Quantile regression with censoring and endogeneity

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 with censoring, with a control variable approach to incorporate endogenous regress...

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Bibliographic Details
Published in:Journal of econometrics 2015-05, Vol.186 (1), p.201-221
Main Authors: Chernozhukov, Victor, Fernández-Val, Iván, Kowalski, Amanda E.
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic methods
Econometrics
Economic models
Economic theory
Estimation
Parameter estimation
Regression analysis
Studies
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Summary: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 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. Our analysis covers two-stage (uncensored) quantile regression with nonadditive first stage as an important special case. We illustrate the computation and applicability of the CQIV estimator with a Monte-Carlo numerical example and an empirical application on estimation of Engel curves for alcohol.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2014.06.017