An Anatomy of Event Studies: Hypothetical Experiments, Exact Decomposition, and Weighting Diagnostics

TL;DR

This paper critically examines event study methodologies, introduces robust weighting estimators, provides a novel decomposition of TWFE estimators, and offers diagnostics and visualization tools to improve causal inference in observational studies.

Contribution

It develops a new decomposition of TWFE estimators, introduces diagnostics for event studies, and enhances understanding of information borrowing in causal analysis.

Findings

Decomposition of TWFE estimator in closed form.

Insights into information borrowing and comparison issues.

New diagnostics and visualization tools for event studies.

Abstract

In recent decades, event studies have emerged as a central methodology in health and social research for evaluating the causal effects of staggered interventions. In this paper, we analyze event studies from experimental design principles for observational studies, with a focus on information borrowing across measurements. We develop robust weighting estimators that increasingly use more information across units and time periods, justified by increasingly stronger assumptions on the treatment assignment and potential outcomes mechanisms. As a particular case of this approach, we offer a novel decomposition of the classical dynamic two-way fixed effects (TWFE) regression estimator for event studies. Our decomposition is expressed in closed form and reveals in finite samples the hypothetical experiment that TWFE regression adjustments approximate. This decomposition offers insights into how standard regression estimators borrow information across different units and times, clarifying and supplementing the notion of forbidden comparison noted in the literature. The proposed approach enables the generalization of treatment effect estimates to a target population and offers new diagnostics for event studies, including covariate balance, sign reversal, effective sample size, and the contribution of each observation to the analysis. We also provide visualization tools for event studies and illustrate them in a case study of the impact of divorce reforms on female suicide.