Efficient Semiparametric Seemingly Unrelated Quantile Regression Estimation

We propose an efficient semiparametric estimator for the coefficients of a multivariate linear regression model — with a conditional quantile restriction for each equation — in which the conditional distributions of errors given regressors are 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 true optimal instruments 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. ∗(corresponding author) Department of Economics, The Pennsylvania State University, 608 Kern Graduate Building, University Park PA 16802, [email protected] †[email protected] We thank the coeditor, two anonymous referees and participants at the Carnegie Mellon departmental seminar and Ari Kang for their useful suggestions. We thank the Human Capital Foundation for their support.