Analysis of the binary instrumental variable model

I first review the potential outcome (Neyman-Rubin) causal model in the context of a simple randomized experiment with a binary treatment (X) and binary outcome (Y). I then consider the situation in which experimental subjects do not comply, so that the treatment to which subjects are randomized (Z) may differ from that which they receive (X). The latter situation is an instance of the binary instrumental variable model. It is well known that this model is not identified by the observed joint distribution p(x,y,z). Consequently many statistical analyses impose additional assumptions, or change the causal estimand of interest in order to achieve identification. Here we take a different approach, directly characterizing and graphically displaying the set of distributions over potential outcomes that correspond to a given population distribution p(x,y,z). This provides insights into the variation dependence between average causal effects for various compliance groups, that are partially identified. The analysis also leads directly to re-parameterizations that may be used for Bayesian inference and the development of models that incorporate baseline covariates. (Joint work with James Robins, Harvard School of Public Health)