Efficient minimum distance estimator for quantile regression fixed effects panel data

This paper develops a new minimum distance quantile regression (MD-QR) estimator for panel data models with fixed effects. The proposed estimator is efficient in the class of minimum distance estimators. In addition, the MD-QR estimator is computationally fast, especially for large cross-sections. We establish consistency and explicitly derive the limiting distribution of the MD-QR estimator for panels with large number of cross-sections and time-series. The limit theory allows for both sequential and joint limits. Monte Carlo simulations are conducted to evaluate the finite sample performance of the estimator. The simulation results confirm that the MD-QR approach produces approximately unbiased estimators with small variances, and is computationally advantageous. Finally, we illustrate the use of the estimator with a simple application to the investment equation model.