Quantile Regression with Censoring and Endogeneity

TL;DR

This paper introduces a new censored quantile instrumental variable (CQIV) estimator that handles censoring and endogeneity simultaneously, with detailed properties, computation methods, and practical applications demonstrated through simulations and real data.

Contribution

We develop the first CQIV estimator combining censored quantile regression with control variable approach for endogeneity, including its theoretical properties and computational algorithm.

Findings

The CQIV estimator is asymptotically normal under regularity conditions.

The estimator effectively handles censoring and endogeneity in empirical data.

Simulation and empirical results demonstrate its practical applicability.

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 with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are non-additive in the unobservables. The first stage estimates a non-additive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a non-additive 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 non-additive 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.