🤖 AI Summary
Standard parallel-trends tests in Difference-in-Differences (DID) estimation merely fail to reject the null of no pre-treatment differences, but cannot actively confirm the assumption’s validity, thereby limiting causal credibility. This paper proposes the first equivalence-testing framework for DID pre-trend assessment: the null hypothesis posits *substantive* pre-treatment trend divergence between treatment and control groups; rejection of this null provides direct statistical support for the absence of meaningful pre-trends. We construct an asymptotically t-distributed test statistic and associated confidence sets within a two-way fixed-effects setting, ensuring theoretical rigor and empirical feasibility. The method naturally accommodates staggered adoption designs. Empirically, it detects subtle yet systematic pre-trend deviations missed by conventional tests—enhancing robustness, reproducibility, and causal interpretability of estimated treatment effects.
📝 Abstract
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.