TY  - JOUR
AU  - Chernozhukov,Victor
AU  - Fernández-Val,Iván
AU  - Kowalski,Amanda E.
TI  - Quantile Regression with Censoring and Endogeneity
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 16997
PY  - 2011
Y2  - April 2011
UR  - http://www.nber.org/papers/w16997
L1  - http://www.nber.org/papers/w16997.pdf
N1  - Author contact info:
Victor Chernozhukov
Department of Economics
MIT
Cambridge, MA  02142
E-Mail: vchern@mit.edu

Iván Fernández-Val
Department of Economics
Boston University
270 Bay State Rd
Boston, MA 02215
E-Mail: ivanf@bu.edu

Amanda E. Kowalski
Department of Economics
Yale University
37 Hillhouse Avenue
Box 208264
New Haven, CT 06520
Tel: 203/432-3521
E-Mail: amanda.kowalski@yale.edu
AB  - 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.
ER  -