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 $G$ and the exposure level $Z$, and define effect modification and causal moderation as the associative and causal effects of $G$ on the effect of $Z$, 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 trends} assumption, that is, mean independence between $G$ 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 $G$. We demonstrate the framework with an empirical application on the role of social capital in famine relief in China.

翻译：本文提出析因双重差分法（FDID），这是一种将经典双重差分法（DID）扩展到事件影响所有单元场景的研究设计。在许多面板数据应用中，研究者利用基线因子的截面变异与事件的时间变异，但相应的估计量通常是隐式的，且应用DID估计量的理由仍不明确。我们将FDID构建为一个具有两个因子（基线因子$G$和暴露水平$Z$）的析因设计，并分别将效应修饰和因果调节定义为$G$对$Z$效应的关联效应与因果效应。在无预期效应和平行趋势的标准DID假设下，DID估计量可识别效应修饰，但不能识别因果调节。识别后者需要一个额外的\emph{析因平行趋势}假设，即$G$与潜在结果趋势之间的均值独立性。我们将该框架扩展到条件有效假设和基于回归的实现方式，并进一步扩展到重复截面数据和连续型$G$。我们通过一项关于中国饥荒救济中社会资本作用的实证应用来展示该框架。