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Panel Quantile Regression with Common Shocks

Harold D. Chiang, Antonio F. Galvao, Chia-Min Wei

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.

Panel Quantile Regression with Common Shocks

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 . We show that the standard FEQR estimator remains asymptotically normal under the mild condition , thereby accommodating empirically relevant regimes, including those with . 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.
Paper Structure (13 sections, 14 theorems, 108 equations, 2 tables)

This paper contains 13 sections, 14 theorems, 108 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Model and Estimation
  3. Asymptotic Theory
  4. Uniform Consistency
  5. Asymptotic Distribution
  6. Statistical Inference
  7. Monte Carlo Simulations
  8. Conclusion
  9. Proof of the Main Results
  10. Proof of Proposition \ref{['prop:consistency']}
  11. Proof of Theorem \ref{['thm:main']}
  12. Proof of Theorem \ref{['thm:covariance_estimation']}
  13. Auxiliary Lemmas

Key Result

Proposition 1

Under Assumptions assump:x_bounded_support and assump:identification and suppose that $(\log N)^2 / T \to 0$, we have $\max_{1 \leq i \leq N}|\hat{\alpha}_i - \alpha_{i0}| \vee \|\hat{\beta} - \beta_0\| \overset{p}{\rightarrow} 0$.

Theorems & Definitions (32)

  • Remark 1: The rationale behind the structures of Equations \ref{['eq:DGP']} and \ref{['eq:DGP_cond']}
  • Proposition 1: Uniform consistency
  • Remark 2: Structure of asymptotic covariance
  • Theorem 1: Asymptotic distribution
  • Remark 3: Comparison with classical FEQR results
  • Remark 4: Intuition behind Theorem \ref{['thm:main']}
  • Remark 5: Weakly correlated common shocks
  • Theorem 2: Robust covariance estimation
  • Remark 6: Estimating $\Sigma$
  • Remark 7: Robustness of the covariance estimator
  • ...and 22 more