Binary quantile regression with local polynomial smoothing

Manski (1975, 1985) proposed the maximum score estimator for the binary choice model under a weak conditional median restriction that converges at the rate of n(-1/3) and the standardized version has a nonstandard distribution. By imposing additional smoothness conditions, Horowitz (1992) proposed a smoothed maximum score estimator that often has large finite sample biases and is quite sensitive to the choice of smoothing parameter. In this paper we propose a novel framework that leads to a local polynomial smoothing based estimator. Our estimator possesses finite sample and asymptotic properties typically associated with the local polynomial regression. In addition, our local polynomial regression-based estimator can be extended to the panel data setting. Simulation results suggest that our estimators may offer significant improvement over the smoothed maximum score estimators. (C) 2015 Elsevier B.V. All rights reserved.