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Quantile regression with censoring and endogeneity

  • Victor Chernozhukov

    ()

    (Institute for Fiscal Studies and MIT)

  • Ivan Fernandez-Val

    (Institute for Fiscal Studies and University of Boston)

  • Amanda Kowalski

    (Institute for Fiscal Studies)

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.

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File URL: http://cemmap.ifs.org.uk/wps/cwp2011.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP20/11.

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Date of creation: May 2011
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Handle: RePEc:ifs:cemmap:20/11
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