Quantile Regression with Censoring and Endogeneity

51 Pages Posted: 26 Apr 2011

See all articles by Victor Chernozhukov

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics; New Economic School

Iván Fernández‐Val

Boston University - Department of Economics

Amanda Kowalski

University of Michigan at Ann Arbor - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: April 23, 2011

Abstract

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.

Keywords: Censored, Quantile, Instrumental variable, Censoring, Endogeneity, Engel curve, Alcohol

JEL Classification: C01, C14

Suggested Citation

Chernozhukov, Victor and Fernandez-Val, Ivan and Kowalski, Amanda, Quantile Regression with Censoring and Endogeneity (April 23, 2011). Cowles Foundation Discussion Paper No. 1797, Available at SSRN: https://ssrn.com/abstract=1822383

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-262f
Cambridge, MA 02142
United States
617-253-4767 (Phone)
617-253-1330 (Fax)

HOME PAGE: http://www.mit.edu/~vchern/

New Economic School

100A Novaya Street
Moscow, Skolkovo 143026
Russia

Ivan Fernandez-Val

Boston University - Department of Economics ( email )

270 Bay State Road
Boston, MA 02215
United States

HOME PAGE: http://people.mit.edu/ivanf

Amanda Kowalski (Contact Author)

University of Michigan at Ann Arbor - Department of Economics ( email )

Ann Arbor, MI
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
44
Abstract Views
864
PlumX Metrics