Exploiting multivariate outcomes in Bayesian inference for causal effects with noncompliance

A Bayesian approach to causal inference in the presence of noncompliance to assigned randomized treatment is considered. It exploits multivariate outcomes for improving estimation of weakly identified models, when the usually invoked exclusion restriction assumptions are relaxed. Using artificial data sets, we analyze the properties of the posterior distribution of causal estimands to evaluate the potential gains of jointly modelling more than one outcome. The approach can be used to assess robustness with respect to deviations from structural identifying assumptions. It can also be extended to the analysis of observational studies with instrumental variables where exclusion restriction assumptions are usually questionable.