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

TL;DR

This paper introduces a new estimator called double DID that leverages multiple pre-treatment periods to enhance difference-in-differences analysis, offering more flexibility, efficiency, and weaker assumptions, especially in staggered adoption settings.

Contribution

The paper develops the double DID estimator that utilizes multiple pre-treatment periods, improving accuracy and flexibility over traditional methods, and extends it to staggered adoption designs.

Findings

Double DID is more efficient than existing estimators.

It requires weaker assumptions about outcome trends.

The method is demonstrated with empirical applications.

Abstract

While a difference-in-differences (DID) design was originally developed with one pre- and one post-treatment period, data from additional pre-treatment periods are 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. 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.