Cluster Robust Covariance Matrix Estimation in Panel Quantile Regression with Individual Fixed Effects

Abstract

This paper develops cluster robust inference methods for panel quantile regression (QR) models with individual fixed effects, allowing 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 estimator (CCM) that solves this problem. The CCM estimator is an extension of the heteroskedasticity and autocorrelation consistent covariance matrix estimator to QR models with fixed effects. The auto-covariance element in the CCM estimator can be substantially biased due to the incidental parameter problem. So we develop a bias correction method. We derive an optimal bandwidth formula that minimises the asymptotic mean squared errors and propose a data driven bandwidth selection rule. We also develop two cluster robust tests and establish their asymptotic properties. Simulation studies show that cluster robust standard errors and tests have excellent finite sample properties. We demonstrate the usefulness of the new methods using two empirical applications.