Quantile regression with censoring and endogeneity

Abstract. In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator handles censor-ing semiparametrically in the tradition of Powell (1986), and it generalizes standard censored quantile regression (CQR) methods to incorporate endogenous regressors in a manner that is computationally tractable. Our procedure combines a control variable approach with the computationally attractive algorithm for the CQR estimator developed by Chernozhukov and Hong (2002). The CQIV estimator is consistent and has a normal limiting distribution that can be estimated consistently via resampling methods. Through Monte-Carlo simula-tion, we show that CQIV performs well relative to Tobit IV in terms of bias and dispersion in a model that satisfies the parametric assumptions required for Tobit IV to be efficient, and it outperforms Tobit in a model with heteroskedasticity. Given the strong parametric assumptions required by Tobit IV, the gains to CQIV relative to Tobit IV are likely to be large in applied work. We illustrate the results with an empirical application on estimation of Engel curves for alcohol. This application demonstrates the importance of accounting for censoring and endogeneity with real data. Date: March 14, 2011. Preliminary and incomplete, comments are welcome. We thank Sukjin Han and seminar participants at Georgetown for useful comments. Sukjin Han provided capable research assistance. Stata software to implement the methods developed in the paper is available in Amanda Kowalski’s web site a