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

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.