  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.
