Expected Shortfall Panel Regression

2026-04-14

AI Summary

This study addresses the gap in modeling Expected Shortfall (ES) for panel data that exhibit both cross-sectional and temporal dependence. It pioneers an extension of ES modeling to the panel data framework by introducing a panel ES regression model with a latent factor structure and develops a two-stage robust estimation procedure: first estimating conditional quantiles and then iteratively estimating ES factor loadings to accommodate heavy-tailed errors and capture cross-sectional dependence. Theoretically, the paper establishes consistency, asymptotic normality, and non-asymptotic error bounds for the proposed estimators. Extensive simulations and empirical analysis demonstrate that the method substantially outperforms existing approaches in parameter estimation and factor recovery, and that the extracted ES factors contain unique risk-pricing information not captured by conventional mean or quantile models.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Security and Privacy: Large-scale security measurements

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.

Problem

• Expected Shortfall
• panel data
• cross-sectional dependence
• tail risk
• latent factor

Innovation

• Expected Shortfall
• panel regression
• latent factor model
• heavy-tailed errors
• non-asymptotic inference