We develop a model that captures important features of debt crises of the Brazilian type. Its applicability to Brazil lies in the fact that (1) in Brazil the macro fundamentals were sound (e.g., a primary surplus, a relatively low debt/GDP ratio, etc.); and (2) in the Brazilian case the trigger appears to be the forthcoming elections, with an expected regime change.

Assaf Razin

Efraim Sadka

English

Research Papers in Economics

NBER WORKING PAPER SERIES
A BRAZILIAN DEBT-CRISIS MODEL
Assaf Razin
Efraim Sadka
Working Paper 9211
http://www.nber.org/papers/w9211
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
September 2002
The views expressed herein are those of the authors and not necessarily those of the National  Bureau of
Economic Research.
© 2002 by Assaf Razin and Efraim Sadka.  All rights reserved.  Short sections of text, not to exceed two
paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given
to the source.A Brazilian Debt-Crisis Model
Assaf Razin and Efraim Sadka
NBER Working Paper No. 9211
September 2002
JEL No. F1
ABSTRACT
We develop a model that captures important features of debt crises of the Brazilian type. Its
applicability to Brazil lies in the fact that (1) in Brazil the macro fundamentals were sound (e.g., a
primary surplus, a relatively low debt/GDP ratio, etc.); and (2) in the Brazilian case the trigger
appears to be the forthcoming elections, with an expected regime change.
Assaf Razin
Department of Economic
Tel Aviv University
Tel Aviv 69978
Israel
and NBER
ar256@cornell.edu A Brazilian Debt-Crisis Model
Assaf Razin and Efraim Sadka
September 2002
Abstract
We develop a model that captures important features of debt crises of the Brazilian type. Its
applicability to Brazil lies in the fact that (1) in Brazil the macro fundamentals were sound (e.g.,
a primary surplus, a relatively low debt/GDP ratio, etc.); and (2) in the Brazilian case the trigger
appears to be the forthcoming elections, with an expected regime change.
1I n t r o d u c t i o n
The IMF accord from August 2002 gave Brazil a critical boost, providing the central bank with an
additional sum totalling $16 bn in international reserves to defend its weak currency, and a promise to
increase the package to $30 bn (if the primary surplus is increased).1 Three-quarters of Brazil’s debt
is in domestic currency, and around a third of this debt is indexed to the dollar. The policy issue is,
therefore, not only the strength of Brazil’s currency, but also the levels and volatility of domestic interest
rates. Since most of Brazil’s local currency debt is short term, and thus eﬀectively indexed to the rate
of interest, Brazil is prone to self-fulﬁlling expectations equilibria, with the country’s risk premium at
the center of analysis.
We employ a model of loans with defaults, due to Townsend (1979), which gives rise to a schedule of
interest rates that depend on the borrower’s credit worthiness.2 The model is applicable to a country that
is characterized by sound macro variables, such as primary surplus, relatively low external debt/GDP
ratio, etc. We derive two types of equilibria: one “good" equilibrium with a steady inﬂow of capital,
1Although only a sum of $6 bn of the new IMF loan will be available in 2002, Brazil’s central bank will have more
ﬂexibility after the accord. The agreement cuts to $5 bn (from $15 bn) the minimum level of reserves the Brazilian Central
Bank promises to hold. Thus, in eﬀect, there is an additional sum of $16 bn that the Central Bank can use to defend the
currency.
2This model was later extended to study the transmission of monetary policy by Bernake and Gertler (1989).
* This paper employs the model developed by Razin and Sadka (2001) in order to shed some light on the recent crisis
in Brazil.
1low public-debt service and a high credit rating; and another, "bad" equilibrium with dried-up capital
inﬂows, high public debt service, doomed growth prospects, and poor credit rating.
2 Analytical Framework
Consider a two-period model of a small, open economy. Suppose for simplicity that capital imports
are channelled solely through ﬁrms borrowing in the world capital markets. Suppose that initially the
country faces a perfectly elastic supply of credit for safe projects at a given risk-free world rate of interest
(r*). The actual rate for any given ﬁrm will, of course, typically be higher depending on the speciﬁc
riskiness of its investment plans. In a subsequent section we will introduce also an element of country
risk.
Suppose there is a continuum of ex-ante identical domestic ﬁrms. Each ﬁrm employs capital input
(K) in the ﬁrst period, in order to produce a single composite good in the second period. We assume
that capital depreciates at the rate δ. Output in the second period is equal to F(K)(1 + ε), where
F(·) is a production function exhibiting diminishing marginal productivity of capital and ε is a random
productivity factor (with zero mean), which is independent across all ﬁrms. The value of ε is bounded
from below by −1, so that output is always nonnegative. It is also assumed that it is bounded from
above, say, by one. We assume that ε is purely idiosyncratic, so that there is no aggregate uncertainty.
For each ε, there will be exactly NΦ(ε) ﬁrms whose output in the second period will be below or equal
to F(K)(1+ε),w h e r eΦ(·) is the cummulative distribution function of ε,a n dN is the number of ﬁrms.
But in the ﬁrst period no one knows who these ﬁrms are. Thus, each ﬁrm faces a probability of Φ(ε)
of having an output below or equal to F(K)(1 + ε) in the second period. To simplify the exposition,
we assume that consumers-savers behave in a risk-neutral way. To further simplify the notation, we
normalize the number of ﬁrms to one; that is, N =1 .
Investment decisions are made by the ﬁrms ex-ante, before the state of the world (that is, ε)i s
known. Since all ﬁrms face the same probability distribution of ε,t h e ya l lc h o o s et h es a m el e v e lo f
investment. They then seek funds to ﬁnance the investment, either at home or abroad. Denote the
gross investment of the ﬁrm by I. Therefore, if its initial stock of capital in the ﬁrst period, carried over
from the preceding period, is (1 − δ)K0, then the stock of capital which the ﬁrm employs in the ﬁrst
period is K =( 1− δ)K0 + I, where δ i st h er a t eo fd e p r e c i a t i o n .
Since credit is extended ex-ante,b e f o r eε is revealed, ﬁrms cannot sign default-free loan contracts
with the lenders. We therefore consider loan contracts which allow for the possibility of default. We
2adopt the "costly state veriﬁcation" framework ¯ a la Townsend (1979) in assuming that lenders make ﬁrm-
speciﬁc loans, charging an interest rate of rj to ﬁrm j. The interest and principal payment commitment
will be honoured, when the ﬁrm encounters a relatively good productivity shock, and defaulted when
it encounters a relatively bad shock. The loan contract is therefore characterized by a loan rate (rj),
with possible default and a threshold value (¯ εj) of the productivity parameter, deﬁned as follows:
F(Kj)(1 +¯ εj)+( 1− δ)Kj =[ Kj − (1 − δ)K0](1 + rj), (1)
and
[1 − Φ(¯ εj)][Kj − (1 − δ)K0](1 + rj) (2)
+Φ(¯ εj)(1 − µ){F(Kj)[1 + e−(¯ εj) ]+( 1− δ)Kj}
=[ Kj − (1 − δ)K0](1 + r∗).
Equation (1) deﬁnes the value of the productivity shock for which the funds available to the ﬁrm
just suﬃce to repay the principal of and the interest on the loan. These funds consist of the output
of the ﬁrm, plus the depreciated stock of capital. This is the expression on the left-hand side equation
of equation (1). When the realized value of εj is larger than (¯ εj),t h eﬁrm is solvent and will thus
pay the lenders the promised amount, consisting of the principal [Kj − (1 − δ)K0], plus the interest
rj[Kj − (1 − δ)K0] as given by the right-hand side of equation (1). If, however, εj is smaller than ¯ εj,
the ﬁrm will be in default. In the case of default, creditors incur a cost in order to verify the true value
of εj and to seize the residual value of the ﬁrm. This cost, interpretable as the cost of bankruptcy, is
assumed to be proportional to the amount seized, µ[F(Kj)(1+εj)+(1−δ)Kj], where 0 <µ≤ 1 is the
factor of proportionality. Net of this cost, the creditors will receive (1 − µ)[F(Kj)(1 + εj)+1− δ)Kj]
. The expected rate of return required by foreign lenders who are the marginal lenders in this capital-
importing economy is naturally r∗. Therefore, the "default" rate of interest, rj,m u s to ﬀer a premium
over and above the default-free rate, r∗, according to equation (2). The ﬁrst term on the left-hand side
of equation (2) is the contracted principal and interest payment, weighted by the no-default probability.
The second term measures the amount seized by the creditors, net of the cost of bankruptcy, and
weighted by the default probability where e−(¯ εj)=E(ε/ε ≤ ¯ εj) is the mean value of ε realized by the
low-productivity ﬁrms. The expression on the right-hand side of equation (2) is the no-default return
3required by foreign creditors.
Observe that equations (1) and (2) together imply that:
[1 − Φ(¯ εj)] +
Φ(¯ εj)(1 − µ){F(Kj)[1 + e−(¯ εj) ]+( 1− δ)Kj}
F(Kj)(1 + ¯ εj)+( 1− δ)Kj =
1+r∗
1+rj . (3)
Because e−(¯ εj) < ¯ εj and 0 <µ≤ 1, it follows that rj >r ∗,,t h ed i ﬀerence being a default premium
(which depends, among other things, on Kj, ¯ εj and µ).
The ﬁrm in this setup is competitive (that is, a price-taker) only with respect to r∗, the international
risk-free rate of return. This r∗ cannot be inﬂuenced by the ﬁrm’s actions. However, rj, Kj and ¯ εj are
ﬁrm-speciﬁc and must satisfy equations (1) and (2). In making its investment (that is, Kj −(1−δ)K0)
and its ﬁnancing (loan contract) decisions, the ﬁrm must take these constraints into account. Because
these decisions are made before ε is known, that is, when all ﬁrms are (ex ante) identical, they all make
the same decision. Therefore, we henceforth drop the superscript j.
Consider now the investment-ﬁnancing decision of the ﬁrm. Its objective is to maximize its net
expected discounted value for its shareholders. Because consumers in this economy compete with
foreign lenders in providing credits to the ﬁrms, they must, in equilibrium, earn the same rate of return
as foreigners, namely, r∗. Hence, the net expected discounted value of the ﬁrm to its shareholders is:
(1 + r∗)−1[1 − Φ(¯ εj)]{F(K)[1 + e+(¯ ε) ]+( 1− δ)K − [K − (1 − δ)K0](1 + r)}, (4)
where e+(¯ ε)=E(ε/ε ≥ ¯ ε) is the mean value of ε for the “high" productivity ﬁrms. Note that the
ﬁrm has a positive value only in the no-default states, that is, only when ε ≥ ¯ ε and it fully repays
the principal of and the interest (r) on the loan. The ﬁrm chooses K, ¯ ε and r so as to maximize the
expression in (4), subject to constraints (1) and (2). Substituting constraint (1) into constraint (2) and
into the objective function (4), we can eliminate the ﬁrm-speciﬁc interest rate r and the optimization
problem of the ﬁrm reduces to:
Max{K,¯ ε}{(1 + r∗)−1[1 − Φ(¯ ε)]F(K)[e+(¯ ε) − ¯ ε]} (5)
subject to:
4[1 − Φ(¯ ε)][F(K)(1 +¯ ε)+( 1− δ)K]+ (6)
Φ(¯ ε)(1 − µ){F(K)[1 + e−(¯ ε) ]+( 1− δ)K} − [K − (1 − δ)K0](1 + r∗)=0 .
A solution to this problem deﬁnes an equal investment level for each ﬁrm (I = K − (1 − δ)K0) and
an equal ﬁrm-speciﬁci n t e r e s tr a t e(r) and an equal default threshold (¯ ε). Note that NI =1is also
the total credit taken by all ﬁrms. The excess of this amount over national saving comprises the capital
imports.
Note from either equation (4) or the maximand in (5) that if a ﬁrm sets ¯ ε =1 , then its net expected
discounted value is zero. (Because in this case the ﬁrm will always default.) If the ﬁrm does not invest
at all, then its net expected discounted value is (1+r∗)−1{F[K0(1−δ)]+K0(1−δ)2} which is positive.
Therefore, it always pays the ﬁrm to set a threshold level ¯ ε that would leave a positive probability of
no default.
Note also that if the world rate of interest (r∗) is suﬃciently high, then the ﬁrm will abstain from
taking loans and making investments. This is because the ﬁrm-speciﬁc interest rate (r) must always
include a default premium over r∗; see equation (3). But at a suﬃciently large interest on its loan, the
ﬁrm will default in all states of nature (that is, for all values of ε). This would contradict our earlier
conclusion that it does not pay the ﬁrm to default in all states of nature.
3 P r i v a t eI n v e s t m e n t ,F i s c a lB a l a n c ea n dC o u n t r yR i s k
We have assumed so far that there is a ﬁx e dp r i m ew o r l dr a t eo fi n t e r e s t(r∗) at which foreign lenders
are willing to extend credit to the government. Naturally, each domestic ﬁrm borrows at higher rates,
depending on its riskiness. In reality, there are varieties of world rates facing governments in diﬀerent
countries, depending on each country’s credit rating. The credit rating is external to our (ex-ante)
identical ﬁrms, but not to the government. It may depend on some aggregate (macro) economic variables
or political factors which are external to the government, but also on some policy variables, such as the
ﬁscal balance, which are endogenous to the government.
Speciﬁcally, suppose that the country’s credit rating depends positively on its aggregate investment
which is external to the government and the ﬁrms, and negatively on the total (including interest
5payments) ﬁscal deﬁcit. Interpret now r∗ as some basic interest rate (e.g., libor rate) and let π be a
country-speciﬁc risk premium, so that the prime rate facing the government is r∗ + π. This π depends
negatively on aggregate investment NI = I and positively on the ﬁscal deﬁcit. (This dependence is
external to the ﬁrm.) That is, the more that a country invests and the smaller its total ﬁscal deﬁcit
(and the rosier look its growth prospects), the lower is the prime interest rate (r∗ + π) it pays on its
credits.
Formally, the analysis now follows the same lines of the preceding section, except that r∗+π replaces
r∗. It is important to emphasize that although π depends on NI =1 , this dependence is external to
the ﬁrm. That is, when choosing I = K −(1−δ)K0, the ﬁrm takes p as exogenously given in the same
way that it views r∗ as exogenous.
4 Boom-Bust Equilibria
Suppose that the government has a primary ﬁscal surplus. It also inherited from the past (previous
governments) a manageable public debt. The total ﬁscal deﬁcit depends naturally on the interest
rate r∗ + π. Now, suppose that there is an equilibrium with a “high" level of domestic investment,
low interest rate cum low ﬁscal deﬁcit. The country-speciﬁc risk premium introduced here would be
"very small", that is, the country gets a "ﬂying colors" credit rating. This is referred to as a "good"
(“boom") equilibrium associated with a sound ﬁscal stance. However, there may be another, "bad"
(bust)" equilibrium with a very high π, a very high interest rate (r∗ + π), no foreign credit, and
“unmanageable" deﬁcit, which is caused by high interest payments. The country may switch abruptly
from the "good" equilibrium to the "bad" equilibrium, if some political factor serves to coordinate and
redirect expectations. Creditors then shift their beliefs about the country’s credit worthiness. These
new beliefs (that the country is at high credit risk) are therefore self-fulﬁlling. Indeed, the country’s
investments dry out.
When public debt is short term, then the debt service is indexed, in eﬀect, to the country’s credit
risk premium. Thus, in the good equilibrium public-debt service is low, whereas in the bad equilibrium
public-debt service is high. These changes in the magnitude of the public-debt service tend to reinforce
the ﬂuctuations of such economy from a "good" to a "bad" equilibrium. However, note that the crucial
feature that can trigger a shift from rosy to gloomy expectations is the dependence of the country risk
on the external (to the ﬁrms and to the government) level of domestic investment. In the absence of
such dependence, there cannot be a shift from a “good" to a “bad" equilibrium. A government that
6exercises a ﬁscal discription will not be derailed to a bad equilibrium.
5C o n c l u s i o n
We develop a model capturing important features of debt crisis. Its applicability to Brazil lies in the fact
that: (1) In Brazil the macro fundamentals were sound (e.g., the primary surplus was around 2.5 percent
of GNP; the debt/GNP ratio was relatively low, etc.), and (2) in the Brazilian case the "coordinator" of
market expectations appear to be the forthcoming elections, with an expected regime change. Whether
Brazil can return to robust growth seems to crucially depend on whether lower interest rates could be
restored. In our model, an external correction of the country’s credit rating can be self-validated in the
sense that it could reduce the country’s prime rate, restore investment and shrink the ﬁscal deﬁcit.
References
[1] Bernanke, Benjamin and Marc Gertler (1989), "Agency Costs, Net Worth and Business Fluctua-
tions," American Economic Review, 79, 14-31.
[2] Razin, Assaf and Efraim Sadka, (2001), "Country Risk and Capital Flow Reversals," Economics
Letters, 72(1), July 73-77.
[3] Townsend, Robert M. (1979), "Optimal Contracts and Competitive Markets with Costly State
Veriﬁcation," Journal of Economic Theory, 21, 265-93.
7

A Brazilian Debt-Crisis Model

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