Regressions under Adverse Conditions

Abstract
We introduce a new regression method that relates the mean of an outcome variable to covariates, given the "adverse condition'' that a distress variable falls in its tail. This allows to tailor classical mean regressions to adverse economic scenarios, which receive increasing interest in managing macroeconomic and financial risks, among many others. In the terminology of the systemic risk literature, our method can be interpreted as a regression for the Marginal Expected Shortfall. We propose a two-step procedure to estimate the new models, show consistency and asymptotic normality of the estimator, and propose feasible inference under weak conditions allowing for cross-sectional and time series applications.

The accuracy of the asymptotic approximations of the two-step estimator is verified in simulations. Three empirical applications show that our regressions under adverse conditions are valuable in such diverse fields as the study of the relation between systemic risk and asset price bubbles, portfolio optimization and dissecting macroeconomic growth vulnerabilities into individual components.