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Board of Governors of the Federal Reserve System

International Finance Discussion Papers

Number 975, June 2009 --- Screen Reader
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NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at http://www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at http://www.ssrn.com/.

Abstract:

Theory predicts that a nation's stochastic intertemporal budget constraint is satisfied if net foreign assets (NFA) are integrated of any finite order, or if net exports (NX) and NFA satisfy an error-correction specification with a residual integrated of any finite order. We test these conditions using data for 21 industrial and 29 emerging economies for the 1970-2004 period. The results show that, despite the large global imbalances of recent years, NFA and NX positions are consistent with external solvency. Country-specific unit root tests on NFA-GDP ratios suggest that nearly all of them are integrated of order 1. Pooled Mean Group error-correction estimation yields evidence of a statistically significant, negative response of the NX-GDP ratio to the NFA-GDP ratio that is largely homogeneous across countries.

Keywords: Global imbalances, external solvency, debt sustainability, Pooled Mean Group estimation

JEL classification: F41, F32, E66

The most significant development in international finance in the last ten years was the emergence of large imbalances in current accounts and net foreign asset positions. Figure 1 shows the evolution of these "global imbalances" since 1997. The U.S. current account deficit rose sharply in this period, reaching a record 6 percent of GDP in 2006 (see Figure 1a), while current account surpluses grew to record levels in Emerging Asia, oil exporting countries, and Japan. In line with these changes, the dispersion of NFA positions widened substantially (see Figure 1b). The NFA position of the United States declined markedly, while those of Japan, Emerging Asia, and the oil exporting countries rose. Recent economic turmoil in the United States has reduced the U.S. current account deficit somewhat, but the nation's large negative NFA position has changed little, and this " stock imbalance" is very likely to persist.

Large and persistent imbalances in the NFA positions of nations pose two central questions that this paper aims to address: First, are these global imbalances sustainable, in the sense of being consistent with external solvency conditions (i.e., with the countries' intertemporal budget constraints)? Second, are there differences in the sustainaibilty of external positions across different country groupings depending on their characteristics (such as income levels or whether countries are net creditors or debtors)?

To answer these questions, we conduct two tests of external
solvency based on recent theoretical results derived by Bohn
(2007):^{2}

(1) Bohn's Proposition 1 (henceforth, PB1) shows that if the NFA series is integrated of order for any finite , then NX and NFA satisfy the intertemporal budget constraint (IBC), and NFA satisfies the associated transversality condition (TC). Hence, PB1 implies that external solvency can be assessed by testing whether NFA is stationary after any finite order of differencing of the original data. This result also illustrates, however, that testing for solvency per se is not very useful, since it is hard to imagine a macroeconomic time series that is not integrated of low order. In addition, Bohn shows that if bounds on debt or nfa exist, testing the null hypothesis of difference-stationarity seems economically uninteresting. Because, with debt limits, is not sufficient for sustainability. Hence, sheding light on the characteristics of the adjustment process that sustains solvency is a more important task, which Bohn tackled with the following result.

(2) Bohn's Proposition 3 (henceforth, PB3) proves that if NX and NFA satisfy an error-correction specification of the form , and is integrated of order for some such that , where is a constant real interest rate, then the IBC holds. This proposition implies that we can assess external solvency by estimating an error-correction " reaction function" between NX and NFA testing for a negative, statistically significant relationship between the two. Evidence that this reaction function exists indicates that NX reacts in the long run to changes in NFA in such a way that NFA grows slower than what a Ponzi scheme implies. Moreover, the magnitude of drives the speed of the adjustment process by which trade surpluses or deficits adjust to larger or smaller NFA positions, and it becomes a key determinant of the long-run average of NFA.

We test PB1 and PB3 using a large dataset covering 51 countries
during the period 1970-2004. We test PB1 by performing standard
Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root
tests of the NFA-GDP ratio (*nfa*) using data for each
individual country separately. Then, we test PB3 by estimating an
error-correction model of *nfa* and the NX-GDP ratio
(*nx*) taking advantage of the panel dimension of the dataset.
We estimate Pesaran et. al.'s (1998) Pooled Mean Group (PMG) and
Mean Group (MG) estimators, and find strong evidence in favor of
the former vis-a-vis the latter. PMG is particularly useful in our
analysis because it models the *nx*-*nfa* relationship as
a long-run relationship common to all countries in the sample, with
homogeneity tests to validate this assumption (v. the MG estimator
that uses country-specific long-run relationships). Moreover, PMG
allows for country-specific short-run deviations from the long-run
relationship.

The results of the unit root tests show that the hypothesis that
a unit root is present in *nfa* data in levels cannot be
rejected for all countries in the sample. The same hypothesis is
rejected, however, for the first-difference of *nfa* in almost
all the countries. Hence, these results provide strong evidence in
favor of the result derived in PB1. In particular, *nfa* is
integrated of order 1 in most countries in our sample, and
therefore the IBC and TC hold.

Our finding that in most countries
implies that both IBC and TC are
satisfied, but it does not show how *nx* adjusts over time so
that its expected present value matches the initial *nfa*
position, and it does not let us identify whether there are
differences in the nature of this adjustment across countries with
different characteristics. The PMG estimation aims to fill these
gaps.

The PMG results show that there is a statistically significant error-correction relation between and both for the full sample of countries and for sub-samples separating emerging from industrial countries, and creditor from debtor countries. The systematic long-run component of responds negatively to movements in , in line with Bohn's PB3, and homogeneity tests cannot reject the hypothesis that this component is similar across countries (v. the null of country-specific components produced by MG estimation).

The long-run response coefficient is estimated at -0.07, which indicates that a one percentage point drop in
leads to a 0.07 percentage points
increase in *in the long run*. This result
also implies that, assuming realistic growth-adjusted real interest
rates (below 7 percent), both and are stationary processes.^{3} The error correction
coefficient is estimated at 0.31, which implies that the adjustment
of to a given change in
has an average half-life of over 1.5 years.

The PMG results also show that is more responsive to movements in in emerging markets than in industrial countries. The response coefficient is 1.6 times larger in the former than in the latter. Keeping other factors constant (i.e. country-specific fixed effects), this difference implies that industrial countries converge to lower long-run averages of that are consistent with external solvency.

Our work is related to the large empirical literature on tests of fiscal and external solvency. Studies include Mendoza and Ostry (2008), Trehan and Walsh (1991), Wickens and Uctum (1993), Ahmed and Rogers (1995), Liu and Tanner (1996), Wu (2000), Wu, Show-Lin and Lee (2001), Engel and Rogers (2006), and Nason and Rogers (2006). The tests we conduct differ from several of the tests conducted in this literature, and in the related literature testing for fiscal solvency, which (with the exception of Mendoza and Ostry) generally test for unit roots in the foreign debt-GDP (or public debt-GDP) and NX-GDP (or primary balance-GDP) ratios; for cointegration between exports and imports (or between fiscal revenues and outlays); or for specific orders of integration in debt (public or external). Bohn (1998, 2005, 2007) showed that failure of these tests cannot be relied on to evaluate solvency because the tests consider only sufficiency conditions that are not necessary for the IBC to hold, and hence can indicate that observed debt dynamics violate solvency, when in fact they do not.

Our tests are in line with the literature on fiscal reaction
functions pioneered by Bohn (1998) with an application to U.S.
data, and extended to a cross-country fiscal panel by Mendoza and
Ostry (2008).^{4} However, these reaction functions were
estimated using fiscal datasets in which public debt and fiscal
balances are stationary as shares of GDP. In contrast, the
hypothesis of unit roots cannot be rejected in our external
accounts data (in levels or in shares of GDP), and hence we cannot
implement Bohn's (1998) reaction function specification for
stationary variables. Instead, we use the more general
error-correction formulation characterized in PB3, which applies
even when the relevant debt stock and net revenue flow variables
are not stationary, and we also conduct the
-order-difference stationarity tests implied by PB1.

Our work is also related to the large and growing literature on
global imbalances. This literature presents opposing views about
the sustainability of the global imbalances, along with
explanations of why the observed NFA dynamics may be consistent or
inconsistent with solvency considerations.^{5} In this context, the
results of our work suggest that global imbalances are consistent
with external solvency. In fact, this can be the case even if
*nfa* is not stationary, but as long as the growth of
*nfa* and the predicted response of *nx* is such that net
foreign liabilities grow at a slower pace than the one implied by a
Ponzi scheme.

The rest of the paper is organized as follows: Section 2 describes the analytical foundations of our empirical methodology. Section 3 presents the results of the empirical tests. Section 4 concludes.

Our methodology for testing external solvency adapts Bohn's (2007) theoretical findings to an open-economy environment. Consider an open economy with the following standard period-by-period resource constraint:

(1) |

where denotes imports, exports, and the interest rate on external assets and liabilities. These variables could be expressed in nominal terms, real terms, or as a ratio to GDP as long as is adjusted accordingly (i.e., if the variables are in nominal terms, is the nominal interest rate; if the variables are in real terms, is the real interest rate; if the variables are ratios to GDP, is the growth-adjusted real interest rate that follows from dividing the gross real interest rate by the gross rate of output growth).

Under alternative standard simplifying assumptions about the
nature of the process, the resource constraint
implies:^{6}

(2) |

where , and . The above expectational difference equation, together with this TC,

(3) |

implies the following IBC:

(4) |

In the subsections that follow, we review Bohn's PB1 and PB3, which are propositions that establish testable predictions about the time-series behavior of NFA and NX that characterize economies for which (3) and (4) hold.

The following proposition from Bohn (2007) states that a
stochastic time series of debt or assets is consistent with its
corresponding IBC if the series is stationary at *any* finite
order of differencing:^{7}

**Proposition 1 PB1**.

**Proof.**See p. 1840 in Bohn (2007).

In our context, PB1 indicates that as long as any finite
difference of NFA is stationary, the NFA positions are consistent
with solvency (i.e., they satisfy 4). Thus, PB1
implies a simple but practical way to test for external solvency.
The intuition, as pointed out by Bohn (2007), is that if NFA is
-order integrated, its -period-ahead conditional expectation is a polynomial that
is *at most* of order . The discount
factor in the TC, however, grows exponentially with .
Since exponential growth dominates polynomial growth of any order,
NFA grows slower than the discount factor in TC as long as NFA is
integrated of any finite order.

Our second test of external solvency looks for a systematic
negative response of *NX* to *NFA* in the form of an
error-correction specification. In particular, Bohn (2007)
established the following result:

**Proposition 2. PB3.**

**Proof.**See p. 1844 in Bohn (2007).

This proposition states that if a country's NX and NFA positions are linked through an error-correction relationship with a coefficient that satisfies the stated conditions, then TC and IBC hold. Existence of such reaction function implies that, implicitly, households, firms and the government adjust their savings and investment plans over time in a manner that is in line with the financing requirements implied by changes in the economy's NFA position. With this response in place, the economy's external liabilities grow at a slower pace than what a Ponzi scheme implies, so that external positions are consistent with the IBC. For countries with more negative , the response of net exports to changes in net foreign assets is stronger. In turn, more negative 's are likely to reflect limitations affecting the financial markets that those countries can access, in terms of the level of financial development and/or the presence of financial frictions.

Efficient estimation of country-specific error-correction reaction functions linking NFA and NX requires large data sets that are generally not available for a large number of countries. The best data available for NFA positions, which is the dataset constructed by Lane and Milesi-Ferretti (2006), covers only the 1970-2004 period. The alternative, therefore, is to exploit the cross-sectional, time-series structure of the data to estimate a panel error-correction specification of the following form:

(5) |

where is an process. This is an error-correction specification in the class of those allowed by PB3.

Following Pesaran et al. (1999), we can nest the above relationship in an auto-regressive distributed lag (ARDL) model in which dependent and independent variables enter the right-hand-side of the model with lags of order and , respectively:

(6) |

where and denote the net exports-GDP and NFA-GDP ratios in country at time respectively, and denotes country-specific fixed effects. is a set of normally distributed error terms with country-specific variances, var.

The above equation can be expressed in terms of a linear combination of variables in levels and first differences, as follows:

where , , , , with , and .

To highlight the long-run relationship, the above equation can be rearranged as:

(7) |

where denotes the long-run relationship between and , and denotes the speed at which NX adjusts towards the long-run relationship following a change in NFA. A negative and statistically significant is sufficient to guarantee that IBC in eq. (4) holds.

We estimate the dynamic panel equation (7) using MG and PMG estimators. MG estimates independent error-correction equations for each country and computes the mean of the country-specific error-correction coefficients and its relevant statistics (see Pesaran and Smith (1995)). This approach produces consistent estimates of the average of the coefficients as long as the country-specific coefficients are independently distributed and the regressors are exogenous. If some of the coefficients are the same for all countries, however, the MG estimates are inefficient. In this case, PMG is efficient (see, Pesaran, et al (1999)). The PMG estimator imposes the restriction that the long-run coefficients are the same across countries, but the intercept, short-term coefficients and error variances can differ. The criterion for choosing whether the PMG estimator is preferred to the MG estimator is a standard Hausman test on the homogeneity restriction that the long-run coefficient is the same for all countries (see Pesaran et al. (1999)).

Using the results from PMG or MG estimation, we can derive estimates of the long-run average positions to which each country converges. For the long-run average of to exist, must be stationary, and this requires that the estimation results satisfy three conditions: and . The first condition is required for the error-correction specification to be well-defined, and the last two follow from PB3. Note that if but , PB3 still holds, but and are not stationary (see Bohn (2007)).

If is stationary, equation (7) and the resource constraint imply that each country's position converges to the following long-run average:

(8) |

Using our PMG results, is the same for all countries in the estimation panel, but there can still be significant heterogeneity in the predicted values of because the estimator still allows for country-specific estimates of and .

Since the stationarity conditions imply and the denominator of the right-hand-side of the above expression is positive, and therefore . The intuition for this result is straightforward: if is positive (negative), the country's long-run trade balance converges to a deficit (surplus), and the resource constraint dictates that in the long run (i.e., net foreign assets are equal to the negative of the annuity value of the trade balance).

It is important to note that also determines whether is a positive or negative function of the parameters that determine it. is a positive (negative) function of or if is positive (negative). This result has an important implication: everything else constant, countries with lower converge to higher (lower) mean positions if is negative (positive). This result is also intuitive. Comparing two net debtor countries (each with ), the one with a stronger response coefficient responds to temporary declines in its by adjusting its trade surplus relatively more, vis-a-vis the alternative of widening more the current account deficit, and the larger surpluses imply a higher (less negative) long-run average of . A similar intuition applies to a comparison of two creditor countries. This suggests that stronger response coefficients can be viewed as evidence that the corresponding countries have more limited access to financial markets, either to borrow or to save, than those that display weaker response coefficients.

The derivation of the IBC eq. (4) followed from a generic setup that applies to a variety of intertemporal open-economy models, as long as TC, and the assumptions about the process that support the expectational difference equation for hold. The latter can be particularly restrictive, however, because they effectively imply that the expected future stream of trade balances in the right-hand-side of (4) can be discounted at a time- and state-invariant average interest rate. This simplification is very useful for the proofs of PB1 and PB3, but it is important to note that the key implications of these propositions still hold in more general environments that do not restrict discount rates in the same way. In particular, we show below that this the case in a canonical general equilibrium model of a small open economy with complete markets of state contingent claims traded at exogenous world-determined prices.

Domestic output () in this economy is an exogenous random process, and there are similar processes driving the output of a large number of identical countries. The world-wide state of nature (i.e., the vector of all country output realizations) follows a stochastic process with the Markov transition density function . Since agents have access to complete international markets of state-contingent claims the small open economy's period-by-period budget constraint is:

(9) |

where is the period- world-determined price of a state-contingent claim that pays one unit of good in state at period . At equilibrium, these prices are equal to the corresponding stochastic marginal rates of substitution in consumption across time and states of nature. Given these prices, and if the appropriate TC holds, the above budget constraint implies the following IBC:

(10) |

where
denotes the marginal
utility of consumption, denotes the subjective
discount factor, and
is the stochastic discount factor. If we denote by the rate of return of a -period-ahead
risk-free asset, we can rewrite the IBC as follows:^{8}

(11) |

If the economy's output process represents purely diversifiable country-specific risk (e.g., if the country-specific output processes are i.i.d. and aggregate into a non-stochastic world-wide income), domestic agents would attain a perfectly smooth consumption path constant across time and states, and the compounded risk-free rate would be . In this case, the small open economy's IBC simplifies to the same expression in (4), and propositions PB1 and PB3 obviously apply.

If domestic agents cannot attain perfectly smooth consumption (which could happen for a variety of reasons, such as a global component in country output fluctuations, the existence of nontradable goods, country-specific government purchases, incomplete markets, etc.), the expressions of the IBC in (4) and (11) are not equivalent. In particular, the co-variance terms in the right-hand side of (11) are not zero, and as a result a constant discount factor equal to the unconditional expectation of the interest rate, as assumed in (4), is not the appropriate discount factor that is consistent with the true solvency condition (11). The correct discount factor is given by the equilibrium asset pricing kernel.

The intuition for why the risk-free rate is not the appropriate discount factor is that, depending on the shocks hitting the economy, the NFA stocks that result from the resource constraint can vary over a wide range and be correlated with sources of risk such as terms-of-trade shocks, foreign demand shocks, etc. As a result, NFA, NX, and asset prices and returns implied by the equilibrium pricing kernel are likely to follow very different stochastic processes, and therefore risk-free interest rates are not appropriate discount rates for the relevant TC. As Bohn (2005) puts it: "not just technically wrong, but also providing a misleading economic intuition."

Eq. (11) also implies an interesting relationship between the economy's initial NFA position and the sequence of conditional covariances of stochastic discount factors and NX. In particular, given the same expected present discounted value of net exports, a Country A with lower covariances than a Country B should display a lower initial NFA position. In turn, assuming a standard isoelastic utility function, the covariances can be re-interpreted as covariances between inverse consumption growth rates and net exports, which can then be related to observed co-movements between these variables (see Section 3.2 below).

A second important implication of eq. (11) is that, as
Bohn (1995 and 2005) showed, it again implies that a reaction
function with a negative, linear response of NX to NFA is
sufficient to guarantee that external solvency holds. Thus, this
sufficiency condition for solvency holds here even with an interest
rate that is generally *not* time- and state-invariant as
assumed in PB3.

Our analysis is based on annual data for the period 1970-2004
covering 21 industrial countries (IC) and 29 emerging markets (EM).
The IC mainly comprise the core OECD countries while the EM are
those listed in Appendix 1. NFA data in U.S. dollars are from Lane
and Milessi-Feretti (2006). Data for NX and GDP in U.S. dollars are
from the International Monetary Fund's *International Financial
Statistics*.^{9} Our sample selection is simply based
on data quality and availability. The sample includes all the
countries for which NFA and NX data start on or before 1990.
Overall, the sample consists of 1742 observations for both the NX
and NFA positions-of which 733 observations correspond to IC group
and 1009 observations to EM group.

We test PB1 using the Augmented Dickey-Fuller (ADF) and
Phillips-Perron (PP) tests to determine the degree of integration
of *nfa* for each country in our sample. We use both ADF and
PP tests because, although they are asymptotically equivalent, they
can differ significantly in small samples (see Hamilton (1999)). We
first test the null hypothesis that *nfa* is integrated of
order 1 (H(0):
) against the alternative that
it is stationary (H(1):
). Second, if the null is
accepted, we test the null hypothesis that the first difference of
*nfa* is integrated of order 1 (i.e., H(0):
) against the alternative
that it is stationary (H(1):
). We continue on this
procedure until we arrive at stationarity at a finite order of
differencing. As detailed, we arrive at stationarity in the first
order of differencing on most cases.

Figure 2 summarizes our main findings. The top panel of the
Figure shows that ADF and PP tests cannot reject the null
hypothesis of a unit root in *nfa* at commonly used
significance levels for all countries in the sample. The bottom
panel shows that when we perform the tests for the first difference
of , however, we reject the null hypothesis
of a unit root in favor of the alternative of stationarity for
almost all of the countries. This means that in most countries
is integrated of order 1. Only for very
few countries (e.g. Belgium, Norway), we cannot reject the
hypothesis of unit roots present in the first differences of
. This evidence suggests that
the observed NFA positions are consistent with external
solvency.^{10} These results do not change
significantly when we allow for the possibility of structural
breaks, intercepts and trend components in the time-series
processes.

To examine the robustness of our findings, we also conducted
tests using the KPSS stationarity test, developed by Kwiatkowski,
Phillips, Schmidt and Shin (1992). In contrast with the ADF and PP
unit root tests, KPSS tests the null that *nfa* is stationary
(H(0):
) against the alternative that
it is integrated of order 1 (H(1):
). In the event the null
hypothesis is rejected, we next proceed to check if the first
difference of *nfa* is stationary (i.e., H(0):
against the alternative
that it is integrated of order 1 (H(1):
. As in the case of the
ADF and PP tests, the results of the KPPS test indicate that
is integrated of finite order.^{11}

We also performed additional robustness tests particularly for
the U.S. The U.S. has a large weight in our analysis because of its
large share of global imbalances. For this exercise, we performed
the aforementioned unit root tests using a long time series data of
covering 1790-2004 from Engel and Rogers
(2005), and data from Curcuru et al. (2008), which is corrected for
valuation changes.^{12} We find that our main findings are
preserved in both datasets, i.e., is
nonstationary in levels but stationary in first differences.

It is important to keep in mind that the usual caveats about inference problems in short samples due to limited power of the tests are relevant for the remainder of our sample. In particular, it is well known that the ADF and PP tests do not have the power to distinguish between a unit root or a near unit root process or between a drifting or trend stationary process. In fact, when we examine the individual AR(1) coefficients for each country (see Figure 3), we find that they span a wide range from 0.59 to 1.06, and that their standard errors are relatively large (ranging from 0.065 to 0.146). Thus, although we could not reject the hypothesis of unit roots in , the possibility remains that due to the low power of the tests the true data generating process is in fact stationary in levels. This, however, would not affect our finding that the data support the hypothesis that the solvency condition holds, since stationarity in levels is also consistent with PB1.

We test PB3 by estimating the dynamic panel equation derived in
the previous Section using PMG and MG estimators. Table 2 reports
results for the full sample combining ICs and EMs and subsamples
separating ICs from EMs. The table is divided in two blocks. Block
1 shows our baseline results, and Block 2 shows results obtained
with the data expressed as ratios of world gdp.^{13} The ARDL lag
structure for each country was selected using the Schwartz Bayesian
criterion. For the majority of countries, specifications without
lagged dependent variables are rejected at conventional levels of
statistical significance. Throughout this section, we examine the
null hypothesis that there is no error-correction relation between
and under both the
PMG and MG estimators, and use -statistics to test
this hypothesis.

The Full Sample panel in Block 1 of Table 2 shows the main results combining all the countries in our sample. The Hausmann -statistic test cannot reject the slope homogeneity restriction, indicating that the PMG estimator is preferred to the MG estimator. The PMG estimates of the long-run response coefficient show a negative and statistically signficant response of to . A reduction (increase) of one percentage point in rises (lowers) by 0.07 percentage points. The estimated error correction coefficient of 0.31 (in absolute value) indicates that the adjustment of to a given change in has an average half-life of just over 1.75 years. Overall, these results for the full sample indicate that PB3 and the external solvency conditions hold.

The IC and EM panels of Block 1 in Table 2 show that the results
of MG and PMG estimation splitting the sample according to whether
countries are industrialized or emerging economies also support the
hypothesis that PB3 holds. The null hypothesis of no
error-correction relation between and
is rejected in both the IC and EM
groups. The -test indicates that PMG dominates MG
for both the IC and EM groups. Comparing across the two groups, we
find that the long-run response coefficient is higher in EMs than
in ICs (-0.085 v. -0.053). Both of
these estimates are statistically significant at a 5 percent
significance level. The error-correction coefficients imply that
the adjustment of to changes in is more protracted in ICs, for which the average
half-life is about years, than in EM, for
which the average half-life is
years.^{14}

The result indicating that the long-run response coefficient of EMs is about 1.6 times larger than that for ICs implies that net exports in EMs need to respond more to changes in net foreign assets in order to support external solvency. As suggested earlier, this difference can be attributed to the underdevelopment of financial markets or the severity of the financial frictions that EMs face compared to ICs.

Table 3 shows the long-run positions that each country converges to. In this table, we report the estimates for only those countries with statistically significant EC coefficient (phi) and intercept (mu). The estimates reported in column 5 are calculated using the formula in (8). The column labeled "nfa for constant mu" calculates the implied estimate for in the formula where the intercept term (mu) is set to the value estimated for the whole sample (All). The purpose of this exercise is to illustrate the potential changes in estimated driven solely by the changes in the EC term (phi). Likewise, the last column shows the estimates for when the EC coefficient is fixed at the estimate for the whole sample to illustrate the importance of the intercept term (mu). The main lesson we derive from this exercise is that although the long-run coefficient (rho) is kept the same, there are marked variations in long-run estimates that each country converges to. The large changes in these estimates are driven by differences in the EC and intercept terms, which, in turn, is affected by the structural differences across countries.

Figures 4a-b illustrate the impulse responses functions of and when the economy is subject to a one-standard-deviation noise shock (figures are shown for only a selected set of countries reported in Table 3 due to space limitations). These impulse responses are calculated using the PMG estimates reported in Tables 4, and setting the initial and positions to their long-run values that they converge to. The main finding is that although can converge back to its long-run equilibrium faster, the adjustment of (i.e., the stock imbalance) can persist much longer. The convergence of the positions to their long-run values in our sample takes from about 10 years up to 50 years. Our exercise also illustrate that although the long-run coefficients are common across EMs and ICs, there is marked variation among countries in their convergence. This exercise affirms that the framework preserves the heterogeneity across countries on how they respond to similar shocks. This heterogeneity arises due to structural differences among these countries as mentioned earlier.

We study next the robustness of our results to the representation of the data. To do so, we study how our results change when we use an alternative representation of the data in which the NX and NFA series are normalized using world GDP instead of country-specific GDPs (Block 2, Table 2). In the latter exercise, the world GDP is simply the sum of the respective GDPs of the countries in the sample, each expressed in U.S. dollars. The purpose of this exercise is to explore if the baseline results are altered by relative country size and by restrictions that force global market clearing.

In Block 2, the results for the Full Sample panel show that again the Hausman -test indicates that the cross-country slope homogeneity restriction cannot be rejected, albeit marginally, and that the PMG estimate of the response coefficient (-0.08) must be chosen over the MG estimator. Moreover, the average half-life of adjustment to the long-run relationship in this scenario is years. These results are very similar to those obtained using the standard and measures based on country GDPs.

The results for the IC panel with world gdp ratios are also similar to those obtained with country gdp ratios, but the results for the EM panel are different. The Hausmann -test cannot reject the long-run homogeneity condition for ICs, which implies that the PMG estimate of -0.057 is preferred to the MG estimator. In addition, the average half life for this country group is 2.6 years. Both of these estimates are very similar to those reported using country gdp ratios. For EMs, however, the Hausmann -test suggests that the hypothesis of long-run homogeneity should be rejected and that the MG estimate of -0.225 should be chosen. This estimate is almost 3 times larger than the one reported earlier. In contrast, the average half-life is estimated at 1.2 years, which is slightly lower than the one reported earlier.

The next robustness test explores the implications of splitting
the sample into creditor countries (also called "High NFA"
countries) and debtor ("Low NFA") countries. Creditor (debtor)
countries are defined as those with above (below) median
using each country's GDP.^{15} The
results of the dynamic panel estimation are shown in Panel 1 of
Table 4. For creditors, the Hausmann -test cannot
reject the cross-country homogeneity restriction and, thus,
indicates that the PMG estimate of -0.095 should
be preferred. The average half-life for this group is estimated at
1.94 years. For debtors, the Hausmann -test
indicates that the cross-country homogeneity restriction cannot be
rejected and that the PMG estimate of -0.061 is
preferred. The average half-life for this group of countries is
estimated at 1.6 years. In summary, these findings suggest that in
terms of its implications for sustainability, there is no
significant behavioral difference between creditor and debtor
countries. However, in terms of long-run
positions creditor countries will converge to higher positions than debtor countries in the long-run.

Next, we explore the importance of trade openness (panel 2, Table 4). Those countries with a volume of trade as a share of GDP higher than the volume for the median country are treated as more open economies, and the rest is treated as less open economies. For both groups, the long-run homogeneity restriction cannot be rejected. The implied PMG estimates are -0.070 (with half life 2.2 years) and -0.065 (with half life 1.4 years) for more open and less open economies, respectively, suggesting that there is no significant difference between these two groups.

We also explore the importance of institutional quality, financial sector development, and capital account openness as shown in panels 3-5, respectively. In all these cases, Hausmann test cannot reject the long-run homogeneity restriction so that the PMG should be the preferred method. These results mainly show that the countries with relatively weaker fundamentals (i.e., less institutional quality, less financial sector development, and less open to capital) need to respond more strongly to the changes in NFA to keep them on a sustainable path (notice that implied PMG estimates for the long-run coefficient is more negative for these groups compared to their counterparts with stronger fundamentals). However, our baseline findings regarding the sustainability of imbalances are preserved in all these cases.

This paper explored whether external solvency conditions hold in existing cross-country data on trade balances and net foreign assets, which largely reflects the recent episode of large and growing global imbalances. We conducted external solvency tests for a panel of 21 industrial and 30 emerging market countries during the 1970-2004 period.

Our solvency tests are based on two propositions postulated by Bohn (2007). The first proposition shows that solvency is satisfied if NFA are integrated of any finite order. When we tested this proposition, we found that we could not reject the presence of unit roots in in levels in all of the countries in our sample, but that unit roots are rejected for the first-differences of in virtually all the countries.

Bohn's second proposition shows that solvency holds if NFA and NX are linked by an error-correction reaction function. Using dynamic panel estimation methods, we found that a statistically significant error-correction relationship between those two series does exist in the data. In particular, we found a systematic, negative long-run response of to changes in . Comparing industrial and emerging countries, we found that the response coefficient of the latter is higher, and that as a result emerging economies converge to higher long-run averages of than industrial countries.

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Following Pesaran et al. (1999), we can nest the relationship in eq. 5 in an auto-regressive distributed lag (ARDL) model in which dependent and independent variables enter the right-hand-side of the model with lags of order and , respectively:

where and denote the net exports-GDP and NFA-GDP ratios in country at time respectively, and denotes country-specific fixed effects. is a set of normally distributed error terms with country-specific variances, var.

Using the following identity in the left-hand side of the equation and the following identities in the right-hand side of the equation and the above equation can be rewriten as follows:

or

or

where , , , , with , and .

To highlight the long-run relationship, the above equation can be rearranged as:

where denotes the long-run equilibrium relationship between and , and denotes the speed at which NX adjust toward their long-run equilibrium following a change in NFA.

The sample comprises 21 industrial countries and 30 emerging markets.

**Industrial Countries:** Australia (AUS), Austria (AUT),
Belgium (BEL), Canada (CAN), Denmark (DNK), Finland (FIN), France
(FRA), Germany (DEU), Greece (GRC), Ireland (IRL), Italy (ITA),
Japan (JPN), Netherlands (NLD), New Zealand (NZL), Norway (NOR),
Portugal (PRT), Spain (ESP), Sweden (SWE), Switzerland (CHE),
United Kingdom (GBR), United States (USA).

**Emerging Markets:** Argentina (ARG), Brazil (BRA), Chile
(CHL), China (CHN), Colombia (COL), Costa Rica (CRI), Ecuador
(ECU), Egypt (EGY), El Salvador (SLV), Hong Kong (HKG), Hungary
(HUN), India (IND), Indonesia (IDN), Israel (ISR), Jordan (JOR),
Korea (KOR), Malaysia (MYS), Mexico (MEX), Morocco (MAR), Pakistan
(PAK), Peru (PER), Philippines (PHL), Saudi Arab (SAU), Singapore
(SGP), South Africa (ZAF), Thailand (THA), Turkey (TUR), Uruguay
(URY), Venezuela (VEN).

Figure 1a. Current Account Balances

Note: * indicates: China, Hong Kong, Indonesia, Korea, Malaysia, Philippines, Singapore, Taiwan and Thailand. ** indicates: Algeria, Angola, Azerbaijan, Bahrain, Rep. of Congo, Ecuador, Equatorial Guinea, Gabon, Iran, Kuwait, Libya, Nigeria, Norway, Oman, Qatar, Russia, Saudi Arabia, Syria, Turkmenistan, UAE, Venezuela and Yemen

Figure 1b. Net Foreign Assets

Note: * indicates: China, Hong Kong, Indonesia, Korea, Malaysia, Philippines, Singapore, Taiwan and Thailand. ** indicates: Algeria, Angola, Azerbaijan, Bahrain, Rep. of Congo, Ecuador, Equatorial Guinea, Gabon, Iran, Kuwait, Libya, Nigeria, Norway, Oman, Qatar, Russia, Saudi Arabia, Syria, Turkmenistan, UAE, Venezuela and Yemen

Figure 2a. The Order of Integration of Net Foreign Assets Positions: Lag = 0

Figure 2b. The Order of Integration of Net Foreign Assets Positions: Lag = 1

Figure 3. The Estimated AR(1) Coefficints: Net Foreign Assets

Figure 4a. Impulse Responses to a One-Standard Deviation Noise Shock: Selected Industrial Countries

Figure 4b. Impulse Responses to a One-Standard Deviation Noise Shock: Selected Emerging Markets

Table 1. Sample Statistics. Period 1970-2004

All | Industrial Countries | Emerging Market Economies | |
---|---|---|---|

Net Exports (% of GDP): Mean | -0.872 | 0.182 | -1.637 |

Net Exports (% of GDP): Median | -0.518 | 0.196 | -1.380 |

Net Exports (% of GDP): Bottom quartile | -3.640 | -1.910 | -5.290 |

Net Exports (% of GDP): Top quartile | 2.410 | 2.430 | 2.410 |

Net Exports (% of GDP): Standard deviation | 8.367 | 4.640 | 10.192 |

Net Exports (% of GDP): Number of observations | 1742 | 733 | 1009 |

Net Exports (% of GDP): Number of countries | 50 | 21 | 29 |

Net foreign assets (% of GDP) : Mean | -17.922 | -9.195 | -24.429 |

Net foreign assets (% of GDP) : Median | -20.831 | -10.021 | -31.037 |

Net foreign assets (% of GDP) : Bottom quartile | -40.105 | -25.303 | -47.638 |

Net foreign assets (% of GDP) : Top quartile | -3.997 | 4.775 | -13.497 |

Net foreign assets (% of GDP) : Standard deviation | 43.021 | 35.082 | 47.071 |

Net foreign assets (% of GDP) : Number of observations | 1716 | 733 | 983 |

Net foreign assets (% of GDP) : Number of countries | 50 | 21 | 29 |

Table 2. Dynamic Panel Estimates of Net Exports on Net Foreign Assets (1970-2004 period)

Full Sample: MG | Full Sample: PMG | Industrial Countries: MG | Industrial Countries: PMG | Emerging Markets: MG | Emerging Markets: PMG | |
---|---|---|---|---|---|---|

As a % of Country GDP: LR Coefficient | -0.186** [0.084] | -0.068*** [0.008] | -0.243 [0.194] | -0.053*** [0.011] | -0.144*** [0.039] | -0.085*** [0.012] |

As a % of Country GDP: EC Coefficient | -0.357*** [0.035] | -0.311*** [0.037] | -0.284*** [0.045] | -0.219*** [0.043] | -0.409*** [0.050] | -0.383*** [0.052] |

As a % of Country GDP: Hausman Statistics | 1.99 | 0.97 | 2.61 | |||

As a % of Country GDP: p-value | [0.33] | [0.33] | [0.11] | |||

As a % of Country GDP: Number of countries | 50 | 50 | 21 | 21 | 29 | 29 |

As a % of World GDP^: LR Coefficient | -0.491 [0.336] | -0.078*** [0.009] | -0.871 [0.813] | -0.056*** [0.013] | -0.225*** [0.068] | -0.093*** [0.012] |

As a % of World GDP^: EC Coefficient | -0.377*** [0.039] | -0.329*** [0.041] | -0.290*** [0.048] | -0.299*** [0.046] | -0.438*** [0.056] | -0.406*** [0.058] |

As a % of World GDP^: Hausman Statistics | 1.52 | 1.00 | 3.95 | |||

As a % of World GDP^: p-value | [0.22] | [0.32] | [0.05] | |||

As a % of World GDP^: Number of countries | 51 | 51 | 21 | 21 | 30 | 30 |

Note: The symbols *, ** and *** indicate statistical significance at the 10%, 5% and 1%, levels, respectively. Standard errors are reported in brackets. The Hausman statistic refers to the test statistic on the long-run homogeneity restriction. The maximum number of lags considered in the estimation is 2. ^Includes the Rest of the World, which is created as the negative of the global external imbalances. The World Output is the sum of the outputs of industrial and emerging market countries in our sample.

Table 3. Long-run NFA

rho | phi | mu | nfa | nfa for constant mu | nfa for constant phi | |
---|---|---|---|---|---|---|

Industrial Countries: Australia | -0.053 | -0.322*** | -1.080** | -45.961 | -10.462 | -67.599 |

Industrial Countries: Japan | -0.053 | -0.337*** | 0.685*** | 27.840 | -9.997 | 42.854 |

Industrial Countries: Netherlands | -0.053 | -0.216** | 1.109** | 70.324 | -15.587 | 69.425 |

Industrial Countries: New Zealand | -0.053 | -0.889*** | -3.386*** | -52.150 | -3.788 | -211.816 |

Industrial Countries: Portugal | -0.053 | -0.380*** | -3.919*** | -141.020 | -8.852 | -245.143 |

Industrial Countries: Spain | -0.053 | -0.395*** | -0.89*** | -31.114 | -8.529 | -56.133 |

Industrial Countries: All | -0.053 | -0.219*** | -0.246** | -15.388 | -15.388 | -15.388 |

Emerging Markets: Brazil | -0.085 | -0.313*** | -0.748* | -22.746 | -33.762 | -18.612 |

Emerging Markets: Chile | -0.085 | -0.499*** | -1.582* | -30.159 | -21.179 | -39.341 |

Emerging Markets: Costa Rica | -0.085 | -0.409*** | -3.428*** | -79.728 | -25.839 | -85.244 |

Emerging Markets: Hong Kong | -0.085 | -0.117** | 1.682* | 136.972 | -90.435 | 41.843 |

Emerging Markets: Hungary | -0.085 | -0.324** | -1.991** | -58.494 | -32.637 | -49.514 |

Emerging Markets: India | -0.085 | -0.468*** | -1.320*** | -26.836 | -22.580 | -32.834 |

Emerging Markets: Jordan | -0.085 | -0.209* | -6.936* | -315.912 | -50.602 | -172.473 |

Emerging Markets: Mexico | -0.085 | -0.315** | -1.117* | -33.747 | -33.548 | -27.791 |

Emerging Markets: Morocco | -0.085 | -0.275*** | -3.317*** | -114.531 | -38.351 | -82.504 |

Emerging Markets: Peru | -0.085 | -0.349*** | -2.271** | -61.974 | -30.309 | -56.489 |

Emerging Markets: Philippines | -0.085 | -0.282** | -2.456** | -82.851 | -37.468 | -61.089 |

Emerging Markets: All | -0.085 | -0.383*** | -1.111** | -27.627 | -27.627 | -27.627 |

Note: The table shows the long-run NFA positions that the PMG model converges to for the countries with significant phi an mu. The last two columns illustrate the respective implied NFA positions if the EC coefficient and intercept terms were kept constant at the value estimated for the whole sample.

Table 4. Panel A. Dynamic Panel Estimates of Net Exports on Net Foreing Assets (As a percent of GDP, 1970-2004 period): Debtor vs. Creditor

Debtor Economies: MG | Debtor Economies: PMG | Creditor Economies: MG | Creditor Economies: PMG | |
---|---|---|---|---|

LR Coefficient | -0.285* [0.162] | -0.061*** [0.010] | -0.087** [0.039] | -0.095*** [0.016] |

EC Coefficient | -0.349*** [0.046] | -0.315*** [0.046] | -0.364*** [0.055] | -0.300*** [0.059] |

Hausman Statistics | 1.91 | 0.05 | ||

p-value | [0.17] | [0.82] | ||

Number of countries | 25 | 25 | 25 | 25 |

Note: The symbols *, ** and *** indicate statistical significance at the 10%, 5% and 1%, levels, respectively. Standard errors are reported in brackets. The Hausman statistic refers to the test statistic on the long-run homogeneity restriction. The maximum number of lags considered in the estimation is 2.

Table 4. Panel B. Dynamic Panel Estimates of Net Exports on Net Foreing Assets (As a percent of GDP, 1970-2004 period): Trade Openness

Less Open Economies: MG | Less Open Economies: PMG | More Open Economies: MG | More Open Economies: PMG | |
---|---|---|---|---|

LR Coefficient | -0.104** [0.041] | -0.065*** [0.012] | -0.267 [0.163] | -0.070*** [0.012] |

EC Coefficient | -0.488*** [0.056] | -0.404*** [0.061] | -0.266*** [0.036] | -0.218*** [0.033] |

Hausman Statistics | 0.99 | 1.48 | ||

p-value | [0.32] | [0.22] | ||

Number of countries | 25 | 25 | 25 | 25 |

Note: The symbols *, ** and *** indicate statistical significance at the 10%, 5% and 1%, levels, respectively. Standard errors are reported in brackets. The Hausman statistic refers to the test statistic on the long-run homogeneity restriction. The maximum number of lags considered in the estimation is 2.

Table 4. Panel C. Dynamic Panel Estimates of Net Exports on Net Foreing Assets (As a percent of GDP, 1970-2004 period): Institutional Quality

More Institutional Quality: MG | More Institutional Quality: PMG | Less Institutional Quality: MG | Less Institutional Quality: PMG | |
---|---|---|---|---|

LR Coefficient | -0.224 [0.164] | -0.055*** [0.011] | -0.147*** [0.041] | -0.083*** [0.012] |

EC Coefficient Hausman Statistics | -0.287*** [0.040] | -0.226*** [0.039] 1.06 | -0.427*** [0.056] | -0.403*** [0.058] 2.79 |

p-value Number of countries | 25 | [0.30] 25 | 25 | [0.09] 25 |

Note: The symbols *, ** and *** indicate statistical significance at the 10%, 5% and 1%, levels, respectively. Standard errors are reported in brackets. The Hausman statistic refers to the test statistic on the long-run homogeneity restriction. The maximum number of lags considered in the estimation is 2.

Table 4. Panel D. Dynamic Panel Estimates of Net Exports on Net Foreing Assets (As a percent of GDP, 1970-2004 period): Financial Sector Development

More Financial Sector Dev.: MG | More Financial Sector Dev.: PMG | Less Financial Sector Dev.: MG | Less Financial Sector Dev.: PMG | |
---|---|---|---|---|

LR Coefficient | -0.235 [0.164] | -0.063*** [0.011] | -0.137*** [0.041] | -0.074*** [0.012] |

EC Coefficient | -0.280*** [0.036] | -0.226*** [0.037] | -0.434*** [0.058] | -0.397*** [0.060] |

Hausman Statistics | 1.11 | 2.56 | ||

p-value | [0.29] | [0.11] | ||

Number of countries | 25 | 25 | 25 | 25 |

Table 4. Panel E. Dynamic Panel Estimates of Net Exports on Net Foreing Assets (As a percent of GDP, 1970-2004 period): Capital Account Openness

More Open to Capital: MG | More Open to Capital: PMG | Less Open to Capital: MG | Less Open to Capital: PMG | |
---|---|---|---|---|

LR Coefficient | -0.230 [0.164] | -0.054*** [0.011] | -0.141*** [0.040] | -0.085*** [0.013] |

EC Coefficient | -0.299*** [0.049] | -0.240*** [0.049] | -0.414*** [0.049] | -0.386*** [0.052] |

Hausman Statistics | 1.16 | 2.16 | ||

p-value | [0.28] | [0.14] | ||

Number of countries | 25 | 25 | 25 | 25 |

1. We thank Shaghil Ahmed, Daniel Beltran,
Betty Daniel, Linda Goldberg, David Romer, Barbara Rossi,
participants of the Global Imbalances workshop at the Federal
Reserve Board for comments and suggestions; Stephanie Curcuru, John
Rogers for kindly sharing their data sets; Paul Eitelman, Justin
Vitanza and George Zhu Yi for excellent research assistance. We
also thank Gian Maria Milesi-Ferretti and Philip Lane for the data
on net foreign asset positions (posted at
`http://www.imf.org/external/pubs/ft/wp/2006/data/wp0669.zip`).
The analysis undertaken in this paper would not have been possible
without their efforts. All remaining errors are exclusively our
responsibility. Correspondence: `Bora.Durdu@frb.gov`,
`mendozae@econ.umd.edu`, `mterrones@imf.org`. The
views expressed in this paper are those of the authors and should
not be attributed to the International Monetary Fund, or to the
Board of Governors of the Federal Reserve System. Return to text

2. Bohn focused on public debt, the primary fiscal balance and the government's IBC, but obviously his results also apply to NFA, NX and the open-economy IBC. One important caveat is that his analysis establishes only sufficiency conditions for solvency. Hence, if our tests yield positive results they do represent evidence indicating that the IBC holds, but failure of the tests does not reject it. Return to text

3. This evidence is contrary to the
country-specific unit root tests that suggested that *nx* and
*nfa* are not stationary. The difference in results is due to
the small-sample problems of unit root tests, and to the fact that
the unit root tests are country specific, while PMG estimation uses
the full panel dataset to identify the error-correction
relationship. Return to text

4. Engel and Rogers (2006) tested for
external solvency in the United States using Bohn's (1998) test.
They estimated a conditional linear reaction function for
and the *negative* of the net
external financial position-to-GDP ratio over the 1791-2004 period.
They obtained a negative and statistically significant response
coefficient, which indicates failure of the sufficiency condition
for external solvency. Return to
text

5. One group of studies (e.g., Summers(2004), Obstfeld and Rogoff (2004), Roubini and Setser (2005), Blanchard, Giavazzi and Sa (2005), Krugman (2006)) argues that these imbalances are not sustainable. On the other hand, other studies (e.g., Backus, Henriksen, Lambert and Telmer (2005), Bernanke (2005), Croke, Kamin and Leduc (2005), Durdu, Mendoza and Terrones (2008), Gourinchas and Rey (2005), Hausmann and Sturzenegger (2005), Henriksen (2005), Mendoza, Quadrini and Rios-Rull (2007), Lane and Milesi-Ferretti (2005), Caballero, Farhi and Gourinchas (2006), Cavallo and Tille (2006), Engel and Rogers (2006), Fogli and Perri (2006), Ghironi, Lee and Rebucci (2006)), argue that the imbalances are an equilibrium outcome of various developments such as differences in business cycle volatility, financial development, demographic dynamics, a `global savings glut,' self insurance against financial crises, or valuation effects. Return to text

6. Three of these assumptions reviewed in Bohn (2007) are: (1) positive and constant, (2) i.i.d with a positive and constant conditional expectation, or (3) is any stationary stochastic process with mean , and subject to implicit restrictions that may be required so that the process of " interest adjusted imports" ( ) has similar statistical properties as . Return to text

7. A common test used to evaluate external solvency is to test if NFA is difference-stationary (integrated of order 1). Rejection of this hypothesis was commonly taken as evidence against external solvency, but PB1 demonstrates that this interpretation is incorrect. Return to text

8. At equilibrium, this interest rate satisfies Return to text

9. Summary statistics are provided in Table 1. Return to text

10. In the case of four transition economies (Lithuania, Poland, Russia, and Slovenia) the tests cannot establish a robust stationarity result. These results, however, are mainly driven by the sample size (for those countries, the sample starts in early 1990s), because the unit root tests tend to be inconclusive in short samples. Return to text

11. The results for KPSS tests are available upon requests. Return to text

12. We thank corresponding authors for kindly sharing their dataset. Return to text

13. We also studied the results where only those countries with statistically significant EC coefficients, and intercept terms (as reported in Table 3) are kept in the sample. We found that the results are robust to the sample selection. Return to text

14. The half-life is calculated as , where denotes the error correction coefficient. The higher is the , the lower is the half-life and the faster is the adjustment. Return to text

15. The list of countries pertaining to each group is available on request. Return to text

This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to text