COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1797 Quantile Regression with Censoring and Endogeneity Victor Chernozhukov, Ivan Fernandez-Val and Amanda Kowalski April 2011 In this paper, we develop a new censored quantile instrumental variable
(CQIV) estimator and describe its properties and computation. The CQIV estimator combines
Powell (1986) censored quantile regression (CQR) to deal semiparametrically with
censoring, with a control variable approach to incorporate endogenous regressors. The CQIV
estimator is obtained in two stages that are nonadditive in the unobservables. The first
stage estimates a nonadditive model with infinite dimensional parameters for the control
variable, such as a quantile or distribution regression model. The second stage estimates
a nonadditive censored quantile regression model for the response variable of interest,
including the estimated control variable to deal with endogeneity. For computation, we
extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the
estimation of the control variable. We give generic regularity conditions for asymptotic
normality of the CQIV estimator and for the validity of resampling methods to approximate
its asymptotic distribution. We verify these conditions for quantile and distribution
regression estimation of the control variable. We illustrate the computation and
applicability of the CQIV estimator with numerical examples and an empirical application
on estimation of Engel curves for alcohol. |
