Addressing lack of common support in causal inference using Bayesian non-parametrics

Causal inference strategies in observational studies that assume ignorability of the treatment assignment also typically require an assumption of common support; problems can arise when trying to estimate causal effects in neighborhoods of the covariate space where there are not both treatment and control units. If ignorability is satisfied, then identifying whether, or for which units, the common support assumption is satisfied is an empirical question. However in high-dimensional covariate space such identification may not be trivial. Methods have been developed in the past two decades can be used to address this problem, yet many require reliance on parametric assumptions and most, if not all, ignore the information embedded in the response variable. We propose a method for identifying common support that addresses both of these issues.