Efficient Estimation of a Triangular System of Equations for Quantile Regression

This paper proposes a one-step sieve estimator of the parameter in the semiparametric triangular model for quantile regression of Lee (2007). The proposed estimator is a penalized sieve minimum distance (PSMD) estimator developed by Chen and Pouzo (2009). We develop the asymptotic theory for the PSMD estimator under a set of low-level conditions. The PSMD estimator is shown to be semiparametrically efficient, and the validity of a weighted bootstrap is established. A small Monte Carlo simulation study shows that our estimator performs well in finite samples