Efficient Multivariate Quantile Regression Estimation

We propose an efficient semiparametric estimator for the multivariate linear quantile regression model in which the conditional joint distribution of errors given regressors is unknown. The procedure can be used to estimate multiple conditional quantiles of the same regression relationship. The proposed estimator is asymptotically as efficient as if the conditional distribution were known. Simulation results suggest that the estimation procedure works well in practice and dominates an equation–by–equation efficiency correction if the errors are dependent conditional on the regressors. ∗Department of Economics, The Pennsylvania State University, 608 Kern Graduate Building, University Park PA 16802, [email protected] †[email protected] We thank participants at the Carnegie Mellon departmental seminar and Ari Kang for their useful suggestions.