English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

While a difference-in-differences (DID) design was originally developed withone pre- and one post-treatment period, data from additional pre-treatmentperiods are often available. How can researchers improve the DID design withsuch multiple pre-treatment periods under what conditions? We first usepotential outcomes to clarify three benefits of multiple pre-treatment periods:(1) assessing the parallel trends assumption, (2) improving estimationaccuracy, and (3) allowing for a more flexible parallel trends assumption. Wethen propose a new estimator, double DID, which combines all the benefitsthrough the generalized method of moments and contains the two-way fixedeffects regression as a special case. We show that the double DID requires aweaker assumption about outcome trends and is more efficient than existing DIDestimators. We also generalize the double DID to the staggered adoption designwhere different units can receive the treatment in different time periods. Weillustrate the proposed method with two empirical applications, covering boththe basic DID and staggered adoption designs. We offer an open-source R packagethat implements the proposed methodologies.

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