Censored Partial Linear Quantile Regression with Endogeneity

This paper considers the estimation of a censored partial linear quantile regression model with endogeneity. Our method extends those for partial linear quantile regression (Lee, 2003, Qu et al. 2024), nonparametric quantile regression (Qu and Yoon, 2015, Belloni et al., 2019), and censored linear quantile regression with endogeneity (Chen, 2018). Our estimation method involves a tractable sequential-multiple-step procedure. We establish the uniform consistency, the uniform representation and the asymptotic normality for the proposed estimators. We further extend our analysis to allow for sample selection. A set of Monte Carlo experiments show that our estimators have a good finite sample performance and an empirical application is given to show the usefulness of our estimators.