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

TL;DR

This paper introduces a functional data approach to event study plots in Difference-in-Differences analysis, enabling honest causal inference with rigorous confidence bands and validity tests.

Contribution

It develops a novel DiD estimator that converges to a Gaussian process, allowing for honest causal inference through equivalence and relevance testing in event study plots.

Findings

Method provides valid confidence bands for causal inference.

Simulation studies demonstrate improved accuracy.

Case studies confirm practical applicability.

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.