2024/07/16 by Yiqing Xu, Anqi Zhao, Xu, Yiqing +3
Decision Sciences · Mathematics · #Advanced Causal Inference Techniques #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Graph theory and applications #Methodology (stat.ME) #Multi-Criteria Decision Making
paper · pdf · doi:10.48550/arxiv.2407.11937
openalex publication_date 2024/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate <i>factorial difference-in-differences</i> (FDID), a research design that extends canonical difference-in-differences (DID) to settings in which an event affects all units. In many panel data applications, researchers exploit cross-sectional variation in a baseline factor alongside temporal variation in the event, but the corresponding estimand is often implicit and the justification for applying the DID estimator remains unclear. We frame FDID as a factorial design with two factors, the baseline factor <i>G</i> and the exposure level <i>Z</i>, and define effect modification and causal moderation as the associative and causal effects of <i>G</i> on the effect of <i>Z</i>, respectively. Under standard DID assumptions of no anticipation and parallel trends, the DID estimator identifies effect modification but not causal moderation. Identifying the latter requires an additional <i>factorial parallel trends</i> assumption, that is, mean independence between <i>G</i> and potential outcome trends. We extend the framework to conditionally valid assumptions and regression-based implementations, and further to repeated cross-sectional data and continuous <i>G</i>. We demonstrate the framework with an empirical application on the role of social capital in famine relief in China. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.