Under what assumptions do Site-by-Treatment instruments identify average causal effects?

The increasing availability of data from multi‐site randomized trials provides a potential opportunity to use instrumental variables methods to study the impacts of multiple hypothesized mediators of the effect of a treatment. We describe nine assumptions needed to identify the impacts 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 non‐trivial and cannot be empirically verified, suggesting that multiple‐site, multiple‐mediator instrumental variables models must be justified by strong theory.