Testing for equivalence of pre-trends in Difference-in-Differences estimation

TL;DR

This paper introduces equivalence tests for the parallel trends assumption in Difference-in-Differences analysis, enabling researchers to more convincingly validate the key pre-trend assumption rather than merely failing to reject it.

Contribution

It develops equivalence testing methods for pre-trends in DiD, extending the standard approach to staggered treatment adoption scenarios.

Findings

Provides formal equivalence tests for pre-trends

Enhances credibility of DiD estimates

Applicable to staggered treatment settings

Abstract

The plausibility of the ``parallel trends assumption'' in Difference-in-Differences estimation is usually assessed by a test of the null hypothesis that the difference between the average outcomes of both groups is constant over time before the treatment. However, failure to reject the null hypothesis does not imply the absence of differences in time trends between both groups. We provide equivalence tests that allow researchers to find evidence in favor of the parallel trends assumption and thus increase the credibility of their treatment effect estimates. While we motivate our tests in the standard two-way fixed effects model, we discuss simple extensions to settings in which treatment adoption is staggered over time.