Making Event Study Plots Honest: A Functional Data Approach to Causal Inference
Chencheng Fang, Dominik Liebl
TL;DR
This paper recasts Difference-in-Differences as a functional data problem, proving that the DiD estimator converges to a Gaussian process in the space of continuous functions and enabling simultaneous confidence bands for the entire event-time trajectory. It develops a practical framework that yields honest inference via equivalence testing in the pre-treatment period and relevance testing in the post-treatment period, with both oracle (continuous-time) and interpolated (practical) implementations. The methodology supports covariate adjustment and staggered adoption, provides uniform inference results, and demonstrates strong finite-sample performance in simulations and two empirical applications. By turning event study plots into rigorous tools for causal inference, the approach enhances credibility and reliability of conclusions drawn from DiD designs in applied settings.
Abstract
Event study plots are the centerpiece of Difference-in-Differences (DiD) analysis, but current plotting methods cannot provide honest causal inference when the parallel trends and/or no-anticipation assumption fails. We introduce a novel functional data approach to DiD that directly enables honest causal inference via event study plots. Our DiD estimator converges to a Gaussian process in the Banach space of continuous functions, enabling powerful simultaneous confidence bands. This theoretical contribution allows us to turn an event study plot into a rigorous honest causal inference tool through equivalence and relevance testing: Honest reference bands can be validated using equivalence testing in the pre-treatment period, and honest causal effects can be tested using relevance testing in the post-treatment period. We demonstrate the performance of our method in simulations and two case studies.