Difference-in-differences with a mediator
Yuhao Deng, Haoyu Wei, Zhongzhe Ouyang
TLDR
This paper introduces a difference-in-differences framework to identify natural indirect, direct, and total causal effects in observational studies.
Key contributions
- Identifies natural indirect, direct, and total causal effects within a difference-in-differences framework.
- Proposes a mediator-adjusted parallel trends assumption for identifiability in treated groups.
- Derives efficient influence functions for multiply robust and nonparametrically efficient estimators.
- Applies methodology to Job Corps data, showing job training increases earnings via employment weeks.
Why it matters
Observational studies often struggle to identify causal mediation effects due to confounding. This work provides a robust difference-in-differences framework, enabling identification of direct and indirect effects. This advances causal inference, allowing researchers to better understand treatment mechanisms in real-world data.
Original 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.
📬 Weekly AI Paper Digest
Get the top 10 AI/ML arXiv papers from the week — summarized, scored, and delivered to your inbox every Monday.