Seminars

Abstract: Causal inference is often focused on average effects, which can hide important aspects of the effect distributions. Here we consider the entire posterior effects distribution by estimating full counterfactual outcome distributions. We propose a methodology for inference on counterfactual distributions which builds upon the martingale posterior framework of Fong et al. (JRSS, B, 2023). This provides a highly flexible approach to estimating densities, distribution functions, and derived quantities such as quantiles, which coherently quantifies the epistemic uncertainty on any target estimand of interest. As the predictive recursions are based on an underlying nonparametric model (a Dirichlet process mixture model), it naturally inherits a robustness with respect to restrictive parametric assumptions. This approach can be applied to marginal or conditional counterfactual distributions and is easily extended to an instrumental variables setup. We illustrate our approach on two well-known data sets, one investigating the impact of vitamin A supplementation on children’s survival rates with one-sided noncompliance (analysed in Imbens and Rubin, Annals of Statistics, 1997) and another on the effect of job training (LaLonde, AER, 1986).