Making Event Study Plots Honest: A Functional Data Approach to Causal Inference

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 assumptions fail. 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 fast and 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-anticipation period, and honest causal effects can be tested using relevance testing in the post-treatment period. We demonstrate the performance of the method in simulations and two case studies.