Bayesian Sensitivity Analyses for Policy Evaluation with Difference-in-Differences under Violations of Parallel Trends

TL;DR

This paper develops a Bayesian framework for difference-in-differences analysis that accounts for violations of the parallel trends assumption, enabling more robust policy evaluation despite pre-treatment dynamics or external shocks.

Contribution

It introduces a formal sensitivity parameter with an autoregressive prior to model violations of parallel trends within a Bayesian DiD framework, with calibration from pre-treatment data.

Findings

Bayesian sensitivity analysis provides robust policy effect estimates.

The method accommodates various prior specifications, including empirical Bayes.

Application to beverage tax data demonstrates practical utility.

Abstract

Violations of the parallel trends assumption pose significant challenges for causal inference in difference-in-differences (DiD) studies, especially in policy evaluations where pre-treatment dynamics and external shocks may bias estimates. In this work, we propose a Bayesian DiD framework to allow us to estimate the effect of policies when parallel trends is violated. To address potential deviations from the parallel trends assumption, we introduce a formal sensitivity parameter representing the extent of the violation, specify an autoregressive AR(1) prior on this term to robustly model temporal correlation, and explore a range of prior specifications - including fixed, fully Bayesian, and empirical Bayes (EB) approaches calibrated from pre-treatment data. By systematically comparing posterior treatment effect estimates across prior configurations when evaluating Philadelphia's sweetened beverage tax using Baltimore as a control, we show how Bayesian sensitivity analyses support robust and interpretable policy conclusions under violations of parallel trends.