Using Multiple Pretreatment Periods to Improve Difference-in-Differences and Staggered Adoption Designs

Abstract

Abstract While a difference-in-differences (DID) design was originally developed with one pre- and one posttreatment period, data from additional pretreatment periods are often available. How can researchers improve the DID design with such multiple pretreatment periods under what conditions? We first use potential outcomes to clarify three benefits of multiple pretreatment periods: (1) assessing the parallel trends assumption, (2) improving estimation accuracy, and (3) allowing for a more flexible parallel trends assumption. We then propose a new estimator, double DID, which combines all the benefits through the generalized method of moments and contains the two-way fixed effects regression as a special case. We show that the double DID requires a weaker assumption about outcome trends and is more efficient than existing DID estimators. We also generalize the double DID to the staggered adoption design where different units can receive the treatment in different time periods. We illustrate the proposed method with two empirical applications, covering both the basic DID and staggered adoption designs. We offer an open-source R package that implements the proposed methodologies.