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Defaultable Debt, Interest Rates and the Current Account Defaultable Debt, Interest Rates and the Current Account Mark Aguiar Federal Reserve Bank of Boston
Gita Gopinath University of Chicago and NBER
Abstract
World capital markets have experienced large scale sovereign defaults on a number of oc-
casions. In this paper we develop a quantitative model of debt and default in a small open
economy. We use this model to match four empirical regularities regarding emerging markets:
defaults occur in equilibrium, interest rates are countercyclical, net exports are countercyclical,
and interest rates and the current account are positively correlated. We highlight the role of the
stochastic trend in emerging markets, in an otherwise standard model with endogenous default,
to match these facts.
JEL Classication: F3, F4
Keywords: sovereign debt, default, current account, interest rates, stochastic trend We thank seminar participants at Brandeis, Chicago, SED (2003), and the Federal Reserve Bank of San Fran-
ciscos conference on Emerging Markets and Macroeconomic Volatility, Enrique Mendoza, Diego Valderrama and two
anonymous referees for useful comments. We particularly thank Fernando Alvarez for helpful comments. Both Aguiar
and Gopinath acknowledge with thanks research support from the Chicago GSB. Gopinath wishes to acknowledge as
well support from the James S. Kemper Foundation. The views expressed in this paper are not necessarily those of
the Federal Reserve Bank of Boston or the Federal Reserve System. mark.aguiar@bos.frb.org Email: gita.gopinath@gsb.uchicago.edu, Tel: (617)4958161. Address: Department of Economics, Harvard Uni-
versity, 1805 Cambridge Street, Littauer Center, Cambridge, MA 02138.
1 1
Introduction
World capital markets have experienced large scale sovereign defaults on a number of occasions, the
most recent being Argentinas default in 2002. This latest crisis is the fth Argentine default or
restructuring episode in the last 180 years.
1
While Argentina may be an extreme case, sovereign
defaults occur with some frequency in emerging markets. A second set of facts about emerging
markets relates to the behavior of the interest rates at which these economies borrow from the
rest of the world and their current accounts. Interest rates and the current account are strongly
countercyclical and positively correlated to each other. That is, emerging markets tend to borrow
more in good times and at lower interest rates as compared to slumps. These features contrast with
those observed in developed small open economies.
In this paper we develop a quantitative model of debt and default in a small open economy, which
we use to match the above facts. Our approach follows the classic framework of Eaton and Gersovitz
(1981) in which risk sharing is limited to one period bonds and repayment is enforced by the threat
of nancial autarky. In all other respects the model is a standard small open economy model where
the only source of shocks are endowment shocks. In this framework, we show that the models
ability to match certain features in the data improve substantially when the productivity process
is characterized by a volatile stochastic trend as opposed to transitory uctuations around a stable
trend. In a previous paper (Aguiar and Gopinath (2004)), we document empirically that emerging
markets are indeed more appropriately characterized as having a volatile trend. The fraction of
variance at business cycle frequencies explained by permanent shocks is shown to be around 50% in
a small developed economy (Canada) and more than 80% in an emerging market (Mexico).
To isolate the importance of trend volatility in explaining default, we rst consider a standard
business cycle model in which shocks represent transitory deviations around a stable trend. We
nd that default is extremely rare, occurring roughly twice every 2,500 years. The weakness of the
1
See Reinhart, Rogo and Savastana (2003).
2 standard model begins with the fact that autarky is not a severe punishment, even adjusting for
the relatively large income volatility observed in emerging markets. The welfare gain of smoothing
transitory shocks to consumption around a stable trend is small. This in turn prevents lenders from
extending debt, which we demonstrate through a simple calculation a la Lucas (1987). We can
support a higher level of debt in equilibrium by assuming an additional loss of output in autarky.
However, in a model of purely transitory shocks, this does not lead to default at a rate that resembles
those observed in many economies.
The intuition behind why default occurs so rarely in a model with transitory shocks and a stable
trend is described in Section 3. The decision to default rests on the dierence between the present
value of utility (value function) in autarky versus that of nancial integration. Quantitatively, the
level of default that arises in equilibrium depends on the relative sensitivity of the two value functions
to endowment shocks. When the endowment process is close to a random walk there is limited need
to save out of additional endowment, leaving little dierence between nancial autarky and a good
credit history, regardless of the realization of income. At the other extreme, if the transitory shock is
iid over time, then there is an incentive to borrow and lend, making integration much more valuable
than autarky. However, an iid shock has limited impact on the entire present discounted value
of utility, and so the dierence between integration and autarky is not sensitive to the particular
realization of the iid shock. At either extreme, therefore, the decision to default is not sensitive
to the realization of the shock. Consequently, when shocks are transitory, the level of outstanding
debt and not the realization of the stochastic shock is the primary determinant of default. This
is reected in nancial markets by an interest rate schedule that is extremely sensitive to quantity
borrowed. Borrowers internalize the steepness of the loan supply curve and recognize that an
additional unit of debt at the margin will have a large eect on the cost of debt. Agents therefore
typically do not borrow to the point where default is probable.
On the other hand, a shock to trend growth has a large impact on the two value functions
3 (because of the shocks persistence) and on the dierence between the two value functions. The latter
eect arises because a positive shock to trend implies that income is higher today, but even higher
tomorrow, placing a premium on the ability to access capital markets to bring forward anticipated
income. In this context, the decision to default is relatively more sensitive to the particular realization
of the shock and less sensitive to the amount of debt. Correspondingly, the interest rate is less
sensitive to the amount of debt held. Agents are consequently willing to borrow to the point that
default is relatively likely. This theme is developed in Section 4.
The next set of facts concerns the phenomenon of countercyclical current accounts and interest
rates. In the current framework where all interest rate movements are driven by changes in the
default rate, the steepness of the interest rate schedule makes it challenging to even qualitatively
match the positive correlation between interest rates and the current account. This is because, on
the one hand, an increase in borrowing in good states (countercyclical current account) will, all else
equal, imply a movement along the heuristic loan supply curve and a sharp rise in the interest
rate. On the other hand, if the good state is expected to persist, this lowers the expected probability
of default and is associated with a favorable shift in the interest rate schedule. To generate a positive
correlation between the current account and interest rates we need the eect of the shift of the curve
to dominate the movement along the curve. A stochastic trend is again useful in matching this fact
since the interest rate function tends to be less steeply sloped and trend shocks have a signicant
eect on the probability of default. Accordingly, in our benchmark simulations, a model with trend
shocks matches the empirical feature of a positive correlation between the interest rate and the
current account. The model with transitory shocks however fails to match this fact. The prediction
for which both models perform poorly is in matching the volatility of the interest rate process.
2
The model with shocks to trend generates default roughly once every 125 years, which is a ten-fold
2
The additional observed volatility may be due to a volatile risk premium, as suggested by Broner, Lorenzoni, and
Schmukler (2004).
4 improvement over the standard model but still shy of the observed pattern for chronic defaulters.
We bring the default rate closer to that observed empirically for Latin America by introducing
third-party bail-outs. Realistic bailouts raise the rate of default dramatically bailouts up to 18%
of GDP lead to defaults once every 27 years. However, the subsidy implied by bailouts breaks the
tight linkage between default probability and the interest rate. Interest rate volatility is therefore
an