Robust Inference for Panel Quantile Regression Models with Individual Fixed Effects and Serial Correlation

Abstract

This paper develops cluster robust inference methods for panel quantile regression (QR) models with individual fixed effects, allowing arbitrary temporal correlation structure within each individual. The conventional QR standard errors assuming independent outcomes can seriously underestimate the uncertainty of estimators and therefore overestimate the significance of effects when outcomes are serially correlated. This is analogous to the well-known size distortion in the OLS estimation of panel data, illustrated by Bertrand, Duflo, and Mullainathan (2004). Thus, we propose a clustered covariance matrix estimator that solves this problem in panel QR models. In addition, we develop two cluster robust tests and establish their asymptotic properties. Unlike OLS, there is no known data transformation in quantile models that effectively remove individual fixed effects, so we use recent advancements in panel QR literature to deal with the incidental parameters problem. Simulation studies show that cluster robust tests have good finite sample properties. We demonstrate the usefulness the new methods using an empirical capital structure example. The results document evidence of strong heterogeneity of the economic drivers across the conditional distribution of market debt ratio.