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

2025-08-04

AI Summary

Violations of the parallel trends assumption in difference-in-differences (DiD) — arising from pre-treatment dynamics or exogenous shocks — frequently bias causal estimates. Method: This paper proposes a Bayesian sensitivity analysis framework that embeds sensitivity parameters directly into the DiD model and imposes an AR(1) prior on latent potential outcomes to capture temporal dependence. It systematically compares three inference strategies — fixed-parameter, fully Bayesian, and empirical Bayesian — to enhance robustness to departures from parallel trends. Contribution/Results: The approach delivers both robustness and interpretability by quantifying assumption sensitivity through posterior distribution comparisons. Applied to the Philadelphia sugary drink tax, the framework yields highly consistent policy effect estimates across diverse prior specifications, demonstrating its validity and practical utility. It provides policymakers and researchers with a more reliable tool for causal inference in quasi-experimental settings.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Address violations of parallel trends in DiD studies
• Propose Bayesian framework for policy effect estimation
• Introduce sensitivity parameter for robust causal inference

Innovation

• Bayesian DiD framework for non-parallel trends
• AR(1) prior models temporal correlation robustly
• Empirical Bayes calibration from pre-treatment data