Expected Shortfall Panel Regression

Abstract: Expected Shortfall (ES) is a coherent measure of tail risk that captures the average loss beyond a quantile threshold. Despite the growing literature on ES regression conditional on covariates, no existing work considers ES modeling in panel data settings where both cross-sectional and temporal dependencies are present. This paper introduces the panel ES regression model with a latent factor structure to capture cross-sectional dependence. We develop a two-stage estimation procedure robust to heavy-tailed errors, recovering the conditional quantile in the first stage and iteratively estimating the ES factor model in the second stage. Theoretically, we establish the consistency and asymptotic normality of the proposed two-step ES estimators and derive non-asymptotic error bounds for both the panel quantile and ES estimators. We also provide a non-asymptotic normal approximation for the standardized ES regression estimator, bridging asymptotic theory and finite-sample practice. Simulation evidence shows that the proposed method delivers substantial gains in both parameter estimation and factor recovery, particularly in the presence of latent tail dependence. An empirical application further indicates that the extracted ES factors carry distinct pricing information that is not captured by conventional mean or quantile-based approaches.