This study develops cluster robust inference methods for panel quantile regression (QR) models with individual fixed effects, allowing for temporal correlation within each individual. The conventional QR standard errors can seriously underestimate the uncertainty of estimators and, therefore, overestimate the significance of effects, when outcomes are serially correlated. Thus, we propose a clustered covariance matrix (CCM) estimator to solve this problem. The CCM estimator is an extension of the heteroskedasticity and autocorrelation consistent covariance matrix estimator for QR models with fixed effects. The autocovariance element in the CCM estimator can be substantially biased, due to the incidental parameter problem. Thus, we develop a bias‐correction method for the CCM estimator. We derive an optimal bandwidth formula that minimizes the asymptotic mean squared errors, and propose a data‐driven bandwidth selection rule. We also propose two cluster robust tests, and establish their asymptotic properties. We then illustrate the practical usefulness of the proposed methods using an empirical application.

中文翻译：

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具有独立固定效应的面板分位数回归中的聚类鲁棒协方差矩阵估计

这项研究为具有个别固定效应的面板分位数回归（QR）模型开发了聚类鲁棒性推断方法，允许每个个体内的时间相关。当结果与序列相关时，传统的QR标准误差会严重低估估计量的不确定性，因此高估了影响的重要性。因此，我们提出了一种聚类协方差矩阵（CCM）估计器来解决此问题。CCM估计器是具有固定效应的QR模型的异方差和自相关一致协方差矩阵估计器的扩展。由于附带参数问题，CCM估计器中的自协方差元素可能会明显偏倚。因此，我们为CCM估计器开发了一种偏差校正方法。我们推导了一个最佳带宽公式，该公式使渐近均方误差最小，并提出了一种数据驱动的带宽选择规则。我们还提出了两个聚类鲁棒性测试，并建立了它们的渐近性质。然后，我们使用经验应用说明了所提出方法的实际实用性。