Alternative diff-in-diffs estimators with several pretreatment periods

This paper deals with the identification of treatment effects using difference-in-differences estimators when several pretreatment periods are available. We define a family of identifying nonnested assumptions that lead to alternative difference-in-differences estimators. We show that the most usual difference-in-differences estimators imply equivalence conditions for the identifying nonnested assumptions. We further propose a model that can be used to test multiple equivalence conditions without imposing any of them. We conduct a Monte Carlo analysis and apply our approach to several recent papers to show its practical relevance.