Analysis of the binary instrumental variable model
Thomas Richardson (University of Washington) and James Robins (Harvard)
The instrumental variable model comprises a randomly assigned
treatment (Z), an exposure variable (X) and a response variable
(Y). It is well known that when all three of these variables are
binary, the potential outcomes model is not identified by the 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 displaying the set of distributions compatible with the observed data. 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 a re-parameterization that may be used for Bayesian inference and the development of models that incorporate baseline covariates.
Time permitting we will discuss extensions to trials in which randomized
treatment (Z) takes more than 2 levels.