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

arXiv: https://arxiv.org/abs/2102.09948 · HTML: https://mlsanity.com/paper/2102.09948/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2021.

## Built on by (most cited first, 1 of 1)

- [The Impact of Generative AI on Collaborative Open-Source Software Development: Evidence from GitHub Copilot](https://mlsanity.com/paper/2410.02091/) (2024)

## Abstract (arXiv)

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.