 2(0.065�0.01). This volatility bound is easily exceeded by estimates of the log SDF derived below.

Applying the approximation in (9) to the expectations terms in (8) and simplifying the result gives

NFAn;t ¼ r

1 � r � Mn;t � Xn;t

� þ 1 2ð1 � rÞ

� Mn;t þ Xn;t

� Et X i¼1

∞ r i�Dmn;tþi � Dxn;tþi�

þ 1 1 � r

� Mn;t � Xn;t

� Et X i¼1

∞ r i�Dtn;tþi � g� þ 11 � r

� Mn;t � Xn;t

� Et X i¼1

∞ r iðktþi � kÞ;

(10)

where Dtn;t ¼ 12 ðDmn;t þ Dxn;tÞ. This expression identifies the three sets of factors determining a country's NFA position in a clear fashion. The first term on the right-hand-side identifies the influence

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290 277

of the current trade balance. This would be the only factor determining the NFA position in the sto- chastic steady state where import growth, export growth and the log SDF followed i.i.d. processes because the terms involving expectations would equal zero. As such, this first term identifies the atemporal influence of trade flows on the NFA position. The remaining terms on the right-hand-side identify the intertemporal factors that were present in (7). In particular they make clear how expec- tations concerning future trade flows and financial conditions, represented by the world SDF, are (approximately) linked to a country's current NFA position.

The influence of future trade and financial conditions on external positions can be further clarified with a simply transformation of (10). For this purpose, I define country n's external position by

NXAn;t ¼ NFAn;t

Mn;t þ Xn;t � r 1 � r TDn;t where TDn;t ¼

Mn;t � Xn;t Mn;t þ Xn;t

:

In words, the country's NXA position is defined as the gap between its current NFA position and the steady state present value of the future trade deficits, all normalized by the current volume of inter- national trade. Combining this definition with (10) gives

NXAn;t ¼ 1

2ð1 � rÞ Et X∞ i¼1

r i�Dmn;tþi � Dxn;tþi� þ 11 � r TDn;tEt

X∞ i¼1

r i�Dtn;tþi � g�

þ 1 1 � r TDn;tEt

X∞ i¼1

r iðktþi � kÞ: (11)

Equation (11) provides us with the (approximate) link between a country's current external position and expectations concerning future trade flows and the SDF that forms the basis for the empirical analysis below. For intuition, consider the effects of news that leads agents to revise their forecasts for future trade deficits upwards. If there is no change in the expected future path of the SDF, according to (7) there must be a rise in assets prices and/or a fall in liability prices that produces a rise in NFA if investors are to avoid participation in a Ponzi scheme. This link is represented by the first two terms on the right-hand-side of (11).

The third term on the right-hand-side of (11) identifies how news concerning the future financial conditions, as reflected by the SDF, affects a country's external position. To illustrate the economic intuition behind this term, consider the effect of news that lowers agents' forecasts of the future SDF but leaves their forecasts for future trade flows unchanged. Under these circumstances, (7) shows that future trade deficits are discounted more heavily so the country's current NFA position is more closely tied to the value of a claim on its near-term deficits. Thus the NFA positions of countries currently running trade deficits deteriorate while the NFA positions of those running current trade surpluses improve. These variations in NFA are reflected one-to-one in NXA.

Equation (11) contains expectations conditioned on the common information set of agents in period t, much of which is unavailable to researchers. To take this into account, let Ft denote a subset of agents' information at t that includes NXAn,t and TDn,t. Taking expectations conditioned on Ft on both sides of (11) and applying the Law of Iterated Expectations, we find that

NXAn;t ¼ 1 2 PV

� Dmn;t � Dxn;t

� þ TDn;tPV

� Dtn;t � g

� þ TDn;tPVðkt � kÞ; (12)

where PVðytÞ ¼ 11�r P∞

i¼1r iE½ytþijFt�. This equation takes the same form as (11) except the agents' ex-

pectations are replaced by expectations conditioned on Ft. Conditioning down in this manner doesn't affect the link between the country's external position and the expectations because information used by agents is effectively contained in Ft via the presence of NXAn,t and TDn,t.

The implications of (12) for forecasting are straightforward. NXA should have forecasting power for any stationary variable ytþk insofar as expected future values of that variable, E½ytþkjFt�, are correlated

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290278

with the present value terms on the right-hand side of (12). Suppose, for the sake of illustration, that yt is independent of the trade flows and that country n's long-run trade deficit is equal to TDn. Then a projection of ytþk on NXAn,t (i.e. a regression without an intercept) would produce a projection coef- ficient equal to

E � ytþkNXAn;t

� E h NXA2n;t

i ¼ 1 1 � r E

2 64TDn;t X∞

i¼1 r iE½ðktþi � kÞjFt�ytþk

E h NXA2n;t

i 3 75

¼ TDn 1 � r

X∞ i¼1

r iℂV½E½ktþijFt�; E½ytþkjFt��

E h NXA2n;t

i ; where ℂV½:; :� denotes the covariance. Notice that in this case the size of the coefficient depends on both the long run trade deficit, TDn, and the covariance between the expectations of ytþk and ktþi over a range of horizons i. In the empirical analysis below, I examine the forecasting power of NXAn,t for future trade flows with yt ¼ Dmt � Dxt and yt ¼ Dtt, and future financial conditions with yt ¼ kt at particular horizons k. I also study the forecasting power of NXAn,t for trade and financial conditions over a range of horizons (i.e. for all k�1) using time series estimates of PVðDmn;t � Dxn;tÞ; PVðDtn;t � gÞ and PVðkt � kÞ.

4. Empirical methods

4.1. Estimating the world SDF

In a fully specified theoretical model of the world economy the world SDF would be identified from the equilibrium conditions governing investors' portfolio and savings decisions. Fortunately, for our purposes, we can avoid such a complex undertaking. Instead, I adopt a “reverse-engineering” approach in which I construct a specification for the SDF that explains the behavior of a set of returns; the returns on the asset and liability portfolios for six of the G7 countries.5 This approach is easy to implement and allows us to empirically examine how prospective future financial conditions are reflected in external positions.

Let ertþ1 denote a k � 1 vector of log excess portfolio returns, eritþ1 ¼ ritþ1 � rTBtþ1, where ritþ1 denotes the log return on portfolio i and rTBtþ1 is the log return on U.S. T-bills. I assume that the log of the SDF is determined as

ktþ1 ¼ a � rTBtþ1 � b'ðertþ1 � E½ertþ1�Þ: (13) This specification for the SDF contains kþ1 parameters: the constant a and the k � 1 vector b. In the “reverse-engineering” approach values for these parameters are chosen to ensure that the no-arbitrage conditions are satisfied for the specified SDF. More specifically, I find values for a and b such that the portfolio returns for the asset and liability portfolios of the six G7 countries and the U.S. T-bill rate all satisfy the no-arbitrage conditions.

Consider the condition for the i'th portfolio return: 1 ¼ Et½expðktþ1 þ ritþ1Þ�: Taking unconditional expectations we can rewrite this condition as

1 ¼ E h exp

� ktþ1 þ ritþ1

�i xexp

� E h ktþ1 þ ritþ1

i þ 1 2 V h ktþ1 þ ritþ1

i :

(14)

5 Unfortunately, the data needed to compute the returns on Canada's foreign asset and liability positions is not available from the IMF database before 2006, so I use the returns of the other six G7 countries.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290 279

When the log returns are normally distributed the second line holds with equality because (13) implies that ktþ1 and ritþ1 are jointly normal. Otherwise, the second line includes an approximation error.

Next, I substituting for the log SDF from (13) in (14) and take logs. After some re-arrangement this gives

a þ E h eritþ1

i þ 1 2 V h eritþ1

i þ 1 2 b0V½ertþ1�b ¼ ℂV

h eritþ1; er

0 tþ1

i b: (15)

This equation must hold for the T-bill return (i.e., when ritþ1 ¼ rTBtþ1, or eritþ1 ¼ 0 ) so

a þ 1 2 b0V½ertþ1�b ¼ 0: (16)

Imposing this restriction on (15) gives

E h eritþ1

i þ 1 2 V h eritþ1

i ¼ ℂV

h eritþ1; er

0 tþ1

i b:

This equation holds for each of the k portfolio returns. So stacking the k equations we obtain

E½ertþ1� þ 1 2 L ¼ Ub; (17)

where U ¼ V½ertþ1� and L is a k � 1 vector containing the leading diagonal of U. Finally, we can solve (16) and (17). Substituting the solutions for a and b in (13) produces the

following expression for the log SDF:

ktþ1 ¼ � 1 2 m'U�1m � rTBtþ1 � m'U�1ðertþ1 � E½ertþ1�Þ: (18)

By construction, equation (18) identifies a specification for the log SDF such that the unconditional no-arbitrage condition, 1 ¼ E½expðktþ1 þ ritþ1Þ�, holds for the k log portfolio returns and the return on U.S. T-bills. This specification would also satisfy the conditional no-arbitrage condition, 1 ¼ Et½expðktþ1 þ ritþ1Þ�, if log returns were independently and identically distributed. However, since this is not the case, we need to amend the specification to incorporate conditioning information.

Consider condition 1 ¼ Et½expðktþ1 þ ritþ1Þ�: Let ut be a valid instrument known to market partici- pants in period t. Multiplying both sides of the no-arbitrage condition by exp(ut) and taking uncon- ditional expectations produces, after some re-arrangement

1 ¼ E h exp

� ktþ1 þ ri;utþ1

�i ; (19)

where ri;utþ1 ¼ ritþ1 þ ut � lnE½expðutÞ�: Notice that (19) takes the same form as (14) used in the con- structions of the log SDF in (18). The only difference is that (19) contains the adjusted log return on

portfolio i, ri;utþ1; rather than the unadjusted return r i tþ1: This means that we can reverse engineer a

specification for the log SDF that incorporates conditioning information if we add adjusted log returns

to the set of returns. Specifically, let eri;u j

tþ1 ¼ ritþ1 � rTBtþ1 þ u j t � lnE½expðu

j t� denote the log excess

adjusted return on portfolio i using instrument ujt. If ertþ1 now represents a vector containing er i tþ1 and

eri;u j

tþ1, the log SDF identified in (18) will satisfy the non-arbitrage condition

1 ¼ E h exp

� ktþ1 þ ritþ1

� ujt i ;

for all the portfolio returns i and instruments ujt included in ertþ1.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290280

Three aspects of this reverse engineering procedure deserve comment. First, equation (18) doesn't necessarily identify a unique SDF that satisfies the no-arbitrage conditions for a set of returns. Indeed, we know as a matter of theory that many SDF exist when markets are incomplete. Rather the speci- fication in (18) identifies one specification for the SDF that satisfies the no-arbitrage conditions. Second, this reverse engineering approach makes no attempt to relate the SDF to underlying macro factors. This complex task is unnecessary if our aim is simply to identify how prospective future financial conditions affect external positions. The third aspect concerns the use of instrumental variables to control for conditioning information. In principle the conditional expectations of market participants that appear in the no-arbitrage conditions equal expectations conditioned on every instrumental variable in their information set. In practice, there is a limit to the number of instruments we can incorporate into the log SDF specification. I chose instruments that have forecasting power for log excess portfolio returns and I examine the robustness of my results to alternative specifications for the log SDF based on different instrument choices.

I consider two empirical specifications for the log SDF. The first, denoted by bkIt, is estimated from (18) without conditioning information. To assess whether the estimates satisfy the no-arbitrage

condition, 1 ¼ E½expðbkItþ1 þ ritþ1Þ ujt�, I estimate regressions of the form:

exp �bkItþ1 þ ritþ1

� � 1 ¼ b1

� fan;t � fln;t

� þ b2

� xn;t � mn;t

� þ vtþ1; (20)

where xn,t, mn,t, fan,t and fln,t denote the logs of exports, imports, the value of foreign assets and foreign liabilities, respectively, for country n. Panel A of Table 1 reports the estimation results for the log returns on the asset and liability portfolios. Notice that the log ratios of assets-to-liabilities and export-to- imports are valid instruments so the estimates of b1 and b2 should be statistically insignificant under the null of a correctly specified SDF. As Panel A shows, this is not the case for the portfolio returns of four countries. The log asset-to-liability ratio has predictive power for German, U.K. and U.S. returns, while the log export-to-import ratio has power for the returns on Japanese assets.

In the light of these results, I incorporate conditioning information in my second specification for

the log SDF, denoted by bkIIt . Specifically, I now add the adjusted log return on U.S. assets, ri;ztþ1 ¼ rAUS;tþ1 þ ðfaUS;t � flUS;tÞ � lnE½expðfaUS;t � flUS;tÞ�, where rAUS;tþ1 is the log return on U.S. assets, to the set of returns used to estimate the log SDF in (18). This specification incorporates information concerning the future value of the SDF that is correlated with variations in the U.S. NFA position. Thus,

Table 1 Forecasting returns.

Asset returns Liability returns

b1 b2 R 2 b1 b2 R

2

A: bkI France 0.059 �0.210 �0.001 0.117 �0.205 0.003 Germany �0.428* 0.669 0.124 �0.442** 0.594 0.129 Italy �1.031 2.436 0.135 �1.009 2.667* 0.143 Japan 0.299 2.304** 0.098 0.327 2.374 0.106 United Kingdom �5.852** 0.324 0.183 �5.843** 0.437 0.177 United States �1.108** 0.216 0.132 �1.059** 0.252 0.115 B: bkII France �0.188 �0.636 0.023 �0.116 �0.610 0.017 Germany �0.083 2.824 0.057 �0.091 2.862 0.059 Italy �0.653 �0.668 0.018 �0.653 �0.453 0.016 Japan 0.742 1.809 0.050 0.774 1.874 0.055 United Kingdom �4.595 2.237 0.052 �4.698 2.529 0.054 United States �0.229 0.515 0.022 �0.163 0.558 0.023

Notes: The table reports the OLS estimates of the regression (20) using the kIt specification for the log SDF in panel A and the k II t

specification in panel B. “**” and “*’’ indicate statistical significance at the 5% and 10% levels, respectively. All regression esti- mated in annual data between 1971 and 2011.

Fig. 1. SDF Estimates.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290 281

faUS;t � flUS;t should not have forecasting power for expðbkIItþ1 þ ritþ1Þ � 1 by construction. To check whether the other instruments retain their forecasting power, I then re-estimate regression (20) with

bkIItþ1 replacing bkItþ1. Panel B of Table 1 reports these regression results. In contrast to Panel A, none of the b1 and b2 coefficient estimates are statistically significant. Notice, also, that the R

2 statistics are (in most cases) an order of magnitude smaller than their counterparts in Panel A. The asset-to-liability and export-to-import ratios do not account for an economically meaningful fraction of the variation in

expðbkIItþ1 þ ritþ1Þ � 1. These findings appear robust to the choice of estimation period and instruments. Re-estimating (20) over a sample period that ends in 2007 gives essentially the same results. I also find

statistically insignificant coefficients in regressions using bkIItþ1 as the log SDF when GDP growth rates and/or lagged returns are used as alternate instruments.6

Fig.1 plots the two estimated SDFs, bKIt ¼ expðbkItÞ and bKIIt ¼ expðbkIIt Þ, together with the inverse of the real return on U.S. T-bills, 1=RTBt . In the special case where the expected excess portfolio returns on assets and liabilities are zero, equation (18) implies that the SDF is equal to 1=RTBt . Thus differences between 1=RTBt and the estimated SDF's arise because the SDFs must account for the expected excess portfolio returns. As the plots clearly show, both estimates of the SDF are more volatile than 1=RTBt . In fact, variations in the log return on U.S. T-bills contribute less than one percent to the sample variance of bkIt and bkIIt . Changes in U.S. T-bill returns do not appear to have an economically significant impact on estimates of the SDF that “explain” returns on asset and liability portfolios in major economies. The plots in Fig. 1 also show that there are numerous episodes where the estimated SDFs are well above one. Ex ante, the conditionally expected value of the SDF, EtKtþ1, identifies the value of a claim to one real dollar next period. So safe dollar assets sold at a premium during periods where these high values for the SDF were forecast ex ante.

6 Recall that specification for kt in (18) was derived using a log normal approximation to evaluate expected future returns. Based of these regression estimates, there is no evidence to suggest that the approximation is a significant source of specifi- cation error for bkIIt .

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290282

4.2. Estimating external positions

The estimates of the log SDF, bkIIt , allow us to pin down the discount rate r ¼ expðg þ kÞ used in computing the NXA positions and the present value terms in equation (12). Recall that g is the un- conditional growth rate for exports and imports, which I estimate to be 0.064 from the pooled average of import and export growth across countries. My estimate of k computed from the average value of bkIIt is �0.59. These estimates, denoted by bg and bk; imply a discount rate of r ¼ expðbg þ bkÞ ¼ 0:586. This is the value I use to construct the NXA measures of each country's external position.

Fig. 2 plots the NXA positions for each country in the dataset between 1980 and 2011. The upper panel shows that the NXA positions for all but one of the G7 countries have remained between ±1 during the past 30 years. The one exception is the Japanese NXA position, which persistently increased from 0.1 to 2.6 during the period. Variations in the NXA positions of countries outside the G7 are generally larger. The plots in the lower panel of Fig. 2 show large improvements in the external po- sitions of India and South Korea while Australia's NXA position has remained largely unchanged. It is also interesting to note that the steady improvement in the NXA position of China in the last twenty years is not nearly as pronounced as the improvement in Japan's position.7 Of course the time series for the NXA positions reflect changes in NFA positions and trade deficits both measured as a fraction of annual trade, NFAn;t=ðMn;t þ Xn;tÞ and ðMn;t � Xn;tÞ=ðMn;t þ Xn;tÞ. Plots for these variables are shown in the Web Appendix.

4.3. Long-horizon forecasts

In principle, variations in the NXA positions could reflect revisions in the expectations concerning the entire path for future imports, exports and the SDF. One way to investigate this possibility would be to estimate regressions of realized present values; i.e.,

Pk i¼1r

iytþi for yt ¼ fDmt � Dxt; Dtt � g; kt � kg, on NXAn;t for some finite horizon k. For example, with r equal to 0.586, ri < 0:01 for i > 8, so a finite horizon of eight or nine years ought to be sufficient for this purpose. Unfortunately, there are two well- known econometric problems with this approach. First, the coefficient estimates may suffer from finite sample bias when the independent variables are persistent and predetermined but not exogenous (see, e.g. Campbell and Yogo, 2006). Second, the asymptotic distribution of the estimates provides a poor approximation to the true distribution when the forecasting horizon is long relative to the span of the sample (see, e.g. Mark, 1995), as it would be here with just a 40 year span.

To avoid these problems, I examine the relation between the NXA positions and P∞

i¼1r ibEtytþi, where

the conditional expectations bEtytþi are computed from VARs. Specifically, let the vector zt ¼ ½yt; :; ::�0 follow a p0 th. order VAR, which can be written in companion form as Zt ¼ AZt�1 þ Ut, where Zt stacks the zt vectors appropriately. I estimate the present value for yt by

dPVðytÞ ¼ 11 � r X∞ i¼1

r ibEtytþi ¼ r1 � r ı1 bA

� I � rbA��1Zt; (21)

where ı1 is a vector that picks out the first row of Zt (i.e., yt¼ı1Zt) and bA denotes the estimated com- panion matrix from the VAR. [The 1=ð1 � rÞ term is included for compatibility with the expression for the NXA position in equation (12)]. I compute present values for trade flows where yt ¼ Dmn;t � Dxn;t or yt ¼ Dtn;t � bg from VARs estimated country-by-country, and for the log SDF with yt ¼ kIIt � bk using a single world-wide specification. In all these calculations r ¼ expðbg þ bkÞ ¼ 0:586.

I estimate the present value terms involving future trade flows (i.e., dPVðDmn;t � Dxn;tÞ anddPVðDtn;t � bgÞ) from VARs that include the import-export growth differential Dmn,t�Dxn,t, trade growth Dtn,t, and the log export-to-import ratio xn,t�mn,t. Below I report results based on first-order VARs estimated separately for each country, n; higher-order VARs give very similar results. In addition, I

7 The span of the sample period is much too short for unit roots tests to provide reliable information on the whether the true process for each country's NXA position is stationary. On the other hand the economic logic embedded in equation (12) implies that NXAn,t is indeed a stationary process, and so my analysis in Section 5 proceeds under this assumption.

Fig. 2. NXA positions.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290 283

considered estimates that included NXAn,t and the log return on U.S. T-bills, rTBt ; in the VARs. The results presented below are robust with respect to the presence of these variables.8

I also use a VAR to compute the present value of the log SDF, dPVðbkIIt � bkÞ. In this case the VAR in- cludes bkIIt � bk, the log return on U.S. T-bills, rTBt ; the U.S. inflation rate, pUSt ; the spread between the real

8 The Web Appendix examines the time series predictability of the import-export growth differential and the trade growth differential across the countries in the sample. It also documents the results of Grange Causality tests from the estimated VARs.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290284

yields on ten and one year U.S. T-bonds, sprUSt , and the average rate of real GDP growth across the G7, DyG7t . In addition, I use the VAR to compute the present value of the log return on U.S. T-bills,dPVðrTBt � brTBÞ, where brTB is the sample average of rTBt . Comparing dPVðbkIIt � bkÞ with dPVðrTBt � brTBÞ proves useful when we examine how future financial conditions are reflected in the NXA positions below.

5. Results

5.1. Forecasting future trade flows

I begin by examining the short-horizon forecasting power of the NXA positions for trade flows. Panel A of Table 2 reports slope coefficients, (heteroskedastic-consistent) standard errors and R2 sta- tistics from regressions of ytþ1 on a constant and NXAn,t for each of the countries, n, over the full sample. Columns I and II show estimates where ytþ1 ¼ Dmn;tþ1 � Dxn;tþ1 and ytþ1 ¼ ðDtn;tþ1 � bgÞTDn;t are the

Table 2 Forecasting trade flows.

A: short horizon forecasts

I II III

Forecast variables

Dmn;tþ1 � Dxn;tþ1 ðDtn;tþ1 � bgÞTDn;t Dmn;tþ1 � Dxn;tþ1 þ ðDtn;tþ1 � bgÞTDn;t coeff std R2 coeff std R2 coeff std R2

Canada 2.407 (1.811) 0.042 0.141 (0.186) 0.014 1.345 (0.885) 0.055 France �0.698 (0.646) 0.028 0.187*** (0.037) 0.386 �0.163 (0.323) 0.006 Germany 4.693 (3.818) 0.036 �0.802*** (0.280) 0.170 1.544 (1.991) 0.015 Italy 5.121 (3.683) 0.046 0.222 (0.236) 0.022 2.782 (1.848) 0.054 Japan 2.338 (1.947) 0.035 �0.210 (0.186) 0.031 0.959 (0.992) 0.023 United Kingdom

1.925 (1.806) 0.028 �0.419*** (0.096) 0.325 0.543 (0.883) 0.009

United States 0.877 (1.822) 0.006 �0.064 (0.199) 0.003 0.374 (0.919) 0.004 Australia �1.279 (4.853) 0.002 �0.308 (0.316) 0.023 �0.947 (2.374) 0.004 China 10.311** (4.929) 0.131 �0.920*** (0.351) 0.192 4.235* (2.395) 0.097 India 0.518 (0.848) 0.009 �0.028 (0.099) 0.002 0.231 (0.457) 0.006 South Korea 2.603** (1.108) 0.124 �1.276*** (0.171) 0.588 0.025 (0.574) 0.000 Thailand 8.945* (5.356) 0.065 �1.688*** (0.656) 0.142 2.785 (2.635) 0.027

B: Long-Horizon Forecasts

Forecast Variables

I II III

dPVðDmn;t � Dxn;tÞ dPVðDtn;t � gÞTDn;t dPVðDmn;t � Dxn;tÞ þ dPVðDtn;t � gÞTDn;t coeff std R2 coeff std R2 coeff std R2

Canada 1.923 (1.244) 0.058 0.144 (0.386) 0.004 2.067 (1.478) 0.048 France �1.123*** (0.315) 0.246 �0.405*** (0.130) 0.199 �1.528*** (0.443) 0.234 Germany 7.750*** (1.530) 0.397 3.233*** (0.699) 0.354 10.982*** (2.213) 0.387 Italy 0.021 (2.105) 0.000 0.237 (0.814) 0.002 0.258 (2.908) 0.000 Japan 3.848*** (0.933) 0.304 0.607 (0.429) 0.049 4.455*** (1.309) 0.229 United Kingdom

5.004*** (0.725) 0.550 2.281*** (0.302) 0.594 7.284*** (0.900) 0.627

United States 3.522** (1.585) 0.112 1.039*** (0.361) 0.175 4.562** (1.898) 0.129 Australia 5.338*** (1.980) 0.157 2.021** (0.969) 0.100 7.359*** (2.498) 0.182 China 12.564*** (2.117) 0.548 2.911*** (0.651) 0.408 15.475*** (2.683) 0.534 India 2.647*** (0.281) 0.695 1.923*** (0.289) 0.531 4.569*** (0.487) 0.693 South Korea 3.216*** (0.449) 0.568 �0.002 (0.251) 0.000 3.214*** (0.650) 0.385 Thailand 13.923*** (2.012) 0.551 4.706*** (0.836) 0.448 18.628*** (2.526) 0.582

Notes: The table reports OLS estimates of the slope coefficients, (heteroskedastic-consistent) standard errors and R2 statistics from regressions of the variables shown at the top of each panel on NXAn,t and (an unreported constant). Each row reports estimates for country n. “***”, ”“**” and “*’’ indicate statistical significance at the 1%, 5% and 10% levels, respectively. All re- gressions estimated in annual data between 1971 and 2011.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290 285

forecast variables, respectively. These are the trade flows that appear in the present value terms that determine the NXA position of country n in equation (12). The estimates in column III use the com- bination of trade flows that appears on the right-hand side of (12).

The results in Panel A of Table 2 show that information contained in the NXA positions concerning future near-term trade flows differs considerably across countries. Among the G7, there is no evidence that the NXA positions contain information about next year's import-export growth differential; none of the estimated slope coefficients are statistically significant at conventional levels. By contrast, the NXA positions of China and South Korea appear to have reasonably strong forecasting power for the differential. In both cases an increase in the NXA position forecasts a rise in Dmn;tþ1 � Dxn;tþ1. Ceteris paribus, this is consistent with equation (12). For perspective on the size of coefficient estimates, the value of 10.3 implies that an increase in the Chinese NXA position of 0.1 forecasts an increase in the growth differential of approximately one percent.

External positions have more widespread forecasting power for trade growth. Column II shows that six slope coefficients are statistically significant at the one percent level. According to (12), an increases in NXAn,t should, ceteris paribus, forecast a rise in trade growth for current deficit countries and a fall in growth for surplus countries. This prediction is not borne out in five of the six countries with significant coefficients. Finally, column III shows the forecasting power of the NXA positions for the combined trade flows. Here there is very little evidence of any short-horizon forecasting power. With the exception of China, none of the estimated slope coefficients are statistically significant at the 10 percent level, and all the R2 statistics are extremely small.

All-in-all, the results in Panel A suggest that variations in prospective near-term trade flows play no more than a minor role in driving variations in external positions. This doesn't mean that future trade flows are irrelevant. On the contrary, changes in external positions could reflect revisions in expec- tations concerning the entire future path for trade flows (i.e. expectations well beyond the one year horizon studied above). The results in Panel B of Table 2 allow us to examine this possibility. Here I report the estimates from regressions of the VAR-based present values of trade flows on a constant and NXAn,t. Notice that these are not forecasting regressions e the dependent variable is not the realized present value of the future trade flows. Rather the regressions measure the degree to which changes in the present value of future trade flows computed from VAR forecasts are reflected in NXAn,t variations.

9

If the forecasting information captured by the VARs is also embedded in agents' expectations that are reflected in the NXA positions, we should expect to find positive and statistically significant slope coefficients.

The results reported in Panel B generally confirm this prediction. The slope coefficients in column I are positive and highly statistically significant for nine countries. And, judging by the R2 statistics, the variations in NXAn,t capture a sizable portion of the variance in the VAR-based present values for the import-export growth differential. This evidence is consistent with notion that the information con- tained in the long-term VAR forecasts for Dmn,tþi�Dxn,tþi is positively correlated with that used to form the actual expectations embedded in the NXA positions. The estimates based on French data prove an exception to this pattern. Here the slope coefficient is negative and highly statistically significant e a counterintuitive finding. The estimates shown in Panel II continue this pattern. In this case the slope coefficients are positive and highly statistically significant in seven countries, with France again proving the exception. Column III shows how the VAR-based forecast for the combined future trade flows relate to external positions. Again, the slope coefficients are positive and highly significant for most countries (except France). It is alsoworth noting that the R2 statistics from these regressions are over 0.5 in the U.K., China, India, and Thailand. The time series variations in the NXA positions of these countries during the past 40 years are quite informative about changes in the VAR forecasts of future trade flows.

Overall, the results in Table 2 are consistent with the view that changing expectations about trade flows far into the future contribute to the year-by-year variations in the NXA positions of many

9 The VAR-based present values used as left-hand-side variables in these regressions include some sampling error. Impor- tantly, the results reported in the table are derived from VARs that do not include NXAn,t, so there is no reason to suspect that this sampling error contributes to the estimated regression coefficients. Furthermore, when I estimate regressions using VAR- based present values that include NXAn,t in the VAR specification, I obtain very similar results.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290286

countries. Expectations concerning near-term trade flows appear far less relevant. These results are broadly consistent with the findings reported by Gourinchas and Rey (2007a). They estimate that changing expectations concerning future trade flows account for approximated 30 percent of the cyclical variations in the U.S. external position between 1952 and 2004. Here variations in the U.S. NXA position are strongly correlated with the forecasts of future trade flows, but not as strongly as the NXA positions of other countries.

5.2. Forecasting future financial conditions

I now consider the influence of prospective financial conditions on country's external positions. Panel A of Table 3 reports on the short-horizon forecasting power of the NXA positions for different measures of future financial conditions. As above, the table shows slope coefficients, (heteroskedastic- consistent) standard errors and R2 statistics from regressions of the forecast variable on a constant and NXAn,t estimated over the full sample. Recall that variations in the expected log SDF only affect NXAn,t insofar as the country is running a current trade surplus or deficit, so the forecast variables are multiplied by the current trade deficit, TDn,t, to be consistent with the right-hand-side of (12).

Table 3 Forecasting financial conditions.

I: short horizon forecasts

I II III

Forecast variables ðbkIItþ1 � bkÞTDn;t �ðrTBtþ1 � rTBÞTDn;t ðbkIItþ1 þ rTBtþ1ÞTDn;t coeff std R2 coeff std R2 coeff std R2

Canada �3.216 (3.567) 0.020 �0.017 (0.084) 0.001 �3.200 (3.562) 0.020 France �2.277*** (0.697) 0.215 0.008 (0.014) 0.008 �2.285*** (0.693) 0.218 Germany 13.258*** (4.172) 0.206 0.005 (0.092) 0.000 13.253*** (4.166) 0.206 Italy �6.327 (3.810) 0.066 0.222*** (0.079) 0.169 �6.549* (3.804) 0.071 Japan 3.439 (2.499) 0.046 �0.146** (0.058) 0.142 3.585 (2.477) 0.051 United Kingdom 6.548** (2.571) 0.143 0.252*** (0.072) 0.238 6.295** (2.589) 0.132 United States 1.834 (4.113) 0.005 0.039 (0.077) 0.006 1.795 (4.104) 0.005 Australia �2.234 (6.107) 0.003 �0.239** (0.099) 0.130 �1.996 (6.093) 0.003 China 6.216 (3.999) 0.079 0.347*** (0.088) 0.357 5.869 (3.992) 0.072 India 5.476** (2.469) 0.112 �0.034 (0.065) 0.007 5.510** (2.474) 0.113 South Korea 6.630*** (1.709) 0.284 �0.083* (0.043) 0.090 6.712*** (1.714) 0.288 Thailand 5.795 (7.428) 0.015 0.727*** (0.165) 0.332 5.068 (7.480) 0.012

II: Long-horizon forecasts

I II III

Forecast Variables dPVðbkIIt � bkÞTDn;t �dPVðrTBt � rTBÞTDn;t dPVðbkIIt þ rTBt ÞTDn;t coeff std R2 coeff std R2 coeff std R2

Canada 2.525 (1.644) 0.057 �0.467*** (0.152) 0.195 2.992* (1.706) 0.073 France 0.812** (0.378) 0.106 �0.146*** (0.039) 0.268 0.959** (0.405) 0.126 Germany �2.153 (2.523) 0.018 0.340* (0.194) 0.073 �2.493 (2.604) 0.023 Italy 2.537 (2.183) 0.033 �0.558** (0.256) 0.109 3.095 (2.400) 0.041 Japan �0.374 (1.167) 0.003 0.299** (0.116) 0.145 �0.672 (1.262) 0.007 United Kingdom �1.371 (1.553) 0.020 0.070 (0.173) 0.004 �1.441 (1.661) 0.019 United States 5.293*** (1.752) 0.190 �0.692*** (0.156) 0.336 5.985*** (1.790) 0.223 Australia 4.777* (2.625) 0.078 �0.148 (0.300) 0.006 4.924* (2.801) 0.073 China 2.721 (1.997) 0.060 �0.318** (0.135) 0.160 3.040 (2.048) 0.071 India �3.247** (1.246) 0.148 0.558*** (0.150) 0.263 �3.805*** (1.341) 0.171 South Korea �3.168*** (0.901) 0.241 0.650*** (0.096) 0.543 �3.818*** (0.973) 0.283 Thailand 0.189 (4.080) 0.000 �0.338 (0.551) 0.010 0.527 (4.500) 0.000

Notes: The table reports OLS estimates of the slope coefficients, (heteroskedastic-consistent) standard errors and R2 statistics from regressions of the variables shown at the top of each panel on NXAn,t and (an unreported constant). Each row reports estimates for country n. “***”, ”“**” and “*’’ indicate statistical significance at the 1%, 5% and 10% levels, respectively. All re- gressions estimated in annual data between 1971 and 2011.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290 287

Column I shows the results when NXAn,t is used to forecast the one-year ahead deviation of the log SDF from its unconditional mean multiplied by the current trade deficit, ðbkIItþ1 � bkÞTDn;t: Recall that, ceteris paribus, an increase in the expected future SDF should raise (lower) the NXA position of a deficit (surplus) country because future trade imbalances are discounted more heavily when valuing current asset and liability positions. So, if revisions in expected near-term financial conditions are a source of NXAn,t variations over the sample, and those expectations are reflected in actual conditions as repre- sented by the SDF estimates, we should see positive and significant slope coefficients in the forecasting equations. The estimates in Column I show that this is the case for four countries: Germany, the U. K., India and South Korea. NXAn,t does not appear to have significant near-term forecasting power across the other countries, with the exception of France; where, once again, the significant negative coeffi- cient is counterintuitive.10

Columns II and III provide further perspective on these findings. Here I show the results from forecasting regressions that include the log return on U.S. T-bills, rTBtþ1: In the absence of arbitrage opportunities 1 ¼ Et½expðbkIItþ1 þ rTBtþ1Þ�, which (approximately) implies that Et½ktþ1 þ rTBtþ1� ¼ �12 Vt½kIItþ1 þ rTBtþ1�; where Vt½:� denotes the conditional variance. Subtracting unconditional expecta- tions from both sides and re-arranging using (18) gives

Et � ktþ1 � k

� ¼ �Et

h rTBtþ1 � rTB

i � 1 2

n Vt½b0ertþ1� � E½Vt½b0ertþ1��

o : (22)

Thus, changing expectations concerning the future SDF must either reflect revisions in expected future T-bill returns and/or changes in perceived risk measured by the conditional variance of future excess portfolio returns on asset and liabilities across the major economies.

Column II shows the regression results when the T-bill returns (multiplied by the trade deficit) are the forecast variable. Here we see a different cross-country pattern of forecasting power. NXA positions have forecasting power for near-term T-bill returns in Italy, Japan, Australia, China and Thailand; all countries where NXAn,t appeared not to forecast the log SDF. When judged by the R

2 statistics, these forecasting results are particularly strong in the Chinese and Thai cases. Column III shows results whenbkIItþ1 þ rTBtþ1 (multiplied by the trade deficit) is used as the forecast variable. Mathematically, the esti- mated slope coefficients are equal to the difference between their counterparts in columns I and II, but economically they show the extent to which changing perceptions concerning near-term risk is re- flected in the NXA positions. Notice that the cross-country pattern of the coefficient estimates closely corresponds to the pattern in column I. To the extent that NXAn,t variations reflect prospective near- term financial conditions, revisions in perceived risk appear more important than expectations con- cerning future returns on U.S. T-bills.

Of course NXAn,t variations may reflect revisions in expectations concerning the SDF further into the future. To gauge the importance of variations in these long-horizon expectations, Fig. 3 plots the estimated present value for the log SDF, dPVðbkIIt � bkÞ, and minus one times the estimated present value of the return on U.S. T-bills, �dPVðrTBt � brTBÞ. The plotted series are computed from a VAR estimated from the full sample. Alternative series derived from a VAR estimated on pre-crisis data (1971e2006) follow a similar pattern. As the figure clearly shows, time series variations in the present value for the log SDF follow a cyclical pattern and are much larger in magnitude than the changes in the present value of the log return on U.S. T-bills. This means that the changing VAR forecasts for the log SDF largely reflect revisions in perceived future risk, represented by the last term on the right-hand-side of (22). For example, the sizable swings in the log SDF between 1998 and 2008 appear to reflect, in turn, a large rise, fall, and rise again in expectations concerning the level of risk well into the future.

To what extent are these estimates of changing risk perceptions reflected in the NXA positions? To address this question, Panel B of Table 3 reports estimates from regressions of the VAR-based present

10 Gourinchas and Rey (2007a) found that the U.S. external position had forecasting power for the return on the net asset position and the return differential between equity assets and liabilities at the quarterly horizon between 1952 and 2004. One possible reason for the difference between their findings and the U.S. forecasting results in Panel A is that NXAn,t exhibits a good deal more persistence than the cyclical component of the U.S. external position they use.

Fig. 3. The Present Value of the log SDF.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290288

values of the log SDF and T-bill returns on a constant and NXAn,t. As in Panel A, the dependent variables in these regressions are multiplied by the trade deficit for consistency with the right-hand- side of (12). The estimates in column I show that the variations in NXA are only weakly related to those in dPVðbkIIt � bkÞTDn;t for many countries. The most notable exception is the U.S., where the estimated slope coefficient is positive, highly statistically significant, and the R2 is 0.19. This finding contrasts with the U.S. estimates in Panel A, where the coefficient is insignificant and the R2 statistic is smaller that 0.01. It suggests that changes in the U.S. external position are in part a reflection of changing perceptions concerning future financial conditions beyond the immediate future, particular future risk. The NXA positions of three other countries also appear to reflect prospective future financial conditions. The estimate slope coefficient on the French NXA position is positive and sig- nificant, but the regression R2 is only 0.1, while those for India and South Korean are negative and significant.

The cross-country pattern of statistical significance changes when we focus on forecasts for U.S. T- bill returns. Column II shows that the NXA positions of many countries are quite closely related to �dPVðrTBt � brTBÞTDn;t: the estimated slope coefficients are significant at the five percent level in eight countries. To interpret these estimates, recall from Table 2 that most country's NXA positions appeared to reflect prospective future trade conditions. Their NXA positions will also reflect long- term forecasts for U.S. T-bill returns insofar as they are correlated with their forecasts for future trade flows. The estimation results in column II reflect these correlations and the importance of expected future trade flows for the determination of NXA across countries. Finally, note that the results in column III closely mirror those in column I. This is due to the fact that the changing VAR forecasts for the future log SDF primarily reflect revisions in the forecasts of risk rather than U.S. T- bill returns (see Fig. 3).

Overall, the results in Table 3 provide only limited support for the view that revisions in expecta- tions about future financial conditions contribute significantly to the changing NXA positions across countries. Although the VAR forecasts reveal sizable and persistent swings in the present value of the log SDF, the NXA positions of most countries are not strongly correlated with this measure of pro- spective financial conditions. The one notable exception to this pattern is the U.S., where variations in the NXA position are strongly correlated with the estimated present value of the future SDF.

M.D.D. Evans / Journal of International Money and Finance 48 (2014) 271e290 289

6. Conclusion

In the absence of Ponzi schemes and arbitrage opportunities, the NFA position of any country must equal the expected present discounted value of future trade deficits, discounted at the cumulated world SDF. In this paper I investigated the forecasting implications of this theoretical insight. To do so, I first developed a measure of a country's external position, NXAn,t, that is simply linked to expectations of future trade flows and the log SDF. I also showed how the SDF can be estimated from cross-country data on returns. With these tools I then studied the near-term forecasting power of 12 country's NXA positions for trade flows and the SDF, and the statistical link between the NXA positions and VAR forecasts for the paths of trade flows and the SDF far into the future.

Overall, my empirical findings support the prediction that the external positions of most countries reflect (in part) expectations about the future path for trade flows. Evidence on the role of future financial conditions is less clear cut. While the VAR forecasts for the log SDF suggest that there have been persistent and sizable variations in the prospective future financial conditions that are relevant for the determination of NXA positions, only the U.S. NXA position is strongly correlated with these forecasts. This suggests that identifying the impact of future financial conditions on many country's NXA positions requires a more structural empirical investigation than the simple forecasting exercise undertaken here. One possibility along these lines would be to extend the VAR methods pioneered by Campbell and Shiller (1987) to allow for the nonlinearity between the trade deficits and the present value terms in equation (12) e a possibility I leave for future work.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.ijrefrig.2014. 05.029.

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