Censored Quantile Instrumental Variable Estimation via Control Functions

In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator handles censoring semi-parametrically 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 computational algorithm combines a control function approach with the CQR estimator developed by Chernozhukov and Hong (2002). Through Monte-Carlo simulation, 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. Given the strong parametric assumptions required by Tobit IV, the gains to CQIV relative to Tobit IV are likely to be large in empirical applications. We present results from an empirical application of CQIV to the estimation of Engel curves for alcohol. This empirical application demonstrates the importance of accounting for censoring and endogeneity with CQIV.