A stochastic algorithm for quantile regression models with fixed effects

In this paper, we present a stochastic algorithm for parameter estimation based on panel quantile regression model. We propose an easy-to-implement estimator based on the proposed algorithm. We profile the quantile-specific fixed effects as functions of the parameters of interest based on the Gaussian mixture representation of the asymmetric Laplace (AL) likelihood and eliminate the fixed effects through a data transformation. Parameters of interest can be estimated via quantile regression. Under a set of sufficient conditions, the proposed estimator is consistent and asymptotically normal when n and T both go to infinity. The proposed estimator is illustrated via both simulations and real data examples.