Panel Quantile Regression with Common Shocks

2026-02-22

AI Summary

This study addresses a key limitation in existing inference methods for fixed-effects panel quantile regression (FEQR), which typically rely on cross-sectional independence and require the time dimension to be much larger than the number of individuals—conditions often violated in real-world panels subject to pervasive common shocks. The paper establishes asymptotic theory for FEQR under cross-sectional dependence driven by such common shocks, demonstrating for the first time that the standard FEQR estimator remains asymptotically normal even when \( T \ll N \). It further reveals the critical role of common shocks in shaping the asymptotic covariance structure. Building on these insights, the authors propose a robust covariance estimator that does not require prior knowledge of the dependence structure and is consistent both with and without common shocks, substantially enhancing the applicability and reliability of FEQR in empirical research.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper develops an asymptotic and inferential theory for fixed-effects panel quantile regression (FEQR) that delivers inference robust to pervasive common shocks. Such shocks induce cross-sectional dependence that is central in many economic and financial panels but largely ignored in existing FEQR theory, which typically assumes cross-sectional independence and requires $T \gg N$. We show that the standard FEQR estimator remains asymptotically normal under the mild condition $(\log N)^2/T \to 0$, thereby accommodating empirically relevant regimes, including those with $T \ll N$. We further show that common shocks fundamentally alter the asymptotic covariance structure, rendering conventional covariance estimators inconsistent, and we propose a simple covariance estimator that remains consistent both in the presence and absence of common shocks. The proposed procedure therefore provides valid robust inference without requiring prior knowledge of the dependence structure, substantially expanding the applicability of FEQR methods in realistic panel data settings.

Problem

• panel quantile regression
• common shocks
• cross-sectional dependence
• fixed-effects
• asymptotic inference

Innovation

• panel quantile regression
• common shocks
• cross-sectional dependence
• robust inference
• asymptotic covariance