Using Multiple Pre-treatment Periods to Improve Difference-in-Differences and Staggered Adoption Design

While difference-in-differences (DID) was originally developed with one pre- and one post-treatment periods, data from additional pre-treatment periods is often available. How can researchers improve the DID design with such multiple pre-treatment periods under what conditions? We first use potential outcomes to clarify three benefits of multiple pre-treatment 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. In a wide range of applications where several pre-treatment periods are available, the double DID improves upon the standard DID both in terms of identification and estimation accuracy. 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.