Difference-in-differences with a mediator

TL;DR

This paper develops a new method for causal mediation analysis within the difference-in-differences framework, allowing identification and estimation of direct and indirect effects in observational studies.

Contribution

It introduces mediator-adjusted parallel trends assumptions and derives efficient estimators for natural effects, enhancing causal inference in observational data.

Findings

Job training increases earnings after controlling for mediating employment weeks.

Proposed estimators are multiply robust and nonparametrically efficient.

Method applied to Job Corps data demonstrates practical utility.

Abstract

Causal mediation analysis is a powerful tool for disentangling the total effect of a treatment into its direct effect on the outcome and its indirect effect mediated through an intermediate variable. However, in observational studies, confounding between treatment and potential outcomes typically renders the total and natural effects non-identifiable. In this work, we advance mediation analysis within the difference-in-differences framework. Under a mediator-adjusted parallel trends assumption and additional conditions, we demonstrate that natural indirect, direct, and total effects are identifiable in the treated group. We further derive efficient influence functions for these estimands, enabling the construction of multiply robust and nonparametrically efficient estimators. We establish the asymptotic properties of these estimators. Applying our methodology to data from the Job Corps Study, we find that job training significantly increases both short-term and long-term earnings, after controlling for the indirect effect through the proportion of weeks employed.