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.

翻译：本文针对固定效应面板分位数回归（FEQR）建立了渐近理论和推断框架，该框架能够对普遍存在的共同冲击提供稳健推断。此类冲击会引发横截面依赖性，这在许多经济和金融面板数据中至关重要，但现有FEQR理论大多忽略该问题——现有理论通常假设横截面独立性且要求$T \gg N$。我们证明标准FEQR估计量在$(\log N)^2/T \to 0$的温和条件下仍保持渐近正态性，从而能够涵盖包括$T \ll N$在内的实证相关数据场景。我们进一步证明共同冲击会从根本上改变渐近协方差结构，导致传统协方差估计量失效，并提出一种在共同冲击存在与否时均保持一致性的简易协方差估计量。因此，所提方法无需预先了解依赖结构即可提供有效的稳健推断，显著拓展了FEQR方法在现实面板数据场景中的适用性。