Under What Assumptions Do Site-by-Treatment Instruments Identify Average Causal Effects?

The increasing availability of data from multisite randomized trials provides a potential opportunity to use instrumental variables (IV) methods to study the effects of multiple hypothesized mediators of the effect of a treatment. We derive nine assumptions needed to identify the effects of multiple mediators when using site-by-treatment interactions to generate multiple instruments. Three of these assumptions are unique to the multiple-site, multiple-mediator case: (1) the assumption that the mediators act in parallel (no mediator affects another mediator); (2) the assumption that the site-average effect of the treatment on each mediator is independent of the site-average effect of each mediator on the outcome; and (3) the assumption that the site-by-compliance matrix has sufficient rank. The first two of these assumptions are nontrivial and cannot be empirically verified, suggesting that multiple-site, multiple-mediator IV models must be justified by strong theory.