Program Evaluation with Right-Censored Data

TL;DR

This paper develops a unified, nonparametric framework for estimating various treatment effects with right-censored outcomes, applicable under multiple assumptions, and provides theoretical guarantees for the estimators' properties.

Contribution

It introduces easy-to-implement, closed-form estimators for treatment effects under right censoring, extending Kaplan-Meier methods with theoretical validation.

Findings

Valid uniform law of large numbers established

Functional central limit theorems proven for estimators

Bootstrap validity confirmed for inference procedures

Abstract

In a unified framework, we provide estimators and confidence bands for a variety of treatment effects when the outcome of interest, typically a duration, is subjected to right censoring. Our methodology accommodates average, distributional, and quantile treatment effects under different identifying assumptions including unconfoundedness, local treatment effects, and nonlinear differences-in-differences. The proposed estimators are easy to implement, have close-form representation, are fully data-driven upon estimation of nuisance parameters, and do not rely on parametric distributional assumptions, shape restrictions, or on restricting the potential treatment effect heterogeneity across different subpopulations. These treatment effects results are obtained as a consequence of more general results on two-step Kaplan-Meier estimators that are of independent interest: we provide conditions for applying (i) uniform law of large numbers, (ii) functional central limit theorems, and (iii) we prove the validity of the ordinary nonparametric bootstrap in a two-step estimation procedure where the outcome of interest may be randomly censored.