Integrate dimension-reduced propensity score methods into doubly robust ATT and DID frameworks

Integrate the kernel-based, dimension-reduced propensity score estimator that uses Kolmogorov–Smirnov conditional-dependence screening with cross-validation refinement into (i) doubly robust estimators of the average treatment effect on the treated (ATT) and (ii) modern doubly robust difference-in-differences estimators, extending the current ATE-focused implementation to ATT and DID settings.

Background

The paper develops a data-driven dimension reduction procedure for conditional density and propensity score estimation, combining a Kolmogorov–Smirnov-based conditional dependence screening step with a cross-validation refinement, and applies it to doubly robust ATE estimation.

In the empirical 401(k) illustration, the authors caution that their analysis focuses on ATE, whereas common empirical strategies like difference-in-differences target ATT. They note that a more direct methodological comparison would require embedding their dimension-reduction approach within doubly robust ATT and modern doubly robust DID frameworks, which they do not undertake in this paper.

Consequently, a concrete extension is to incorporate the proposed dimension-reduced propensity score estimator into doubly robust ATT estimation (e.g., as in Shinozaki and Matsuyama, 2015) and into modern doubly robust DID procedures (e.g., Sant’Anna and Zhao, 2020).