A Gravity Model of Sovereign Lending: Trade, Default, and Credit
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

One reason why countries service their external debts is the fear that default might lead to shrinkage of international trade. If so, then creditors should systematically lend more to countries with which they share closer trade links. We develop a simple theoretical model to capture this intuition, then test and corroborate this idea. [JELF15, F33]


One reason why countries service their external debts is the fear that default might lead to shrinkage of international trade. If so, then creditors should systematically lend more to countries with which they share closer trade links. We develop a simple theoretical model to capture this intuition, then test and corroborate this idea. [JELF15, F33]

A Gravity Model of Sovereign Lending: Trade, Default, and Credit

While the age of gunboat diplomacy as a mechanism of credit enforcement has long passed, sovereign default is still an exceptional event. This stylized fact indicates that while the source of a sovereign default penalty is still controversial, sovereigns behave as if they consider default costly. Many models of sovereign debt in the literature (e.g., Bulow and Rogoff, 1989a, 1989b) introduce explicit default penalties to rationalize this fact. These sanctions are primarily considered to be methods of inhibiting trade. Bulow and Rogoff (1989a) discuss the difficulties countries would experience in their trade subsequent to default, including complications associated with avoiding seizure and the interruption of short-term trade credit.

Nevertheless, there are a number of reasons why one might doubt the existence of default penalties. (Bulow and Rogoff (1989b) themselves admit that it is unclear whether private creditors enjoy the ability to induce their governments to enforce claims on sovereign borrowers. Kletzer and Wright (2000) argue that most penalties in models of sovereign lending are not “renegotiation-proof.” That is, Kletzer and Wright argue that both parties could do better subsequent to a full or partial sovereign default, if the creditor resists levying a destructive penalty from which (s)he would receive no immediate benefit. In brief, there is considerable uncertainty concerning the viability of penalties for sovereign default. Thus, empirical evidence regarding such penalties warrants attention.

Unfortunately, there are only a limited number of empirical studies concerning such penalties. Ozler (1993) provides evidence of positive, albeit small, premia charged to countries with default histories. Cline (1987) notes that Bolivia and Peru experienced interruptions in their flows of short-term trade credits subsequent to debt renegotiation. In a recent paper, Rose (2002) provides empirical support for the role of trade as a sovereign enforcement mechanism. His paper shows that sovereign Paris Club reschedulings are followed by economically and statistically significant reductions in international trade.

The evidence of Cline and Rose centers on the interruption of international trade as a mechanism for sovereign debt repayment. If one believes that the primary penalties for enforcing sovereign debt obligations are trade related, then creditors originating from nations with strong bilateral trade ties with a debtor nation should have a comparative advantage in lending to that nation.

In this short paper, we explore this idea. We first present a theoretical model of international lending where a debtor optimally chooses its borrowing from different creditors. These creditors are identical except that they are located in countries that differ by the strength of their bilateral trade ties with the debtor. We show that in equilibrium, the pattern of borrowing favors the creditor with higher bilateral trade volume with the debtor. We then test and corroborate this idea using an annual panel data set including bilateral trade and international banking claims from 20 creditor and 149 debtor countries from 1986 through 1999. Using instrumental variable (and other) techniques, we find a significantly positive effect of bilateral trade on bilateral lending patterns. That is, debtors tend to borrow more from creditors with whom they share more international trade ties.

While our empirical results support the trade sanction sovereign debt model derived in the paper, the evidence does not necessarily refute pure “reputation-based” models of sovereign debt in which the penalty for default is exclusion from access to future borrowing (e.g., Eaton and Gersovitz, 1981; Kletzer and Wright, 2000; or Wright, 2002), or with mixed models where some combination of direct sanctions and reputational penalties are applied, such as Kehoe and Levine (1993).1 However, it appears that reconciling reputation-based models with the data without introducing new inconsistencies requires the introduction of some friction, such as superior information sets to creditors from those countries engaged in greater bilateral trade.2

Our theoretical model is presented in the next section. We then present the data set and methodology and test the model. The paper ends with a brief summary.

I. A Model of Sovereign Borrowing with Trade-Related Default Penalties

In this section we develop a simple borrowing model in which a sovereign debtor allocates its borrowing across different creditor nations, when default penalties are based on proportional losses in bilateral gains from trade.

We assume that there are three countries: one borrower country, i, and two creditor countries, a and b. Let r represent one plus the world risk-free interest rate. All countries are assumed to be small and therefore take r as given. Lending banks in the creditor countries are risk-neutral and therefore willing to extend unlimited funds at levels consistent with an expected return equal to r.

The model has two periods. In the first period, the representative agent in lender country j (j = a, b) extends a loan of magnitude Lij in return for the promise of a fixed payment Dij in the second period. In the second period, the agent in debtor country i makes its default decisions. If the debtor chooses to service its country j debt it pays Dij. If the debtor defaults, it suffers a penalty equal to a fraction θ of its gains from bilateral trade with country j, where 0 < θ < 1.

Bilateral gains from trade are exogenous and equal to γTij, where γ is a positive constant and Tij is a random variable reflecting total trade between country i and country j in the second period. Expectations of Tij are unbiased and satisfy


where E1(Tij) represents the period one expected value of Tij and εi is an i.i.d. disturbance term with expected value 0 and a symmetric and single-peaked distribution on the interval εi ∈ [e, ē]. Let F(ε) represent the distribution of ε, that is, the probability that εi ≤ ε, and f(ε) represent its density. The creditor nations are assumed to only differ in their expected trade volume with the debtor country, with E1(Tia) > E1 (Tib).

The expected utility function of the representative agent in country i satisfies


where U′ > 0, U″ < 0, Cit represents consumption in country i in period t(t= 1,2), and (β represents the debtor's discount rate. The specification that debtor utility is linear in expected second-period consumption is made for analytic simplicity, but drives none of our results.

Debtor income, Yit, is exogenous in both periods. Debtor first-period consumption satisfies


Since no new funds are obtained in period 2, the debtor's default decision on debts from each creditor nation is based on maximizing expected second-period consumption. Conditional on service on its debt obligations to country j, debtor second-period consumption satisfies


where jk and g (Dik, εi) represents the gains from trade net of the cost of debt service on the debtor's country k debt obligations given that the debtor makes its utility-maximizing default decision on its obligations to that country.

Similarly, conditional on default on obligations to country j, debtor second-period consumption satisfies


It follows that the debtor chooses to default on country j when Dij > θγTij.

Define εij* as the realization of εi that leaves the debtor indifferent between default and repayment. εij* satisfies


Equilibrium in the model is defined as the pair of debt obligations (Dia, Dib) that maximize expected debtor utility subject to both creditors' zero-profit conditions. The creditors' zero profit conditions satisfy


where j= a,b.

Utility maximization for the debtor can be characterized in terms of two decisions, the overall borrowing level, Li, and the allocation of debt across the two creditors, Dia and Dib Consider first the allocation decision. Given total borrowing Li, maximizing expected utility subject to the creditors' zero-profit conditions yields the first-order condition


Equation (8) demonstrates that the debtor skews its borrowing allocation toward the nation from which the impact of a marginal increase in borrowing on its probability of default is smaller. Since the creditors' risk premia are symmetric functions of default risk, equalizing the marginal cost of the last dollar borrowed in each country implies borrowing more from the country that would have a lower probability of default if borrowing levels were equal. Of course, doing so pushes up the probability of default in this country relative to the other, and narrows the difference between these probabilities.

This result implies that the optimal allocation of borrowing across countries mitigates the disparities in default risk across countries. This result fits well with historical experience, as countries typically default on all of their creditors simultaneously, or not at all. It should be stressed, however, that the result is an equilibrium outcome of the model, rather than simply assumed.3

Totally differentiating (8) with respect to Lia and E(Tia) yields


where the denominator can be signed as negative by the debtor's second-order condition.

Equation (9) yields our first result. Holding total lending constant, the share of lending originating in country a is increasing in the expected volume of trade with country a.

We can now confront the debtor's overall borrowing decision. Maximizing expected utility in equation (2) over the choice of Li subject to the creditors' zero-profit conditions and the debtor's optimal debt allocation rule yields the first-order condition


where by (6) and (7), the partial term satisfies


Totally differentiating with respect to Li and E1(Tia) yields


where the denominator can be signed as negative by the debtor's second-order condition.

Our results demonstrate that an increase in the expected volume of bilateral trade with an individual country is associated with both an increase in overall borrowing and an increase in the share of overall borrowing originating in that country. Consequently, the model predicts a positive correlation between expected bilateral trade volumes and bilateral lending. In the next section, we test this prediction.

II. Empirics

Gravity Methodology

We are interested in estimating the effect of international trade on international debt. However, international borrowing may itself encourage trade; alternatively, both borrowing and trade may be jointly driven by common factors. That is, it is important for us to consider the possibility that international borrowing and trade are simultaneously determined.

We solve this problem using instrumental variables. The popular “gravity” model of bilateral international trade provides a wealth of potential instrumental variables. Many variables that are known to be important determinants of international trade are unlikely to be important determinants of international lending patterns. For instance, a pair of landlocked countries engages in less international trade, while a pair of physically large countries or those that share a common land border trade more. But international lending patterns are unlikely to be affected by such features.4 We use such variables as instrumental variables for trade in a model of bilateral lending.

Since conditions that lead two countries to be more integrated are likely to lead to more financial activity between them, our specification for bilateral international borrowing levels follows the gravity model of international trade closely:


where i and j denotes countries, t denotes time, and the variables are defined as:

  • Cijt denotes the value of real lending from i to j at time t,

  • Xijt denotes the average value of real bilateral trade between i and j at time t,

  • Y is real GDP,

  • Pop is population,

  • D is the distance between i and j,

  • Lang is a binary variable that is unity if i and j have a common language,

  • Cont is a binary variable that is unity if i and j share a land border,

  • FTA is a binary variable that is unity if i and j belong to the same regional trade agreement,

  • Landl is the number of landlocked countries in the country pair (0, 1, or 2).

  • Island is the number of island nations in the pair (0, 1, or 2),

  • Area is the land mass of the country,

  • ComCol is a binary variable that is unity if i and j were ever colonies after 1945 with the same colonizer,

  • CurCol is a binary variable that is unity if i and j are colonies at time t,

  • Colony is a binary variable that is unity if i ever colonized j or vice versa,

  • ComNat is a binary variable that is unity if i and j remained part of the same nation during the sample (e.g., the United Kingdom and Bermuda),

  • CU is a binary variable that is unity if i and j use the same currency at time t,

  • Tτt is a comprehensive set of year-specific intercepts,

  • β and γ are vectors of nuisance coefficients, and

  • εij represents the myriad other influences on bilateral credit, assumed to be well behaved.

The coefficient of interest to us is φ, the effect of bilateral trade between countries i and j on commercial bank claims by creditor country j on debtor nation i.

We estimate the model with a number of techniques below. We begin by using ordinary least squares (OLS) with standard errors that are robust to clustering (since pairs of countries are likely to be highly dependent across years). We then use instrumental variables, dropping some of the regressors from the right-hand side of the equation and using them as instrumental variables. Finally, we employ fixed- and random-effects panel data estimators, with and without instrumental variables. We use both fixed- and random-effects estimators extensively below.

The Data Set

We use a subset of the panel data set of Glick and Rose (2002); the interested reader is referred to Glick and Rose for more details.

For the regressand we use consolidated foreign claims of reporting banks on individual countries.5 These bank loans are provided by the Bank for International Settlements (BIS) in millions of U.S. dollars for 20 creditor countries and almost 150 borrowing countries.6 Not all of the areas covered are countries in the conventional sense of the word; we use the term “country” simply for convenience. (The creditor countries and debtor countries are listed in the appendix.) The data are provided semi-annually from 1986; we average the data to annual series by simple averaging. We convert nominal bank claims to a real series by deflating by the U.S. CPI (1982–1984 = 1). Almost half the claims are reported to be zero. This makes the log transformation potentially important and questionable; we investigate it further below.

Table 1.

OLS Estimates of Effect of Trade on Claims

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Equation estimated is Claimsi,j,t = φTradei,j,t + βXi,j,t + εi,j,t. Robust standard errors (clustered by country-pairs) recorded in parentheses. Intercepts and year effects not recorded.

The most important regressor is the level of international trade. We use bilateral trade flows taken from the IMF's Direction of Trade Statistics data set, deflated by the U.S. CPI.7 To this we add population and real GDP data (in constant dollars).8 We exploit the CIA's World Factbook for a number of country-specific variables. These include: latitude and longitude, land area, landlocked and island status, physically contiguous neighbors, language, colonizers, and dates of independence. We use these to create great-circle distance and our other controls. We obtain data from the World Trade Organization to create an indicator of regional trade agreements, and we include: EEC/EC/EU, US-Israel FTA, NAFTA, CACM, CARICOM, PATCRA, ANZCERTA, ASEAN, SPARTECA, and Mercosur. Finally, we add the Glick and Rose (2002) currency union dummy variable.

Descriptive statistics for the data set are tabulated in the appendix.


We begin our investigation by estimating equation (12) with OLS. Our results appear in Table 1.

Our default estimates include the entire set of regressors (i.e., all 14 coefficients are estimated, as well as the set of time-specific intercepts). In this specification, the estimate of the all-important φ coefficient is 0.54, with a robust standard error of 0.04. This elasticity is not only consistent with our theory, but is highly significant. With a t-statistic of over 15, the coefficient is different from zero at any reasonable level of statistical significance. The effect is also economically significant; an increase in trade of 1 percent is associated with an increase in bilateral lending of over 0.5 percent, all other things being equal. Of course, since there are capital flows above and beyond the bank lending that we consider (through, for example, stock and bond markets, as well as foreign direct investment), even this considerable elasticity should probably be considered a lower bound.

The rest of the table provides a series of robustness checks. For instance, the second row reports φ if the other controls are dropped from the equation (i.e., we set β = γ = 0); in this case, the effect is even more significant. Since many of the creditor countries have not extended loans to some of the debtor countries, many observations of the dependent variable are zero and are thus dropped from the equation estimated in natural logarithms. Therefore, the third and fourth rows of the table report comparable estimates of φ when both trade and bank claims are included in untransformed levels. Yet φ remains statistically significant when the key relationship is estimated in levels.9

The fifth and sixth rows of the table move away from panel data analysis to cover only cross sections for two years in the middle of the sample, 1990 and 1995. However, the results are essentially unchanged from the default specification. The seventh and final row includes only observations between industrial countries (i.e., those with IFS country codes less than 200). If anything, the results become mysteriously larger; they certainly remain positive and highly significant in both the economic and statistical senses.10

To summarize, the effect of international trade on bank claims seems positive, significant, and robust in simple OLS estimation. The question is whether this result stands up to greater econometric scrutiny.

III. Results

We now proceed to instrumental variables estimation. We use five instrumental variables for (the log of) trade: (the log of) distance between the countries; the land border dummy; the number of landlocked countries; the number of island nations; and the log of the product of the countries' area. We accordingly set the appropriate β coefficients to zero (i.e., drop them from the equation, leaving the remaining variables as controls). The estimates are tabulated in Table 2a.

Despite the use of instrumental variables that are both plausibly exogenous and correlated with trade, the key results do not change with IV estimation. The default estimate is somewhat smaller, averaging perhaps 0.4. But it remains economically and statistically significant; it is also robust to a number of econometric perturbations.11

Table 2a.

IV Estimates of Effect of Trade on Claims, Geographic Instruments

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Equation estimated is Claimsi,j,t = φTradei,j,t + βWi,j,t + εi,j,t. Robust standard errors (clustered by country-pairs) recorded in parentheses. Intercepts and year effects not recorded. Instrumental variables for trade are: distance; land border; number landlocked; number of island nations; log of area.
Table 2b.

IV Estimates of Effect of Trade on Claims, Excludable Instruments

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Equation estimated is Claimsi,j,t = φTradei,j,t + βZi,j,t + εi,j,t. Robust standard errors (clustered by country-pairs) recorded in parentheses. Intercepts and year effects not recorded. Instrumental variables for trade are: common language; regional trade agreement; same nation.

Table 2b reports sensitivity analysis with respect to the set of instrumental variables. Instead of the five geographic variables, we use three whose coefficients are usually insignificant in OLS estimates of equation (14): the common language dummy; the regional trade agreement dummy; and the same nation dummy. Again, the estimates of φ seem economically and statistically significant.12

Table 3.

IV Estimates of Effect of Trade on Claims, Controlling for Total Claims/Debt

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Equation estimated is Claimsi,j,t = φTradei,j,t + εWi,j,t + εi,j,t. Robust standard errors (clustered by country-pairs) recorded in parentheses. Intercepts and year effects not recorded. Instrumental variables for trade are: distance; land border; number landlocked; number of island nations; log of area.

The middle column of Table 3 adds a control for the (log of the) total credit extended by the creditor country, as suggested by our theoretical analysis; the right-hand column controls for the (log of) total debt incurred by the debtor country. Again, the results remain economically and statistically significant.

Finally, Table 4 reports results when panel estimators are used instead of more traditional regressions. The middle columns report OLS fixed- and random-effects estimates of φ for a variety of different specifications. The former takes into account all country-pair factors that influence trade whether measured or not, and is thus an exceptionally good robustness check. The right-hand column reports instrumental variables estimates using a random effects estimator (the fixed-effect estimator is infeasible since the geographic variables are time-invariant). Yet despite all the econometric firepower, the estimate of φ remains significant; it has a t-statistic of almost 9 and an economically large effect.13

We conclude that our hypothesis that bank credit is extended across international borders along the lines of international trade is corroborated.

IV. Summary

It is plausible to believe that countries service their foreign debts at least in part to avoid the reduced trade that typically follows international default. If so, sovereign borrowers will enjoy superior credit terms from creditor countries for which this penalty is disproportionately high. In this paper we have provided a simple theoretical model that formalizes this intuition. We have also empirically investigated and confirmed the hypothesis that international trade patterns determine lending patterns.

Table 4.

IV Estimates of Effect of Trade Level on Claims, Panel Estimators

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Equation estimated is Claimsii,j,t = φTradei,j,t + βWi,j,t + εi,j,t. Robust standard errors (clustered by country-pairs) recorded in parentheses. Intercepts and year effects not recorded. Instrumental variables for trade are: distance; land border; number landlocked; number of island nations; log of area.

In future work it would be interesting to extend this analysis to other forms of international lending, above and beyond bank loans. We think this is a good place to pass the torch to others.


Descriptive Statistics

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Creditor Countries with Claims Reported

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Debtor Countries with Claims Reported

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*Rose is B.T. Rocca Jr. Professor of International Trade and Economic Analysis and Policy in the Haas School of Business at the University of California, Berkeley, NBER research associate, and CEPR Research Fellow. Spiegel is Senior Research Advisor, Economic Research Department, Federal Reserve Bank of San Francisco. We thank Rob Feenstra for a comment that helped inspire this paper; Rose thanks INSEAD for hospitality while part of this paper was written. We also thank Gerd Haeusler, Phillip Lane, Nancy Marion, Paulo Mauro, Michael Mussa, and participants at the IMF's Fourth Annual Research Conference, and especially Mark Wright, for comments. A current (PDF) version of this paper and the STATA data set used in the paper are available via the Internet at: http://faculty.haas.berkeley.edu/arose.


While the Kehoe and Levine model allows for asset seizure, it does not consider interruptions of trade in spot markets, which might be considered analogous to the direct trade sanctions in our model below.


See Wright's (2003) comments on our paper below. Wright argues that the assumption of superior information sets held by primary trading partners may give those partners comparative advantages in lending in pure reputation models with the additional assumption of continuous trade in goods to avoid the “excessive gross flows” problem.


In the limiting case where the εij 's are distributed uniformly, the equilibrium borrowing allocation results in the debtor defaulting on both creditors or none.


If bank lending reflects trade credits, coefficient estimates from our IV estimation may be biased upwards. As our estimated effect is large, however, it is unlikely that correction for this bias would eliminate our results.


Our measurement of cross-border obligations may contain errors from a number of sources. First, the use of consolidated data may not correctly assign the risk of banks' foreign branches. Second, “outward risk transfers” are sometimes used to transfer risks to residents of other countries, and our data set would not pick these up. Still, as these errors fall in the regressand of our model they only make the effect of trade harder to find and do not appear to introduce any bias issues.


These data are available via the Internet at: http://www.bis.org/publ/qcsv0206/hanx9b.csv and are part of the International Banking Statistics published regularly in the BIS Quarterly Review. For technical reasons we usually ignore a few observations from Ireland and Spain; adding these makes little difference in general to our results.


Bilateral trade on FOB exports and CIF imports is recorded in U.S. dollars; we deflate trade by the U.S. CPI. We create an average value of bilateral trade between a pair of countries by averaging all of the four possible measures potentially available.


Wherever possible, we use World Development Indicators (taken from the World Bank's WDI 2000 CD-ROM) data. When the data are unavailable from the World Bank, we fill in missing observations with comparables from the Penn World Table Mark 5.6, and (when all else fails) from the IMF's International Financial Statistics. The series have been checked and corrected for errors.


Box-Cox tests imply that the natural logarithmic transformation is quite reasonable, and that the level transformation is rejected in favor of the log transform.


Though if we include only developing country borrowers, our estimate remains significant at 0.53 (standard error of 0.04).


Again, if we include only developing country borrowers, our estimate remains significant at 0.38 (standard error of 0.08).


If we use lags (e.g., of the GDP terms) as instrumental variables, our key result of a positive effect of trade on borrowing is not changed.


Lending may be motivated by servicing FDI, rather than the sovereign risk issues considered in the theory above. To test this, we add a control in the form of the natural logarithm of FDI sourced from the creditor country. We obtained the bilateral FDI data from the OECD's International Direct Investments Yearbook 1980–2000. This data set is annual and unavailable for many countries in our sample, containing only some 2,600 observations. When we add this control to our default IV regression (in logs, with controls) its coefficient is indeed positive and significant. Still, the log of trade retains an economically and statistically significant coefficient of 0.62 (with a robust standard error of 0.11).