When some groups violate 'parallel trends', study the groups that don't: a new local DiD estimand for staggered treatments
This paper addresses a common problem in difference‑in‑differences studies. These studies assume that, without the policy or event being studied, treated and comparison groups would have followed the same time path. That assumption is called “parallel trends.” When some treated groups break that rule but others do not, the usual average treatment effect on the treated (ATT) can be biased and hard to interpret.
The authors propose changing the question rather than trying harder to defend the original one. They define a credible‑subpopulation local ATT (LATT). LATT is the average effect only for the cohorts whose pre‑treatment trends look credible. In other words, they restrict attention to the subset of cohorts for which the parallel‑trends assumption is plausible. Under parallel trends for those selected cohorts alone, LATT is point‑identified. That is a weaker and often more realistic identifying assumption than requiring parallel trends for every treated cohort.
How do they estimate it? The method reweights standard group‑time effect estimates (the building blocks used in staggered‑adoption designs) toward the selected cohorts. The selection can be done in two ways. It can be ex‑ante, using outside knowledge or a data split, or data‑driven, by screening cohorts whose estimated pre‑treatment differences are close to flat. Because the selection can depend on the same data used for estimation, the authors pair the point estimate with honest sensitivity bounds. These bounds follow the sensitivity analysis approach of Rambachan and Roth (2023) and quantify how large a post‑treatment trend could be while remaining consistent with the observed pre‑trends.
The method has clear strengths and limits. It buys credibility by narrowing the target to cohorts where the identifying assumption is plausible. Simulations in the paper show the advantage grows when pre‑treatment trends are informative about what might happen after treatment. But pre‑trend tests can be weak in practical samples, and a flat pre‑treatment path does not guarantee no post‑treatment drift. If pre‑trends are uninformative, selecting a subpopulation buys little and can give a misleading sense of precision. The authors also stress practical requirements: groups must be large enough to estimate pre‑trends, and the screening rule and its inferential role must be handled carefully.