Instrumental variable quantile regression under random right censoring

TL;DR

This paper develops a semiparametric instrumental variable quantile regression method for models with endogenous variables and right censoring, providing estimation, inference, and validation through simulations and real data application.

Contribution

It introduces a novel estimation approach for quantile regression with endogenous regressors under right censoring, including asymptotic properties and bootstrap inference.

Findings

Estimator is asymptotically normal.

Bootstrap procedure is valid for inference.

Method performs well in finite samples.

Abstract

This paper studies a semiparametric quantile regression model with endogenous variables and random right censoring. The endogeneity issue is solved using instrumental variables. It is assumed that the structural quantile of the logarithm of the outcome variable is linear in the covariates and censoring is independent. The regressors and instruments can be either continuous or discrete. The specification generates a continuum of equations of which the quantile regression coefficients are a solution. Identification is obtained when this system of equations has a unique solution. Our estimation procedure solves an empirical analogue of the system of equations. We derive conditions under which the estimator is asymptotically normal and prove the validity of a bootstrap procedure for inference. The finite sample performance of the approach is evaluated through numerical simulations. An application to the national Job Training Partnership Act study illustrates the method.