other assessments. As such, the DVA can be seen as a screening and filtering system to identify countries that are potentially at risk.

# **6 Conclusion**

This paper describes a methodology for analyzing public debt vulnerability. Four distinct elements make up this framework: (1) A Fundamental Index identifies vulnerable countries by mapping default risk to changes in fundamentals; (2) a Default Probability Index measures the degree of weakened perceptions regarding risk; (3) a Count Index maps expert opinion to debt vulnerability; and (4) a Theory Index estimates debt thresholds that vary by the probability of a panic for each market access country in the study.

The Fundamental Index consists of a large set of variables related to debt vulnerabilities and summarizes risks by looking at available low-frequency data. The Fundamental Index shows rising/abating vulnerabilities by country.

Two default probabilities are calculated to create the Default Probability Index. One uses required primary balances and actual primary balances to produce a debt sustainability default probability related to a government’s ability to finance its debts. The other one uses interest rate spreads to produce measures of defaulting expectations. The two default probabilities track each other for most of the sample, but diverge just before default. The difference between the two probability estimates is a proxy for a probability of a panic - if markets perceive a higher risk than what the fundamentals suggest, then it can lead to an increase in roll-over risk.

Thresholds from the IMF-WBG DSAs are used in the construction of the Count Index. The index measures the proportion of variables of a country that exceed a threshold. Countries that have many variables exceeding their thresholds are more likely to default.

The Theory Index of the framework consists of identifying debt thresholds that are indicative of risky, safe, and default regions. These debt-to-GDP thresholds are time varying as opposed to static thresholds typical of DSAs. They measure an angle of default related to what it ought to be. The theoretical model controls for debt maturity, spreads, and a panic probability to model endogenous default.

The four indices are used as predictors of sovereign default. Three statistical methodologies are applied. A classical logit regression, a LASSO logit regression, and random forests. The latter two methodologies apply machine learning techniques to maximize the prediction aspect of the framework.

The results suggest that the four indices do better than rules of thumb and standard estimates in identifying defaults, with a LASSO type regression yielding the highest level of precision.

This framework is distinct from traditional early-warning systems. In addition to flagging vulnerable countries, outputs help identify sources of vulnerability and hence provide a policy angle to reduce risks. The theoretical model, as an example, illustrates that debtto-GDP thresholds are unique to countries as opposed to applying a single threshold to all countries that fall within an income group. In addition, the Fundamental Index decomposes the variability of vulnerability into a set of variables.

The framework can be improved with access to more data. Some data are not publicly available for all countries - such as implicit and explicit government guarantees, which 27