Causal mediation with instrumental variables

Mediation analysis is a strategy for understanding the mechanisms by which treatments or interventions affect later outcomes. Mediation analysis is frequently applied in randomized trial settings, but typically assumes: a) that randomized assignment is the exposure of interest as opposed to actual take-up of the intervention, and b) no unobserved confounding of the mediator-outcome relationship. In contrast to the rich literature on instrumental variable (IV) methods to estimate a total effect of a non-randomized exposure, there has been almost no research into using IV as an identification strategy in the presence of both exposure-outcome and mediator-outcome unobserved confounding. In response, we define and identify novel estimands -- complier interventional direct and indirect effects (i.e., IV mediational effects) in two scenarios: 1) with a single IV for the exposure, and 2) with two IVs, one for the exposure and another for the mediator, that may be related. We propose nonparametric, robust, efficient estimators, and apply them to a housing voucher experiment.