Cohort-Anchored HonestDiD

Abstract

HonestDiD sensitivity analysis (Rambachan and Roth, 2023) is usually applied to event-study coefficients aggregated across cohorts. Under staggered adoption, the treated cohorts contributing to these coefficients change with event time, as do their control groups with estimators that use not-yet-treated units. Therefore, the restriction on the aggregated coefficients and the corresponding inference does not have a clear interpretation. This paper proposes to do the HonestDiD sensitivity analysis on a cohort basis. The restriction is placed on each cohort's block bias, which captures its violation of parallel trends relative to the units untreated when it first adopts treatment. The restriction on the block bias maps to the restriction on the estimation bias through an invertible linear decomposition. In simulations, the proposed cohort inference keeps nominal coverage when parallel trend violations differ across cohorts, where the inference based on aggregated coefficients can fail. Applying the method to Callaway and Sant'Anna (2021) and Bailey and Goodman-Bacon (2015), I highlight the trade-off between interpretable imposed restrictions and the precision demands of cohort inference.