The canonical difference-in-differences (DD) estimator contains two time periods, ”pre” and ”post”, and two groups, ”treatment” and ”control”. Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper shows that the two-way fixed effects estimator equals a weighted average of all possible two-group/two-period DD estimators in the data. A causal interpretation of two-way fixed effects DD estimates requires both a parallel trends assumption and treatment effects that are constant over time. I show how to decompose the difference between two specifications, and provide a new analysis of models that include time-varying controls.

标准差值 (DD) 估计量包含两个时间段，“前”和“后”，以及两组，“处理”和“控制”。然而，大多数 DD 应用程序利用在不同时间接受治疗的单元组之间的差异。本文表明，双向固定效应估计量等于数据中所有可能的两组/两期 DD 估计量的加权平均值。双向固定效应 DD 估计的因果解释需要平行趋势假设和随时间恒定的处理效应。我展示了如何分解两个规范之间的差异，并提供对包含时变控制的模型的新分析。