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Commercial banks and LDC debt reduction.


Much empirical literature examines the foreign debt servicing capacity of lesser developed countries (LDCs) before and after the onset of the LDC debt crisis in 1982 (Abassi and Taffler, 1982; Avramovic et al., 1968; Cline, 1984; Edwards, 1984; Dhonte, 1975; Feder and Just, 1977; Feder, Just, and Ross, 1981; Frank and Cline, 1971; Grinols, 1976; Kharas, 1984; Mayo and Barrett, 1978; Saini and Bates, 1978; Sargen, 1977; Schmidt, 1984.) Of particular concern to most of these studies are the factors that may influence the probability that a country will default on, or be forced to reschedule, its foreign debts. Using a variety of statistical methodologies, the studies identify several macroeconomic variables that are statistically linked to higher default probabilities in indebted LDCs. (For a review of the empirical literature on LDC default probabilities, see McDonald, 1982; Saini and Bates, 1984; and Eaton, Gersovitz, and Stiglitz, 1986.)

The LDC debt literature, however, has failed to address the question of how international creditor banks have responded to those macroeconomic factors found to be systematically related to the probability of default (defined here as the probability that a bank is repaid less than the face value of debt). This question has taken on even greater importance since the onset of the LDC debt crisis in which a succession of indebted LDCs, beginning with Mexico in August of 1982, found that they no longer could service their external debts at existing levels and terms. Faced with the very real prospect that widespread LDC default could shake the world financial and trading systems and the economic and political stability of debtor countries, the international financial community struggled for years to find an appropriate policy response to the crisis.

The cooperation of the creditor banks was key to the success of any LDC debt policy. Thus, some theory of how banks responded to high expected LDC default probabilities was needed. Toward the latter part of the 1980s, a theory that gained prominence offered an intuitive, albeit controversial, framework within which to explain bank behavior in response to high expected LDC default probabilities. This theory posited that banks' optimal strategy in certain situations may be to reduce their claims on indebted LDCs (see, for example, Krugman, 1989; Sachs, 1986). This theory was perhaps best represented by Krugman's (1989) debt-relief Laffer curve, which demonstrated that when high default probabilities existed, reducing a country's debt burden actually could increase the expected value of the debt (see section II for a more on-depth discussion of the debt-relief Laffer curve). Implicit in this theory was the assertion that a bank's incentive to reduce its claims on a country is positively related to the prospect that the country will default.

The rapidly growing volume of voluntary market-based debt reduction beginning around 1985 seemed to bear out the theory that a bank's optimal strategy may be to reduce its outstanding LDC claims. From 1985 through 1488, the yearly total of market-based debt reduction--as measured by instruments such as debt-equity swaps, debt buybacks, local currency payments, or local currency conversions--increased from $742 million to $18.2 billion. Then in March of 1989, U.S. Treasury Secretary Nicholas Brady made debt reduction the new cornerstone of the official LDC debt policy. (The Brady Plan replaced the failed Baker Plan, which in 1987 called for the banks to increase net lending flows to troubled LDC debtors by $20 billion over three years.) The so-called Brady Plan was targeted to a relatively small group of highly indebted middle-income countries, that owed nearly 85 percent of all LDC commercial bank debt in 1989.

The Brady Plan was based on at least three key assumptions. First, debtor countries would be willing to undertake appropriate economic reforms in exchange for significant debt reduction. Second, the introduction of involuntary, or concerted, mechanisms in the debt reduction process would overcome the banks' incentive to free ride on the ether banks. Finally, and as implied by the debt-relief Laffer curve, the banks would find it in their interests to reduce their outstanding LDC claims, given high expected default probabilities.

Since the introduction of the Brady plan, 13 countries (Argentina, Brazil, Bulgaria, Costa Rica, Dominican Republic, Ecuador, Jordan, Mexico, Nigeria, Philippines, Poland, Uruguay, and Venezuela) have signed Brady agreements resulting in total debt reduction of over $71 billion, or nearly 20 percent of middle-income country commercial bank debt. (The percentage of debt reduction in each country ranged from a low of 18 percent in Brazil to a high of 80 percent in Nigeria.) Negotiations with other debtors within the framework of the Brady Plan are continuing.

Market-based debt reduction measures also have continued outside the framework of the Brady Plan. These have averaged around $8 billion a year since 1990, down from an average of almost $15 billion a year from 1988 through 1990. The slowdown in market-based reduction measures has resulted in part from the increase in formal Brady deals, which have displaced market-based measures in several cases, and from the increase in the secondary market prices of debt for countries participating in Brady deals.

Despite the relative success of the Brady Plan, a fundamental assumption underlying the plan remains untested--the assumption that the incentive to grant debt reduction is a function of the expected probability of default. The purpose of this paper is to test this assumption empirically. To do so, the paper tests whether debt reduction totals to highly indebted middle-income countries have been related systematically and positively to the expected probability of default, as measured by established macroeconomic indicators of LDC default probabilities.


The debt-relief Laffer curve (figure 1) captures the intuitive notion that debt service ability is not independent of a country's debt burden. The fact that the debt curve traces the 45 degree line at lower debt levels illustrates that at lower debt levels, the probability that the debt is fully repaid is relatively high. As the nominal value of the debt grows, the probability of default also grows, and the expected value (which is equal to the face value of the debt times the probability of repayment) increases at a decreasing marginal rate, thus diverging from the 45 degree line. At point x in figure 1, the slope of the curve becomes zero. At all points to the right of x, the probability of repayment is sufficiently low to make any increase in the debt's nominal value reduce its expected value. At the same time, when a country lies to the right of x, the bank can increase its expected value of debt collection by reducing the country's debt obligation, thereby moving the country left along the curve toward point x.

When a country's debt burden exceeds a level it is able to repay, the debt acts as a marginal tax on the country. If the country performs better than anticipated, the benefits will tend to flow to the country's international creditors rather than to the country. This outcome discourages economic reform. The debt overhang burden also falls on the domestic population through taxation, including capital taxation, thus discouraging investment at the margin. (For discussion of the intuition behind the debt-relief Laffer curve, see, for example, Krugman, 1989; Sachs, 1986.)

According to this reasoning, the larger debt level, the greater the probability of nonpayment, and the greater the subjective discount for the country's debt in the secondary LDC loan market. Debt reduction thus increases the probability of the remaining debt's repayment, thereby increasing its market value. If the country lies to the right of point x, the increase in the remaining debt's market value more than compensates for the write-off loss, and the expected value of the bank's claims increases. However, if the country lies to the left of point x, the increase in the remaining debt's market value does not compensate for the write-off loss, and the expected value of the bank's claims falls.

Purcell and Orlanski (1988), Claessens (1990), and Claessens et al. (1991) provide empirical evidence for the existence of a debt-relief Laffer curve. All three studies attempt to measure a debt-relief Laffer curve using secondary market prices for LDC debt and various default probability indicators. Purcell and Orlanski and Claessens find that the debt Laffer curve peaks at relatively high levels of debt, such that only a few countries exist on the wrong side of the curve. However, Claessens et al. find the curve to be flat over the range that covers most debtors, implying that large amounts of debt reduction could be purchased for relatively small amounts of money. Claessens et al. estimate that collectively reducing the debt of 17 highly indebted countries by $200 billion would increase the average market price of their debt from 40 cents to 56 cents, leaving the banks just as well off as they were before the reduction.

Comparisons of predeal and postdeal secondary market prices of the debt of countries participating in Brady deals reveal further evidence for the debt-relief Laffer curve. Such comparisons generally find that the postdeal prices often are significantly higher than the predeal prices. Claessens and Diwan (1994) examine the predeal and postdeal secondary market prices for six Brady countries (Mexico, Philippines, Costa Rica, Venezuela, Uruguay, and Argentina). They calculate that the value of the banks' LDC loan portfolios, as measured by secondary market prices, increased by an aggregate of $14.8 billion as a result of the Brady deals. The deft-relief Laffer curve predicts precisely this type of outcome. (Note, however, that the analysis here does not test for the existence of a debt-relief Laffer curve. Rather, it tests whether the banks have behaved as if they believed a debt-relief Laffer curve exists.


Specifying the empirical model involves deriving a debt-relief Laffer curve. The derivation begins with the assumption that the probability of repayment is a linear function of the debt size relative to the size of the country's economy:

(1) [Mathematical Expression Omitted]

A number of factors determine the probability of default. An unobserved "indexing" variable called z reasonably summarizes these factors. Presumably, no matter how favorable this index variable may be, some probability of default still exists. Likewise, if this index becomes sufficiently "bad," the probability of repayment will be zero. Assuming that high values of z correspond to bad conditions, one can model the probability of repayment by country i at time t as:

(2) [Mathematical Expression Omitted]

Where [] is the probability of repayment, [] is the face-value of the outstanding debt, [] GDP, and [] the indexing variable.

If z goes to negative infinity (i.e., wonderful conditions), the probability of re payment is one for all debt levels. As z goes to zero (i.e., terrible conditions), the probability of repayment goes to zero for any debt level (except zero). Figure 2 illustrates this relationship. The solid line indicates a set of good conditions. The dashed line indicates a set of poor conditions. As z rises toward zero, the line in figure 2 becomes steeper.

The next step is to examine the expected value of the debt, EV:

(3) [Mathematical Expression Omitted]

One can find the maximum value for E{[]} taking the derivative of equation 3 with respect to []:

(4) [Mathematical Expression Omitted]

Note that the maximum value will not occur when exp{[]}[]/[][greater than or equal to] 1, for this would imply an expected value of zero.

Hence the first portion of equation 4 is set equal to zero and then solved for []:

(5) [Mathematical Expression Omitted]

Since equation 5 gives the maximum possible expected value for a given face value, one can assume that banks will forgive any debt beyond this level, []*. However, since banks cannot issue negative debt forgiveness, they will keep the debt level constant if it lies below []*. One thus can express the amount of debt forgiveness as:

(6) [Mathematical Expression Omitted]

Substituting equation 5 into equation 6, subtracting this from ['] and dividing by [] gives:

(7) [Mathematical Expression Omitted]

Finally, taking the natural logarithm of both sides yields an equation fit for estimation:

(8) [Mathematical Expression Omitted]

Figure 3 plots the debt Laffer curve implied by equation 3. The left-hand side of equation 8 is the natural log of the horizontal distance from the origin to point V* in figure 3.

One can interpret the left-hand side of equation 8 as the level of debt to GDP after subtracting any debt reduction. Or put more intuitively, it is the new level of debt that the bank is targeting (with an adjustment for country size). If the debt is beyond the maximum point, V*, banks will reduce the debt to the optimal level via debt reduction. If the debt already is below V*, banks will not reduce the debt. Factors other than debt reduction may influence the actual debt size (for example, the bank may extend new loans to the country), and some of these may be beyond the lender's control. Therefore, the dependent variable differs from the actual value of the debt observed following debt reduction. Instead, it gives a measure of the value of debt lenders want to hold.

Conditions that give a low probability of repayment will be associated, ceteris paribus, with low values on the right-hand side of equation 8 because poor conditions lower the optimal value of the debt, V*, and lead to more debt reduction. Good conditions will lead to a higher value for V* and to lower amounts of debt reduction. In fact, in some cases, banks will not forgive any debt at all because the optimal value of the debt will be well above the actual value. This means that the left-hand side of equation 8 is a censored variable.

Attention next turns to the specification of the indexing variable, z. Since the analysis here estimates over a panel of data, it assumes that z includes country-specific fixed shocks, as in equation 9:

(9) [Mathematical Expression Omitted]

One can use a standard fixed-effects approach here to estimate the [v.sub.i's] along with the matrix b, as in equation 10:

(10) [Mathematical Expression Omitted]

Here [] is the matrix of exogenous variables, and [D.sub.I] is a matrix of I-1 country dummies.

If X is concatenated with the D matrix and b with the v vector, the result is:

(11) [Mathematical Expression Omitted]

One can subsume the term in b from equation 8 into the coefficient on the constant term in b and combine equations 8 and 11:

(12) [Mathematical Expression Omitted]

Assuming that [] is normally distributed allows one to proceed with maximum likelihood estimation. Estimating this model involves using PROC LIFEREG in SAS. Note that the negative sign on [[] in equation 12 implies that the coefficients estimated will be the opposite sign of the elements of z. In other words, elements of z that increase the probability of repayment by lowering z will have positive estimated values.

In the model used here, ordinary least squares yield biased coefficient estimates due to censoring. The panel nature of the data potentially leads to inconsistency of coefficient estimates if fixed-effects are ignored. However, a TOBIT regression with fixed effects in equation 12 will give estimates with all the usual desirable properties of maximum likelihood estimation (see Greene, 1993, pp. 691-706, for an excellent discussion of the topic). Thus, the TOBIT method provides a way to model the theorized nonlinear nature of debt reduction and to explain how different variables affect the amount of debt reduction observed. (In a significant number of cases, this amount will be zero since negative amounts of debt reduction are impossible.)


A. The Dependent Variable

The analysis here computes regressions from a data set of 29 indebted middle-income countries (see table 1). The selection of the middle-income countries for the data set reflects the fact that all U.S. debt initiatives, as well as the bulk of debt reduction, have focussed primarily on this group of countries. Observations begin in 1985 and end in 1993. Before 1985, debt reduction totals were zero or negligible for nearly all the countries in the data set, and 1993 is the last year for which complete data are available for the countries in the data set.

Countries in the Data Set

Algeria Dominican Republic Nigeria
Argentina Ecuador Panama
Bolivia Egypt Peru
Brazil Honduras Philippines
Cameroon Hungary Poland
Chile Jamaica Senegal
Colombia Jordan Uruguay
Congo Mexico Venezuela
Costa Rica Morocco (Former) Yugoslavia
Cote d'Ivoire Nicaragua

Debt reduction totals-F in the dependent variable ln[(V-F)/Y]-are from the World Bank's World Debt Tables and are measured by the present value of the "amounts that have been netted out of the stock of debt using debt conversion schemes, such as buybacks and equity swaps, or the discounted value of longterm bonds that were issued in exchange for outstanding debt." Unfortunately, the World Bank does not separate debt reduction totals by the type of conversion scheme.

B. Default Probability Indicators

The empirical analysis includes 11 macroeconomic indicators of default probability. Eight of the 11 variables have appeared in previous empirical studies of LDC default probabilities. These eight variables are statistically significant in one or more of the earlier studies. In addition to these traditional macroeconomic indicators of debt-servicing capacity, the model used here also includes additional variables not considered in earlier empirical studies (variables 8, 10, and 11 below). Bank-specific variables are omitted because aggregate bank-specific variables for all of the banks in each of the many creditor countries are unavailable. Moreover, because the creditor countries use different accounting conventions, using inter-country bank variables would raise serious questions about the comparability of data.

Past studies on LDC default probabilities establish that the default incentive is a function of a number of macroeconomic factors, including the economic performance of the debtor country (Cohen and Sachs, 1986; Krugman; 1987, Nunnenkamp,1989), the debtor country's expected costs and benefits of default (Crawford, 1987; Eaton and Gersovitz, 1981; Krugman, 1989; Nunnenkamp and Picht, 1988; Sachs, 1984), and exogenous economic shocks (Nunnenkamp, 1989). Accordingly, variables 1 through 5 below measure the economic performance of the debtor country. Specifically, variables 1 through 3 measure the country's liquidity position, or alternatively, its ability to generate sufficient foreign exchange in the short term to meet its debt service obligations. Variables 4 and 5 measure the debtor country's long-term economic prospects and long-term debt servicing capacity. Variables 6 through 8 measure some of the potential costs and benefits of default. Finally, variables 9 through 11 present alternative measures of the effect of exogenous economic shocks on the probability of default. Poorer economic performance, higher (lower) expected net benefits (costs) of default, and exogenous economic shocks all are generally associated with a higher expected probability of default.

According to equation 12, a negative coefficient in the TOBIT regression implies a positive relationship between the explanatory variable and the level of debt reduction, whereas a positive coefficient implies an inverse relationship with the level of debt reduction. Intuition suggests that when z rises, the probability of default rises, and the debt Laffer curve shifts to the left (figure 3). This leads banks to forgive more debt and leads to a lower value for the dependent variable. Thus, z and the dependent variable move inversely. (The discussion of the explanatory variables below and in the second column of table 2 indicate the predicted direction of the coefficient signs.)


1) Ratio of total interest due on the country's external debt to exports of goods and services (Avramovic et al., 1964; Cline, 1984; Edwards, 1984; Feder and Just, 1977; Feder et al., 1981; Frank and Cline, 1971; Sargen, 1984; Schmidt, 1984). Foreign exchange earnings from exports typically provide the funds for debt service payments. Consequently, the interest due-export ratio serves as the most common indicator of short-term debt servicing capacity. A higher ratio indicates a larger adjustment burden for a given shortfall in export receipts. The hypothesis is that this variable is positively correlated with the level of debt reduction. (Predicted sign: -.)

2) Ratio of international reserves to imports (Cline, 1984; Dhonte, 1975; Feder and Just, 1977; Feder et al., 1981; Frank and Cline, 1971; Mayo and Barrett, 1978; Saini and Bates, 1978). This variable measures the country's ability to accommodate shortterm exchange earnings fluctuations. The larger reserves are relative to imports, the more they are available to service the country's external debt, thereby making debt service interruptions less likely. The hypothesis is that this variable is inversely related to the level of debt reduction. (Predicted sign: +.)

3) Ratio of the current account balance to exports (Cline, 1984; Edwards, 1984; Saini and Bates, 1978). The current account deficit is roughly equal to the debtor country's short-term new financing requirements. Dividing the current account balance by exports normalizes for economy size. The hypothesis is that this variable is inversely related to the level of debt reduction. (Predicted sign: +.)

4) Ratio of investment to GDP (Avramovic et al., 1964; Edwards, 1984; Kharas, 1984; Mayo and Barrett, 1978). This ratio measures the country's propensity to invest. The rate of investment will tend to reflect the country's prospect for future economic growth. The hypothesis is that this variable is inversely related to the level of debt reduction. (Predicted sign: +.)

5) Rate of inflation (Abassi and Taffler, 1982; Avramovic et al., 1968; Dhonte, 1975; Edwards, 1984; Mayo and Barrett, 1478; Saini and Bates, 1978; Sargen, 1977). Some argue that inflation exacerbates balance of payments problems by reducing the value of the country's currency in the world market (see, for example, McDonald, 1982). The hypothesis is that this variable is positively related to the level of debt reduction. (Predicted sign: -.)

6) GDP per capita (Dhonte, 1975; Feder and Just, 1977; Feder et al., 1981; Frank and Cline, 1971; Saini and Bates, 1978; Schmidt, 1984). Under an assumption of a declining marginal utility of income, lower income countries will tend to be less willing and less able to sustain large resource transfers abroad and, consequently, more willing to default on their foreign loans. The hypothesis is that this variable is inversely related to the level of debt reduction. (Predicted sign: +.)

(7) Ratio of exports of goods and services to GDP (Avramovic et al., 1968; Feder et al., 1981; Schmidt, 1984). The ratio of exports to GDP is an indicator of the debtor country's stake in maintaining harmonious relations with its trading partners/international creditors. Some also argue that countries with larger exports relative to GDP will tend to have more foreign exchange remaining after debt service, all else being equal, and thus will be less likely to default on their foreign loans (see, for example, Feder et al. 1981). The hypothesis is that this variable is inversely related to the probability of default and the level of debt reduction. (Predicted sign: +.)

8) Interest arrears as a percentage of outstanding commercial bank debt. The level of outstanding interest arrears has grown steadily since the onset of the debt crisis. Most of the so-called problem debtor countries have at one time or another accumulated (often substantial) interest arrearages. Moreover, interest arrears are perhaps the most serious violation of a debtor country's contractual obligations. Thus, the accumulation of interest arrears threatens to cut off the debtor country not only from new bank credits but from other sources of international capital as well. Because a common belief is that the primary disincentive to default is exclusion from international capital markets, the presence and size of interest arrears appears to be a good indicator of a debtor country's expected net benefits of default. Consequently, the hypothesis is that the ratio of arrears to outstanding debt is positively related to the probability of default and debt reduction. (Predicted sign: -.)

9) Ratio imports of goods and services to GDP (Dhonte, 1975; Edwards, 1984; Frank and Cline, 1971; Mayo and Barrett, 1978; Saini and Bates, 1978). This variable measures the openness of the debtor country's economy. A relatively open economy is generally believed to be more vulnerable to balance of payments crises and exogenous economic shocks. The hypothesis is that this variable is positively related to the level of debt reduction. (Predicted sign: -.) (Note the potential here for introducing severe multicollinearity into the model. The current account balance is approximately equal to exports of goods and services minus imports of goods and services--with unilateral transfers being the third, but typically small, component. This explains why the authors have chosen to normalize imports and exports in the model by GDP and the current account balance by exports.)

10) Terms of trade. The deterioration in the terms of trade among debtor countries have played a major role in the onset and continuation of the LDC debt crisis. A weakening in a country's terms of trade means that the country must now export more units of goods or services to buy a single unit of imports. This fact implies a higher probability of default because fewer export earnings are now available to pay foreign creditors (see also Eaton et al., 1986). Thus, the expectation is that the worsening of a country's terms of trade is positively related to the probability that the country will default on its foreign loans, and therefore to the level of debt reduction. (Predicted sign: -.) (In the analysis here the terms of trade are real exchange rates vis-a-vis the G7 nations derived from the Penn World Table [Mark 5] [Summers and Heston, 1991]. The Penn World Data are from the Worldwide Web site at the address [http://cansim.epas.] at the University of Toronto. The values used express the number of U.S. goods per unit of domestic goods. Thus, a low value for the terms of trade indicates that foreign goods are relatively less expensive than G7 goods. By this definition, a "worsening" of the terms of trade would be an increase in its value.)

11) Rate of industrial country real GDP per capita growth. During the early 1980s, the recession in industrial countries, which are the major export market for developing countries' goods, significantly contributed to the onset of the debt crisis. Lower rates of industrial country economic growth reduce the demand for debtor country exports, causing debtor countries more difficulty in earning the foreign exchange necessary to service their external debts in addition to meeting all their other foreign exchange needs. Thus, the hypothesis is that this variable is inversely related to the level of debt reduction. (Predicted sign: +.)

The analysis here chooses explanatory variables for which the hypothesized effect on the probability of default is, for the most part, widely recognized and theoretically straightforward. Thus, using these variables in a regression can test whether LDC creditor banks have responded to high expected default probabilities by reducing their LDC claims. Data for the explanatory variables are from the United Nations, International Monetary Fund, and the World Bank. All monetary values in the data set are measured in real U.S. dollars, and all explanatory variables take on year t-1 values.


Table 2 reports the results of six regressions run on alternative specifications of the empirical model. In addition to the coefficient estimates and t-statistics, table 2 also reports the value of the log-likelihood for each regression as well as a pseudo-[R.sup.2]. Constructing a pseudo-[R.sup.2] involves estimating a baseline model which includes 28 of 29 country dummies and a constant, and then incorporating the baseline model into the following formula to compute the pseudo-[R.sup.2] value:

(13) [Mathematical Expression Omitted] where, ln L is the log likelihood for the model specification in question, and [lnL.sub.B] is the log-likelihood for the baseline specification. Equation 13 will approach one only as the log-likelihood goes to infinity. It will be zero if the log-likelihood is the same as the baseline model.

Regression 1 regresses the dependent variable on all 11 regressors in the model using the TOBIT method from equation 12. In this regression, six of the 11 independent variables have statistically significant coefficients. Of these, four are in the predicted direction. Of the 11 point estimates, six carry the predicted sign.

The potential presence of multicollinearity among the regressors call the results in regression 1 into question. By construction, some of the variables in the model are related. For example, imports-GDP and exports-GDP both use GDP in their construction. If multicollinearity is present among the regressors, large variances of the regression coefficients, and thus imprecise parameter estimates, will result even when the regressors as a group explain the data well. This seems to be the case in regression 1. The high pseudo-R2 indicates strong explanatory power for the model as a whole. A likelihood ratio test of this model versus the baseline model discussed above gives a test statistic of 40.37, which is significant at the 0.01 level of confidence. In contrast, only one of the regressors has a coefficient statistically significant at the 0.01 level. Hence, this regression model exhibits the signs of collinearity.

A straightforward test of multicollinearity involves constructing a matrix of simple correlations of all the regressors in the model. A commonly used rule of thumb states that if the correlation coefficient between the values of two regressors is greater than 0.8 in absolute value, then collinearity is a serious problem. By this method, the simple correlations between investment-GDP and per capita GDP and between exports-GDP and imports-GDP exceed 0.8 in absolute value, thus suggesting probable collinearity among these two pairs of variables.

Since joint collinearity of several variables also is possible, a second test for collinearity often is desirable. One such method involves conducting matrix decompositions following Belsley et al. (1980). This method extracts eigenvalues and eigenvectors from the set of regressors in order to construct a series of condition indices that are equal to the square root of the ratio of the largest eigenvalue to the eigenvalue in question. When condition indices are large, the X'X matrix is close to singular, and the data are said to be ill-conditioned. A collinearity problem exists when a component associated with a high condition index contributes strongly to the variance of two or more variables. This method produces two large condition indices whose principal components explain over 80 percent of the variance of investment-GDP and per capita GDP and over 90 percent of the variance of exports-GDP and imports-GDP. Thus, both diagnostic exercises confirm the existence of significant collinearity between investment-GDP and per capita GDP and between exports-GDP and imports-GDP.

Investment-GDP and imports-GDP are statistically significant in regression 1, but regression 2 drops both from the model to control for the presence collinearity. Regression 3 excludes per capita GDP and exports-GDP, the two collinear variables that are not statistically significant in regression 1. To further test the robustness of the estimates, regression 4 drops inflation, interest arrears-debt, and the terms of trade from the model. Neither of these three variables is statistically significant in regressions 1 through 3 (and across all other tested specifications of the model). Finally, regressions 5 and 6 alternately drop the two sets of collinear variables from the model, together in each case with the three robustly insignificant variables.

Table 2 shows that the parameter estimates are fairly stable across the six alternative specifications of the empirical model. The notable exception is the coefficient of exports-GDP. That coefficient goes from insignificantly positive to significantly negative in the absence of imports-GDP with which it is highly collinear. Of the six specifications, however, regression 3 appears to best represent the data because it controls for collinearity without a loss of explanatory power. The basis for this conclusion is a series of likelihood ratio tests comparing regressions 2 through 6 with the full model in regression 1. The last line in table 2 reports the results of these tests. These results show that only regression 3 offers a basis for not rejecting the null hypothesis that the omitted variables are unimportant.

Starting with the measures of economic performance, the coefficients for each of the three liquidity measures are statistically significant. The coefficients for the interest-export ratio and the reserves-import ratio point in the hypothesized direction, indicating that liquidity problems, as measured by these two variables, are associated with higher levels of debt reduction. However, the coefficient for the current account-export ratio points in the opposite direction, suggesting instead an inverse relationship between liquidity concerns and the level of debt reduction.

Regarding the two long-term economic performance measures, the coefficient for the investment-GDP ratio is significant and negative while that for the inflation rate is insignificant. The negative coefficient for the investment-GDP ratio is opposite to that predicted, suggesting that the level of debt reduction is positively related to a country's long-term economic prospects.

Among the variables measuring the expected costs and benefits of default, the arrears-debt ratio has no significant effect on the level of debt reduction. GDP per capita and exports-GDP do not appear in regression 3; however, both are statistically significant in regressions 2 and 5, which drop investment-GDP and imports-GDP from the model. In each of these two regressions, signs of both coefficients are opposite to those predicted. The evidence therefore suggests an inverse relationship between the probability of default, as measured by the expected costs and benefits of default, and the level of debt reduction.

Among the variables measuring the effect of exogenous shocks on the level of debt reduction, both the imports-GDP ratio and industrial country growth are statistically significant and in the predicted direction. The terms of trade variable, on the other hand, is statistically insignificant. This result indicates that the level of debt reduction tends to rise in response to adverse economic shocks.

The results in table 2 support the conclusion that the level of debt reduction is a function of the expected probability of default. Of the 11 default probability indicators, eight are statistically significant. Moreover, the results also support the more general hypotheses concerning the level of debt reduction as a function of debtor country economic performance (including liquidity measures and long-term economic prospects), the expected costs and benefits of default, and exogenous economic shocks.

Testing this last conclusion formally, involves performing a series of likelihood ratio tests (table 3). The tests estimate five new models--with one subset of variables omitted in each case--and then compare the resulting log-likelihood values to the log-likelihood value from regression 1 by constructing a set of likelihood ratio statistics. Table 3 shows that each of the likelihood ratio statistics is statistically significant at the 0.05 level of confidence or better. Thus, in each case, one can reject the hypothesis that each of the categories of variables is unrelated to the level of debt reduction. Rather, each category of variables appears to exert important effects on debt reduction levels, even though the exact effects of specific variables may be less clear.


The evidence supports a general relationship between debt reduction and the expected probability of default but fails to establish a consistent direction of this relationship. That is, the results on balance do not indicate that the banks have behaved systematically in a manner consistent with a belief in a debt-relief Laffer curve. The banks do appear to have responded to high expected default probabilities by increasing the level of debt reduction in some cases, but the evidence likewise suggests that they have responded in the opposite manner in other cases. These findings tend to confirm an earlier study (Wolfer and Phillips, 1995) that tests the determinants of the annual variation in the outstanding loan totals to nine LDC debtor countries of 61 U.S. commercial banks. Using an empirical model similar to the one in the analysis here (but also including several bank-specific variables), the earlier Woller and Phillips study also failed to find a consistent relationship between bank behavior and expected LDC default probabilities.

Within the different categories of variables, however, the results are less ambiguous. For variables measuring long-term economic prospects and the expected net benefits of default, the results point uniformly to an inverse relationship between debt reduction and the expected probability of default. For variables measuring exogenous economic shocks, the observed relationship is unambiguously positive. Finally, for the three liquidity measures in the model, the direction of the relationship is, on balance, positive.

Some possible explanations for the "incorrect" signs in table 2 exist. Under the Brady Plan, only those countries undertaking appropriate economic reforms ostensibly are eligible for debt reduction. This policy attempts to avoid the moral hazard problems that rewarding poor economic performance with debt reduction would create. A typical economic reform program is designed to improve a country's balance-of-payments position so as to ensure sufficient foreign exchange flows for debt service and to lay the groundwork for future economic prosperity. The coefficient signs for investment-GDP, current account-exports, and exports-GDP may reflect this policy, although this explanation does not account for the "correct" signs of the interest due-exports and reserves-imports ratios.

The negative coefficient for GDP per capita possibly reflects the fact that the countries with the most debt typically receive the most debt reduction. Among the countries in the sample set, those countries with the highest GDP per capita also tend to have the most debt outstanding. Given equal probabilities of default, the banks will be much more likely to reduce, say, Brazil's debt burden, with an average of $60 billion outstanding, than that of Cameroon, with an average of $532 million of debt outstanding. In other words, not all default probabilities are created equal.

The concerted features of the Brady Plan also may influence the results. Once the banks' representatives and the debtor reach a reduction agreement, all creditors of a certain class are required to participate. To prevent free riding, several mechanisms, such as regulatory and political pressure and various types of financial and legal engineering, are employed. Thus, certain banks possibly are "coerced" into participating in Brady agreements, even though this may not be their preferred strategy.

Finally, the banks necessarily consider a wide range of factors other than expected default probabilities in deciding whether to reduce their claims on indebted LDCs. These other factors may include, for example, the condition and structure of their overall loan portfolio, long-term strategic and tax considerations, the actions of competitors, and capital adequacy issues. Indeed, Woller and Phillips (1995) find that bank-specific strategic factors and internal capital constraints are far more important determinants of bank behavior than are traditional default probability indicators.


This paper examines the relationship between the expected probability of default on commercial bank LDC loans and the level of debt reduction granted to indebted LDCs. It tests this relationship by regressing debt reduction totals for 29 indebted middle-income countries on 11 default probability indicators over the years 1985 through 1993. The results confirm a statistically significant relationship between the expected probability of default and debt reduction levels. However, the results are indeterminate as to the overall direction of this relationship. Thus, the evidence is insufficient to conclude whether the banks have behaved systematically as if they believed a debt-relief Laffer curve exists.

These findings suggest that an incentive structure more complex than that implied by the debt-relief Laffer curve has motivated the behavior of the LDC creditor banks. Consequently, future empirical research on the commercial banks and LDC debt reduction might benefit from more closely exploring these other factors in addition to, or in place of, the traditional macroeconomic indicators of expected default probabilities.



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GARY M. WOLLER and KERK PHILLIPS, Woller is Assistant Professor, Institute of Public Management, J. Willard and Alice S. Marriott School of Management, Brigham Young University; Phillips is Assistant Professor, Department of Economics, Brigham Young University. The authors are grateful to two anonymous referees for helpful comments.
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Title Annotation:lesser developed country
Author:Woller, Gary M.; Phillips, Kerk
Publication:Contemporary Economic Policy
Date:Apr 1, 1996
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