metadata: authors: 0: author: Eaton,Jonathan W.
docna: 0: docna: Sovereign debt : a primer
docty: Policy Research Working Paper
subtopic: Debt Relief and HIPC,Governance Diagnostic Capacity Building,Public Sector Economics,Capital Markets and Capital Flows,Capital Flows,External Debt,International Trade and Trade Rules,Economic Forecasting,Macroeconomic Management,Public Finance Decentralization and
            Poverty Reduction,Debt Markets
teratopic: Finance and Financial Sector Development
abstracts: cdata!: The troublesome debts of many developing
            countries have spawned much literature on why countries
            borrow, on what debt contributes to growth, on why countries
            repay, and on how to deal with existing debt. The author
            provides an analytical primer on the following aspects of
            sovereign debt : 1) the basic accounting concepts associated
            with debt and some data associated with external borrowing;
            2) debt as a component of an optimizing model of borrowing
            in a competitive loan market, when the borrower faces an
            intertemporal budget constraint; 3) debt as a component of
            recent models of endogenous growth; 4) problems arising from
            sovereign risk, including problems of liquidity,
            enforcement, and revenue-raising to finance repayment; 5)
            incentives to repay; 6) options available to a creditor
            whose debtor is unwilling to meet current debt-service
            obligations; and 7) debt buybacks. The author concludes that
            in the absence of any efficiency cost imposed by outstanding
            debt, how much a buyback benefits the borrower depends on
            how much buying back debt reduces what is available for
            repayment later. The author also concludes that if there are
            efficiency losses associated with debt, debt forgiveness can
            benefit both a debtor nation and its creditors. Contrary to
            claims in the literature, this outcome does not require that
            a reduction in the face value of debt raise its market
            value, and the debtor benefits even though the buyback
            raises the market price of the debt.
repnme: repnme: Sovereign debt : a primer
display_title: Sovereign debt : a primer
listing_relative_url: /research/1992/02/699745/sovereign-debt-primer
topicv3: Debt Relief m1326505 452,Trade m1326924 698,Capital Markets m1326967 332,Treasury m1327009 1045,Market Failures m1327149 1068
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Finance and Financial Sector Development
origu: International Economics Department
no_of_pages: 92
author_keys: 0: author_key: 632776
model_extractions: **Policy R, search|**

# **Debt and International Finance**

WPS 855

- This paper a product of the Debt and Intemational Finance Division, Intemational Economics - Department is part of a larger effort in the department to understand the relationship of external borrowing to economic development. Copies of this paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Sheilah King-Watson, room S8-040, extension 31047 (83 pages). February 1992.

The troublesome debts of many developing countries have spawned much literature on why countries borrow, on what debt contributes to growth, on why countries repay, and on how to deal with existing debt. Eaton provides an analytical primer on the following aspects of sovereign debt:

* Incentives to repay. Maintaining access to credit markets can by itself be a reason to repay enot. h to sustain substantial debt levels.

* Options available to a creditor whose debtor is unwilling to meet current debt-service obligations.

- The basic accounting concepts associated with debt and some data, particularly about the net resource transfers associated with extemal borrowing.

The mechanics of debt and growth im"'lcd in the Harrod-Domar and two-gap growth models. Eaton points out how this analysis can yield misleading conclusions about the sustainability of debt and the determinants of solvency.

* Debt as a component of an optimizing mod A of borrowing in a competitive loan market, when the borrower faces an intertemporal budget constraint.

* Debt as a component of recent models of endogenous growth. Eaton concludes that what debt contributes to growth depends greatly on the source of growth.

_e_ Debt buybacks. Eaton concludes that in the absence of any efficiency cost imposed by outstanding debt (so that the only implications of the formn and extent of repayment are for the distribution of surplus between borrower and lender), how much a buyback benefits the borrower depends on how much buying back debt reduces what is available for repayment later.

Eaton also concludes that if there are efficiency losses associated with debt (a "debt overhang"), debt forgiveness can benefit both a debtor nation and its creditors. Contrary to claims in the literature, this outcome does not require that a reduction in the face value of debt raise its market value (a "debt Laffer curve"), and the debtor benefits even though the buyback raises the market price of the debt. The efficiency argument for buybacks is inconsistent with the case for lengthening the debt's maturity.

* Problems arising from sovereign risk, including problems of liquidity, enforcement, and revenue-raising to finance repayment (and the attendant problem of capital flight).

I The Policy Research Working Paper Serics disseminates thc findings of work under way in the Bank. An objective of the series

| is to get these findings out qtuickly, even if presentations are less than fully polished. The findings, interpretations, and conclusions in these papers do not necessarily represent official Bank policy.

Produced by the Policy Research Dissemination Center
# SOVEREIGN DEBT: A PRIMER

# Jonathan Eaton

# TABLE OF CONTENTS

|1. Introduction|1|
|---|---|
|2. Some Easic Concepts and Magnitudes|4|
|3. Debt and Growth: "Knife-Edged"<br>Analysis|6|
|3.1 The Mechanics of Debt Dynamics|7|
|3.2 Stability and the "Debt Trap"|9|
|3.3 Steady-State Debt and Ponzi Schemes|9|
|3.4 Two-Cap Models|11|
|3.5 Implications of the "Knife-Edge"<br>Models|14|
|4. Intertemporal Optimization, the Budget Constraint, and Solvency|16|
|5. Debt and Growth: "Endogenous Growth" Models|23|
|5.1 The Lucas Model|23|
|5.2 The Cohen Model|29|
|6. Sovereign Risk|32|
|7. The Incentive to Repay|39|
|7.1 Sanctions|39|
|7.2 Maintaining a Reputation for Repayment|40|
|8. Dealing with Nonpayment|49|
|9. Buybacks and Swaps: Market-%ased Debt Reductior.<br>Schemes|57|
|9.1 "Average" and "Marginal" Debt:<br>Are Buybacks Boons or Boondoggles?|58|
|9.2 Buybacks as a Cure for Debt Hangovers|61|
|10. Conclusion|65|
|REFERENCES|66|
|APPENDIX: Flows From Private Creditors|69|
# SOVEREIGN DEBT: A PRIMER

# 1. Introduction

The recent debt problems of a number of developing countries, and the potential demand for foreign capital by formerly socialist countries, raises a number of basic questions about the role of sovereign debt in e-onomic development and growth. My purpose here is to provide a basic, albeit analytic, introduction to some issues raised by foreign borrowing, especially foreign borrowing by sovereign governments from private creditors.

The paper is not meant to be a survey of the literature. A number of issues are ignored, and I have not attempted to provide a complete set of references to the literature.' Indeed, a number of important contribuzions are unmentioned. Rather, I have tried to identify areas: (i) where recent analytic developments may provide useful tools, or at least food for thought, for the applied economist; (ii) that are likely to present pitfalls; or (iii) where the existing literature seems to have generated confusion. I have then attempted to provide rudimentary frameworks: (i) for applying existing analytic tools to applied problems; (ii) to show where traditional analysis can leae one astray; (iii) to clarify what I find to be misleading or confusing points in the existing literature.

Section 2 presents some basic accounting distinctions, and discusses data on the debt to private creditors of a number of large sovereign debtors.

II refer readers to Glick and Kharas (1984), Eaton, Gersovitz, and Stiglitz (1987), Eaton and Taylor (1987) and Eaton (1989a) for treatments of a wider range of issues and more comprehensive bibliographies.
-2-

Sections 3 and 5 concern the contribution<sup>of debt to growth. Section 3</sup> revie-s traditional nonoptimizing<sup>or "knife-edge"</sup> models of borrowing, such as the Harrod-Domar and the two-gap<sup>models. Here I discuss such notions as</sup> "debt-traps" and "ionzi schemes.'<sup>In Section 4 I turn to intertemporal</sup> optimization, introducing the intertemporal budget constraint and the "transverselity condition" on borrowing.<sup>A particular purpose is to point out</sup> where knife-edged analysis can<sup>mislead. Section 5 then considers borrowing in</sup> a recent class of optimizing<sup>growth models in which the rate of growth is</sup> endogenous. While the focus,<sup>as in the nonoptimizing literature, is on the</sup> relationship between debt and<sup>growth, the methodology is quite different. I</sup> consider two particular contributions<sup>to this literature, one by Lucas (1988)</sup> and one by Cohen (1991) and<sup>point out how different assumptions about the</sup> source of growth have very different<sup>implications for the role of foreign</sup> borrowing in economic development.

Sections 3 through 5 consider<sup>debt in a world in which debt contracts</sup> with sovereign debtors are automatically<sup>and costlessly honored. Hence, as</sup> long as a nation has the resources<sup>to pay its creditors what it owes, it does</sup> so. The remain' sections consider<sup>problems that arise from a sovereign</sup> government's potential inability<sup>to appropriate domestic resources to service</sup> debt, or its unwillingness to<sup>service debt. Section 6 discusses four</sup> particular issues: (i) the<sup>excess burden associated with taxing domestic</sup> resources to repay debt (the<sup>"public finance" problem), (ii) the "liquidity"</sup> problem, (iii) the "enforcement" problem, and the "information" problem. Section 7 considers the incentives<sup>a sovereign debtor has to service its debt,</sup> and what these incentives imply<sup>about how much debt it can sustain. A</sup> particular issue is whether<sup>a nation's desire to maintain a "reputation for</sup> creditworthiness" alone can provide an incentive<sup>to service debt, a point</sup>
-3 -

about which a great deal of confusion was recently introduced. In section 8 I review the options facing creditors whose sovereign debtors are not paying what they owe. Here I discuss debt relief, the role of official lenders, and the notions of a "debt overhang" and the "debt Laffer curve.' In Section 9 I turn to "market-based" debt reduction schemes, such as various swap arrangements and debt buybacks. Section 10 concludes with a brief review of other issues.
-4-

# 2. Some Basic Concepts and Magnitudes

Some simple distinctions among the various stocks and flows associated with debt should be made. Starting with stocks, one distinction is between disbursed and undisbursed debt, the second consisting of commitments made by lenders that have not been drawn upon, and therefore are not yet accumulating interest. Part of disbursed debt is interest arrears, accumulated unpaid interest obligations. Henceforth, by "debt" (or D t) I mean "disbursed debt." Turning to flows, debt service payments in period t (DS t) consist of interest payments (IPt) and principal repayments (PRt) associated with disbursed debt. Thus DSt = IPt + PR . The net flow in period t (Bt) is new borrowing (loan disbursements plus accumulation of arrears' in period t (NB t) less repayments of principal, i.e., Bt - NBt -PRt. This is the amount by which the nominal stock of disbursed debt changes in period t. Hence (denoting the change in variable x as x), Bt - Dt.

Finally, the net transfer in period t (NT t) equals the net flow less interest payments or, 3quivalently, new borrowing less debt service, i.e., NTt Nt = = Bt t - - IPt t = NB = t - DS t' . This concept is especially critical in that it represents the net flow of real resources from creditors to the debtor. A positive value means that creditors are contributing resources to the debtor country while a negative value means that creditors are taking resources away. A hypothetical observer privy to a nation's complete set of international transactions concerning goods and services (other than interest payments) and its foreign aid receipts could ascertain the net resource transfer even if it could not observe any balance sheets or financial transactions.

The appendix presents annual data on disbursements, principal and
-5-

interest payments and the consequent net resource transfers between twenty-six higtily-indebted countries and their private creditors during 1970-1988. Values are in current U.S. dollars. A negative number (in parentheses) indicates a net resource transfer to the creditor.

For each country, the botton row gives the 1969 present value of the net transfer, where the 3-month U.S. Treasury Bill rate serves as discount factor. For each country, the upper figure in the final column is the number of times the net resource transfer changed sign during the nineteen year period. The lower figure is the 1969 present value of the cumulative net resource transfer as of tbe end of 1988.

Two observations are worth making. One, to be taken up later, is that net resource transfers change signs quite often, on average every three or four years. Second, as of the end of 1988, only three of the twenty-six countries had made net resource transfers to creditors over the entire period: Costa Rica, Jamaica, and Yugosiavia. For the rest, the relationship between private creditors and debtors has meant a significant real net transfer from private creditors (as a group) to the borrower.
-6-

# 3. Debt and Growth: "Knife-Edged" Analysis

How does debt relate to the growth of the debtor? Early on, economists put the Harrod-Domar growth model, due to Harrod (1939) and Domar (1946), to work to answer this question. This framework describes an economy very simply with four parameters: (1) the capital-output ratio, 1/a, (2) the savings ratio out of income, s, (3) the rate of growth of the effective labor force, n, and (4, the rate of depreciation of the capital stock 6. These variables are assumed exogenous and constant over time.

For a closed economy, the growth rate "warranted" by savings and w technology, g , is given by: This relationship follows from the fact that the change in the capital stock AK is given by investment, which equals savings or sQ, where Q is output less depreciation 6K. Dividing both side by K gives the result. Since Q is proportional to K, Q and K grow at the same rate. An obvious problem is that g may not equal the natural growth rate n, the "knife-edge" problem.

Rosenstein-Rodan (1961), for example, used this formulation to calculate "aid requirements," meaning the amount of foreign aid needed to bring the warranted growth rate into line with the natural rate. Assuming that a constant share s' of foreign aid is saved, and treating aid as a fraction a of output, the warranted rate adjusted for aid becomes: w g (s + s'a)a - 6, (3.2)
**-Z/-**

so required aid as a share of output 1.s a* - (n + 6 - sa)/Qs'.2

# 3.1 The Mechanics of Debt Dynamics

The model can also be applied to foreign debt. Denote net foreign debt at any time t as DL and the ratio of debt to outplt as dt. If r is the interest rate (assumed constant) then period interest payment obligations are rDt, while net borrowing is Dt. The net transfer is Dt - rDt.

The issue of identifying the appropriate income concept for savings now arises. To be quite general, let s denote the savings rate out of output, s' the dissavings rate out of interest payments, and s" the savings rate out of net borrowing. Thus: Since Dt/Kt - ad + adtKt/Kt, where dt Dt/Yt, the ratio of debt to output:/ The rate of change of the ratio of debt to output is therefore: 2In Eaton (1989a) I provide more complete references on applications of Harrod-Domar analysis to aid and debt problem-.
-8-

# (with time subscripts omitted).

If the debt-output ratio is maintained at some constant level d then the d warranted growth rate allowing for debt, g , is: The long-run effect of of a lpermanent change in the rat4n of debt to output on growth can be obtained by differentiating this expression with respect to d. The result is that higher debt raises growth if and only if s"(sa-6) > s'r. If, say, the dissavings rate out of interest payments equals - the savings rate out of nev borrowing (s' s') then higher debt raises the growth rate if and only if the warranted growth rate for the.-closed economy exceeds the interest rate.

A Similarly, if a particular growth rate g (such as the natural rate) is to be sustained with a constant ratio of debt to output, then the debt-output ratio must attain a level: If _s' -_ s" .ien the sign of this expression depends upon the relationship **A** between the target growth rate g, the warranted growth rate gw and the interest rate. Positive debt is called for either when the warranted rate and interest rate both exceed the target rate or both are exceeded by the target rate.
-9-

# 3.2 Stability and the "Debt Trap"

Stability requires that d be negative when<sup>d is just above d and positive</sup> when d is just below d. Differentiating<sup>(3.5) with respect to d gives:</sup> which must be negative for stability.<sup>Hence, if s'-s", stability requires</sup> that the actual growth rate exceed<sup>the interest rate.</sup> If this condition is not satisfied<sup>then an increase in debt above d</sup> raises interest obligations more than<sup>it raises the additional borrowing that</sup> can occur to maintain a steady d.<sup>Ever-increasing</sup> amounta of debt relative to output are thus needed to finance<sup>debt service payments. A nredicament of</sup> this sort is sometimes called a<sup>"debt trap."</sup>

# 3.3 Steady-State Debt and Ponzi<sup>Schemes</sup>

If the stability condition is satisfied<sup>then, from (3.7), the</sup> steady-state debt-output ratio<sup>is positive or negative dependinguponwhether</sup> the desired growth rate exceeds<sup>or is exceeded by the warranted rate. For the</sup> economy to grow faster than what<sup>is warranted by domestic saving requires</sup> positive debt. Since the stability<sup>condition is satisfied, new borrowing is</sup> always sufficient to repay interest<sup>on old debt and finance additional</sup> investment without raising the<sup>ratio of debt to output.</sup> This analysis has led to the<sup>conclusion that a debtor country is</sup> "solvent" or "creditworthy" if it grows at a faster rate than<sup>the interest</sup>
-10-

rate, as countries occasionally do and as many of the current highly-indebted countries did during the 1970s.

There are several reasons, however, why this criterion is a misleading indicator of a country's creditworthLness.

First, it is unlikely that the underlying parameters of the analysis, such as the capital-output and savings ratios, will remain constant over the long term.

A second, related, reasor. is that the stock of net debt itself should have implications for a country's savings behavior. The assumption that savings depends on income flows implies that, other things equal, as a country becomes more indebted it saves less (since its interest obligations rise). But it might seem reasonable to assume that as a country becomes more indebted, anticipated future debt-service obligations would raise savings.

Third, and most important, if a country's output perpetually grew faster than the interest rate and it maintained a constant debt-output ratio, then net borrowing would perpetually exceed interest payments, meaning that the net t' ansfer associated with debt would forever be positive. This is inconsistent with rational behavior on the part of lenders. It the stock of debt could forever grow faster than the interest rate then any debtor could successfully set up a "Ponzi" scheme, using new borrowing to pay off old debt. Demand for debt to finance such schemes would eventually drive the world interest rate to at least the growth rate of loanable funds.

The second objection can be overcome by introducing an explicit direct feedbcc', from the stock of debt to domestic savings. Say that for each additional unit of debt, domestic savings increases by a. With this modification, accumulation of debt per unit of output becomes:
-11 -

> <sup>s"g-a < 0. The</sup> Stability is now guaranteed by the condition that s'r<sup>-</sup> steady-state ratio of debt to output associated<sup>with a growth rate g is then:</sup>

Note that, as before, the condition for<sup>stability implies that a country</sup> become a de,tor to maintain a growth rate permanently<sup>in excess of the rate</sup> warranted by domestic resources. Even if s'<sup>_=_s", however, it need not be the</sup> case that creditors make perpetual net transfers<sup>to the country to raise its</sup> growth rate. Going into debt can raise a country's<sup>growth rate even when the</sup> country is making net transfers to creditors.<sup>Indebtedness raises the growth</sup> rate by raising domestic savings.

# 3.4 Two-Gap Models

The Harrod-Domar model, and the analysis of debt<sup>dynamics that follows</sup> from it, assume a single, homogeneous output<sup>that can also serve as the</sup> capital stock. The amount of output allocated<sup>toward investment, and the</sup> incremental capital-output ratio thus<sup>limit the growth rate.</sup> The two-gap model posits that output requires not only<sup>physical capital</sup> that can be produced domestically, but an imported input (that could also be a capital good) that is not produced domestically.<sup>Both domestic capital and</sup> the imported input are essential for production,<sup>and the standard assumption</sup> is that they are needed in fixed proportions.<sup>If Kd denotes the stock of</sup>
-12-

domestic capital and Kf the stock of the imported input then<sup>output Q is given</sup> by:

# - Q min[aKcd,oPKfI

where P is some positive parameter.

If domestic savings is a proportion s of income Y, in the absence of foreign aid, lending, or depreciation (6-0) the growth<sup>rate "warranted" by</sup> domestic savings is now s/K where # - l/a + _1/fi._ For the economy to grow at this rate, however, requires an investment of foreign capital If equal to a share _s/pK_ of output each period. Obtaining this foreign capital with domestic savings does not pose an additional problem if it can be purchased at a given price with domestic output. The analysis assumes, however, that this is not the case, but rather that the supply of foreign capital has an upper bound proportional to capacity. If<sup>_f_</sup> denotes<sup>the</sup> availability of foreign capital relative to capacity then the<sup>warranted growth</sup> rate can be sustained as long as eo > s/K. Otherwise, the availability<sup>of</sup> foreign capital, rather than domestic savings, limits growth, and the<sup>maximum</sup> sustainable growth rate is cfi. In this case increases in the<sup>domestic savings</sup> rate do not increase growth.

Th's framework has been called the "two-gap" model because<sup>there are now</sup> two possible resource gaps that keep the actual<sup>growth rate below the growth</sup> rate of the labor force, or the "natural" growth rate.<sup>One is the gap in</sup> domestic savings. The other is the gap in foreign exchange.

Say that foreign exchange is indeed the binding gap, so that in the absence of foreign debt growth is constrained to Pe. Foreign<sup>borrowing</sup> obviously provides an additional source of foreign exchange,<sup>but servicing</sup>
-13-

debt is an additional use. Again, denoting total foreign debt in period t by Dt and the ratio of debt to output as dt, the growth rate "warrant.;J" by the f availability of foreign capital, g , becomes: If in the long-run a constant ratio of debt to output is maintained, so f that dt - 0 and dt - d, then the warranted growth rate g is given by: The basic implications are qualitatively similar to those of the Harrod-Domar analysis: First, the long run effect of an increase in d on gr is positive or negative as fe exceeds or is exceeded by r. As in the basic Harrod-Domar model, if the growth rate in the absence of borrowing exceeds the interest rate then net borrowing has the long-run effect of increasing growth even further while, if in the absence of borrowing the warranted growth rate is lower than the interest rate, net borrowing lowers the warranted growth rate.

Say that the economy tries to use borrowing to acbieve a target growth rate g. The long-run level of debt necessary to do this is given by: Again, as with the Harrod-Domar model, a positive level of debt is implied
-14-

only when the target rate is either below the warranted rate and the interest rate or above these two rates.

Finally, for any given growth rate g, the change in the debt-output ratio is given by: Again, stability requires a growth rate in excess of the interest rate. As in the simpler Harrod-Domar model, the stability condition implies that a positive permanent level of debt is associated with growth above the warranted rate.

# 3.5 Implications of the "Knife-Edge" Models

The Harrod-Domar and two-gap models have been popular tools for analyzing the debt problems of developing countries. For one thing, they allow the analyst to make long-term projections with a minimal amount of data. Nevertheless, there are at least two reasons why they can yield very misleading results: First, there is little reason to think that the magnitudes they treat as constants should be. Opportunities for substitution between capital and other factors imply that the capital-output ratio should rise with nore investment. In fact, capital-output ratios can fluctuate wildly. Similarly, the savings rate should depend on more than current income and the stock of debt. A framework should base its assumptions about how investment affects output and about savings on a more complete description of technology and the intertemporal trade-offs facing the economy.
-15-

Second, and more fundamentally, the analysis makes unreasonable assumptions about the resources that a competitive world loan market can be expected to provide a borrowing country. Stability in these models requires a growth rate in excess of the world interest rate. But if the country maintains a constant debt-output ratio then its debt must also grow faster than the interest rate. Creditors must always lend the country more than what it owes to service past debt so that it never needs to make net resource transfers to its creditors. Moreover, the faster it grows, the more resources it can perpetually obtain from the rest of the world. This state of affairs is unsustainable, however. In order for the country not, at some point, to exhaust the world supply of funds, world wealth must also grow forever at least as fast as the country. But then anyone could always borrow whatever was needed to repay past debts. Attempts to do so would drive the world interest rate up to at least the growth rate of world wealth, however. While we have observed growth rates far in excess of interest rates, the phenomenon has necessarily been a temporary one. The next section discusses how the constraints that world capital markets impose on borrowers render the scenarios created by the knife-edge models infeasible.
-16-

# 4. Intertemporal Optimization, the Budget Constraint,<sup>and Solvency</sup>

A critical shortcoming of the<sup>knife-edge analysis is that savings</sup> behavior, which is closely<sup>tied to the accumulation of foreign debt, is not</sup> related to rational intertemporal<sup>decision-making</sup> on the part of the borrowing country or its creditors.

A very basic formulation that<sup>introduces a motive for borrowing _onsiders</sup> a small borrowing country as<sup>an entity with a given income stream, with per</sup> period output Q t . The country's behavior is governed<sup>by that of a</sup> representative, constituent individual (or dynasty)<sup>that seeks to maximize the</sup> discounted value of its utility<sup>from consumption. A common simplification is</sup> that utility is additively<sup>separable across time, and that utility in any</sup> period t is a concave function<sup>u(Ct) of consumption Ct in period t.</sup> Consumption cannot be negative.<sup>The representative individual discounts</sup> future consumption by some factor<sup>A(which equals one over one plus its</sup> discount rate, as it is more<sup>conventionally</sup> defined). Hence 0 is between<sup>zero</sup> and one, with values nearer one<sup>implying less discounting of the future. It</sup> can borrow and lend in intornational credit markets at an interest<sup>rate r,</sup> which I will usually treat<sup>as a constant to simplify notation.</sup> Consider a time 0 when the<sup>country's foreign debt is zero. As of that</sup> point, its objective can be<sup>described as maximizing a function of the form:</sup> Each period t it chooses to<sup>borrow some net amount Bt (defined as new</sup> borrowing less repayments<sup>of principal on old debt), but must pay interest</sup>
-17 -

rDt 1 on debt accumulated as of the end of the previous period. What is left over for consumption is then: while debt at the end of period t is: Iterating the second part of equation (4.3) backward to period 0 gives: Debt in period t is just the cumulative discounted net resource transfers since period 0 (when debt was zero).

Obviously, if the country faces absolutely no limit on what it can borrow in any period, it can attain an arbitrarily high level of consumption in any period without defaulting by financing debt-service obligatione with new borrowing. What keeps a country from pursuing such a borrowing strategy?

The problem is that allowing a country to do this would be inconsistent with rational lender behavior. Sensible lenders would not enter into transactions with a country that would imply a loss. This means that, as of period 0, the anticipated discounted value of resource transfers that they would provide the country not exceed 0, or that:
-18-

This last condition is often called the intertemporal budget constraint.

Dividing (4.4) by (l+r) gives: Expressions (4.5) and (4.6) imply the following restrictions on debt: _Solvency_ Substituting (4.6) into (4.5) gives, for any period t: Since consumption cannot be negative, this condition implies that: where the present discounted value of the borrowing country's remaining income stream. Condition (4.7), often called the solvlncy constraint, states that debt in any period cannot exceed this amount if lenders are to find their relationship with the borrower profitable.
-19-

In principle, the right hand side of (4.7) could be infinite, in which case the constraint disappears. This would mean that the country's<sup>current</sup> and future resources are infinitely valuable, which could happen<sup>if the</sup> country grew on average at a rate in excess of the interest<sup>rate.</sup> Presumably, the demand for borrowing on the part of such a country<sup>would</sup> suffice to drive the world interest rate up to the point at which the constraint became binding. As mentioned, some of the literature on external debt talks of "solvency" as a condition that its growth rate exceed<sup>the</sup> interest rate. For a country to be permanently solvent in this sense implies that it have resources that are infinitely valuable, in which case any level of debt is consistent with solvency. It is unlikely that any country<sup>meets</sup> this criterion. A growth rate in excess of the interest rate is almost surely a temporary phenomenon. On the other hand, as discussed below, almost all sovereign borrowers are probably solvent in the sense that the discounted present value of their national resources exceeds the value of their external debt.

_The "Transversality Condition"_ Together, (4.5) and (4.6) imply that often called the transversality condition: In order to realize a collective positive return on their loans, foreign creditors cannot allow<sup>the discounted</sup> value of debt in the infinite future to be positive.<sup>As is clear from (4.3) a</sup> borrowing strategy that never required making net resource<sup>transfers to</sup>
-20-

creditors would require that debt grow at or<sup>above the rate of interest,</sup> violating (4.8). Note that the condition allows<sup>Dt to remain positive, i.e.,</sup> the country can remain a net debtor forever.<sup>Debt just can't grow, on</sup> average, faster than the interest rate.

The country's problem then, can be<sup>seen as choosing NTt in each period t</sup> to maximize U0 subject to either (4.5) or (4.8).<sup>Setting this problem up as a</sup> constrained maximization, it becomes: where A is the shadow price associated with<sup>the solvency condition.</sup> The first-order conditions for a maximum<sup>are:</sup> With nonsatiation (so that the marginal utility<sup>of consumption is always</sup> strictly positive), A is strictly positive,<sup>meaning that the constraint is</sup> binding. Optimal borrowing thus implies that<sup>condition(4.5)</sup> hold with equality, or that: One implication of (4.10) is that,<sup>given the discounted present value of</sup> initial resources W0, international borrowing and lending completely<sup>separate</sup> the timing of consumption from<sup>that of production. The intertemporal</sup> budget constraint is the only link between<sup>the two. Hence, given the present</sup> r-s s ,1 ,4
-2,..-

discounted value of resources, the timing of<sup>their availability should have no</sup> implications for consumption.

A second implication of (4.10) is that consumption<sup>rises or falls over</sup> time depending upon whether (l+r)p is larger or<sup>smaller than one, or whether</sup> the world interest rate is higher or lower<sup>than the country's time discount</sup> rate.

As an example, consider a borrowing country<sup>whose representative</sup> consumer has a one-period utility function: where the (nonnegative) parameter a corresponds to the (constant,<sup>in this</sup> case) elasticity of the marginal utility<sup>of income, or, equivalently, the</sup> degree of relative risk aversion. The solution<sup>involves choosing:</sup> Say that Qt grows at a constant<sup>rate g. Then</sup> while the present discounted value of current<sup>and future resources in any</sup> subsequent period is (l+g) WO. Debt at the end of<sup>period t-l is then:</sup>
-22-

The country becomes a debtor if 1+g > [(1+r)#] / and a creditor otherwise. Note that debt grows faster the higher the exogenous growth rate of income, the higher the discount factor, and the lower the rate of interest.

The analysis can be extended to incorporate a productive role for capital. As long as the production technology and other factors of endowmenit are exogenous, however, little in this analysis is affected. Say, for example, that output in period t is a function F(Kt,L ,t), where Lt is a set of exogenous factor supplies such as labor and land, and where F is homogeneous in Kt and Lt. Optimal investment requires investing up to the point at which FK r, wl.re FK is the marginal product of capital. Let * K (Lt,t) denote the value of K consistent with optimal investment. Defining Qt - F(K*,Lt,t) and redefining fore5gD debt Dt as Dt + Kt - Kof where K is the period 0 capital stock. and Dt is derived as before, the analysis follows as above.

In this case, even in the long run, in contrast to what "knife-edge" analysis discussed above suggests, the growth rate is invariant to the level of debt, and to economic policy more ger.erally. It is deterrnined only by exogenous changes in technology and factor supplies. However, the recent growth models we turn to next reintroduce reasons why debt has implications for growth.
-23-

# 5. Debt and Growth: "Endogenous Gr^wth" Models

The revival of interest in growth theory in the 1980s, spurred by papers of Romer (1986) and Lucas (1988), suggests a richer relationship between debt and growth. While the literature rests on more neoclassical assumptions about tastes and technology than the "knife-edge" 4nalysis, in some ways it resembles them more than the neoclassical analysis that intervened. In particular, it revives the notion that foreign debt has implications for the long-run growth rate. Unfortunately, the literature is too undeveloped to provide any robust results. Consider the following two models that have very different implications for how changes ia world credit market conditions affect growth.

# 5.1 The Lucas Model

The following analysis draws on Lucas (1988): Consider an economy with a technology given by:

**t t** ~~~~~ tt **tt**

where Qt is output, K t is the capital stock, Lt is the labor force, and Ht represents the state of "technological knowledge" of a typical worker in the economy, all at period t. The variable ut, which lies between zera and one, represents the share of an average worker's time spent working, rather than developing technological knowledge. (Assume for now that all workers spend the same amount of tiwe working, regardless of their knowledge. We later show
-24-

that they will in fact do so.) The capital share is P, which lies between zero and one, and y is a nonnegative parameter.

A worker's technological knowledge contributes to current output in two ways. First, it increases the productivity of the worker with that knowledge in proportion. Hence worker i with knowledge Hit in period : working a fraction of his time uit contributes u itHit to the labor force that period. The worker captures the return to this aspect of his knowledge by earning a proportionately higher wage. Second, if Ht is the average state of knowledge in the economy, output is affected beyond what is implied by the contribution of H to the effective labor force in proportion H't. Returns to capital and t ~~~~~~~~~~~~~~~t effective labor exhaust production, so these general returns are not appropriated.

Separating these two roles for technological knowledge, the production relationship can be rewritten: where Et = utHtLt, the effective labor force. The wage (per unit of effective labor) is thus: There is only one produced good, which can be used for investment or for consumption. (Issues concerning the relative price of capital are thus not addressed: The price is one.) Hence the capital stock grows according to the relationship Kt = It - WKC, where, again, 6 is the rate of depreciation (assumed constant).
-25-

Workers inherit a given state of technological knowhow. They can add to the existing state by allocating time toward that purpose, which takes away from their efforts toward current production. The increase in the state of technical knowhow in period t is given by the function: where e is some nonnegative parameter. Note that a given amount of effort at acquiring new knowledge makes a contribution that is proportional to the existing stock of knowledge in period t. Hence gH Ht/Ht, the growth rate in the stock of knowledge, is: Aside, then, from the two contributions that knowhow makes to production that have already been mentioned (augmenting the current effective labor force in production and enhancing current productivity generally) knowledge increases the productivity of time spent adding to technological knowledge (learning).

Each period t the representative individual chooses a level of consumption ct and an allocation of time between work and learning u . The standard assumption is that preferences are intertemporally additively separable and display constant relative risk aversion. Denoting the discoun_ factor by p and the elasticity of the marginal utility of consumption by _a,_ at any period 0 the individual's problem (taking into account the growth of his household) is to choose ct and ut each period to maximize:
-26-

subject to the equation of motion for wealth Wt where r is the interest rate (again treated as<sup>constant) and wt the wage per</sup> unit of effective labor, and the equation of motion<sup>for an individual's state</sup> of knowledge: To examine the role of foreign capital consider<sup>two versions of the</sup> model, one in which all capital investment is financed<sup>by national saving</sup> (financial autarky) and another in which the<sup>capital market is open</sup> internationally, so that the economy we examine can borrow or lend<sup>at a given</sup> constant world interest rate r.

As does Lucas (1988), I focus on a balanced<sup>growth path or steady state,</sup> in which output and the capital stock grow<sup>at the same rate g. In a</sup> competitive equilibrium, both under financial<sup>autarky and with foreign</sup> borrowing, if - > 0 then the stock of knowledge grows<sup>at gH, where</sup>

- if this rate lies below the maximum feasible<sup>ratef.</sup> Here, as before n L/L, the rate of growth of the labor force (again assumed<sup>constant). If</sup><sup>**-y**-0 or</sup>
-27-

if g H> f the economy achieves a steady state<sup>in which the stock of human</sup> capital is constant, so that the economy reaches a point<sup>after which u-</sup> 1. There is no further growth growth in output or wages.<sup>(A no-growth outcome</sup> can also occur whenever c < r, although positive<sup>steady-state growth may also</sup> be a possibility.) If a strictly positive growth rate is feasible,<sup>however, output and the</sup> capital stock grow at: while the wage rate grows at: Somewhat surprisingly, as long as strictly positive steady-state<sup>growth</sup> is feasible, the interest rate r affects growth positively<sup>while the</sup> productivity of time spent acquiring knowl_dge<sup>eaffects growth negatively.</sup> The reason is that when future income is discounted<sup>more and when time spent</sup> developing knowledge is less productive, more<sup>growth in wages is needed to</sup> compensate workers for investing in developing knowledge.<sup>Less paradoxically,</sup> if the interest rate exceeds a level r,<sup>where</sup> strictly positive steady-state growth is no<sup>longer viable. Instead, the</sup> steady-state outcome is no growth.

Say, for example, that the labor force grows<sup>at an annual rate of 2 per</sup>
-28-

cent while the maximum feasible steady<sup>state growth in technology</sup><sup>_(f)_</sup> is 6 per cent, and f - y - 1/3. Ongoing growth requires<sup>an interest rate below 11 per</sup> cent.

If the interest rate is in fact<sup>10 per cent then technological knowledge</sup> grows at 4 per cent while output<sup>and the capital stock grow at 6 per cent.</sup> The wage grows at 2 per cent.

# _A Closed Economy_

If the economy has no access to foreign<sup>capital, so that the accumulation</sup> of domestic physical capital is<sup>fully financed through domestic savings, then</sup> the steady-state interest rate<sup>is r5, where:</sup> and where gc is the growth rate<sup>in per worker consumption, which, with</sup> balanced growth, is equal to g-n.<sup>Substituting this term into the expression</sup> for gH above gives, as the growth<sup>rate in knowledge:</sup> Say that the degree of relative<sup>risk aversion is 1. (Empirical estimates</sup> for most economies place it between<sup>one and three.) The growth rate in</sup> knowledge is then 2n+e-p.<sup>Because of their effect on the interest rate,</sup> population growth and the productivity<sup>of time spent acquiring new technology</sup> now enhance growth, while discounting<sup>reduces it. The feasibility of positive</sup> growth now requires that the<sup>discount factor not exceed twice the rate of</sup>
-29-

labor force growth.

## _An Open Economy_

Say instead that the economy can borrow and lend at a constant world interest rate r. In this case individuals' decisions about investment in human capital are independent of their own preferences, in our case of the parameters p and a. The rate of growth depends only on the technological parameters and the world interest rate. Access to the world capital market can raise the growth rate (1) if domestic taste parameters are such that positive growth is feasible with borrowing but infeasible under autarky or (2) if the steady-state growth rate under autarky is positive but below that under free capital mobility.

# 5.2 The Cohen Model

Cohen (1991) develops an alternative, somewhat simpler discrete-time endogenous growth model that is more in keeping with the assumptions of the two-gap literature. In particular, output is proportional to the capital stock. Hence, in period t, Qt aKt, where a is an exogenous constant. The capital stock evolves according to the law of motion: where, again, S is the rate at which capital depreciates. Following assumptions that appear in an earlier investment literature, Cohen assumes that investment uses resources beyond what is needed to contribute to the
-30-

capital stock. In particular, adding an amount It (gross of depreciation) requires a sacrifice of current resources of Jt, where: The parameter 0 is meant to capture capital installation costs.

As in the Lucas model, the competitive equilibrium of an open economy facing a given world interest rate will entail the maximization of the present discounted value of output at world prices. The consequent growth rate of output g° is given by: The expression for the growth rate of a closed economy with a representative agent with strictly ccncave preferences is more complicated. Since general results are hard to come by, I provide some numerical calculations. Table 1 presents the growth rates for the open and closed economies under alternative parameter values for a, the discount factor f,<sup>r,</sup> 6, and 0. In order to maintain more or less comparable discount factors for the closed and open cases, P is set equal to l/(l+r) (although, as<sup>with the</sup> Lucas analysis, if consumption is growing then the interest rate<sup>will exceed</sup> th( discount rate).

Note that, in contrast with the Lucas model, the growth rate of the open Cohen economy falls when the interest rate goes up. This is simply because a higher world interest rate makes it less worthwhile to allocate<sup>resources</sup> toward future rather than toward current consumption, while higher growth does not increase the return to investment in physical capital. In the Lucas
-31-

model, on the other hand, higher growth increases the return to human capital. Hence higher growth is needed to offset the effect of a higher interest rate, which reduces the incentive to accumulate human capital.

Also not surprising is the result that growth is higher when capital is more productive and is lower the higher the depreciation rate and the cost of installation, as reflected in the parameter 0. Note that the open economy grows as fast or faster than the closed economy when both grow at positive rates, but grows as slow or slower when both rates are negative. Whatever tendency of motion the economy has, its direction is exaggerated by openness.

To conclude, both the Cohen and Lucas models, as well as a number of other treatments of endogenous growth, provide a means of relating foreign indebtedness to long-run growth. Unfortunately, at this stage the literature has not provided any general conclusions about such essential issues as the relationship between the world interest rate and the growth rate.
# TABLE 1

|alpha|beta|r|delta|phi|open|closed|
|---|---|---|---|---|---|---|
|0.60|0.95|0.05|0.05|100.00|0.05|0.01|
|0.60|0.94|0.06|0.05|100.00|0.01|0.00|
|0.60<br>|0.93<br>|0.07|0.05|100.00|0.00|-0.00|
|0.60|0.92|0.08|0.05|100.00|-0.01|-0.00|
|0.60|0.92|0.09|0.05|100.00|-0.01|-0.01|
|0.60|0.91|0.10|0.05|100.00|-0.02|-0.01|
|0.60|0.90|0.11|0.05|100.00|-0.02|-0.01|
|0.60|0.89|0.12|0.05|100.00|-0.02|-0.02|
|0.60|0.88|0.13|0.05|100.00|-0.02|*0.02|
|0.60|0.88|0.14|0.05|100.00|-0.03|-0.02|
|0.60|0.87|0.15|0.05|100.00|-0.03|-0.02|
|1.00|0.95|0.05|0.05|100.00|ERR|0.04|
|1.00|0.94|0.06|0.05|100.00|ERR|0.03|
|1.00|0.93|0.07|0.05|100.00|ERR|0.03|
|1.00<br>|0.92|0.08|0.05|100.00|ERR|0.02|
|1.00<br>|0.92|0.09|0.05|100.00|0.04|0.02|
|1.00|0.91|0.10|0.05|100.00|0.03|0.01|
|1.00|0.90|0.11|0.05|100.00|0.02|0.01|
|1.00|0.89|0.12|0.05|100.00|0.01|0.01|
|1.00|0.88|0.13|0.05|100.00|0.00|0.00|
|1.00|0.88|0.14|0.05|100.00|-0.00|-0.00|
|0.60|0.91|0.10|0.10|100.00|-0.08|-0.06|
|0.60<br>|0.91<br>|0.10|0.05|200.00|-0.03|-0.03|
|1.00|0.91|0.10|0.10|100.00|-0.05|-0.04|
|1.00|0.91|0.10|0.05|200.00|-0.02|-0.01|

THE COHEN MODEL: GROWTH RATES UNDER ALTERNATIVE PARAMETER VALUES
-32-

# 6. Sovereign Risk

All the analysis so far rests on an assumption that sovereign debtors will meet debt service obligations to foreign creditors as long as they remain solvent, meaning that debt obligations do not exceed the present discounted value of national resources. There are reasons why sovereign debt may pose problems before the solvency constraint bites', however.

## _The Public Finance Problem_

An issue in the case of sovereign debt is the solvency of the sovereign government itself, as opposed to that of the nation as a whole. Even if the government perfectly represents the interests of the population, the administrative cost and excess burden of taxation can reduce the resources that a government can obtain to meet a debt-service obligation below what is available nationally. The problem debtor countries do in fact seem to have particular difficulty raising tax revenue. The capital flight phenomenon suggests the extent to which a significant portion of nctionally-owned resources may lie beyond the grasp of a sovereign debtor.

In fact, depending on how debt-seru'ice obligations are financed, even a small amount of debt can, in some circumstances, have a devastating effect on investment and government revenue. To make the argument in its starkest terms, consider a government that relies on proportional taxation of capital income for all of its tax revenue. Hence T - tg(K), where T is tax revenue, t is the tax rate on income from investment, which is itself a function g(K) of the amount inv3sted K; g is increasing and concave in K.
- 33.-

Say that the government owes an amount D to foreign creditors, and D must be covered by tax revenue. Potential investors know that the government owes w D, and can invest their funds elsewhere and earn a return r . Investing in the debtor country earns them an after-tax return rH _ (l-t)g'(K). Investors must decide where to invest before the actual tax rate is known. (It does not matter for our purposes whether these potential investors are nationals or foreigners; all that matters is that investment income in the debtor country is taxed while foreign investment income is not.) In order to meet its debt-service obligations the government sets a tax-rate t - D/g(K). Hence the after-tax rate of return is which can be increasing in K for K near zero but decreases in K or.ce K becomes very large. If we assume that individual investors are small relative to the total number (so that each investor ignores the effect of his own investment on the total amount K) investmont will occur up to the point at which r (K) r if K is strictly positive, while if then K 0 is an equilibrium outcome. The reason is that the income from any investment by a single, small investor acting on his own will be taxed at a very high rate, since the tax base will be so small.

Figure 1 illustrates a quite possible relationship between r (K), K and rw. At K , [l-D/g(K*)]g'(K*) - r . Investment is sufficient to allow a competitive after-tax return even after enough is collected to repay the debt.
w r <!-- Start of picture text --> /~~<br>~~~~~~~~~~~~~~~~ H )HK F'I (K)<br>I<br>I~~~~~~~~~~~~~~~<br>_. LK<br>K" K<br><!-- End of picture text --> FIGURE 1
34(Also, at K*, r (K) is declining in K so that K is locally stable.) Aowever, condition (6.1) is also satisfied. When the initial amount of capital is zero, a small level of investment is taxed at such a high rate it is not worth making.

The model, which is developed further in Eaton (1987), illustrates several points: First, it suggests why debt might be associated with capital flight, as domestic investors invest elsewhere to avoid the tax obligations associated with debt. Note that K* could exceed D, so that the equilibrium with positive investment could involve a positive net resource transfer, while the equilibrium wich no investment would involve a negative one.

Second, it su,gests that governments with large debt obligations would do better to rely on taxes that fall on internationally immobile factors, like land.

Third, it suggests why a government could benefit from being able to commit itself somehow to a particular tax rate in advance of investment decisions.

Why, given the public finance problems associated with sovereign borrowing, was so much borrowing done by governments rather than by private entities? There are irobably many reasons. But given the nature of contract enforcement and bankruptcy procedures in many debtor countries, lending to private borrowers would not have avoided problems associated with sovereign risk. Lenders would have had to rely on the borrower's government to enforce loan contracts and to administer bankruptcy procedures fairly. In fact, much of what was borrowed privately was ultimately assumed by borrower governments, even when loans were not guaranteed by the borrower's government.

Diaz-Alejandro (1984) tells of private Chilean banks that borrowed
-35-

substantial amounts from foreign commercial banks. The loans were n-ot guaranteed by the Chilean government. The Chilean banks invested the funds quite recklessly, and ultimately went bankrupt. The foreign commercial banks persuaded the Chilean government to assume the liabilities, threatening to worsen the government's own credit terms if it didn't. The point seems to be that the foreign commercial banks did not distinguish between private borrowers in Chile and the Chilean government, and held the government responsible for the outcome of all of its investments there.

# _The Liquidity Problem_

Another problem that is frequently mentioned in discussion of debt repayment is that of liquidity: A sovereign debtor may be solvent, but<sup>not</sup> have resources available to meet a cutrent debt-service obligation. If the borrower is truly creditworthy, however, the question arises as to why creditors won't lend what is needed to meet the current obligation. This issue comes up in our discussion of the options facing a creditor in dealing with a debtor not paying what it owes in section S.

# _The Enforcement Problem_

Most domestic borrowing occurs in a context in which creditors have significant legal rights over the assets of debtors. In the case of<sup>secured</sup> debt, specific assets that the creditor can seize in the event of default serve as collateral. In the case of unsecured debt, a default can lead to the general liquidation of the debtor's assets, with the proceeds distributed to creditors. In either case, the transfer of assets from debtor to<sup>creditor in</sup>
-36-

the event of nonpayment serves the dual purpose of placing a lower bound on what the creditor can recover if default does occur, and providing an incentive for the debtor not to default in the first place.

If in fact creditors can seize all of the debtor's assets, and can realize a return on them that is at least as high as what the debtor could, then the lenders can issue up to the discounted present value of the debtor's income without risk. The solvency constraint is thus the relevant upper bound on what can safely be lent.

In the context of sovereign debt, however, a creditor's legal remedies do not usually provide him the means to obtair a significant portion of the debtor's assets. The czeditor might be able to use its own legal system to obtain the debtor's foreign assets, but to the extent that the debtor is a net debtor, these will not suffice to compensate lenders. The natural question then is what incentive a sovereign debtor has to repay any (net) debt since it does not stand to lose assets of comparable value in the event of default.

Answers to this question are the topic of Section 7. First, however, some implications of the enforcement problem deserve mention.

# _Credit Rationing and the Monitoring of Indebtedness_

A creditor's inability to enforce aspects of loan contracts has several implications for the relationship between creditors and debtors, which I illustrate in a simple, two-period framework.

Say that in the first period a debtor borrows some amount L, incurring a - debt service obligation D L(l+r) in the second period. Here r, of course, is the interest rate on the loan.

Say that payment of anything less than what is owed causes the debtor to
-37-

suffer a penalty equivalent to the loss of an amount P of income in period 2. Hence the debtor will pay all that it owes if D < P, and default if D > P. (For simplicity, I resolve indifference on the debtor's part in favor of the creditor.) Creditors, who realize this and can monitor total indebtedness, will ensure that L(l+r) does not exceed P. As long as indebtedness satisfies this constraint, loans are perfectly safe, and competitive lenders should w provide them at the safe world interest rate r However, the debtor may want to borrow more than P/(l+r w) at this rate. But if it does it will default the next period. Lenders will therefore constrain loans not to exceed this amount. The consequence is credit rationing: competitive lenders provide less than what the debtor wants to borrow at the interest cate they charge. The interest rate does not rise in response to this excess demand because total indebtedness in the next period would then exceed P, ensuring default. No risk premium could compensate lenders for certain default.

Credit rationing requires that creditors know the debtor's total debt. In this simple example, if they were ignorant of it, there could be no competitive lending at all. If there were, the debtor would borrow more than what it would be willing to repay and then default. Knowing this, no one would lend.

This result points to the role of accurate information about the stock of total indebtedness in sovereign debt. In this situation the debtor benefits from public observability of its total indebtedness. If its level of debt could not be observed, it could not borrow.

Lack of information need not close the loan market entirely. Following Kletzer (1985), say that the cost of default is nearly infinite with some probability Xr and P < c with probability 1-Xr. A loan requiring repayment of
-38 -

P or less is then perfectly safe, since it will be repaid in any event, while a loan requiring repayment of more than this amount will be repaid only with probability X (when the cost of default is very high). If indebtedness is unobservable then risk-neutral lenders will charge an interest rate rU (l-n+r **)/r** to compensate for the risk of default. But, as Kletzer (1985) shows, if debt is observable the debtor may prefer to have loans rationed at P/(l+r) in order to benefit from improved credit terms.
-39-

# 7. The Incentive to Repay

A common assumption is that default on a current debt-service obligation will prevent a borrower from obtaining new credit, at least in the current period. But losing access to current credit provides an incentive to meet a current debt-service obligation if and only if potential new lending exceeds current debt-service obligations, so that the debtor receives a net resource transfer from creditors if it repays, but would receive nothing if it did not.

As discussed in section 3, however, creditors can earn a competitive return on sovereign lending only if the debtor at some point makes net resource transfers to its creditors. As the data in the Appendix show, sovereign debtors have in fact made large net resource transfers to their creditors during the 1980s. The question then, is why sovereign debtors make net resource transfers to their creditors.

# 7.1 Sanctions

Much of the literature on sovereign debt has simply asserted that the debtor suffers some exogenously-specified penalty beyond the loss of current new lending if it defaults. A particular justification for this assumption is that default allows creditors to intercept payments that the debtor might make to foreign exporters, or payments that it might receive from foreign importers. The cost of evading the creditor's attempts to intercept these payments (through barter arrangements, for example) would reduce the debtor's gains from trade.

Say that this penalty causes the debtor to incur a loss with a value in
-40-

terms of its permanent income of P if it defaults. If, subsequent to the default, the borrower can resume transacting at the world interest rate then the desirability of default depends on a comparison of the discounted value of net resource transfers to current creditors associated with the debt, which should correspond to the current value of the debt itself, and the cost of the penalty.

A common assumption is that P depends positively upon the debtor's subsequent income. Why it should is not clear. If default leads to a deterioration in the terms of trade then the argument must be made that the gains from trade increase with income. There is no presumption that they do. Growth in income might be "import biased," for example, so that higher income implies less reliance on foreign trade.<sup>3</sup> Nevertheless, the assumption that the cost of default, and hence how much foreign creditors can extract from a sovereign debtor, is central to a number of major results on debt forgiveness and debt buybacks, the topics of sections 8 and 9.

# 7.2 Maintaining a Reputation for Repayment

Another reason why a debtor might choose to repay debt is to maintain access to foreign credit markets on favorable terms. Historically, widespread default on loans to developing countries has lead to a subsequent loss of access to credit markets. Episodes of widespread default among Latin American debtors was followed by a virtual loss of access to credit markets for these countries. Subsequent to a series of defaults in the 1930s, for example, Latin American countries were unable to raise money from private international capital markets until the 1970s.

3See the discussion in Gersovitz (1983).
-41-

There is, however, disagreement about the extent to which an individual developing country's repayment performances affected its credit terms relative to those of developing countries as a whole. Hence it is not clear to what extent creditors distinguished among individual countries in relating credit terms to past performance, or judged developing countries as a group. Eichengreen and Portes (1990) indicate that, during the 1920s and 1930s, credit terms did reflect previous repayment within that period, but that a record of default in the 1930s did not worsen credit availability in the 1970s. Ozier (1989a), on the other hand, using a sample that excludes countries that did not exist in the 1930s, finds that among countries that existed in both periods, a history of successful repayment in the 1930s improved credit terms in the 1970s. Furthermore, Ozler (1989b) finds that a history of successful repayment within the 1970s improved subsequent credit terms within the period. Nevertheless, even if creditors lump developing countries together in assessing their creditworthiness, a loss of access to foreign credit markets can serve as an incentive for an individual debtor to repay. Group treatment of developing country debtors by creditors simply introduces a negative externality to a country's default decision.

As Bulow and Rogoff (1989b) have emphasized, losing access to loans from foreign credit markets does not suffice, by itself, to serve as an incentive to repay. If a sovereign debtor in default can somehow continue to enforce its own loan contracts with its own foreign debtors at the world interest rate then, if the only consequence of default is inability to borrow again, at some point a debtor will be called upon to transfer so much to its creditors that it would prefer to default and invest what it owes on its own account. From then on it can remain a net creditor and do at least as well as it could have if it repaid and borrowed again.
-42-

The question arises as to why a sovereign debtor in default could itself enforce a loan contract. The discussion up through section 5 implicitly assumed two-sided automatic enforcement, that the country in question will repay its debts as along as it has the resources to do so, and could rest assured that the rest of the world would repay any loans it made. Other literature (e.g., Eaton and Gersovitz, 1981, Grossman and van Huyck, 1988) implicitly assumes no automatic enforcement: Any credit arrangement would be honored only as long as credit arrangements had always been honored in the past. Kletzer and Wright (1990) have shown that, as long as all parties to any credit arrangement face (even temporary) exclusion from credit markets as a consequence of default then positive amounts of borrowing and lending can be sustained. Bulow and Rogoff's contribution is to show that reputation alone will not sustain lending if there is one-sided automatic enforcement in the credit market.

The result has been misinterpreted, however, to mean that a threatened loss of access to international credit markets in general (financial autarky) is insufficient to sustain borrowing and repayment. See, for example, Cohen (1991, p. 94). Sustaining nonzero net transfers requires, however, that at no point in the relationship between the borrower and lenders is it certain that subsequent net resource transfers from one to the other will be in just one direction.

The following model illustrates how the threat of financial autarky can sustain some transfer of resources between a borrower and the rest of the world.

For simplicity, consider the simple economy treated in Section 4 with an exogenous output Qt each period t facing a constant world interest rate r. At any period t its utility is given by u(C t) where Ct is period t consumption.
.43the function u is incrtasing and concave. The country's discount factor is _6_ < l/(l+r). Its present discounted value utility Ut at any time t is thus: The country's debt evolves according to the equation: Net resource transfers NTt - C - Qt are subject to the solvency constraint: So far, all is just as in section 4. In addition, however, the enforcement constraint requires that, at any time, maintaining its relationship with the interrational financial community is at least as advantageous as severing its ties (by failing to make a net resource transfer that is expected of it), and enduring financial autarky thereafter, consuming its endowment. Hence, at each period t it must be the case that the consumption path Cr provided by particip?.ion in world financial markets satisfies: Sensible creditors will restrict the debtor to debt and repayment profiles that satisfy not only the solvency constraint (7.2) but the
-44-

enforcement constraints (7.3) as well. The debtor's problem is thus to maximize (7.1) subject to (7.2) and (7.3). The relevant optimization problem is now given by the Lagrangian: where A is again the Lagrange multiplier associated with the solvency constraint (7.2) while pt are the (undiscounted) Lagrange multipliers associated with the enforcement constraints (7.3).

The first-order conditions for a maximum are now: Raising consumption in any period not only contributes to utility directly but contributes toward relaxing the enforcement constraints of the current and prior periods.

Say that u(C ) - log(C ), (l+r)p < 1, and Qt - Q if t is even while Qt **t t** QH if t is odd, where QH > QL > 0. Hence income fluctuates between a high and low value. Since consumption is subject to declining marginal utility, the country has an interest in maintaining access to the world capital market to smooth consumption.

From the perspective of any period in which income is low, the present value of future resources discounted at the world interest rate is:
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In the absence of any enforcement problem the optimal consumption profile satisfies: The assumption that 6 < l+r implies that, absent any enforcement constraint, consumption would diminish over time, approaching zero as t becomes large. Since the country is more impatient than world capital markets, it exchanges present for future consumption.

At some critical point t*, then, it would be the case that the C < QL t for all t 2 t*. From that point on the optimal borrowing program would call upon the country to make net resource transfers to creditors every period. Obviously the country would do better to default on its debt and consume its endowment thereafter. Hence the enforcement constraint must affect the consumption path. How much borrowing can still occur?

If Q > (l+r)#Q then the consumption smoothing motive to maintain creditworthiness is not enough to sustain any borrowing at all: The anticipated decline in output is not sufficient to provide an incentive to repay debt in good times in order to borrow in bad times. Otherwise, however, a debtor will be willing to make a positive net resource transfer to creditors when output is high in order to borrow again when output is low.

As in the unconstrained program, initially the debtor borrows in order to raise current consumption. At some point, however, debt reaches a level at which the borrower is indifferent between maintaining access to the international capital markets and defaulting. From that point onward, debt can no longer increase over time. Instead, when output is low the debtor
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receives a net resource transfer from its<sup>creditors but makes a net resource</sup> transfer back when output is high. In high<sup>output periods the debtor is</sup> indifferent between repaying and defaulting,<sup>but in low output periods (when</sup> it receives a net resource transfer from creditors)<sup>it is strictly better off</sup> than under financial autarky.

Once the enforcement constraint binds,<sup>it binds in every high output</sup> period thereafter, and the level of debt<sup>is the same in each subsequent high</sup> output period. How large the maximum<sup>debt level can be depends on the present</sup> value of the net resource transfer over the cycle<sup>that the debtor is prepared</sup> to make in order to avoid financial autarky.

Tables 2A and 2B provide magnitudes of<sup>indebtedness and net transfers (2A</sup> for the case in which output cycles between<sup>8 and 12, a 20 per cent standard</sup> deviation, and 2B for the case in which<sup>it cycles between 9 and 11, a 10 per</sup> cent standard deviation) for various values<sup>ofP("beta"), and R-</sup> l+r; CH and CL are consumption levels when output<sup>is high and low, respectively, while</sup> QH-CH and QL-CL are the corresponding net<sup>resource transfers from debtor to</sup> creditor. (The first is always positive<sup>and the second always negative.).</sup> The maximum amount of debt at the beginning<sup>of a high output period is given</sup> in the column DMAX.

The final column cortipares DMAX with the value of debt incurred<sup>in the</sup> previous (low-output) period times R. If the difference is<sup>positive then the</sup> debtor in fact can borrow enough before<sup>the enforcement constraint becomes</sup> binding to remain a net debtor thereafter.<sup>Otherwise, the enforcement</sup> constraint binds immediately and the debtor<sup>cannot initially borrow enough to</sup> remain a net debtor over the cycle. Instead,<sup>it can only borrow DMAX/R when</sup> output is low. The net transfer it then<sup>makes to creditors when output is</sup> high not only fully repays debt but includes,<sup>in addition, a net investment to</sup>
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finance consunption when output is again low.

The tables reveal several relationships: How much debt can be sustained depends positively on the variability of output and the discount factor, and negatively on the interest rate. Moreover, the effect of output variability is dramatic: An order of magnitude more debt relative to average income can be sustained when output fluctuations are 20 per cent rather than 10 per cent. Also notable is the sensitivity of the maximum debt level to the interest rate.

Finally, note that increases in P offset by reductions in R that maintain R. constant increase the maximum sustainable debt level. An interpretation is that high frequencv fluctuations (say, over the season) allow for more debt to be accumulated than low frequency fluctuations (say over the business cycle).

The analysis is simple. For example, there are no allowances for uncertainty, growth, and investment. Intro-4ng these factors will not<sup>4</sup> affect the basic point of the exercise, that maintaining access to credit markets is a sufficient reason to service debt.

In fact, domestic investment opportunities provide an additional reason to want to maintain access to credit markets. The expected return on investment opportunities may also fluctuate. If a country must finance its own investment, taking advantage of investment opportunities may then force consumption to fluctuate. Access to international capital markets allo4s it to vary its investment level in response to changes in domestic opportunities without completely offsetting movements in consumption.

Annual data on net resource transfers presentLd in the Appendix indicate that, during the 1970s and 1980s, the direction of flow of funds between debtor countries and international capital markets changed on average ar:-nd 5
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times. Possibly, there was much more variation within the year.4 4Using a model very similar to the one developed here, Cohen (1991) claims that avoiding financial autarky cannot, by itself, provide an incentive to service debt (p. 94). What he actually shows is that avoiding financial autarky cannot be the reason for making net resource transfers two periods in a row. If it is the reason in the second period then, in that period, the debtor must be indifferent between repayment and autarky. In the previous period, then, making a net resource transfer must bring utility strictly below the autarky level.
# TABLE 2A

|R=1 +r|beta|CH|CL|QH-CH|QL-CL|DMAX|DMAX-<br>R*(CL-CL)|
|---|---|---|---|---|---|---|---|
|1.00i|G.90|10.40|9.37|1.60|-1.37|111.50|110.13|
|1.005<br>|0.90|10.39|9.39|1.61|-1.39|22.99|<br>21.59|
|1.010|0.90|10.36|9.42|1.64|-1.42|11.93|10.50|
|1.020|0.90|10.31|9.47|1.69|-1.47|6.41|4.92|
|1.030<br>|0.90|10.27|9.52|1.73|-1.52|4.59|3.03|
|1.040|0.90|10.22|9.56|1.78|-1.56|3.68|2.05|
|1.050|0.90|10.17|9.61|1.83|-1.61|3.14|1.45|
|1.060|0.90|10.13|9.66|1.87|-1.66|2.79|1.03|
|1.070|0.90|10.08|9.71|1.92|-1.71|2.54|0.71|
|1.080|0.90|10.04|9.76|1.96|-1.76|2.36|0.46|
|1.090|0.90|9.99|9.80|2.01|-1.80|2.22|0.26|
|1.100|0.90|9.95|9.85|2.05|-1.85|2.12|0.08|
|1.001|0.85|10.73|9.1;,|1.27|-1.13|73.05|71.92|
|1.005|0.85|10.71|9.15|1.29|-1.15|15.15|14.00|
|.0i0|0.85|10.68|9.17|1.32|-1.17|7.92|6.74|
|1.020|0.85|10.64|9.22|1.36|-1.22|4.32|3.07|
|1.030|0.85|10.59|9.27|1.41|-1.27|3.13|1.82|
|1.040|0.85|10.54|9.32|1.46|-1.32|2.54|1.17|
|1.050|0.85|10.49|9.37|1.51|-1.37|2.19|0.76|
|1.060|0.85|10.45|9.41|1.55|-1.41|1.97|0.47|
|1.070|0.85|10.40|9.46|1.60|-1.46|1.81|0.25|
|1.080|0.85|10.36|9.51|1.64|-1.51|1.70|0.07|
|1.090|0.85|10.32|9.56|1.68|-1.56|1.61|-0.09|
|1.100|0.P5|10.27|9.60|1.73|-1.60|1.55|-0.22|
|1.110|0.85|10.23|9.65|1.77|-1.65|1.49|-0.34|
|1.120|0.85|10.19|9.70|1.81|-1.70|1.45|-0.45|
|1.130|0.85|10.15|9.75|1.85|-1.75|1.42|-0.55|
|1.140|0.85|10.11|9.79|1.89|-1.79|1.40|-0.64|
|1.150|0.85|10.07|9.84|1.93|-1.84|1.38|-0.74|
|1.001|0.95|10.09|9.60|1.91|-1.60|155.24|153.64|
|1.005|0.95|10.07|9.62|1.93|-1.62|31.88|30.25|
|1.010|0.95|10.05|9.64|1.95|-1.64|16.47|14.81|
|1.020|0.95|10.00|9.69|2.00|-1.69|8.77|7.05|
|1.030|0.95|9.Q5|9.74|2.05|-1.74|6.22|4.43|
|1.040|0.95|9.91|9.79|2.09|-1.79|4.95|3.09|
|1.050|0.95|9.86|9.84|2.14|-1.84|4.20|2.27|

MAXIMUM DEBT LEVELS SUSTAINABLE THROUGH "REPUTATION" OH = 12, OL 8
# TABLE 2B

|R=1 +r|beta|CH|CL|OH-CH|OL-CL|DMAX|DMAX-<br>R*(CL-OL)|
|---|---|---|---|---|---|---|---|
|1.001|0.90|10.51|9.47|0.49|-0.47|11.54|11.08|
|1.005<br>|0.90|10.49|9.49|0.51|-0.49|2.51|2.02|
|1.010|0.90|10.46|9.51|0.54|-0.51|1.39|0.87|
|1.020|0.90|10.42|9.56|0.58|-0.56|0.84|0.27|
|1.030<br>|0.90<br>|10.37<br>|9.61|0.63|-0.61|0.67|0.04|
|1.040|0.90|10.32|9.66|0.68|-0.66|0.59|-0.10|
|1.050|0.90|10.27|9.71|0.73|-0.71|0.54|-0.20|
|1.060|0.90|10.23|9.76|0.77|-0.76|0.52|-0.28|
|1.070|0.90|10.18|9.81|0.82|-0.81|0.50|-0.36|
|1.080|0.90|10.14|9.85|0.86|-0.85|0.50|-0.42|
|1.090|0.90|10.09|9.90|0.91|-0.90|0.50|-0.49|
|1.100|0.90|10.05|9.95|0.95|-0.95|0.50|-0.55|
|1.001|0.85|10.80|9.19|0.20|-0.19|1.90|1.71|
|1.005|0.85|10.78|9.21|0.22|-0.21|0.46|0.25|
|1.010|0.85|10.76|9.24|0.24|-0.24|0.29|0.05|
|1.020|0.85|10.71|9.29|0.29|-0.29|0.21|-0.08|
|1.030|0.85|10.66|9.34|0.34|-0.34|0.20|-0.15|
|1.040|0.85|10.62|9.38|0.38|-0.38|0.19|-0.21|
|1.050|0.85|10.57|9.43|0.43|-0.43|0.20|-0.26|
|1.060|0.85|10.52|9.48|0.48|-0.48|0.20|-0.31|
|1.070|0.85|10.48|9.53|0.52|-0.53|0.21|.<br>-0.35|
|1.080|0.85|10.43|9.58|0.57|-0.58|0.22|-0.40|
|1.09C|0.85|10.39|9.63|0.61|-0.63|0.23|-0.45|
|1.100|0.85|10.35|9.67|0-65|-0.67|0.24|-0.50|
|1.110|0.85|10.30|9.72|0.70|-0.72|0.25|-0.55|
|1.120|0.85|10.26|9.77|0.74|-0.77|0.27|-0.59|
|1.130|0.85|10.22|9.81|0.78|-0.81|0.28|-0.64|
|1.140|0.85|10.18|9.86|0.82|-0.86|0.29|-0.69|
|1.150|0.85|10.14|9.91|0.86|-0.91|0.30|-0.74|
|1.001|0.95|10.22|9.72|0.78|-0.72|28.18|27.45|
|1.005|0.95|10.20|9.74|0.80|-0.74|5.96|5.22|
|1.010|0.95|10.18|9.77|0.82|-0.77|3.19|2.42|
|1.020|0.95|10.13|9.82|0.87|-0.82|1.82|0.99|
|1.030|0.95|10.08|9.86|0.92|-0.86|1.37|0.48|
|1.040|0.95|10.03|9.91|0.97|-0.91|1.15|0.20|
|1.050|0.95|9.99|9.96|1.01|-0.96|1.03|0.02|

MAXIMUM DEBT LEVELS SUSTAINABLE THROUGH "REPUTATION" QH = 11, OL 9
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# 8. Dealing with Nonpayment

If in fact the sanctions that creditors impose on a debtor in default take the form of a trade embargo, rather than a seizure of its assets, the problem arises as to why the creditor community would ever impose sanctions. Bulow and Rogoff (1988b) develop an argument which separates private creditor banks from the rest of the creditor countries. Default gives banks the legal right to seize any assets of any debtor in default in the creditor community, which reduces or eliminates potential gainful trade between the creditor community as a whole and the debtor country. Both lose but the banks either do not suffer or even gain if some trade remains. The banks' legal rights may even allow them to extract some transfers from the creditor country public, who are willing to pay the banks (or give the debtors money to pay the banks) in order to forestall default and maintain trade with the debtor.

A remaining question is why t'.e creditor community protects these creditor rights if it is not in their interest to do so. In fact, legal issues surrounding "state doctrine" suggests that the claims of private creditors could be quite shaky if exercising them is not in the public interest. Alexander (1987) provides a discussion.

The fact that declaring a borrower to be in default may not convey<sup>nearly</sup> as much benefit to a creditor in an international context, compared with a domestic context, makes the disposition of sovereign debts relatively more difficult to ascertain. In particular, a creditor way be much more<sup>willing to</sup> finance debt-service obligations with "new money" if declaring default<sup>does</sup> not convey much in the way of privileges.

Consider the general situation of a creditor confronted with a<sup>debtor</sup>
-50-

that owes more than it is able or willing to transfer. There are four options: (i) lending the difference (which could take the form of rescheduling, tolerating arrears, or providing "new money"); (ii) finding another creditor to lend the difference; (iii) forgiving the difference; or (iv) declaring the borrower in default and seeking a legal remedy.

The following simple example, which draws on several in the literature, illustrates the situation. A debtor with current income Y owes D now and D next period. It only comes up with R1 < D1 this period, however. There are two possible outcomes in period 2: either the debtor has a high GDP, YH, in which case the debtor is for some reason willing to pay whatever is owed, or income is Y and the debtor repays R2 < D2. (Why the debtor is willing to pay more when income is high than when it is low is not modeled.) The probability n(e) that income is high depends positively on the debtor's effort e in period 1, which could, for example, reflect its investment in exportable commodities, fiscal reform, etc. Effort reduces current income.

In period 1, then, the debtor chooses e to maximize: where RH is whatever is owed in period 2.

A unit of effort costs the debtor 1 now and provides it an expected return ff'(e)(YH-R2_YL +RL), where ff'(e) is the increase in the probability of high income from an extra unit of effort. The amount of effort that the debtor will want to undertake to increase the probability of high income is thus a positive function of the difference between income after repayment in the two periods. Hence we can write the equilibrium amount of effort as e(YH-R _-YL_ +RL). Most significantly, the amount of effort that the debtor will 2 2
-51-

want to expend falls as R rises.

# _Formal Bankruptcy and Legal Remedies_

Consider now the various options<sup>available to the creditor, beginning</sup> with (iv) a formal declaration of default<sup>and subsequent legal remedy. It is</sup> not entirely clear, in the context of<sup>sovereign debt, what this would mean.</sup> But one interpretation of this course of action is that it allows<sup>the creditor</sup> to take some of the debtor's current<sup>assets within territory subject to the</sup> jurisdiction of the creditor's legal system.<sup>Once the disposition of these</sup> assets was adjudicated, however, any<sup>remaining claim that the creditor has</sup> against the sovereign would be wiped clean.<sup>6</sup> Say that this course of action yields the<sup>creditor an expected net gain G</sup> and the creditor an expected direct loss<sup>L. Since the period 2 debt is</sup> canceled the debtor would then find<sup>it worthwhile to expend an amount</sup> e(YHYL ). This is the socially efficient amount,<sup>since the debtor recovers</sup> all the gains from its effort. All distortion<sup>imposed by the debt itself is</sup> eliminated. To the extent that L<sup>exceeds G, however, bankruptcy itself</sup> introduces inefficiency; and there are reasons to think that the inefficiencies associated with sovereign bankruptcy are significant,<sup>although</sup> we have little direct evidence.

# _New Money_

Consider as the next option (i): lending<sup>the difference. The creditor</sup> 6lt is not the case, as is occasionally claimed, that by setting aside a loan loss reserve or "writing down"<sup>a debt a creditor cancels it. Taking</sup> these actions does not relinquish any<sup>legal rights.</sup>
-52-

gets R1 now and increases its period 2 debt by (D1-R1)(l+r ), where rL is the interest rate on what is rolled over. But this amount is paid if and if Y - YH. The debtor's period 2 obligation grows to D2 +(D -R )(l+r ), so that its optimal level of effort falls to e[YH-D +(D -R )(l+rL)-Y +RL. The 2 1<sup>-R</sup> 1<sup>)(+)Y+</sup> 2<sup>].Th</sup> creditor can expect to get R +w(e)[D2+(D -R )(l+rL)] + [l-ir(e)]R L since the creditor pays R1 now for sure and D2+(D -R )(l+r ) the next period with probability w(e[YH-D2+(D -R )(l+r )-YL+R2]) and RLwith remaining probability. Here the debt burden is at its maximum, but if income is high the creditor recovers the most.

# _Forgiveness_

Turn now to option (iii), forgiving the current shortfall. Again the creditor receives R for sure now, but receives D2, the original obligation, next period with probability lr[e(YH-D L YRL)]. Hence the period 2 debt 2 + 2)I ec h eid2db obligation and the consequent amount of effort on the part of the debtor to achieve a high income are somewhere in between what they are in the case of a rollover and a cancellation.6 In comparing options (i) and (iii), the creditor trades off the size of the period 2 obligation wich the likelihood that the obligation will be paid off. The higher the debt obligation, the less effort the debtor is likely to put into ensuring that circumstances will be such that it will pay.

6 L Note, by the way, that formally, through the choice of r , financing a postponement of repayment includes debt forgiveness (r - -100%) and cancellation (r -D2/(D -R )xlOO%) as special cases. We are thinking, however, of rollovers as occurring at either the actuarially fair rate or at least at the risk-free rate. A rollover at anything less than the actuarially fair rate involves an element of forgiveness.
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# **_The "Debt Laffer Curve"_** _and_ **_Debt Relief_**

The general situation, illustrated by this example, in which an increase in a debtor's debt can actually lower<sup>its expected net resource transfers to</sup> its creditors (and hence, presumably,<sup>the market value of its debt) has been</sup> called a "debt Laffer curve." Obviously,<sup>zero obligations imply zero</sup> transfers and have zero value, so the<sup>relationship between the face value and</sup> market value of the debt must be nondecreasing<sup>over a range. But at some</sup> point, the aigument goes, the disincentive<sup>effects associated with a high</sup> nominal debt burden create such a disincentive<sup>to bring about conditions for</sup> full repayment that more nominal debt<sup>means less, on average, will be repaid.</sup> The phenomenon has implications for issues<sup>other than what creditors</sup> should do about unpaid debt. If, for<sup>example, adding to the future debt</sup> burden reduces the value of the<sup>debt, then it is quite likely that subtracting</sup> from it will increase the value of the<sup>debt. Regardless of what the debtor</sup> pays in period 1, creditors may<sup>find it in their collective interest to reduce</sup> period 2 debt service obligations below<sup>D2, say to D2, in order to raise e</sup> and, therefore, w.

Note that the possibility of<sup>a debt Laffer curve in this example requires</sup> that there be at least two possible<sup>outcomes that bear the following</sup> relationship to each other.<sup>In one state the debtor pays less than what it</sup> owes, and what it does pay in that<sup>state does not increase unit for unit with</sup> what it owes. In another state the debtor<sup>pays more, and what it does pay</sup> strictly increases with what it<sup>owes, and the marginal effect of what it owes</sup> on what it pays in this state<sup>is greater than the effect on what it pays in</sup> the state in which it pays less.
-54-

More generally, say that in the low income state the debtor pays RL(D2) H~~~~~~~~~~~~~ while in the high income sitate it pays R (D2). Effort as a function of D2 is then e[Y - Y + R (D2) - R (D2)]. For an increase in debt to decrease e L H requires that R L(D2) rise by strictly less than R H(D2) when D rises. 2 2 ~~~~~~~~~~~~~2 What the creditor can expect to get in period 2 is: so that for an increase in e to raise the expected payment requires that RH(D2) > R (D2).

These conditions were all satisfied in our example since R H(D D and L L R (D)2 R2. They would not be satisfied if, for example, the debtor was expected to pay the same amount regardless of income (if R (D2) - RL(D2) - D2) or if whatever it was expected to repay in either state was independent of D2. The typical assumption is as in the example, that nominal debt affects what a debtor repays only when it repays the full amount. In that case the possibility of a debt Laffer curve requires a belief that there is a significant likelihood that the full amount of the debt will be paid off. Otherwise, the face value of the debt is irrelevant.

# _Coordination, Free Riders, and New Lenders_

A natural question raised by the debt Laffer curve is why, if reducing the face value of a country's debt raises its actual value, don't lenders take advantage of the relationship by forgiving debt, to the point at which its market value is maximized.

One explanation is that reducing the face value requires coordination
- 55-

among lenders, each of whom benefits from debt relief by others. The explanation is incomplete, however. It would still pay for a single purchaser to buy up all (or at least a major portion) of the outstanding debt, and then reduce the debt. The initial holders might appropriate much of the gain, but an offer contingent on 100 per cent participation would still leave a reward to anyone trying to consolidate the debt and achieve the gain.

Demirguc-Kunt and Diwan (1990) have suggested deposit insurance as a reason for the market's failure to consolidate debt and achieve potential efficiency gains. They distinguish between sound and unsound banks. Unsound banks may actually prefer to hold an assel: with a more variable return even if its expected return is lower. The reason is that if the return is low or even average the bank will fail, and bank owners will not suffer the entire loss, but a high return will ensure survival, so that the owners will enjoy the gain. Hence unsound banks may actually consider the debt to be more valuable if it is not written down (since there is some chance of a high return) and may not be willing to sell the debt at its market value to a sound bank. One might ask, then, why unsound banks don't buy all the debt. The answer is that they lack the funds to do so by virtue of their unsoundness.

Proponents of a public buyout of the debt, for instance Kenen (1990) and Sachs (1990), have also made use of the debt Laffer curve argument. The idea is that, since market failures have rendered the private markets incapable of writing-down the debt, a public institution should correct the failure by buying up the debt and realizing the Laffer curve gain itself.

Obviously, the soundness of such an institution hinges on the position of the relevant debtors on the debt Laffer curve. If debtors are on the "wrong" (downward-sloping) side of the curve then the institution could make money, or at least avoid a loss, by realizing the gains from debt relief. If debtors
-56-

are on the upward-sloping portion, however, no such efficiency gains<sup>exist,</sup> and if it buys the debt at anything above<sup>market value it will lose, unless,</sup> of course, it has some advantage over private<sup>creditors in collecting payment.</sup> There is little reason to see why it<sup>should. Existing public institutions do</sup> not seem to have succeeded in achieving<sup>net resource transfers from their</sup> debtors to the extent that private creditors<sup>have. More evidence on this</sup> question, however, would be enlightening.

Public involvement in the debt crisis may,<sup>however, provide sovereign</sup> debtors an option that is rarely available<sup>domestically. Consider the</sup> remaining response to a recalcitrant debtor,<sup>option (ii), finding another</sup> lender to lend the difference between what<sup>the debtor owes and what it is</sup> willing to pay. It is rarely the case that<sup>a loan will be worth more to</sup> another private lender than it is to the original<sup>lender. Nevertheless,</sup> public desire to avoid financial disruption and possible<sup>inefficiencies</sup> associated with default has created<sup>pressure for a public takeover of the</sup> debt: Already, on an ad hoc basis, official lending<sup>agencies have lent</sup> problem debtors some of the difference<sup>between what they owe and what they</sup> want to pay their private creditors. Various<sup>proposals for debt relief</sup> institutionalize this response.
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# 9. Buybacks and Swaps: Market-Based Debt Reduction Schemes

Various schemes have been proposed, some of which have been implemented, in which debtor countries buy back their debt on the secondary market. The original loan covenants typically prohibit debtor buybacks. Hence overt buybacks require that creditors waive these prohibitions. Debtor governments may nevertheless be able to buyback covertly, through third parties, for example. In fact, creditors have now permitted debtor buybacks in a number of circumstances.

Buybacks have taken several forms;

1. Simple buybacks using the debtor's own resources.

2. Simple buybacks using donated resources.

3. "Swap" arrangements, whereby the government exchanges debt for domestic currency at some stated price. The use of this currency is tied to particular purposes such as direct foreign investment (in the case of debt-equity swaps) or environmental protection (debt-for-nature swaps).

Swaps can be decomposed into a simple buyback with a subsidy to direct foreign investment (in the case of debt-equity swaps) or to environmental protection (in the case of debt-for-nature swaps). The amount of the subsidy depends upon the price at which debt is repurchased and on the exchange rate offered.

Discussion has focused on the buyback component of the scheme, which can be analyzed in isolation from the swap component. A particular controversy surrounds the extent to which buybacks benefit debtors. One claim is that they benefit creditors at the expense of debtors. Another is that they benefit both. I present, in very simple form, examples in which each result
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emerges, and discuss the assumptions driving the different outcomes.

# 9.1 "Average" and "Marginal" Debt: Are Buybacks Boons or Boondoggles?

Bulow and Rogoff J988a) argue that, in the case of sovereign debt, buybacks out of the debtor's own resources benefit creditors at the expense of debtors, and that creditors appropriate the lion's share of funds donated to a debtor to buy back debt.

Consider a two-period case in which the debtor owes an amount D in period 2. How much it will pay to service any level of debt in period 2 is an amount R that has a probability distribution F(R), which, critically, is independent of D. What it actually will pay is the minimum of R and D, so if R exceeds D i. pay-<sup>4</sup> -ts debt in full, while otherwise it pays R atAd defaults on the rest. (For simplicity, all magnitudes are discounted to period 1 prese.:t values.) Creditors know all this, so they anticipate an expected payment V(D) that is a function of the face value of the debt D: The first term reflects what creditors get when R is less than D, the realized value of R. The second term is the probability that R exceeds D times repayment in that case, D. Since V(') is the expected amount of repayment in period 2, if the market is risk-neutral then V(D) should equal the period 1 market value of the debt.

The marginal value of debt is the effect of an increase in one unit of its face value on its market value. Differentiating with respect to D, the
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marginal value is: Since the distribution of R is assumed<sup>to be independent of D, this</sup> expression reduces to 1-F(D),<sup>the probability of full repayment. In this case</sup> the only effect of increasing nominal<sup>debt by one unit is to increase</sup> repayment by one unit if full<sup>repayment is made. Otherwise it has no effect.</sup> The average value of a unit of debt p<sup>will equal V(D)/D or:</sup> This amount corresponds to expected<sup>payment per unit of debt. It exceeds</sup> 1 - F(D) as long as some payment occurs<sup>even if full repayment is not made,</sup> but the price cannot exceed one.

When the debtor buys up its own debt,<sup>the presumption is that it should</sup> pay at least the average price p,<sup>since this is the value of the claim that</sup> the seller is sacrificing. In fact,<sup>buybacks have occurred at prices near or</sup> above the market price.<sup>7</sup> To give buybacks the best chance of helping<sup>the</sup> debtor, I treat the case in which buybacks<sup>take place at the market price.</sup> The effect of the buyback on what the debtor<sup>pays subsequently is the</sup> marginal value V'(D) minus the extent<sup>to which resources used for the current</sup> buyback (p) reduce what will be available<sup>for repayment subsequently. Say</sup> that every dollar spent on buybacks reduces<sup>funds available for repayment by a</sup> 70ne finding is that debt bought back through<sup>negotiations with creditors</sup> costs much more than the market<sup>price, while auctions lead to prices close to</sup> the market value.
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fraction A. If one unit of debt is bought back at price p then what the - debtor is willing to pay for any level of debt falls from R to R Ap.

How a buyback of one init of debt affects what the debtor ultimately transfers to the creditor thus has three components. First, there is the transfer entailed in the buyback itself, equal to to the average price p - V(D)/D. Then there is the consequent change in the face value, which reduces expected repayment by the marginal value of the debt V'(D) - 1 - F(D). Finally, there is the expected reduction in what the debtor will pay when there is incomplete payment, which equals AF(D)p, the probability of incomplete payment F(D) times what is spent on the buyback p times the effect of buybacks on resources available for repayment A. The total effect, then is: Since 1 2 p > 1 - F(D), this amount is positive if A 0, as Bulow and Rogoff (1988a) claim is the case for sovereign debt, and negative if A - 1, which they consider to be the case for corporate debt.

Hence a crucial issue is how much the buyback reduces what is available for later repayment. If future resources are significantly reduced, (A near one) then the buyback is a boon for the debtor. A unit of debt reduction costs p. But it reduces its net resource transfer by nearly p if it fails to repay fully and by 1 > p if it does repay fully.

But if the resources used to buy debt does not affect what creditors can later hope to collect (as might be the case when funds were donated for that purpose) then spending p now only reduces payments (by 1) if full repayment is made, which occurs with probability 1-F(D), but not at all otherwise. Since p
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exceeds the probability of full repayment, the debtor<sup>loses. The scheme is a</sup> "boondoggle" for the creditor.

An empirical issue is the effect that buybacks<sup>have had on the value of</sup> remaining debc. The value of A determines<sup>how the price of remaining debt</sup> responds to the buyback. Differentiating the<sup>expression for p -V(D)/D at B,</sup> the amount of debt bought back, and evaluating<sup>at B-0 gives:</sup> Hence, under Bulow-Rogoff presumption that the<sup>buyback does not affect</sup> - resources available for repayment (A 0) the<sup>price of remaining debt rises</sup> - after a buyback (since p 2 1 F(D)). In the<sup>limiting case in which there is</sup> no possibility of all debt being paid off<sup>(F(D)-1) then dp/p-</sup> E/D - -dD/D; so that pD is unchanged. The value of remaining<sup>debt outstanding is</sup> unaffected by the buyback since it has no effect<sup>on what the creditors expect</sup> to receive subsequently.

On the other hand, if resources used for a<sup>buyback decrease what is</sup> available for repayment unit for unit (A<sup>-</sup> 1) then the price of remaining debt falls after a buyback. Only in the limiting<sup>case in which repayment is</sup> - assured, so that p 1, is there no effect.

# 9.2 Buybacks as a Cure for Debt Hangovers

So far, this analysis assumes that there<sup>is no excess burden associated</sup> with debt, so that the only question arising<sup>from the buyback is how it</sup> affects the net resource transfer from<sup>debtor to creditor. Since total</sup> resources are given there is no potential<sup>for a nec gain to both parties.</sup>
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In f%ct, one argument in favor of buybacks is their rotential to eliminate inefficiencies associated with the debt overhang.<sup>8</sup> A very stark example that illustrates how they could builds on the public finance constraint introduced in section 6.

Say that a government initially owes an amount D in a future period. It can raise an amount T < D by taxing rescurces in inelastic supply (like land) but must raise the rest by taxing the return to capital investment projects. These projects yield F(K) before tax, where K is the amount invested.

- F(O) 0, and F is increasing, but at a diminishing rate. If K is positive then the tax rate t is set so that D - T0 + tF(K). The after-tax return on domestic investment r H(K) is thus:

At K - 0 the marginal return to investment is negative infinity, since all the proceeds of any investment will be taxed to try to pay the debt. Hence, as long as there is a foreigr. investment opportunity (earning r ), then no investment (capital flight) is an equilibrium. There may also be another equilibrium with investment sufficient to repay the debt and provide a competitive return. Say that this investment amount is K*. In the flight equilibrium only T0 is repaid, while in the second, all is repaid.

Say that the expectation is that K* will be invested with probability i. Then the value of the debt i3 V(D) - (l-ff)T0<sup>+ irD,</sup> and the price p(D) - (l-ff)T0/D + ff.

Consider now a buyback of an amount B of nominal debt. If the probability of capital flight remains l-w as long as the possibility remains tSee, for example, Krugman (1989) and Helpman (1990).
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then buying back an amount B < D - T will occur at a price i + (l-w)TO/D. Debt service will be reduced by B with probability Xr and by -ApB with probability 1-Xf. The net effect on net resource transfers to creditors is: which, as before, is positive if A - 0 but negative if A - 1.

Consider, however, a buyback B > D-To if A - 0. Such a buyback ensures that nondistortionary taxes suffice to repay the remaining debt the next period. The possibility of a tax on investment is eliminated. Hence the probability of repayment is raised to one.

If creditors realize the extent of the buyback, the price of debt will rise to one, so debt must be bought at par. The debtor must spend B now and D-B the next period on debt. Hence the buyback makes full repayment certain. But the debtor's expected income over the two periods rises from w[F(K*)-D] + (l-w)[r K*-TO] to F(K*)-D, which is an increase as long as F(K*)-r K* 2 D-To, or as long as the difference between national incomes in the no-fliglht and flight cases exceeds the difference in debt repayment between those two casjs. The buyback benefits both parties in this example by eliminating possible distortions due to delay. Since capital is inelastically supplied in the short run but elastically supplied in the long run, fvture taxes to finance repayment provide more scope for distortion than curren. taxes. Hence a buyback, by moving more of the repayment up front, may require less distortionary taxation than the original repayment schedule.

Note, however, that if this argument has merit then the frequert claim that lengthnening maturities will alleviate debt problems is invalid. On the contrary, to impose the minimum excess burden, repayment is to be gotten over
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with quickly. Delay just increases the potential distortions imposed by raising the revenue needed to repay.

# _Buybacks and the Laffer Curve_

Note that the buyback may benefit both parties even though the situation is nct characterized by a "debt Laffer curve," contrary to claims that appear in the literature. Forgiving any amount of debt B less than D-T0 will cause expected repayment to fall by nB, while forgiving an amount in excess of D-T will cause expected repayment fall from iD - (1-n)T0 to below TO' In neither case does debt forgiveness increase the value of the debt.

In conclusion, a debt buyback can benefit a debtor. This requires, however, either that funds used to buy back debt reduce what is available subsequently for repayment (in which case the buyback is necessarily at the expense of the creditor) or that it reduce or eliminate a distortion associated with a debt overhang (in which case the buyback can benefit the creditor as well).
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# 10. Conclusion

Clearly, the issue of sovereign debt raises a large number of complex issues that have yet to be fully worked out. A reason that much work remains to be done is that most economic thinking has posited that contracts are automatically enforceable. But lack of enforceability is key to the sovereign debt problem. Morecver, sovereign debt raises issues that are intrinsically political as well as more traditionally economic. For sovereign debt to be amenable to economic analysis, our tool kits must be enlarged to allow for an analvsis of political outcomes.

Limitations of space and time have forced me to ignore a number of important issues that have received attention. Examples are the literature on bargaining between debtors and creditors (for example, Bulow and Rogoff (1989a) and Fernandez and Rosenthal (1990)), work on nontraded goods and the real exchange rate (see, e.g., Glick and Kharas (1984), Alexander (1987)), and the implications of land values and monopoly rents for foreign indebtedness (see, e.g., Eaton (1988,1989b)).

While much theoretical and empirical work remains to be done, it is clear from the experience of the last decade that international capital markets have not functioned smoothly: There is lictle reason to think that current institutional arrangements can achieve an outcome in which the marginal productivity of capital is the same everywhere. What capital movements have occurred have led to financial crisis, political conflict and government bailouts. An outstanding research issue is h- to motivate international financial institutions to do a better job.