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External Debt, Adjustment, and Burden Sharing: A Unified Framework



We introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that are characterized by persistent excess volatility in returns to capital. We explore a quantitative case for theselearning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time-series data for U.S. stock returns and per-capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can be explained by changes in investor expectations against a background of relatively small changes in fundamental factors.
No. 73, November 1992
published by the International Finance Section of the
Department of Economics of Princeton University. Al-
though the Section sponsors the Studies, the authors are
free to develop their topics as they wish. The Section
welcomes the submission of manuscripts for publication
in this and its other series. Please see the Notice to Con-
tributors at the back of this Study.
The authors of this Study are Ishac Diwan and Dani
Rodrik. Ishac Diwan is a Senior Economist at the World
Bank. He is the co-editor of Dealing with the Debt Crisis
(1989) and author of a number of articles on issues of
external debt. Dani Rodrik is Professor of Economics and
International Affairs at Columbia University, a Research
Associate of the National Bureau of Economic Research,
and a Research Fellow of the Centre for Economic Policy
Research. He is the co-author of Eastern Europe and the
Soviet Union in the World Economy (1991) and co-editor
of The Political Economy of Turkey (1990) and The Eco-
nomics of Middle-East Peace (forthcoming 1993).
PETER B. KENEN, Director
International Finance Section
No. 73, November 1992
Peter B. Kenen, Director
Margaret B. Riccardi, Editor
Lillian Spais, Editorial Aide
Lalitha H. Chandra, Subscriptions and Orders
Library of Congress Cataloging-in-Publication Data
Diwan, Ishac,
External debt, adjustment, and burden sharing : a unified framework / Ishac Diwan
and Dani Rodrik.
p. cm.—(Princeton studies in international finance, ISSN 0081-8070 ; no. 73)
Includes bibliographical references.
ISBN 0-88165-245-8 (pbk.) : $9.00
1. Debts, External—Mathematical models. 2. Debt relief—Mathematical models. 3.
Structural adjustment (Economic policy)—Mathematical models. I. Rodrik, Dani. II.
Title. III. Series.
HJ8015.D59 1992
336.3—dc20 92-40298
Copyright © 1992 by International Finance Section, Department of Economics, Princeton
All rights reserved. Except for brief quotations embodied in critical articles and reviews,
no part of this publication may be reproduced in any form or by any means, including
photocopy, without written permission from the publisher.
Printed in the United States of America by Princeton University Press at Princeton, New
International Standard Serial Number: 0081-8070
International Standard Book Number: 0-88165-245-8
Library of Congress Catalog Card Number: 92-40298
Without Conditionality 12
With Conditionality 14
Without Conditionality 16
With Conditionality 20
IFIs as Sources of Economic Information 22
Distributional Implications of Conditionality 23
Does Conditionality Require Lending by IFIs? 24
When IFIs Have No Prior Exposure 27
When IFIs Have Prior Exposure 28
Without Conditionality 43
With Conditionality 45
1 Composition of Debt Stocks of the Severely Indebted
Middle-Income Countries (SIMICS), 1982-1990 2
2 Composition of Net Transfers to the Severely Indebted
Middle-Income Countries (SIMICS), 1982-1990 3
3 Behavior of Net Transfers by the Severely Indebted
Middle-Income Countries (SIMICS), 1982-1990 7
4 Adjustment Costs for Early-Adjustment Countries 9
5 Upper Bounds on L
/Y 20
1 Second-Period Outcomes with No Adjustment or Overhang 12
2 Second-Period Outcomes with Adjustment but No Overhang 13
3 Second-Period Outcomes with Adjustment and Overhang 30
4 Second-Period Outcomes with Overhang but No Adjustment 35
We would like to thank—without incriminating—Giuseppe Bertola, John Wilton, and
an anonymous referee for helpful suggestions, and Dany Cassimon and Juergen Oedinius
for research assistance. The study reflects the views of the authors and not those of the
institutions with which they are affiliated.
The debt crisis initiated in August 1982 by the Mexican moratorium on
debt service has gone through many phases. Policymakers focused first
on the banking aspect of the crisis. A concerted response, led by the
International Monetary Fund (IMF) and the U.S. Federal Reserve,
allowed the commercial banks to reduce their exposure over time and
to boost their loan loss reserves. By 1985, the banking sector was no
longer in a state of imminent collapse, and attention turned to the
economic crisis in the highly indebted countries. Official intervention
concentrated on generating incentives and support for policies that
would allow the debtors to grow out of their debt problem.
By 1989, although several debtor countries were beginning to grow
again, it became clear that adjustment policies alone would not resolve
the debt crisis. The burden of providing new money had shifted con-
siderably to the International Financial Institutions (IFIs; see Tables 1
and 2), and a multilateral lending crisis loomed on the horizon. The
IFIs had begun to reduce their involvement, and adjustment programs
were failing for lack of sufficient financial support.
The Brady Plan,
announced in 1989, emphasized for the first time the need for com-
mercial-bank debt reduction, to be undertaken simultaneously with
adjustment programs financed by additional loans from the IFIs.
Several debt packages based on these principles have since been
negotiated for Mexico, Costa Rica, the Philippines, Venezuela, and
The debt crisis and the efforts to resolve it have raised three sets of
analytical issues. The first of these relates to the question of the debt
overhang, defined by Krugman (1988, p. 82) as “the presence of an
existing, ‘inherited’ debt sufficiently large that creditors do not expect
with confidence to be fully repaid.” The existence of a deep market
discount on the debt of a highly indebted government is prima facie
Net transfers to the IMF turned positive by 1986, when the credits granted in 1982
came due. Net transfers to the World Bank turned positive by 1988.
evidence of a debt overhang of this sort. The full resolution of the debt
(billions of dollars and percentages)
Share of Total Debt
Year Total Debt IFIs
1982 294 7.4 18.9 63.3 10.4
1983 348 7.1 18.2 64.5 10.3
1984 376 7.0 18.4 65.7 9.0
1985 416 8.3 22.7 60.0 9.0
1986 456 10.0 23.2 58.2 8.6
1987 500 11.6 25.1 55.2 8.1
1988 501 11.3 24.8 55.9 8.1
1989 496 11.9 25.7 53.3 9.1
1990 482 13.8 26.1 44.6 15.5
OTE: The SIMICS are Argentina, Bolivia, Brazil, Chile, the
Congo, Costa Rica, Côte d’Ivoire, Ecuador, Honduras, Hungary,
Mexico, Morocco, Nicaragua, Peru, Philippines, Poland, Senegal,
Uruguay, and Venezuela.
OURCES: World Bank, World Debt Tables, and authors’ com-
crisis requires that the debt overhang be eliminated and (in what
amounts to the same thing) that full repayment is expected by lenders.
Under what circumstances is this likely to come about?
It is widely recognized that the elimination of an overhang requires
the adoption of adjustment policies by the debtor country. The second
set of analytical issues therefore revolves around the question of
adjustment. There is little disagreement about the nature of the domes-
tic policies required: budgets must be brought under control, prices
liberalized, and exports stimulated by exchange-rate and other policies.
But when will governments have the incentive to undertake such
measures, and will adjustment be enough to eliminate the overhang?
The third set of issues has to do with the sharing of the burden of
debt relief among creditors. Under the Brady Plan, IFIs have borne
the brunt of new lending, while commercial banks have provided debt
and debt-service reduction (DDSR). What does this division of labor
imply for the distribution of the burden between these two kinds of
creditors? Further, what does any particular burden-sharing arrange-
ment imply for the elimination of the overhang and for returning the
debtors to creditworthiness?
(billions of dollars)
Total Net
1982 8.1 3.8 3.9 −3.9 4.3
1983 −2.4 8.5 3.1 −13.1 −1.0
1984 −12.0 5.2 1.4 −16.5 −2.2
1985 −19.5 2.7 0.5 −21.1 −1.7
1986 −23.9 0.7 −1.1 −21.1 −2.4
1987 −23.1 −3.1 0.0 −16.9 −3.1
1988 −30.2 −3.6 −0.2 −23.9 −2.5
1989 −24.4 −2.7 −2.3 −15.9 −3.5
1990 −39.6 0.4 −5.0 −25.3 −9.7
OURCES: World Bank, World Debt Tables, and authors’ com-
These issues, and especially the first two, have been analyzed exten-
sively. The typical research strategy, however, has been to take one
question at a time and to work with minimodels designed to make
particular minipoints. In view of the interrelationship among the issues,
we take a different approach here. We present a unified framework in
which all three sets of issues can be addressed in an internally consis-
tent manner. We use this framework to develop our arguments, and we
answer a sequence of questions along the way:
(1) What inefficiencies, if any, are caused by the presence of a debt
(2) Under what circumstances are new lending, debt reduction, or
both required to resolve the crisis?
(3) Under what circumstances is the presence of IFIs required to
arrange efficient deals between commercial creditors and debtors?
(4) Why do debtor governments need conditionality to undertake
reforms that are good for them?
(5) How is burden sharing accomplished under Brady Plan arrange-
Our objective is to clarify the issues and analytics, rather than to
present a solution to any specific model of bargaining.
It might be useful to state at the outset some of our main points.
The literature on the debt overhang has focused on the overhang’s
disincentive effect; it is alleged to discourage investment and income-
increasing adjustment measures because any increase in the debtor’s
income is likely to lead to an increase in its debt-service payments. We
argue that this disincentive effect is generally small, so that debt
reduction does not lead to important efficiency gains on this account.
Instead, we highlight the inefficiency created by the liquidity constraint
faced by overly indebted countries. This constraint is a natural conse-
quence of the overhang, because (1) new creditors are deterred from
lending because they expect to be “taxed” by the old creditors, who
stand to gain disproportionately, and (2) even if some new money is
available, debtor governments will be unable to commit themselves
credibly not to spend the additional resources on consumption. The
result is that investment and adjustment opportunities that are profit-
able at the shadow (world) interest rate go unexploited.
Conditional lending by IFIs can, under certain circumstances, untie
the knot. The ability to exercise conditionality is a source of compara-
tive advantage for IFIs relative to the old creditors. Conditionality can
overcome the time inconsistency introduced in the debtor govern-
ment’s policy by the shortage of liquidity and can prevent the debtor
government from squandering new money on consumption. The result-
ing efficiency gains can be shared between the debtor, the old credi-
tors, and the new creditors. In the absence of debt reduction by the
commercial banks, however, new lending by IFIs would transfer a
disproportionate amount of these gains to the banks. Hence, the role of
debt reduction is to create the “headroom” needed for these new and
more efficient creditors to step in without subsidizing the old creditors.
Put differently, we argue that the presence of the overhang necessi-
tates a three-sided bargain: the debtor government will undertake
adjustment policies only if additional resources are provided; the IFIs
can safely lend those resources only if commercial banks undertake
debt and debt-service reduction (DDSR); commercial banks, in turn,
will provide debt reduction only if, through conditionality, the IFIs can
make the debtor government adjust. These considerations provide a
plausible rationale for the tripartite arrangements among commercial
banks, IFIs, and debtor governments that we are now observing under
the Brady Plan.
Our framework has some implications for the design of such arrange-
ments. First, the higher the prior exposure of IFIs to the debtor
country, the smaller the debt and debt-service reduction that must be
provided by commercial banks. Second, under a certain “fairness”
criterion for burden sharing among creditors (which we call the pro-
portional-distribution rule), efficiency-enhancing packages will generally
fall short of completely eliminating the overhang. Third, deals with
“fair” burden sharing cannot rely on market buybacks and must involve
concerted debt reductions, because the price paid for debt in market-
based buybacks is the equilibrium price after debt reduction. Fourth,
presenting commercial banks with a menu of debt-reducing options can
fruitfully combine the desirable characteristics of both concerted and
voluntary debt-reducing mechanisms. We shall discuss and illustrate
these points using a unified analytical framework.
We begin with the problem of a government that has a debt overhang
and that must decide whether or not to undertake an adjustment
program (Chapter 2). Adjustment could eliminate the overhang, but, in
the absence of external financing, the immediate costs would be too high
relative to the future benefits. We then look at the set of strategies
available to the commercial banks and characterize the types of arrange-
ments that the creditors and debtor could work out, with and without
conditionality (Chapter 3). Next, we turn to the design of debt-relief
packages, asking how the basic parameters of the package affect the
distribution of the burden between commercial creditors and IFIs
(Chapter 4). We also analyze the burden-sharing issue in the context of
arrangements of the Brady type, in which debt is repurchased at a price
(Chapter 5) and creditors are offered a menu of options (Chapter 6).
It is the interdependence between the actions of foreign creditors and
the investment decisions in the debtor country that renders the debt
problem complicated and conceptually interesting. From the creditors’
perspective, it is desirable that the debtor undertake all appropriate
investment projects, as this increases the likelihood that the debt will
be repaid. The overhang and the constraint on foreign borrowing,
however, distort the intertemporal relative prices faced by the debtor
and result in inefficient investment decisions. Understanding how this
inefficiency comes about is critical, for any “solution” to the debt crisis
is in large part an attempt to deal with this problem.
The existing literature has focused largely on the role of the debt
overhang as a tax on future output. In this particular explanation, the
disincentive effect of the overhang arises from the likelihood that an
increase in the output of a country in overhang will lead also to an
increase in its debt service. Therefore, the proceeds of domestic
investment will be shared with foreign creditors. In principle, this acts
just like a tax on investment, decreasing the social return to domestic
investment (see Krugman, 1988; Sachs, 1984; Cohen, 1990; Helpman,
1989; and Corden, 1989).
Conceptual and empirical problems with this story greatly diminish
its relevance. There is no compelling conceptual reason to believe that
an aggregate “tax,” if it exists, will be internalized in private investment
behavior: from the perspective of an individual investor, the aggregate
transfer to creditors is an exogenous constant and is thus unaffected by
the investor’s decisions. Consequently, even if the social disincentive
were large, the private disincentive would still be small.
Furthermore, the importance of the overhang “tax” on investment is
much in doubt empirically. From all indications, both the average and
marginal tax rates implied by debt service are small. Net transfers to
creditors rarely exceed 4 to 5 percent of gross national product (GNP).
The marginal tax rates are, if anything, even lower. Table 3 shows the
results of regressing net transfers on gross domestic product (GDP)
and other variables. We find that, on average, less than two cents of
any dollar increase in income is actually captured by creditors (see also
Eaton, 1990). Moreover, this tax seems to be imposed by official
creditors rather than commercial creditors. Single-country investment
equations (for example, Borensztein, 1990, for the Philippines,
(billions of dollars)
Dependent Variables
Independent Variables
Net Transfers
Net Transfers to
Commercial Banks
Net Transfers to
Official Sector
Total Debt 0.1251
Commercial Debt 0.0997
Official Debt 0.0835
GDP 0.0182
Exports of Goods
and Services
Dummy for
IMF Program
N 171 171 171
0.84 0.79 0.57
OTE: Positive net transfers indicate transfers to the creditors (see also Table 1).
Standard errors are in parentheses. Regressions include country and year dummies.
Significant at 1-percent level
Significant at 5-percent level
OURCE: World Bank, World Debt Tables.
Schmidt-Hebbel, 1989, for Brazil, and Morisset, 1991, for Argentina)
and panel regressions (for example, Ozler and Rodrik, 1992) often find
a negative relation between indebtedness and investment. Such regres-
sions, however, do not shed light on the precise channel of causality
that links high debt to low investment.
In light of these considerations, we think it is appropriate to de-
emphasize the tax-on-future-output aspect of the overhang. We high-
light, instead, the factor of illiquidity, which we believe has much
greater empirical relevance. The real cost of the overhang is that many
high-yielding investments in debtor countries go unexploited because
these countries are shut out of credit markets and cannot borrow. One
particular set of such investments is called “adjustment policies.” Just
like other investments, adjustment policies have benefits in the long run
but costs in the short run (see below).
The first step in our analysis focuses on the interaction between the
adjustment decision and the actions of creditors. We consider a debtor
government that has to decide whether or not to adjust. For the
moment, we treat parametrically the extent of debt reduction and/or
new lending that creditors grant this government. For each combination
of debt reduction and new lending, we seek to determine whether the
government undertakes adjustment policies and whether the country
remains in overhang. In other words, we trace out the adjustment and
overhang consequences of every possible debt-relief package offered by
the creditors. To emphasize the difference made by conditionality, we
work out in parallel the cases of both nonconditional and conditional
Our view of adjustment policies followed by debtor countries has two
key features. The first, primarily for analytical convenience, is that
adjustment is an all-or-nothing affair. Governments choose either to
adjust or not. This rules out the possibility, which certainly exists in
reality, that the amount of adjustment effort may vary depending on the
circumstances. Because we will view the adjustment decision as the
consequence of rational cost-benefit calculus, however, practical benefits
flow from treating the adjustment decision as a binary one. For one
thing, this treatment leads to more realism than the smooth case in
which the marginal costs and benefits of the adjustment effort are
continuously balanced, and the country gains nothing—thanks to the
envelope theorem—from an increase in adjustment induced by a change
in, say, external lending. Moreover, our formulation will allow us to
downplay the “tax” aspect of the debt overhang, which, as we argued
above, has limited empirical content.
The second feature, which is critical to the story that follows, is that
adjustment requires incurring some fixed costs immediately, whereas the
benefits of adjustment come, not immediately, but over time; in the con-
text of a two-period model, they arrive in the second period. This is a
realistic representation of most policy reforms. Any stabilization program
that works is likely to be recessionary in the short run. Structural
reforms likewise create costs in the short run, either economic or
political costs. It is this feature that makes adjustment programs formally
identical to investment; in each case, a cost is incurred immediately to
reap a reward in the future.
Some support for this view is provided in Table 4, which shows that
(percentage points)
Period Dummies Loss in GNP
t = −2 −2.4
t = −1 −3.1
t = 0 −5.1
t = 1 −4.7
t = 2 −2.0
t = 3 −2.3
N = 125 R
= 0.119
OTES: The independent variable is the deviation of annual
growth in GDP per capita, adjusted for terms-of-trade shocks,
from the trend of growth in GDP per capita during 1960-1980.
The adjusted annual growth rate of GDP per capita is from
Summers and Heston (1988). The trend of growth in each
country was computed by regressing growth in GDP per capita
on a time variable.
Period dummies: t = 0 refers to the year in which an IMF
program was first signed between 1977 and 1987; t =−i refers
to i years and t = j refers to j years after.
Data set: Early-adjustment countries are those having re-
ceived two structural-adjustment loans from the World Bank,
the first in or before 1985. All had IMF standby agreements.
OURCE: World Bank, Adjustment Lending Policies for Sus-
tainable Growth, 1990.
economic performance typically follows a U-shaped pattern in countries
undergoing adjustment. Countries that have undertaken adjustment
programs with intensive support from the IMF and the World Bank
have lost on average 3.1 percent of output in the year before the
program, 5.1 percent in the first year of the program, 4.7 percent in the
second year, and 2.0 percent in the third year. These estimates correct
for trend growth and for terms-of-trade shocks. Nevertheless, they
This view is consistent with the justification often provided for adjustment lending by
IFIs. Ernest Stern (1991, p. 4), the World Bank vice president who played a key role in
initiating structural-adjustment loans, writes: “We provide quick-disbursing loans because
the actions being undertaken by the government have some balance of payments impact,
some additional costs that we can help defray.” See Gavin (1991) for a coherent exposition
of this view in a well-specified theoretical model.
should be taken with a grain of salt. On the one hand, they are biased
upward, because these countries would have lost growth opportunities
by not adjusting. On the other hand, countries that choose to adjust are
likely to be those for which adjustment costs are the lowest, and this
selection bias is likely to lower our estimates of the short-run costs.
We now turn to a more formal analysis of the adjustment decision. The
government starts out with an inherited debt that carries a face value D.
In the first period, it is offered a package from the commercial banks
that consists of debt reduction in amount B and new loans in amount L.
We shall look more closely at the banks’ incentive to offer some debt
relief in the next chapter; for the moment, we take B and L as given.
Confronting this package, the government decides whether or not to
undertake an adjustment program. Adjustment “costs” a fixed amount,
K, in period one but increases output from Y to Y(1 +
) in period two.
The government enters period two with an existing stock of debt
amounting to R(D B + L), in which R is 1 plus the world interest rate.
If it fails to repay the debt in full, creditors are able to penalize the
country by a fraction,
, of output. At this point, we do not have to take
a stand on whether
represents a transfer to creditors or is a dead-
weight loss. The essential point is that the debtor suffers a cost when it
interrupts debt service.
The presence of an overhang at the outset is
ensured by assuming that the country would not choose to repay the
debt in full in the absence of adjustment and/or debt reduction because
the cost of repaying it in period two exceeds the penalty for default, that
is, RD >
We assume that the government seeks to maximize a conventional
welfare function, in which second-period utility is linear in consumption.
Following Froot (1989), we represent the government’s problem as
Government’s decision problem (without conditionality)
max W = U(C
Y + L K , if adjust,
s.t. C
Y + L , otherwise.
These costs can include exclusion from international borrowings and interference with
international trade flows. Much has been written showing how international lending can
be supported by indirect sanctions and how the severity of such sanctions determines
credit ceilings. See, in particular, the seminal work of Eaton and Gersovitz (1981), Kletzer
(1984), and Bulow and Rogoff (1989a). For surveys of the literature on sovereign lending,
see Eaton, Gersovitz, and Stiglitz (1986) and Kletzer (1988).
max [Y(1 + )−R[D B + L,(1−)Y(1 + )] , if adjust,
max [Y R(D B + L), (1
)Y] , otherwise.
U(.) is assumed to be concave to guarantee an interior solution. Because
the government can always choose not to repay the debt when that
choice is profitable, second-period consumption is the larger of the
levels with and without default. For completeness, we allow for the
possibility that the overhang may be eliminated even in the absence of
adjustment (thanks to sufficient debt relief B), even though banks will
have no incentive to provide DDSR in such a case.
In what follows, we
assume that the government remains credit rationed in all relevant cases,
so that it views increased borrowing as always desirable. This is guaran-
teed by assuming U >
R throughout (that is, for all relevant C
The formulation above assumes that creditors have no control over
what the government chooses to do with the new loan, L. This can be
seen by noting that C
equals Y + L rather than Y when the government
chooses not to adjust. Under conditional lending, however, the govern-
ment is forced to adjust whenever L > 0. Therefore, conditionality
changes the problem faced by the government, which now reads as
Government’s decision problem (with conditionality)
max W = U(C
Y + L −K,ifadjust,
s.t. C
Y , otherwise.
max [Y(1 +
)−R(D B + L), (1 )Y(1 + )] , if adjust,
max [Y R(D B), (1
)Y] , otherwise.
This is different from the problem defined by (1) in that L is set to zero
in the nonadjustment states.
There are four possible outcomes in the second period, each of which
describes a different zone in (B, L) space:
Zone I: no adjustment, no overhang;
Zone II: adjustment, no overhang;
The overhang will not be eliminated unless R (D + L B) ␾⌼, which cannot be
true unless B > L, because RD >
␾⌼ by assumption. Note, also, that no debt payments
are due at the end of the first period in this model. In the presence of first-period debt
repayment, new money will be equivalent to debt-service relief in the first period.
If the debtor is provided with less than L
in new lending, it may still
choose to adjust. But it will do so only if it also receives enough debt
reduction to eliminate the overhang. This is shown in Figure 1. When
L < L
,aB high enough to eliminate the overhang will push the
debtor from zone IV (no adjustment and overhang) to zone II (adjust-
ment and no overhang). Debt reduction enhances the adjustment
incentive in this region because the implicit investment tax (discussed
previously) goes away when the overhang disappears. In the absence of
the overhang, the productivity benefit of adjustment appears larger.
When the availability of new lending falls below L
, however, no
amount of debt reduction will be enough to prompt the debtor to
In this case, the inability to smooth consumption through
borrowing shows its bite. In the absence of borrowing, the marginal
utility of consumption stays high enough in the first period relative to
the second period to leave adjustment a bad bargain. The magnitude of
B can then determine only whether or not the debtor remains in
To summarize, we note some of the key features of the outcomes
depicted in Figure 1. First, debtor government will always choose to
adjust for a sufficiently large amount of new lending, even in the
absence of conditionality. The primary reason is that adjustment is
assumed to be a good bargain for the country when it can borrow at
world interest rates. Second, a sufficiently large amount of debt reduc-
tion will always eliminate the overhang. Still, the country generally needs
both new money and debt reduction to eliminate the overhang and get
the government to adjust (that is, to reach zone II). One alone will not
always do the trick. New money tends to enhance the incentive to adjust
by alleviating the short-run costs, but it renders overhang more likely
down the line. Debt reduction works against the overhang but has
uncertain effects on the incentive to adjust. In terms of Figure 1, debt
reduction increases the likelihood of adjustment only when L lies
between L
and L
. The appropriate strategy, therefore, must involve a
bit of both.
With Conditionality
The results under conditional lending are qualitatively very similar to
those just discussed. In particular, the basic geometry of the partitions
in Figure 1 remains unchanged (save for some second-order differences
discussed in the Appendix). Once again, both debt reduction and new
Formally, there is no guarantee that L
will be positive. We assume for this discussion
that it is.
lending are required to achieve debt reduction and simultaneously to
eliminate the overhang.
Conditionality, however, has important effects on the sizes of the
various zones in Figure 1. Conditionality enlarges the set of (B , L)
combinations under which the debtor government finds it advantageous
to adjust. Therefore, the no-adjustment zones (I and IV) shrink in favor
of the adjustment zones (II and III). The enlargement is indicated in
Figure 2 by the shaded areas: zone II (adjustment with no overhang) is
now larger by the single-hatched area, and zone III (adjustment with
overhang) is now larger by the double-hatched area.
The reason is easy to understand. Conditionality changes the nature
of the bargain between creditors and the debtor government by making
the package conditional on adjustment being undertaken. It therefore
alters the cost-benefit calculus of the government, which has now to
compare the cost of adjustment against the cost of having to give up
external financing. When the choice is between adjusting with new
money and not adjusting without new money, it will take a lower amount
of external financing to purchase adjustment compared to the case in
which new money is disbursed unconditionally. Moreover, we shall show
that the debtor could end up being better off with conditionality, as the
alternative may be no deal at all once the creditors’ behavior is endogen-
ized. For similar discussions of conditionality, see Sachs (1989) and
Claessens and Diwan (1990).
As in the previous case, we can define the minimum amount of new
lending required to purchase adjustment, irrespective of overhang status.
It is denoted by L
in Figure 2, with the subscript indicating that it
applies to the case of conditional lending. In the Appendix, it is shown
that L
has the same qualitative properties as L
, except that it is always
= L
(, , , K)<L
. (3)
Once again, the debtor will adjust for L
L < L
, but only if sufficient
debt reduction is provided to eliminate the overhang. For any given L,
however, less debt reduction is necessary for this purpose, just as less
new money is now required to prompt adjustment (see Figure 2).
Note, finally, that L
< L
The presence of conditionality therefore reduces the magnitude of
lending required to elicit adjustment policies from the debtor. We shall
show in the next chapter that this greatly increases the likelihood that
there will be efficiency-enhancing bargains between debtors and
In the previous chapter, we looked at the debtor’s behavior in response
to combinations of new money and debt reduction offered by creditors.
The debtor’s decision on adjustment, together with the package offered
by the creditors, determined whether the overhang would be eliminated.
We now turn to the behavior of the creditors themselves. We focus,
first, on the case without conditionality and ask under what circum-
stances commercial banks will have the incentive to offer a package of
new money and debt reduction and what such a package would look
like. In other words, we ask under what circumstances the debtor
government and the banks can reach mutually advantageous bargains in
the absence of conditionality. The answers to these questions will
provide the benchmark against which to evaluate the possible bargains
with IFI conditionality.
Without Conditionality
Let us assume that commercial banks can overcome the coordination
problem inherent in their interactions with the debtor government and
can thus act collectively. We should expect them to be aware of the
possibility, portrayed in Figure 1, that they can influence the behavior
of the government by offering an appropriate package of new money and
debt reduction. Let us first discuss the returns to banks in different
zones of Figure 1.
When the country is in overhang, the face value of the debt out-
standing is irrelevant to the banks’ payoffs. We denote by
the net
transfer, expressed as a proportion of the debtor’s GDP, that creditors
receive in the case of overhang. As discussed earlier, this transfer is
probably small at the margin. The regression results in Table 3 suggest
is around 1.8 percent for creditors as a whole. The transfer is
bounded above by the cost incurred by the debtors,
, because that cost
includes deadweight losses such as the loss of trade credits and foregone
trading opportunities. The banks’ payoff in period two can therefore be
written as
Y(1 + )−RL , when the country adjusts (zone III)
(B, L)=
Y RL , otherwise (zone IV) . (4)
Note that banks’ payoffs are independent of B as long as the overhang
prevails, because B affects only the face value of the debt in this case.
Also note that the opportunity cost of the new money, RL, should be
subtracted from period-two payoffs. Giving new money makes sense to
the banks only if it makes the country adjust. Such “defensive lending”
is meant to increase the share of the old debt that will be repaid
(Krugman, 1985). Expression (4) makes it clear that the banks’ iso-
profit loci are vertical lines in zones III and IV, where there is over-
hang. For lower L (less new lending), bank payoffs are higher.
In the no-overhang zones, the analogous expression for bank payoffs
(B, L)=R(D B) (zones I and II) . (5)
L does not enter this expression because we assume that the interest
charged on the new loans matches the opportunity cost of funds,
making banks indifferent to lending when they can recover their
money. We could have assumed that banks receive excess payoffs on
their loans to creditworthy clients without altering qualitatively any of
the subsequent results. In any case, expression (5) makes bank iso-
profit curves horizontal lines in zones I and II, with lower lines repre-
senting higher payoffs.
To abstract from bargaining issues, let us suppose that banks move
first and can make a take-it-or-leave-it offer to the debtor country.
What will they do? By inspecting Figures 1 and 2 in conjunction with
the bank iso-profit lines, we can see that there are three possibilities:
(1) No deal. This outcome is represented by the origin in Figures 1
and 2, with B = L = 0. In this case, the government chooses not to
adjust, and the country remains in overhang. Incidentally, a small
amount of debt reduction (small in that it does not push us into zone
I) would not hurt the banks or benefit the country, as it would not
affect the country’s decision concerning repayment in the second
(2) The banks offer a package that consists of L
new money and
debt reduction ranging between zero and B
. One such package is
indicated by point X in Figure 2. The country gets enough financing to
adjust, but the banks are indifferent as to whether or not the overhang
This is due to the absence of uncertainty in this model. When period-two outcomes
are uncertain, hanging on to the higher face value has an option value for the banks,
arising from the possibility that the debt will be serviced fully in some good state of
is eliminated, because they can extract no more that Y(1 + ) from
the country; they get the same return whether they provide debt
reduction (the minimum needed to eliminate the overhang), no debt
reduction at all, or something between the two.
(3) The banks offer a package that consists of L
< L
, and B
< B
but just enough to eliminate the overhang and induce the country to
adjust. This package is shown as point Y in Figure 1. It puts us just
inside zone II, eliminating the overhang while ensuring adjustment.
Such a package is feasible only when the border separating zones II
and IV has an interior minimum, as in Figure 1, or is positively sloped
Banks want to ensure that the overhang is eliminated in
this case, unlike case (2) above; otherwise, the country would rationally
choose not to adjust, reducing the banks’ payoff. A slight reduction in
B starting from point Y would put the country in a no-adjustment zone.
In summary, the alternative offers are (1) no deal, (2) a package that
ensures adjustment but may or may not eliminate the overhang, and
(3) a package that ensures both adjustment and return to creditworthi-
ness. One of these three will dominate all other possible deals.
We have next to determine whether packages like (2) and (3) domi-
nate the no-deal option. The critical consideration here is the fact that,
even when the overhang is eliminated, banks can extract no more than
the fraction,
, of the increment in domestic output, Y, resulting from
adjustment. Consequently, they will have no incentive to spend more
than this amount to “purchase” adjustment.
This can be put a bit more formally. Consider bank payoffs when the
package (B
, L
) is offered. They are (B
, L
)=(0, L
)=Y(1 + )−
. With no deal, banks get (0, 0) = Y. Therefore, the condition for
the package to be offered is
Y(1 + )−RL
Y, implying
( , , , K) ␣␪Y/R . (6)
The right-hand side is the discounted value of the fraction of the
productivity increase captured by the creditors. The left-hand side is
the amount of new lending. This condition has a straightforward
intuitive explanation. The minimum amount of new money required to
induce the country to adjust must be less than the additional payment
to the creditors when the debtor does adjust. If L
falls short of this
value, banks will offer a deal.
See the Appendix for a discussion of this issue.
It can be shown that an increase in the effectiveness of adjustment
, and in the share of the debtor’s income transferred to credi-
, make it easier for this condition to be fulfilled. Correspondingly,
an increase in the cost of default,
, and in the short-run cost of
adjustment, K, render the condition more stringent.
What kind of practical guidance does expression (6) provide as to the
likelihood of a mutually advantageous deal? The right-hand side of the
inequality depends on two critical parameters,
and , both of which
are observable in principle. For
, a range of 1 to 4 percent of GDP
would seem reasonable for most highly indebted countries. The mar-
, as estimated in Table 3, is about 1.8 percent, while the average
is somewhat larger. An estimate of , which measures the permanent
productivity benefit of adjustment, can be made by conventional
techniques, such as those used at the World Bank and the IMF. Let us
assume, to be generous, that adjustment can increase the level of
output permanently by something in the range of 10 to 40 percentage
points. Further, we take R to be 1.1.
Putting all these pieces together, we get the numbers shown in Table
5. These numbers satisfy the sufficient condition (6). The table should
be read as follows: For example, when
is 2 percent and adjustment
provides a 20-percent permanent increase in the debtor’s income, the
largest increase in exposure banks are willing to accept during the
whole adjustment period is 0.36 percent of the country’s GDP. If this
amount of new money is enough to make the country undertake the
required adjustment once the money is disbursed, then banks will be
willing to offer such a package. Because adjustment episodes cannot be
expected to succeed in fewer than three to five years, the numbers in
the table must be divided by a factor of three to five to yield the
maximum annual disbursement that banks will be willing to offer. This
translates into very small annual flows, much smaller than the amounts
countries regularly obtain from the IFIs in exchange for adjustment
Hence, these illustrative calculations are not encouraging with
respect to the likelihood that banks and debtor countries will discover
mutually advantageous bargains on their own. The main problems are
twofold. First, when the creditors’ share of the productivity gain from
adjustment is small, their incentive to put up new money to “purchase”
adjustment is correspondingly low.
Second, when debtors are credit
In fact, taken literally, the results in Table 3 suggest that, at the margin, may not
be different from zero for commercial creditors. This would rule out the possibility that
banks, acting on their own, would be willing to offer any new money.
constrained, a lot of new money is needed to induce them to undertake
(percentage points)
Creditors’ Share of Income ()
1 2 3 4
10 0.09 0.18 0.27 0.36
20 0.18 0.36 0.54 0.73
30 0.27 0.54 0.82 1.09
40 0.36 0.73 1.09 1.45
OTE: is the permanent increase in
the level of GDP due to adjustment.
adjustment; they would rather use the money to increase consumption.
With Conditionality
The inclusion of IFIs in creditor-debtor arrangements may help with
both problems mentioned above. It will help with the first if the IFIs
are somehow better than commercial banks at capturing part of the
increase in the debtor’s income. The regressions results in Table 3
suggest that this may be the case. More importantly, thanks to condi-
tionality, IFI participation will help with the second problem. The
presence of conditionality relaxes substantially the constraint embodied
in expression (6).
To see this effect, consider the type of package that creditors might
be willing to offer the government when conditionality is present. The
relevant options are (1) no deal (L = B = 0) and (2) a package that
consists of L = L
and (B between 0 and B
). Other options are domi-
nated by one of these two because creditors’ profits are increasing in
the southern direction in zone II and because the slope of the border
separating zones II and IV is unambiguously negative under condition-
ality (see the Appendix).
The creditors will prefer a debt package to inaction under a condi-
tion analogous to the previous one, namely,
(, , , K) ␣␪Y/R . (7)
There is also a distinct possibility that the creditor group as a whole would not be able
to provide an efficient level of new money because of coordination problems within the
group. Each bank has an incentive to free ride on other banks’ contributions without
providing a fair share of the burden (see, for example, Sachs, 1986).
But L
< L
, as shown previously, so this is a less restrictive condition
than the one in the absence of conditionality. In other words, condi-
tionality expands the range of mutually beneficial bargains between
banks and the debtor government. This is because less new money is
required to purchase adjustment when lending is conditional.
For conditionality to make much difference in practice, however, the
gap between L
and L
has to be a meaningful number. Can we say
anything about the size of the gap?
We can arrive at some rough approximations by undertaking a few
manipulations. Remember that L
is defined as the level of new lend-
ing that makes the debtor indifferent between adjusting (thereby
incurring the short-term cost K) and not adjusting (thereby foregoing
the productivity improvement
). Therefore, L
is implicitly defined by
U(Y + L
K)+(1 )Y(1 + )=U(Y + L
)+(1 )Y .
Similarly, L
is implicitly defined by
U(Y + L
K)+(1 )Y(1 + )=U(Y)+(1 )Y .
(Note that L = 0 in the conditional case if the debtor chooses not to
adjust.) Combining these two equations, we can write
U(Y + L
)−U(Y + L
K)=U(Y)−U(Y + L
Now assume that utility is logarithmic. Rearranging terms, we get
log(Y + L
) log Y = log(Y + L
K) log(Y + L
We can interpret each side of this equation as approximating a percent-
age change. As long as L
, L
and K are small relative to Y, this will not
a bad approximation. Hence,
/Y (L
)/(Y + L
and simplification yields
K/(Y + L
) . (8)
This is an interesting result, showing that the ratio of L
to L
is roughly
of the order of the short-run adjustment cost relative to GDP. As it is
difficult to imagine that adjustment costs will exceed 10 percent of
income, L
will normally be a very small fraction of L
. In fact, the
evidence in Table 4 suggests that K may be of the order of 2 percent
of GDP. Correspondingly, L
must be very small. If this illustrative
calculation is any guide, conditionality can make a big difference
indeed. By greatly reducing the requisite inflow of new money, it
considerably enlarges the parameter space within which a mutually
advantageous bargain between creditors and debtors becomes possible.
An important caveat, of course, is that conditionality must be rela-
tively effective or at least be perceived as such. There is a vast litera-
ture on conditionality that makes it clear the process rarely operates in
the idealized fashion we have modeled here.
World Bank and IMF
studies tend to claim limited success for adjustment programs, but
other analysts have raised questions about these conclusions. The main
empirical difficulty is that it is not easy to isolate the effect of adjust-
ment lending from other phenomena affecting a country’s performance,
such as external shocks, prevailing distortions, and the extent of in-
volvement of other lenders.
Because conditionality cannot be perfect, the IFIs are exposed to
two sources of risk. The first is the risk that conditionality will not work
because of weak monitoring or faulty design. We say nothing in this
study about the ways to reduce this type of risk. The second risk is that
the IFIs’ loans will not be fully repaid because the line of creditors is
too long relative to the debtor’s repayment capacity. The core of our
analysis is concerned with the reduction of this second risk.
IFIs as Sources of Economic Information
IFI participation can have other advantages besides conditionality. In
particular, IFIs can play a positive role by acquiring and disseminating
useful economic information. Mutually advantageous bargains can be
ruled out not only by the inability of governments to commit them-
selves credibly to adjustment, but also by asymmetric information.
In general, commercial banks are poor judges of the cost of adjust-
ment, K, or the productivity enhancement,
, in individual countries.
Under asymmetric information of this sort, they are likely to be more
conservative in spending new money than they would have been under
complete information. This is all the more likely because debtors will
have the incentive to “cheat” by claiming low K or high
, factors that
make adjustment more likely and profitable, in order to qualify for new
loans. In a “pooling” equilibrium, deserving countries will be denied
mutually beneficial packages. In a “separating” equilibrium, countries
Particularly informative are Polak (1991), Kenen (1986), Sachs (1989), Finch
(1989), and the reports on adjustment lending by the World Bank (1988, 1990, and
1992). For a game-theoretic treatment of conditionality, see Mosley (1987).
will have to invest in costly signals to qualify for those packages.
either case, some efficient outcomes will be ruled out.
The IFIs themselves cannot observe perfectly all of the relevant
debtor characteristics. They can be somewhat better than the banks at
monitoring debtors, however, in view of the specialized skills and
different incentives of their staff.
Debtor countries are subject to
almost continuous analysis by desk economists in the IFIs. To the
extent that IFIs can disseminate “harder” information, they will allow
some deals to be struck that may have otherwise been missed.
Distributional Implications of Conditionality
Consider the effect of conditionality on the debtor’s welfare. The
debtor’s welfare is increasing in L as long as the debtor remains credit
constrained, and it is also increasing in B in the no-overhang regions
(in the presence of an overhang, changes in B have no effect). There-
fore, the debtor becomes better off as we move in the northeasterly
direction in Figures 1 and 2. This leads to the important conclusion
that, as long as banks choose not to offer a deal in the absence of
conditionality, the debtor country will always be at least as well off
with conditionality as without. In this instance, conditionality benefits
the debtor because it provides it with the ability to precommit and
therefore avoid the damage caused by the dynamic inconsistency of
adjustment policy. Note, however, that, when creditors move first and
can make a take-it-or-leave-it offer, they can skim off the entire surplus
from the debtor; when the debtor is offered (L
, B
), it is indifferent
between adjusting and no deal. In practice, the surplus is likely to be
shared between the creditors and the debtor.
There is another possibility. Suppose that banks offer a package that
includes both debt reduction and new money, even in the absence of
IFI involvement. In terms of Figure 2, the point X will offer a higher
return to the banks than if they do nothing. With conditional lending,
the banks can do better; they can offer a package consisting of lower L
and lower B. The banks will now be better off, whereas the debtor
government will be worse off. In this case, banks will have been willing
to “bribe” the government to adjust, and conditionality will have
Acharya and Diwan (1989) study the possibility that market-based debt buybacks
are used to signal the willingness of a country to undertake adjustment. Rodrik (1989)
analyzes the case of a well-meaning government attempting to distinguish itself from a
purely redistributive government that is not interested in reform.
See Gwyne (1986) for a now classic account of the short-sightedness in commercial-
bank lending practices.
reduced the needed bribe. Note that banks in this situation will now
have the incentive to “game” against the IFIs, trying to draw them into
the action. The debtor will be harmed if they succeed, however, which
was not so in the previous case.
Our second conclusion is, therefore, that conditionality and IFI
involvement will not always improve the outcome from the combined
perspective of the banks and the debtor. The debtor, in particular, can
be made worse off. The essential criterion is whether the banks are
willing to offer a package in the absence of IFI involvement. If not,
IFI involvement will improve matters for both sides as long as there
are genuine efficiency gains initially. If the banks offer a package
without IFI involvement, the IFIs would have to set conditions to
ensure that the gains are not appropriated disproportionately by the
banks. Remember, however, that the second situation is unlikely in
view of the illustrative calculations given above. Hence, the chance that
IFI involvement will actually hurt the debtors is perhaps not great.
Does Conditionality Require Lending by IFIs?
One point has thus far been finessed in the discussion. Why could IFIs
not simply put their imprimatur on adjustment programs and monitor
program implementation, without lending money? We have seen, after
all, that, once conditionality is in place, commercial banks should be
willing to come up with the requisite new lending, provided there are
efficiency gains.
A situation in which IFIs provide only conditionality and no money
of their own, however, is unlikely to be acceptable to either the banks
or the debtor government. Consider the banks first. Commercial banks
are apt to be suspicious of the quality of the monitoring done by the
IFIs if the latter have little incentive to do a good job. They will
naturally want the IFIs to put their own resources at risk alongside
those of the banks. The debtor governments, for their part, are less
likely to accept conditionality imposed by a foreign institution, with all
the meddling in domestic policy that this entails, when it comes with-
out any resources directly attached to it. The IFIs are often suspected
of doing the commercial banks’ dirty work for them; if conditionality
This point is developed in Claessens and Diwan (1990).
Bulow and Rogoff (1989b) argue that, because creditor-country taxpayers have a
vested interest in maintaining normal trade with the debtor country, they can sometimes
be bargained into making side payments to both lenders and borrowers through dis-
bursements by the IFIs.
comes without money, what better proof can there be that this is
indeed the case?
Another reason why IFIs provide money is to protect their previous
exposure. Remember that the primary motive for banks to lend good
money after bad is to improve the chances of recovering previous
debts. The IFIs may have a similar incentive.
In their roles as creditors, commercial banks and IFIs differ in at least
two respects. First, the prior exposure of the IFIs to the debtor may be
substantially different from that of the bank group. Second, IFIs do
not, as a rule, provide debt and debt-service reduction. These differ-
ences between the two groups raise questions regarding the distribu-
tion of the burden of debt relief between them. What is an appropriate
burden-sharing rule when the two classes of creditors differ in these
respects? How do the basic parameters of the debt-relief package—the
share of new money coming from IFIs, the magnitude of DDSR—
relate to the distribution of the burden between the two classes? When
is a “fair” distribution of the burden compatible with the elimination of
the debt overhang?
Answers to these questions are critical for designing packages that
achieve their objective. To provide a framework, we build on the
results of the previous chapters and proceed step by step to consider
the various elements of a package. Starting in this chapter with the
simplest case, we consider a package in which the proportion,
, of the
new money L is supplied by IFIs and (1
)L is provided by the
commercial banks. In addition, banks undertake to write off B amount
of debt. This is tantamount to a portion of the debt being retired at a
price of zero. In the next chapter, we shall consider arrangements
more reminiscent of actual Brady deals, in which debt is retired at a
positive price and IFIs provide the resources necessary for the repur-
The IFIs will not provide conditional loans unless they are assured
of receiving some minimum repayment. In general, this repayment may
be smaller than the cost of capital if the IFIs’ objective function also
includes other elements such as the welfare of the debtor countries or
the preservation of international trade. Still, some measure of profit-
ability must certainly be one of the IFIs’ objectives in the long run.
An important ingredient of the analysis is the relative seniority of IFI
and commercial debt. Our crucial assumption is that the repayment to
the IFIs will be reduced in the presence of a large commercial debt.
As a result, the IFIs will not make loans to over-indebted countries
unless the previous creditors provide some debt relief. This assumption
is satisfied when IFIs are not senior to commercial creditors in a
strictly me-first sense. There is no firm evidence on the issue of senior-
ity, but recent work casts serious doubt on IFI seniority. Demirguc-
Kunt and Fernandez-Arias (1992) find that the disbursement of IFIs’
loans to noncreditworthy countries does not have any significant effect
on the price of commercial debt in the secondary market, suggesting
that such loans are in fact junior. By contrast, official bilateral debt
significantly reduces the price. Bulow and Rogoff (1992) argue that
IFIs will be treated as senior as long as their claims on a country are
small enough to allow for positive future net disbursements and as long
as bilateral donors find the services rendered by the IFIs valuable
enough for the donors to earmark disbursements to the debtor so the
debtor can meet his obligations to the IFIs. In other cases, however,
they argue that IFIs are unlikely to be repaid first.
We can see from Tables 1 and 2 that the IFIs’ and bilateral lenders’
share of new money was larger than that of commercial lenders pro-
portional to exposures. As a result, the former’s share of total debt
increased over time. To understand how different types of arrange-
ments divide the burden and the future payoff between the two catego-
ries of lenders, we begin with the case in which the IFIs have no prior
exposure to the problem debtor.
When IFIs Have No Prior Exposure
In the case of no prior exposure, IFIs have no interest in defensive
lending. If they are nonetheless compelled to lend, they must be
guaranteed full repayment. Otherwise, they would end up subsidizing
commercial banks. Full repayment, in turn, can be guaranteed only
when the debtor’s overhang is eliminated. A debt package in this case
therefore requires that the commercial banks provide enough DDSR to
eliminate the overhang and return the debtor to full creditworthiness.
To understand these points, consider the return to the IFIs when
they provide L = L
, the minimum amount of new money needed to
induce the debtor to adjust. When the overhang is eliminated, which
occurs when the commercial banks provide DDSR of exactly B
, the
IFIs are repaid in full. They receive
. If banks provide DDSR
smaller than B
, the country still adjusts but remains in overhang.
Because IFIs are unlikely to be treated in practice as fully senior to
commercial banks, assume that they receive only a prorated share of
total repayments. This works out to be
/(D B + L
)][␣␪Y(1 + )] ,
which falls short of full repayment.
In the latter case, IFIs effectively end up subsidizing the banks. To
see this, note that the return to the banks when the overhang is elimi-
nated through debt reduction is
)=Y(1 + )−RL
The appropriately prorated return when the overhang remains is
{[D +(1−
]/(D + L
)}[Y(1 + )] .
With a bit of algebra, it can be shown that
Y(1 + )−RL
<{[D +(1−)L
]/(D + L
)}[Y(1 + )]
for any feasible value of
, because R(D + L)>Y(1 + ). Therefore,
banks will actually prefer to maintain the debtor in overhang when IFI
conditionality buys adjustment, as this is a way of transferring resources
from the IFIs to themselves. For this to happen, however, the IFIs
must be willing to accept less than the market (or normal) return on
their lending to the debtor.
To avoid a cross subsidy from the IFIs to the banks, it is thus neces-
sary that banks provide sufficient debt reduction (here B
eliminate the overhang completely. In other words, IFIs can make the
normal return on their loan only if the banks complement the IFI
lending by debt reduction large enough to eliminate the overhang. By
doing this, banks will be worse off than if they are subsidized by IFIs
but better off than if IFIs stay entirely on the sidelines.
Moreover, if
L > L
, so that the debtor also shares in the efficiency gains, we must
have B > B
to ensure elimination of the overhang. In this case, each
additional dollar of new money has to be matched by an extra dollar of
debt reduction (see Figure 2).
When IFIs Have Prior Exposure
In more realistic cases, IFIs will also have some prior exposure to the
problem debtor. Consequently, they will be asked to partake in the net
burden of the debt package. When they do so, some of the logic of the
previous argument survives in an appropriately amended fashion.
Under an intuitive “fairness” criterion defined below, commercial banks
have to provide a certain amount of debt reduction as long as the IFIs’
share of new money exceeds their share of the existing debt. An impor-
To see that banks are still better off having a deal even when IFIs require them to
undertake sufficient debt reduction to eliminate the overhang, note that R(D B
Y(1 + )−RL
> Y, because L
< ␣␪Y/R as long as efficiency gains exist from a debt
package; compare expression (7).
tant corollary, however, is that the debtor will have to remain in
overhang after the deal is completed.
To clarify these points, we derive the set of feasible bargains that
can be struck between the commercial creditors and IFIs. We start by
noting that, when conditionality is imposed, debt reduction does not
affect the adjustment behavior of the debtor country. It only changes
the distribution of future debt service between creditors. Creditors that
offer debt reduction in effect reduce their future claim on the pool of
resources to be paid out,
Y(1 + ). Unless the IFIs get a large enough
return on their involvement, they can threaten to withhold support.
Similarly, unless the banks get a large enough share, it will be in their
interest to remain on the sidelines. Generally, there are many arrange-
ments that satisfy these two constraints.
We first derive the IFIs’ participation constraint. The IFIs will not
impose conditionality and finance a share of the new money required if
their payoff will be decreased by the operation. We argued above that
this rule is likely to apply even when taken with a grain of salt. We
simply assume that IFI participation occurs whenever
␻␣Y Y(1 + )−RL ,
is the proportion of debt initially held by IFIs and =(D +
L)/(D B + L) is the post-deal IFI exposure. The inequality is satis-
fied whenever the net return to IFIs with the package exceeds or
equals the net return without the package. This defines the combina-
tion of minimum debt relief, B, and maximum share in new money,
that is necessary for IFIs to get involved. Treating the inequality as an
equation, we get the IFIs’ indifference frontier shown in Figure 3:
= B (, L, , , ).
Note that B
can be zero when is large enough or L and are small
Similarly, the banks’ participation constraint requires that they do
better with the package than without it, that
)Y (1 )Y(1 + )−(1−)RL RBp ,
where p is the expected ex post price of debt given by
p =
Y(1 + )/R(D B + L).
This defines the maximum combination of DDSR, B
, and new loans,
)L, that can be offered by banks:
Define p as the pre-deal secondary-market price, p = Y/RD. The
net financial gains from the program, T, are given by the difference
between the capital gain on the existing stock of debt, RD(p p), and
the capital losses on the new loans, RL(1 p), and on the forgiven
debt, RBp. It can be shown that the net financial gain, T = RD(p p)
RL(1 p)−RBp is equal to the real gain,
Y RL, using the
definitions of p and p. Because the IFIs do not engage in debt relief,
the net payoff to them, I, is given by the difference between a share
of the total capital gain and a share of the loss on new loans. PDR
requires that
which can be rewritten as
ωD(p p) τL(1 p )
D(p p) L(1 p ) Bp
Because all creditors share proportionally in the net financial gain
(τ ω)
(1 p )
under PDR, the net payoff per dollar of exposure is the same for all of
them. To see this, note that the payoff to the IFIs per dollar of expo-
sure is given by (I +
Dp)/RD, and, under fair burden sharing (that
is, using [9]), this is equal to
(T + Dp)/RD =[Y(1 + )−RL]/RD f . (11)
Similarly, it is easy to show that the banks also receive f per dollar of
initial exposure. Thus f can be interpreted as the “fair” exit price, equal
to the future payoff per dollar of debt if the country adjusts, net of the
present value of the required new loans.
Equation (10) can be used to derive the following implications of PDR:
First, when
= , that is, the share of the new loan provided by the
IFIs is equal to their initial exposure share, debt reduction is unneces-
sary, that is, B = 0. The reason for this result is simple. When the
sharing of the burden of providing new loans is “fair,” the sharing of
the future payoff will also be “fair.” In these circumstances, it will be
“unfair” to ask the commercial creditors for some further contribution
in terms of debt relief.
Second, when
> , that is, when the IFIs provide a more-than-
proportionate share of the new money, then B must necessarily be
positive. In this situation, banks must bear an additional burden to
make up for their proportionally smaller loss on the new loan. This can
be done by restricting the banks’ share of the future payoff, and DDSR
will do that. This rule can be also turned around. When banks offer
debt relief, PDR requires that their loss be made up by reducing their
share of the new loan.
Third, as long as
> 0 and > , the debtor must remain in over-
hang after the debt deal is completed. The reason is that the IFIs must
share the burden when
> 0, but they do not provide DDSR and will
thus remain whole unless the new price of debt, p, remains below
unity. The point can also be made by using equation (9). As p goes to
1, the right-hand side goes to
D(1 p)/[D(1 p)−B], which is
larger than
. For the same reason, banks cannot be asked under PDR
to provide enough debt reduction to return the debtor to full credit-
In practice, the secondary-market discount has rarely disappeared
following deals of the Brady type. This is consistent with the third
point above, in that the overhang should disappear under PDR only in
the limiting case in which the IFIs have no initial exposure. There may
be other reasons, however, for the failure of the debt price to go to
unity after a debt deal is completed. One possibility is that IFIs are
subsidizing the banks by not asking for enough debt reduction. More-
over, we have so far assumed that IFI participation buys conditionality
with certainty. In practice, doubts may remain as to the quality of the
conditionality, and these will be reflected in the secondary-market
Finally, consider the debtor country’s welfare. As argued above, the
country may lose if unconditional lending occurs in the absence of IFI
involvement. It may thus try to bargain for more new money than L
(possibly as much as L
). Note, further, that, although debt reduction
does not directly affect economic behavior in the debtor economy, but
rather redistributes the burden of financing between different credi-
tors, it may still have indirect effects. When the creditors are locked
together in bargaining, there is uncertainty in the debtor country as to
whether an adjustment program with external financial support will
materialize. This may depress economic activity. A debt-reduction
agreement signals that the burden-sharing issue has been resolved and
that an adjustment program with adequate support will materialize.
The announcement effect then has positive value for the debtor.
We now turn to schemes that are closer to actual Brady deals, in which
IFIs provide the resources to retire a portion of the debt at some price
below par and also provide additional adjustment loans.
In the
“pure” debt-reduction schemes discussed above, this debt repurchase
took place at a zero price. More generally, the repurchase will take
place at a negotiated price,
. We shall show that the efficiency gains
of the debt package can be divided between the banks and the IFIs in
any desired manner by appropriately selecting the price and the level
of debt repurchase. Under “fair” burden sharing, however, the repur-
chase price must be below the post-deal market price. That in turn
necessitates a concerted approach to debt reduction rather than a
voluntary approach.
We suppose that the debt package has three components: (1) an
adjustment loan of
from the IFIs, in return for conditionality; (2)
an IFI loan to the country of
B, to be used to retire B debt at price
< 1; and (3) agreement by the banks that they will put up (1 )L
new money and will sell off B debt at price
. We shall take as given
here and look at different pairs of
and B to see how the deal can be
structured to split the gains. We assume that
> .
The “participation” constraints of the IFIs and the creditor banks,
discussed in the previous chapter, now depend on the exit price
. The
IFIs will not participate unless B B
= B(, L, , , , ), with
/ > 0 as long as is small enough. When is close enough to p,
the IFIs will be losers. This is discussed more formally below in the
context of the proportional-distribution rule. The analogous participa-
tion constraint for the banks is given by B B
= B(, L, , , , ),
/ > 0 for < p. When exceeds p, banks will of course
be happy to sell more debt. Note that the minimum price at which
banks are willing to sell the entire debt stock is the pre-deal market
price, p =
Y/RD. The range of feasible, mutually advantageous pro-
grams is shown by the shaded area in Figure 4. The closer we move to
the B
schedule, the more the banks benefit from the program. The
For a description of the Brady deals signed by the time of writing this study, see
Claessens and Diwan (1992).
figure shows the general tendency for the requisite amount of debt
reduction to increase as the repurchase price rises. We also note from
Figure 4 that banks are willing to “sell off” as much as B
of debt at a
zero price (that is, to provide B
of pure debt reduction). Debt buy-
backs at any price above B
transfer resources to the banks.
Finally, we repeat the application of the proportional-distribution
rule (PDR) to this case of costly debt reduction. The cost of debt
reduction, B
, is financed by the IFIs in addition to their contribution
of a share
of L. In practice, there are limits on the ratio B/L, which
the World Bank and the IMF set at between 20 and 25 percent.
Following the logic of the previous chapter, the PDR now requires
in which p is now given by
ωD(p δ) τL(1 p ) Bδ(1 p )
D(p δ) (L Bδ)(1 p ) B(p δ)
Some algebra leads to
αY(1 θ)
R[D B(1 δ) L]
which is equal to (10) when
= 0. This expression shows that, under
ωD(p δ) τL(1 p ) Bδ(1 p )
D(p δ) (L Bδ)(1 p ) B(p δ)
PDR, B must increase as
increases. That is because banks are now
getting an early payoff compared to the pure relief case. As a result,
the IFIs require a larger share of the future payoff, and this is
achieved with larger buybacks. This arrangement can work, however,
only as long as
< p and the implied B is smaller than (1 )D.At
< p, the whole commercial debt will have to be retired.
One important implication is that PDR is incompatible with being set
equal to p. The “fair” exit price for debt must lie below the post-deal
market price.
Rewriting (14) as G(B,)=p(B)[L( )+B(1 )+B]+L( )+B =
0, we have
B/ =−G
, where G
= B[1 p(1 )] > 0, and G
)+Bd(1 )+B]−p[(1 )+]+, which is negative when is small, and
equal to zero when
< p. Note that, as gets smaller, there is more room
to increase before G
becomes zero. Thus, B() is convex in , with a vertical
asymptote at p. In Figure 4,
can be read as the point at which B(
) is equal to
A more important problem with the concerted approach is caused by
heterogeneity among the commercial banks. If creditors differ with
respect to their valuations of a country’s debt, a concerted buyback that
does not discriminate among banks and yet does not hurt any bank
must occur at the reservation price of the bank with the highest valua-
tion; for a discussion of heterogeneous valuation, see Diwan and
Kletzer (1992). Attempts to discriminate between creditors require
unobservable information and create moral hazard. The market mecha-
nism is more efficient on this score, in that it allows creditors to self
select, with only those with low valuations selling out at a particular
offer price. Some of the desirable characteristics of the market-based
approach, however, can be included in a concentrated package by
offering the banks a menu of choices.
Recent agreements have focused on a menu of options from which
individual creditors will select after the agreement has been approved.
Such a menu is a contract, which may be partly implicit, defining a
future opportunity set for the lenders. The menu approach requires
that lenders commit to choose ex post from a restricted set of options.
By combining concerted and voluntary characteristics, the menu
approach to debt reduction retains the advantages, but not the inconve-
niences, of pure market and concerted mechanisms. In the first round,
options and their relative prices are negotiated; in the second round,
each creditor freely chooses his preferred option. Overall, the differen-
tiation allowed by the menu produces larger actual relief, given the
willingness of the banks as a group to offer debt relief (see Diwan and
Spiegel, 1991, for a formal treatment).
For a menu of options to allow individual creditors to choose differ-
ent options voluntarily, the values of all options must be comparable.
Interestingly, this works out mechanically when the menu includes exit
and relending options, because each unchosen option becomes more
valuable as banks flock to a different one. In equilibrium, all options
will have comparable values. The menu approach thus allows us to
regard the IFIs as similar to any other creditor, except that they choose
to provide new money rather than debt reduction. We shall show that
any menu the IFIs and banks voluntarily adopt will necessarily satisfy
the PDR. To illustrate this claim, we develop below an equilibrium
analysis of the simplest case, in which all commercial banks are similar.
Suppose that the debtor and creditors (including the IFIs) have
agreed on a simple menu of options represented by the pair (
, n).
For each dollar of claim they hold, creditors can choose either to exit
at a price
or to reschedule the loan and lend n additional dollars. To
show that both options will have the same value in equilibrium, let D
stand for the debt stock after the implementation of the agreement and
N for the total amount of new money. We have
= R (D B + N) , (15)
p =
Y(1 + )/D
, (16)
n = N/(D B) . (17)
Lenders choose between the two options in a manner that maximizes
the values of their assets subject to the terms of the menu (
, n). After
the deal is implemented, debt prices are expected to be higher, at p >
p =
Y/RD. A creditor that chooses to relend n dollars will have its old
claim revalued. Its new claim n, however, will be valued only at p,
implying a capital loss of (1 p). Thus, the opportunity cost of with-
holding a unit of debt back from repurchase at price
is p(1 + n)−n.
This implies that, when p exceeds (
+ n)/(1 + n), the new-money
option is preferable to the exit option. Less debt will then be sold and
more new money offered, resulting in less debt reduction than expected.
This leads to an increase in D
, using equation (15), and thus to a
decrease in p using equation (16). As creditors are price takers when
they optimize ex post and because the expected present value of debt,
p, is strictly concave, portfolio-value maximization by the creditors has
a unique solution. In equilibrium, we must then have
p =(
+ n)/(1 + n) . (18)
The system of equations (15) to (18) can be solved for B, N, D
, and p
as a function of the menu (
, n). Any such menu (, n) will then produce
an equilibrium (B, N) in which all the creditors obtain a payoff exactly
equal to
, whether they exit or relend. Therefore, all menus (, n)
involve a proportional distribution of the net gains. In particular, a
menu offered to all creditors, IFIs as well as commercial banks, will
achieve a proportional sharing of the burden across both classes of
creditors, and the requirements of PDR will necessarily be satisfied
(once again, we leave aside the question of whether this involves fair
burden sharing or not).
For a menu to be able to support the conditional adjustment pro-
gram, however, (
, n) should be chosen to make sure that enough new
money is raised to finance adjustment, L
, and buybacks, B. Which
menus raise exactly L
=(N B)? To answer this question, we feed
equations (15) and (16) into (18) and obtain
Y(1 + θ)/R(D B + N)=( + n)/(1 + n)
+[N/(D B)]}/{1 + [N/(D B)]} (19)
using (17), which implies that
Y(1 + )=R(D + L
) when N B is
set equal to L
. Solving for , we get =[Y(1 + )−RL
]/RD f,
using (11). Hence, when
is set equal to the “fair” exit price f, any n
will produce a menu that raises exactly L
on a net basis. We should
not be surprised to find that
= f is necessary to achieve a deal that
raises L
of net financing. Both options must have the same value, and
proportional burden sharing with sufficient financing provides a payoff
equal to f per dollar of initial debt. It is perhaps more surprising that,
= f, the only effect of varying n is to increase the equilibrium
volume of both buybacks and new money, with no net effect on the
total liquidity, L, that is raised.
To see this more clearly, let us look at how the equilibrium (B, N) and the net
financing raised, N B, vary as the new money call, n, is increased. We do not impose
the requirement that N
D be equal to L
. Differentiating (19) with respect to n and
rearranging, we get
N/n =[Y(1 + )−N]/( + n)>0
for small enough n. The effect of n is ambiguous. On the one hand, an increase in n
raises the amount of new money for any given set of choices by banks. On the other
hand, an increase in n makes exit more desirable and thus reduces the base for the new-
money call. The total effect is positive as long as n does not exceed some maximum level
(the debtor would not want to be on the declining part of the new money curve). When
IFIs are keen on delivering their share of the burden of new loans rather than in the
form of debt reduction, n should be set large enough to produce an equilibrium with a
new-money contribution that is large enough to accommodate their exposure. A larger
IFI exposure should lead to a larger n under proportional burden sharing. Similarly, to
see the effect of n on the amount of debt reduction achieved in equilibrium, differenti-
ate (17) with respect to n to get
B/n = −[(N/n)n N)]/n
As the new money call, n, is increased, the exit option becomes more desirable than the
relending option. In equilibrium, however, both options must be equally desirable. As a
result, more debt reduction will be achieved in order to raise further the ex post debt
price p and increase the attractiveness of the relending option. Increasing n thus leads
to larger buybacks and more new money in equilibrium. What is the net effect on (N
B)? Using the above, we find that (N B)/n =(D/n)(f ) 0asf , and there-
fore the amount of net funds received is invariant to n when
= f, that is, under propor-
tional burden sharing. Thus, the only effect of a change in n is indeed to accommodate
different sets of preferences of the creditor group.
This essay has covered a lot of ground. We have tried to present a
framework in which the roles of the debt overhang, adjustment lending
with conditionality, and arrangements of the Brady type involving new
money and DDSR can be understood and evaluated.
We began with the observation that the chief inefficiency engen-
dered by the existence of a debt is the inability of the debtor country,
hampered by illiquidity, to finance desirable investments, including
adjustment programs. This illiquidity effect on investment must be
distinguished from the disincentive effect on which much writing has
focused. The debt overhang is responsible for an investment shortfall,
but we have argued that the shortfall is not the result of an artificial
reduction in investment incentives but of a lack of liquidity.
Nevertheless, calls for new money and renewed lending will not
solve the problem. The overhang makes it impossible for countries to
attract voluntary loans from new groups of creditors. In the absence of
seniority, new loans enter the same pool as old loans and instantly
metamorphose into claims as poor as the old loans. Of course, these
new loans may have led the country to undertake the investments it
was previously unable to make and may have eliminated the overhang
altogether. But, as long as the old claims stand undiminished, the new
lenders will have to share with the old lenders the fruits of any im-
provement in creditworthiness. This depresses the return to the poten-
tial new lenders and keeps them from doing business with the debtor.
We then turned to the adjustment decision of the debtor govern-
ment. We showed that a credit-constrained government will undertake
an adjustment program that has immediate costs but eventual benefits
only if a sufficient amount of external lending is available. Further-
more, although many governments would be happy to receive new
money in exchange for undertaking adjustment, many would rather use
the new money for consumption rather than investment and will do so
in the absence of conditionality . Hence, conditionality buys a commit-
ment to adjust, preventing the best from being the enemy of the good.
Because an adjustment program benefits old creditors as well by
increasing the debtor’s ability to make debt-service payments, commer-
cial banks may be prepared to finance the program on their own. We
showed, however, that the amount of new lending required to “pur-
chase” adjustment in the absence of conditionality (that is, without the
involvement of IFIs) can be much larger than the amount required
when conditionality is present. The amount of new money banks will
be willing to offer is constrained by their share of the resulting in-
crease in productivity, and that share is quite low in practice. Adjust-
ment lending with conditionality therefore greatly expands the set of
efficiency-increasing bargains between creditors and debtors.
We next turned to the implications of IFI participation for the
design of a financing package. The efficiency gains arising from the
three-way bargain between the debtor, banks, and IFIs can be split in
many ways. Any desired division can be achieved by an appropriate
selection of (1) the amount of new money received by the debtor in
return for adherence to an adjustment program, (2) the shares of the
new loan provided by the two creditor groups, and (3) the sharing
between the two creditor groups of the future repayment made by the
country. The higher the loan, the better off is the country. The banks
are better off and the IFIs worse off when the banks provide a smaller
share of the loan and get a larger share of the future repayment. Of
course, the constraint that the debtor, the banks, and the IFIs be at
least as well off with a deal as without one limits the set of bargains.
When the IFIs have no prior exposure to the debtor country but are
expected to provide new money to support an adjustment program, the
banks must provide enough debt relief to return the country to credit-
worthiness and allow the IFIs to earn a “normal” return on their
investment. When the IFIs have prior exposure, however, adjustment
lending also improves the IFIs’ ability to collect on their old debts, and
this reduces the amount of relief that banks need to offer. We focused
the analysis on a proportional-distribution rule (PDR) under which the
returns to the various creditors are shared in proportion to their initial
exposure. Under such a rule, adjustment lending by IFIs requires debt
or debt-service reduction by commercial banks. This is true whenever
the IFIs’ share of new money exceeds their share of the outstanding
debt stock, as was the case throughout the 1980s. The point of DDSR
in our framework is not to create appropriate incentives for the debtor,
as in much of the overhang literature, but to ensure that IFIs and
banks are treated equitably. Debt reduction creates the “headroom”
required for the more efficient IFIs to come in without subsidizing
other creditors.
We also showed, however, that PDR precludes a complete elimina-
tion of the overhang and full return to creditworthiness (unless the
IFIs have no prior exposure at all). If PDR were to do that, bringing
the post-deal price to unity, the IFIs (which do not provide DDSR)
would remain whole, while the banks would take a loss on their DDSR.
For the same reason, banks cannot be asked, under PDR, to provide all
the debt reduction needed to return the debtor to full creditworthiness.
We then generalized our framework to include Brady-type deals in
which IFIs lend the debtor the resources needed to retire some of the
debt, and commercial creditors are presented with a menu of options.
We showed that, under PDR, the exit price at which debt is retired
must be below the post-deal price. Furthermore, the higher the IFIs’
share of the new money, the lower must be this exit price. These
requirements rule out market buybacks, for the only equilibrium price
at which debt can be repurchased in the market is the equilibrium
price after debt reduction. This finding provides a justification for the
concerted approach characteristic of arrangements of the Brady type.
Some of the advantages of the market-based approach are recovered
by offering a menu of options to commercial creditors. Such a menu
allows the heterogeneity of banks’ valuations to be reflected in their
choices. For all options on a menu to be chosen voluntarily, their
values must be identical in equilibrium, and this condition satisfies
PDR automatically. We showed that this condition is met naturally
when the menu contains exit and new-money options, because each of
these options becomes more valuable as the other option is picked by
an increasing number of banks. The menu approach also allows us to
treat IFIs just as any other creditor group that happens to choose
relending over exit.
We close by noting that our analysis of debt reduction extends to all
forms of new finance that provide efficiency gains. One notable exam-
ple is direct foreign investment. Just as with adjustment lending, it is
necessary to convince prospective foreign investors that their profit
remittances will not be crowded out by debt-service payments to
existing creditors. Debt reduction represents a credible commitment on
the part of banks that they will effectively allow seniority to subsequent
This appendix provides more details on the derivation of the zones in
Figures 1 and 2.
Without Conditionality
Substituting for C
and C
in the maximand (1), we can express the
government’s decision rule as follows:
Adjust if: U(Y + L K)+ max [Y(1 + )−R([D B + L)] ,
)Y(1 + )] U(Y + L)+ max [Y R(D B + L),
)Y] . (A1)
As this makes clear, the net benefits of adjustment depend on whether
the debt overhang is eliminated in period two or not. If it is eliminated,
consumption in period two becomes
Y(1 +
)−R(D B + L)orY R(D B + L).
If the overhang continues, consumption in period two is independent
of both L and B and equals (1
)Y(1 + )or(1−)Y. The cost-
benefit calculus therefore has different properties depending on the
status of the overhang.
Consider the demarcation between overhang and no-overhang zones.
It is defined by those combinations of B and L that leave the govern-
ment indifferent between repaying the debt in full and paying the
penalty (
times output). Hence, it is described by the equations
R(D B + L)=
Y(1 + ) , when adjusting, and
R(D B + L)=
Y , when not adjusting.
These are two 45-degree lines, with the first relevant in zones II and
III, and the second relevant in zones I and IV. They capture the
following simple intuitions. First, when the government is just short of
default, an additional dollar of new lending has to be offset by an
additional dollar of debt reduction to keep the government from
crossing over. Second, when the government chooses to adjust (and
output rises to Y(1 +
), the no-overhang region becomes larger and
the overhang region smaller.
Turn now to the loci that separate the adjustment zones from the
no-adjustment zones. The relevant locus is easy to describe when an
overhang prevails. Here we have the equality
U(Y + L K)+
(1 )Y(1 + )=U(Y + L)+(1 )Y ,or
U(Y + L)−U(Y + L K)=
(1 )Y . (A2)
This defines implicitly a level of L, L
, which makes the equality hold.
When the country remains in overhang, the government will choose to
adjust for all L greater or equal to L
. In equation (2) of the text, L
written as a function of the various parameters in (A2). Note that L
does not depend on B, for the face value of the inherited debt stock is
of no consequence when overhang prevails. Therefore, the demarcation
between zones III and IV (the adjustment and no-adjustment zones,
both in overhang) is perfectly vertical in Figure 1.
The corresponding locus in the absence of overhang is more tricky to
describe. Suppose that the government would be in overhang if it did
not adjust, the relevant case for much of the discussion in the text.
Here, the relevant equality is
U(Y + L K)+
[Y(1 + )−R(D B + L)] = U(Y + L)
(1 )Y ,or
U(Y + L)−U(Y + L K)+
R(D B + L)=( + )Y . (A3)
This defines a schedule along which the government remains indiffer-
ent between adjusting and not adjusting. The relation between L and B
along this schedule is given by
dB/dL =1−(
[U(Y + L K)−U(Y + L)] , (A4)
which is of ambiguous sign because the expression in the square
brackets is positive as long as U′′ <0.
The explanation for the ambiguity is as follows. A dollar increase in
B increases the net benefit from adjusting by
R dollars (because this
is the discounted present value of the increase in second-period con-
sumption when adjusting). Should L be increased or decreased to
offset the added incentive to adjust? An increase in L will reduce the
benefit of adjusting insofar as it reduces the discounted value of
second-period consumption; because overhang prevails when not
adjusting, L does not affect second-period consumption when the
government does not adjust. But an increase in L will also reduce the
net cost of adjusting insofar as it contributes to the smoothing of
consumption. If the first effect dominates the second, that is,
R >
[U(Y + L K)−U(Y + L)], L should be increased. Otherwise, L
should be reduced. As long as U′′′ > 0, there are only three possibili-
ties: (1) dL/dB is initially negative in the relevant range and then turns
positive; (2) dL/dB is negative throughout; (3) dL/dB is positive
throughout. Figure 1 is drawn assuming the first possibility, whereas
the no-conditionality locus in Figure 2 is drawn assuming the second.
One final case must be considered to complete the description of
Figure 1. Suppose that the government will not be in overhang if it
does not adjust. In this case, the locus that describes indifference to
adjustment is given by the equality
U(Y + L)−U(Y + L K)=
␤␪Y . (A5)
This defines implicitly a level of L, L
, which makes the equality hold.
It is independent of B (as is L
), and it is easy to check that L
< L
This explains the vertical line separating zones III and I in Figure 1.
With Conditionality
The government’s decision rule now becomes
Adjust if: U(Y + L K)+
max [Y(1 + )−R(D B + L),
)Y(1 + )] U(Y)+ max [Y R(D B), (1 )Y] . (A6)
We can now proceed to locate the four zones of possible outcomes as
before. Because conditionality affects only the incentive to adjust, not
the demarcation between overhang and no-overhang zones, we focus
exclusively on the former.
In the presence of an overhang, the locus that separates the adjust-
ment zone from the no-adjustment zone is given by
U(Y)−U(Y + L K)=
(1 )Y . (A7)
This defines implicitly a level of L, L
, which makes the equality hold.
Suppose, next, that the government will be in overhang if it does not
adjust but otherwise will not. The relevant equality is
U(Y + L K)+
[Y(1 + )−R(D B + L)] = U(Y)+(1 )Y ,
U(Y)−U(Y + L K)+
R(D B + L)=( + )Y . (A8)
The relation between L and B along this schedule is given by
dB/dL =1−(
U(Y + L K)<0, (A9)
with the negative sign unambiguous as long as the government remains
liquidity constrained (that is, U >
R). In this case, unlike the no-
conditionality case, an increase in L always increases adjustment
incentives. The schedules for conditionality and no conditionality are
related as follows: (1) the two meet when L = 0, and (2) the schedule
for conditionality always lies below the schedule for no conditionality.
Finally, suppose that the government will not be in overhang if it
does not adjust. The locus that describes indifference to adjustment is
given by
U(Y)−U(Y + L K)=
␤␪Y , (A10)
which defines implicitly a level of L, L
, which makes the equality
hold. Once again, this is lower than the corresponding level under no
conditionality, (that is, L
< L
). Figure 2 shows the new configuration
and the way it relates to its analogue in the absence of conditionality.
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Notice to Contributors
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