Censored Quantile Regression with Many Controls

TL;DR

This paper introduces a new estimation method for censored quantile regression models that effectively handles high-dimensional controls using double/debiased machine learning, ensuring valid inference and consistent, asymptotically normal estimators.

Contribution

It extends censored quantile regression to high-dimensional settings by integrating double/debiased machine learning for valid inference on low-dimensional parameters.

Findings

Estimator is consistent and asymptotically normal.

Performs well in numerical simulations.

Applied to study 401(k) eligibility effects.

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.