Censored Quantile Regression with Many Controls

Abstract: This paper develops estimation and inference methods for censored quantile regression models with high-dimensional controls. The methods are based on the application of double/debiased machine learning (DML) framework to the censored quantile regression estimator of Buchinsky and Hahn (1998). I provide valid inference for low-dimensional parameters of interest in the presence of high-dimensional nuisance parameters when implementing machine learning estimators. The proposed estimator is shown to be consistent and asymptotically normal. The performance of the estimator with high-dimensional controls is illustrated with numerical simulation and an empirical application that examines the effect of 401(k) eligibility on savings.