Asymptotics and bootstrap inference for panel quantile regression models with fixed effects

This paper studies panel quantile regression models with fixed effects. We formally establish sufficient conditions for consistency and asymptotic normality of the quantile regression estimator when the number of individuals, n, and the number of time periods, T , jointly go to infinity. The estimator is shown to be consistent under similar conditions to those found in the nonlinear panel data literature. Nevertheless, due to the non-smoothness of the criterion function, we had to impose a more restrictive condition on T to prove asymptotic normality than that usually found in the literature. We also examine the practical ability of bootstrap procedures for inference in quantile regression models for panel data. The finite sample performance of the estimator and the bootstrap procedures are evaluated by Monte Carlo simulations.

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