World capital markets have experienced large?scale sovereign defaults on a number of occasions, the most recent being Argentina?s default in 2002. This latest crisis is the fifth Argentine default or restructuring episode in the last 180 years. 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 counter cyclical and positively correlated with each other. That is, emerging markets tend to borrow more in good times and at lower interest rates than in 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 financial autarky. In all other respects the model is a standard small open economy model where the only source of shocks is domestic productivity shocks. In this framework, we show that the model?s ability to match the facts in the data improve substantially when the productivity process is characterized by a volatile stochastic trend as opposed to transitory fluctuations 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 percent in a small developed economy (Canada) and more than 80 percent in an emerging market (Mexico). This characterization captures the frequent switches in regimes these markets endure, often associated with clearly defined changes in government policy, including dramatic changes in monetary, fiscal, and trade policies.
To isolate the importance of trend volatility in explaining default, we first consider a standard business?cycle model in which shocks represent transitory deviations around a stable trend. We find that default occurs extremely rarely roughly two defaults every 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, as we demonstrate through a simple calculation à 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 that explains why default occurs so rarely in a model with transitory shocks and a stable trend, consider that the decision to default rests on the difference between the present value of utility (value function) in autarky versus that of financial 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 transitory 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 difference between financial 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 difference between integration and autarky is not sensitive to the particularly 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 reflected in financial 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 effect 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 shock?s persistence) and on the difference between the two value functions. The latter effect 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 benefit of borrowing is higher as well. The option to default provides insurance against repayment in bad states. With trend shocks, a given shock has a magnified effect on permanent income and thus on consumption. This additional consumption volatility increases the value of insurance.
However, we find that quantitatively the demand for insurance varies little across our two specifications once we constrain the models to produce the same volatility of income at business?cycle frequencies. Rather, we show that the important difference between an economy with trend rather than transitory shocks lies in the equilibrium price of insurance. However, reflecting the role of default in providing insurance, we show that as we double the volatility of either trend or transitory shocks, ceteris paribus, the rate of default roughly doubles as well.
The next set of facts concerns the phenomenon of counter cyclical 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 even qualitatively to 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 (counter cyclical current account) will, all else being 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 effect 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 significant effect on the probability of default.
Accordingly, in our benchmark simulations, a model with trend shocks matches qualitatively the empirical features of counter cyclical current accounts, counter cyclical 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. This might not be surprising since we rely only on default rates as an explanation for movements in interest rates. The roles of risk premia and external shocks have been set aside.
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