Quantile Regression with Censoring and Endogeneity
Massachusetts Institute of Technology (MIT) - Department of Economics; New Economic School
Boston University - Department of Economics
Amanda Ellen Kowalski
National Bureau of Economic Research (NBER); Yale University
April 23, 2011
Cowles Foundation Discussion Paper No. 1797
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.
Number of Pages in PDF File: 51
Keywords: Censored, Quantile, Instrumental variable, Censoring, Endogeneity, Engel curve, Alcohol
JEL Classification: C01, C14working papers series
Date posted: April 26, 2011
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