Penalized Quantile Regression Estimation for a Model with Endogenous Individual Effects

Abstract. This paper proposes a penalized quantile regression estimator for panel data that explicitly considers individual heterogeneity associated with the covariates. We provide conditions under which the estimator is asymptotically Gaussian, and the harshness of the penalization can be determined by minimizing asymptotic mean squared error. We investigate finite sample and asymptotic performance in terms of quadratic loss in a class of quantile regression estimators for panel data. The evidence suggests that the penalized approach can significantly reduce the variability of existing quantile regression estimators for models with endogenous individual effects, without introducing bias. An empirical application illustrates the use of the approach.