Cohort-Anchored Robust Inference for Event-Study with Staggered Adoption

Abstract

This paper proposes a cohort-anchored framework for robust inference in event studies with staggered adoption, building on Rambachan and Roth (2023). Robust inference based on event-study coefficients aggregated across cohorts can be misleading due to the dynamic composition of treated cohorts, especially when pre-trends differ across cohorts. My approach avoids this problem by operating at the cohort-period level. To address the additional challenge posed by time-varying control groups in modern DiD estimators, I introduce the concept of block bias: the parallel-trends violation for a cohort relative to its fixed initial control group. I show that the biases of these estimators can be decomposed invertibly into block biases. Because block biases maintain a consistent comparison across pre- and post-treatment periods, researchers can impose transparent restrictions on them to conduct robust inference. In simulations and a reanalysis of minimum-wage effects on teen employment, my framework yields better-centered (and sometimes narrower) confidence sets than the aggregated approach when pre-trends vary across cohorts. The framework is most useful in settings with multiple cohorts, sufficient within-cohort precision, and substantial cross-cohort heterogeneity.