Difference-in-differences with variation in treatment timing

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 twoway 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. Published by Elsevier B.V.

Automated summary

The paper explores the relationship between the two-way fixed effects estimator and all possible two-group/two-period DD estimators, showing that it is a weighted average. A causal interpretation of two-way fixed effects DD estimates requires meeting the parallel trends assumption and constant treatment effects over time.