- In the crisis zone, the economy is vulnerable to a self-fulfilling crisis and the government’s optimal policy is to default only if it could not roll over its stock of debt. Countries that fall in this zone are susceptible to uncertain shocks. These countries might find themselves in a crisis without even knowing that they are at risk when an uncertain shock were to materialize.

- In the default zone, the interest payments are so large that the government would choose to default even if investors were willing to refinance the stock of debt. Countries in the default zone can be considered vulnerable since they are estimated to face an elevated risk of default in the event of a crisis.

To produce outputs, the model requires a set of calibrated parameters. The model requires an estimate of the probability of a panic (proxied by the subjective default rates identified above<sup>10</sup> ); the maturity composition of public debt;<sup>11</sup> the structural levels of revenues and expenditures; output loss upon a default; and the average yield to maturity.

As an example Cole and Kehoe (1996) illustrates the usefulness of these models in the case of Mexico. Mexico was not facing imminent default right before the 1994-1995 crisis. Yet, public debt was high and the share of short-term debt was high. Mexico had debt levels that were in the crisis zone due to **short maturity bonds** . In 1994, there was political turmoil followed by the assassination of the ruling party’s presidential candidate Luis Donaldo Colosia. Subsequently, Mexico defaulted. Mexico could have been better prepared to address a potential shock by increasing its maturity structure and issuing bonds in local currency. Also, the government might have pursued fiscal consolidation more forcefully if there had been more awareness about the risk of default (Cole and Kehoe, 1996). The Theory index would then have picked up if Mexico was getting close to the default zone and would have coded it as a value of 3.

Figure 12 below illustrates an output for a hypothetical country given a set of calibrated parameters. In this chart, the y-axis expresses the future debt-to-GDP ratio, while the x-axis the current debt-to-GDP ratio. The red line is a 45-degree line. Any value above the red line suggests that government’s optimal policy (black line) is to increase the debt-to-GDP ratio. On the contrary, any value below the red line implies an optimal policy of reducing future debt-to-GDP ratios. In this scenario, the lower threshold is about 70 percent of GDP and it divides the safe zone from the crisis zone. The upper threshold is about 90 percent of GDP and it divides the crisis zone from the default zone. Above this level, debt drops to a value of zero given that the country’s optimal decision is to default even if investors were willing to refinance the stock of debt. Hence, investors will not lend to this country and the future debt level drops to a value of zero.

Finally, once we compute the time varying probability of a panic, we can express the thresholds also as a varying function of time. In Figure 13, we illustrate this for South Africa and Argentina in the sample using a simple 1 period maturity. The upper and risky thresholds change over the sample period. Argentina breaches the threshold by 2018, while South Africa is reaching the upper threshold as it accumulates more debt. Interestingly, the

> 10Due to computational restrictions, we have created a mapping between the theoretical model’s probability of panic and the subjective probability. The probability of panic is 0.4 times the subjective probability.

> 11We obtained maturity rates on non-concessional borrowing for 42 countries from 5 regions using Bloomberg. To increase the sample size to 159 countries, we used the average rate of the 42 countries for each of the 5 regions.

19