sovereign defaults on a number
of occasions, the most recent being Argentinas default in 2002.
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. That is, emerging
markets on average borrow more in good times and at lower interest rates as compared
to slumps. Our ability to match these facts within the framework of an otherwise
standard business cycle model with endogenous default relies on the importance of a
stochastic trend in emerging markets. We wish to thank participants at the Chicago Graduate School of Business lunch workshop and Society
for Economic Dynamics (2003) meetings for useful comments. We particularly thank Fernando Alvarez for
helpful comments. Both Aguiar and Gopinath acknowledge with thanks research support from the Chicago
Graduate School of Business during writing of this paper. Gopinath wishes to acknowledge as well support
from the James S. Kemper Foundation. mark.aguair@gsb.uchicago.edu gita.gopinath@gsb.uchicago.edu
1 1
Introduction
World capital markets have experienced large scale sovereign defaults on a number of oc-
casions, the most recent being Argentinas default in 2002. This latest crisis is the fth
Argentine default or restructuring episode in the last 180 years (Reinhart, Rogo and Savas-
tana (2003)). While Argentina may be an extreme case, sovereign defaults occur with some
frequency in emerging markets. 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 re-
garding emerging markets: defaults occur in equilibrium, interest rates are countercyclical,
net exports are countercyclical, and interest rates and the current account are positively
correlated. That is, emerging markets 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.
Our approach follows the classic framework of Eaton and Gersowitz (1981) in which
risk sharing is limited to one period bonds and repayment is enforced by the threat of
nancial autarky. A key ingredient of our approach is to model the income process of
emerging markets as characterized by a volatile stochastic trend that dominates the volatil-
ity of transitory shocks. In a previous paper (Aguiar and Gopinath (2004)), we document
empirically that the fraction of variance at business cycle frequencies explained by perma-
nent shocks is around 50% in a small developed economy (Canada) and more than 80%
in an emerging market (Mexico). This characterization captures the frequent switches in
regimes these markets endure, often associated with clearly dened changes in government
policy, including dramatic changes in monetary, scal, and trade policies. There is a large
literature on the political economy of emerging markets in general, and the tensions behind
the sporadic appearances of pro-growth regimes in particular, that supports our emphasis
on trend volatility (see, for example, Dornbusch and Edwards(1992)).
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 occurs extremely rarely roughly two defaults every
2 2,500 years. The intuition for this is described in detail in Section 3. The weakness of the
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 over
the last 150 years.
To see the intuition behind why default occurs so rarely in a model with transitory
shocks and a stable trend, consider that 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 shocks to productivity. To see why transi-
tory shocks imply infrequent default, consider when productivity is close to a random walk.
While a persistent shock has a large impact on the present value of expected utility, the
impact of such a shock is similar across the two value functions. That is, with a nearly
random walk income process, 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 par-
ticularly 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
3 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
(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. For a given
probability of default, the cost of an additional unit of debt is therefore lower in a model
with trend shocks (and in which agents internalize the interest rate schedule). Agents are
consequently willing to borrow to the point that default is relatively likely. This theme is
developed in Section 4.
Note that this intuition stresses that the marginal cost of borrowing is lower in the
presence of trend shocks. It is also the case that the marginal benet to borrowing is
higher as well. The option to default provides insurance against repayment in bad states.
With trend shocks, a given shock has a magnied eect on permanent income and thus
on consumption. This additional consumption volatility increases the value of insurance.
However, we nd that quantitatively the demand for insurance varies little across our two
specications once we constrain the models to produce the same volatility of income at
business cycle frequencies. Rather, we show that the important dierence between an
economy with trend rather than transitory shocks lies in the equilibrium price of insurance.
However, reecting the role of default in providing insurance, we show that as we ceterus
paribas double the volatility of either trend or transitory shocks, the rate of default roughly
doubles as well.
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 tends to imply a
4 negative correlation between the current account and interest rates. An increase in borrow-
ing 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 de-
fault 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 eects on the probability of default. Accordingly, in
our benchmark simulations, a model with trend shocks matches the empirical feature of
countercyclical current accounts, countercyclical interest rates and a positive correlation
between the two processes. The model with transitory shocks however fails to match these
facts. The prediction for which both models perform poorly is in matching the volatility of
the interest rate process
The model with shocks to trend generates default roughly once every 125 years. This
matches the rate observed in many emerging markets. However, it falls short of the extreme
rates seen in Latin America. For exam