Probabilistic Causal Panel Analysis

Abstract

Many causal panel estimators construct counterfactuals using weights or latent structure estimated directly from observed outcomes, making treatment-effect estimates sensitive to observation noise. Bayesian hierarchical models can account for this noise and borrow information across related observations, but existing Bayesian approaches to causal panel analysis generally combine outcome modeling and counterfactual imputation in estimator-specific formulations that can require bespoke sampling algorithms. We develop a framework that learns the latent untreated panel with a probabilistic model and applies established causal estimators to its posterior draws. The model accommodates non-Gaussian observations and structured pooling, while re-estimation across draws propagates uncertainty through counterfactual imputation. We establish conditions for posterior consistency of counterfactual imputation, characterize how pooling affects imputation risk, and develop fast cross-validation for model selection and calibration of predictive uncertainty for treatment effects. Our results show that probabilistic modeling can improve counterfactual imputation, particularly when observation noise is substantial and the pooling structure is informative.