Double DID: Relax Parallel Trends Assumption with Multiple Pretreatment Periods

• In Event: Causal Inference for Time-Series Data

Abstract

Difference-in-Differences (DID) is one of the most popular methods to estimate the causal effect with time-series cross-sectional data. However, it is well known that the parallel trends assumption required for identification might be too strong in many applications. In this article, we develop double difference-in-differences (double DID), which relaxes the parallel trends assumption by using multiple pre-treatment periods. It only requires that changes in the trends are the same between treatment and control groups. If the parallel trends assumption holds, the proposed estimator based on the generalized method of moments is more efficient than the standard DID. Because pre-treatment trends are incorporated into a built-in model selection procedure, researchers do not need to separately evaluate whether the parallel trends assumption holds in pre-treatment periods. We illustrate this method with an application to a study about the causal impact of recentralization on public services. The proposed methodology is implemented in a forthcoming R package.

Authors

• Naoki Egami, Princeton University

• Soichiro Yamauchi, Harvard University