Quantile regression and sample selection, a control function approach

Arellano and Bonhomme (2017) considered nonparametric identification and semiparametric estimation of a quantile selection model, and Arellano and Bonhomme (2017s) extended the estimation approach to the case with censoring. However, there are some major drawbacks associated with the approach in Arellano and Bonhomme (2017s). In this paper we consider nonparametric and semiparametric identification of the quantile selection model with censoring, and we further propose a semiparametric estimation procedure by making some major adjustments to Arellano and Bonhomme’s (2017, 2017s) approaches to overcome the above mentioned drawbacks. Our estimator is shown to be consistent and asymptotically normal. A Monte Carlo study indicates that our estimator performs well in finite samples. Our method is illustrated with a CPS data to study wage inequality.