Board of Governors of the Federal Reserve System
International Finance Discussion Papers
Number 924
March 2008
A Solution to the Default Risk-Business Cycle Disconnect
Enrique G. Mendoza
And
Vivian Z. Yue
NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate
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A Solution to the D efault R isk-Bu siness C ycle Disconn ect
∗
Enrique G. Mendoza
Universit y of M aryland and NBE R
Vivian Z. Yue
New York University
March 2008
Abstract
Models of business cycles in emerging economies explain the negative correlation be-
tween country spreads and output by modeling default risk as an exogenous interest rate
on working capital. Models of strategic default explain the cyclical properties of sovereign
spreads by assuming an exogenous output cost of default with special features, and they
underestimate debt-output ratios by a wide margin. This paper proposes a solution to
this default risk-business cycle disconnect based on a model of sovereign default with
endogenous output dynamics. The model replicates observed V-shaped output dynamics
around default episodes, countercyclical sovereign spreads, and high debt ratios, and it
also matches the variability of consumption and the countercyclical fluctuations of net ex-
ports. Three features of the model are key for these results: (1) working capital loans pay
for imported inputs; (2) imported inputs support more efficient factor allocations than
when these inputs are produced internally; and (3) default on the foreign obligations of
firms and the governm ent occurs simultaneously.
JEL Code: E32, E44, F32, F34
Key Words: Business
cycles, so vereign default, emerging economies
∗
We thank Cristina Arellano, Andy Atkeson, Fernando Broner, Jonathan Eaton, Jonathan Heathcote, Pat
Keho e, Naraya na Kocherlakota, Guido Lorenzoni, Andy Neumeyer, Victor Rios-Rull, Mark Wright, and Tom
Sargent for helpful comments and suggestions. We also acknowledge comments by participants at seminars
and conferences at NYU, CUNY, Federal Reserve Bank of Kansas City, SUNY-Albany, Federal Reserve Bank
of Minneapolis, SED 2007 Annual Meeting in Prague, LACEA 2007 Annual Meeting in Bogota, and the
CREI-CEPR 2007 Conference o n Sovereign Risk in Barcelona.
1Introduction
Three key empirical regularities characterize the relationship between sovereign debt and
economic activity in emerging economies:
(1) Output displays V-shaped dynamics around default episodes. Recent default episodes
have been associated with deep recessions. Arellano (2007) shows that GDP deviations from
trend in the quarter in which default occurred were -14 percent in Argentina, -13 percent
in Russia and -7 percent in Ecuador. Using quarterly data for 39 developing countries over
the 1970-2005 period, Levy-Yeyati and Panizza (2006) show that the recessions associated
with defaults tend to begin prior to the defaults and generally hit bottom when the defaults
take place. Tomz and Wright’s (2007) study of the history of defaults for industrial and
developing countries during the period 1820-2004 reports that the frequency of defaults is
at its maximum when output is at least 7 percent below trend. They also found, ho wever,
that some defaults occurred with less severe recessions, or when output is not below trend in
annual data.
(2) Interest rates on sovereign debt and domestic output are negatively correlated. Neumeyer
and Perri (2005) report that the cyclical correlations between these interest rates and GDP
range from -0.38 to -0.7 in five emerging economies, with an average correlation of -0.55.
Uribe and Yue (2006) report correlations for seven emerging economies ranging from zero to
-0.8, with an average of -0.42.
1
(3) External debt as a share of GDP is high on average, and high when countries default.
Foreign debt was about a third of GDP on average over the 1998-2005 period for the en tire
group of emerging and developing countries as defined in IMF (2006). Within this group,
the highly indebted poor countr ies had the highest average debt ratio at about 100 percent
of GDP, followed by the Eastern European and Western Hemisphere countries, with averages
of about 50 and 40 percent of GDP respectively. Reinhart et al. (2003) report that the
external debt ratio during default episodes averaged 71 percent of GDP for all developing
countries that defaulted at least once in the 1824-1999 period. The default episodes of recent
years are in line with this estimate: Argentina defaulted in 2001 with a 64 percent debt ratio,
and Ecuador and Russia defaulted in 1998 with debt ratios of 85 and 66 percent of GDP
respectively.
These empirical regularities have proven difficult to explain. On one hand, quantitative
business cycle models can account for the negative correlation between country interest rates
and output if the interest rate on sovereign debt is introduced as the exogenous interest rate
faced by a small open economy in which firms require working capital to pay the wages bill.
2
On the other hand, quan titative models of sovereign default based on the classic setup of
1
Neumeyer and Perri used data for Argentina, Brazil, Ko rea, Mexico and the Philippines. Uribe and Yue
added E cuador, Peru and South Africa, but exclude d Korea.
2
See Neumeyer and Perri (2005), U ribe and Yue (2006) and O viedo (2005).
1
Eaton and Gersov itz (1981) can generate countercyclical sovereign spreads if the sovereign
country faces stochastic shocks to an exogenous output endowment.
3
These models require
exogenous output costs of default with special features in order to support non-trivial levels
of debt together with observed default frequencies, but ev en with these costs they either
produce mean debt ratios under 10 percent of GDP or underestimate default probabilities
by a wide margin.
4
Thus, there is a crucial disconnect between business cycle models and
sovereign default models: the former lack an explanation of the default risk premia that drive
their findings, while the latter lack an explanation of the business cycle dynamics that are
critical for their results.
The country risk-business cycle disconnect raises three important questions: Would a
business cycle model with endogenous default risk still be able to explain the stylized facts
that models with exogenous country risk have explained? Can a model of sovereign default
with endogenous output dynamics produce the large output declines needed to support high
ratios of defaultable debt as an equilibrium outcome? Would a model that endogenizes
both country risk and output dynamics be able to mimic the V-shaped dynamics of output
associated with defaults, and the countercyclical behavior of default risk?
This paper aims to answer these questions by studying the quantitative implications of a
model of sovereign default with endogenous output fluctuations. The model borrows from the
sovereign default literature the workhorse Eaton-Gersovitz recursive formulation of strategic
default in which a sovereign borrower makes optimal default c hoices by comparing the payoffs
of repayment and default. In addition, the model borrows from the business cycle literature
a transmission mechanism that links default risk with economic activity via the financing
cost of working capital. We extend the two classes of models (sovereign debt and business
cycle models) by developing a framework in which the equilibrium dynamics of output and
default risk are determined jointly, and influence each other via the interaction between
foreign lenders, the domestic sovereign borro wer, and domestic firms. In particular, a fall in
productivit y in our setup increases the likelihood of default and hence sovereign spreads, and
this in turn increases the firms’ financing costs leading to a further fall in output, which in
turn feeds back into default incentives and sovereign spreads.
We demonstrate via numerical analysis that the model can explain the three key empirical
regularities of sovereign debt mentioned earlier: The model mimics the V-shaped pattern
of output dynamics around defaults with large recessions that hit bottom during defaults,
yields countercyclical in terest rates on sovereign debt, and supports high debt-GDP ratios on
3
See, for example, Aguiar and Gopinath (2006), Arellano (2007), Yue (2006), and Bai and Zhang (2005).
4
Arellano (2 00 7 ) obtains a mean debt ratio of 6 pe r cent of GDP assuming an output cost of default such
that income is the maximum of actual output or 0.97 of average output while the economy is in financial
autarky. Aguiar and Gopinath (2006) obtain a m ean debt ratio of 27 percent assuming a cost of 2 percent of
output per qu arter, but the default freq uenc y is only 0.02 perce nt (in their m od el without tren d shocks and
debt bailouts). Yue (2006) assumes the same output cost in a mo del with renegotiation calibrated to observed
default frequ enc ies, but obtains a mean debt ratio of 9.7 percent of o utput.
2
average and in default episodes. These results are obtained requiring only a small fraction of
firms’ factor costs to be paid with working capital (only 10 percent of the cost of imported
inputs). Moreover, the model matches key business cycle features like the variability of
consumption and the countercyclical behavior of net exports.
These results hinge on three key assumptions of the model: First, producers of final
goods obtain w orking capital loans from abroad to finance purchases of imported intermediate
goods. Second, these producers can choose optimally to employ domestic intermediate goods
instead of imported inputs, but this shift entails an efficiency loss. Third, the gov ernme nt
can divert the firms’ repayment of working capital loans when it defaults on its own debt, so
that both agents default on their foreign obligations at the same time, and the interest rates
they face are equal at equilibrium.
The transmission mechanism that connects count ry risk and business cycles in our model
operates as follows: Final goods producers maximize profits and choose optimally whether
to use imported inputs or inputs produced in the domestic economy. These two inputs are
perfect substitutes in the production technology, but imported inputs have a higher financing
cost because they need to be paid in advance using working capital, while domestic inputs
require costly reallocation of labor away from final goods production into intermediate goods
production. Thus, a shift from imported to domestic inputs causes an efficiency loss in
production of final goods due to the reallocation of labor.
5
The choice of imported v. domestic inputs by final goods producers depends on the
country interest rate (inclusiv e of default risk), which drives the financing cost of working
capital, and on the state of total factor productivity (TFP). When the country has access
to world financial markets, they choose imported intermediate goods if the country interest
rate is low enough and/or TFP is high enough for the efficiency loss from using domestic
inputs to exceed the higher financial cost of imported inputs. That is, final goods producers
trade off the higher financing cost of imported inputs for the enhanced efficiency in the use
of labor services (which are fully allocated to final goods production). In this situation,
fluctuations in default risk affect the cost of working capital and thus induce fluctuations in
factor demands and output. Conversely, above (below) a threshold value of the interest rate
(TFP) firms choose to use domestic inputs because the financing cost of imported inputs
exceeds the efficiency loss due to domestic labor reallocation, with labor services now being
allocated to both final and intermediate goods production.
When the economy defaults, both the government and firms are excluded from world credit
markets for some time, with an exogenous probability of re-entry as is common in the recent
5
This efficiency loss can be mode led in different ways. We can obtain similar results as t he ones shown
in this paper by modeling the efficiency loss as resulting from costly sectoral reallocation of capital, given an
exogenous amount of aggregate capital, or from foreign inputs that are “superior” to d omestic inputs in the
sense that they support higher TFP. The efficiency loss can also result from changes in capacity utilization,
which can be linked to the choice of imp orted v. domestic inputs using Finn’s (1995) setup.
3
