Revisiting Event Study Designs

TLDR

The paper develops a framework for difference‑in‑differences designs with staggered treatment adoption and heterogeneous causal effects. The authors derive an efficient, imputation‑style estimator for staggered‑adoption designs, characterize its asymptotic properties, provide inference tools and tests, and extend the framework to time‑varying controls, triple‑differences, and non‑binary treatments, validating it with simulations and an empirical application. They show conventional regression‑based estimators are biased without strong homogeneity assumptions, and in an empirical study of U.S.

Abstract

We develop a framework for difference-in-differences designs with staggered treatment adoption and heterogeneous causal effects. We show that conventional regression-based estimators fail to provide unbiased estimates of relevant estimands absent strong restrictions on treatment-effect homogeneity. We then derive the efficient estimator addressing this challenge, which takes an intuitive "imputation" form when treatment-effect heterogeneity is unrestricted. We characterize the asymptotic behavior of the estimator, propose tools for inference, and develop tests for identifying assumptions. Extensions include time-varying controls, triple-differences, and certain non-binary treatments. We show the practical relevance of these insights in a simulation study and an application. Studying the consumption response to tax rebates in the United States, we find that the notional marginal propensity to consume is between 8 and 11 percent in the first quarter — about half as large as benchmark estimates used to calibrate macroeconomic models — and predominantly occurs in the first month after the rebate.