Within-group Estimators for Fixed Effects Quantile Models

This paper provides within-group estimators for fixed effects quantile models. We apply the quantile coupling transformation to well approximate fixed effects quantile models by fixed effects Gaussian models. Our estimators enjoy three advantages: (1) fixed effects are eliminated by within-group estimators, so that ours is computationally fast without involving the increasing Hessian matrix with respect to the dimension of fixed effects (Koenker, 2004); (2) the rates of convergence and asymptotic normality are derived, where the limit theory allows for both sequential and joint limits; (3) estimates under the potential mis-specification can be interpreted as solutions of minimizing least squared mis-specification errors.