Modeling Frailty-Correlated Defaults Using Many Macroeconomic Covariates

Abstract

We propose a new econometric framework for estimating and forecasting the default intensities of corporate credit subject to observed and unobserved risk factors. The model combines common factors from macroeconomic and financial covariates with an unobserved latent (frailty) component for discrete default counts, observed contagion factors at the industry level, and standard risk measures such as ratings, equity returns, and volatilities. In an empirical application, we find a large and significant role for a dynamic frailty component even after controlling for more than eighty percent of the variation in more than hundred macroeconomic and financial covariates, as well as industry level contagion dynamics and equity information. We emphasize the need for a latent component to prevent the downward bias in estimated default rate volatility at the rating and industry levels and in estimated probabilities of extreme default losses on portfolios of U.S. debt. The latent factor does not substitute for a single omitted macroeconomic variable. We argue that it captures different omitted effects at different times. We also provide empirical evidence that default and business cycle conditions depend on different processes. In an out-of-sample forecasting study for point-in-time default probabilities, we obtain mean absolute error reductions of more than forty percent when compared to models with observed risk factors only. The forecasts are relatively more accurate when default conditions diverge from aggregate macroeconomic conditions.