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.We gratefully acknowledge the financial support by the Ministerio Economía y Competitividad (Spain), through grant ECO2015-65204-P. Ricardo Mora also acknowledges the financial support from the grants MDM 2014-0431, and MadEco-CM (S2015/HUM-3444)