Factorial Difference-in-Differences
Yiqing Xu, Anqi Zhao, Peng Ding

TL;DR
This paper introduces factorial difference-in-differences (FDID), a new research design extending DID to settings with all units affected by an event, clarifying estimands and assumptions for effect modification and causal moderation.
Contribution
It formulates FDID as a factorial design, defines effect modification and causal moderation, and extends DID assumptions and methods to more complex data settings.
Findings
FDID clarifies effect modification and causal moderation identification.
Additional assumptions are needed for causal moderation.
Framework applied to social capital's role in famine relief in China.
Abstract
We formulate factorial difference-in-differences (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 and the exposure level , and define effect modification and causal moderation as the associative and causal effects of on the effect of , 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 \emph{factorial parallel…
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Taxonomy
TopicsAdvanced Causal Inference Techniques · Multi-Criteria Decision Making · Graph theory and applications
