Semiparametric Bespoke Instrumental Variables

Many proposals for the identification of causal effects in the presence of unmeasured confounding require an instrumental variable or negative control that satisfies strong, untestable exclusion restrictions. In this paper, we will instead show how one can identify causal effects for a point exposure by using a measured confounder as a 'bespoke instrumental variable'. This strategy requires an external reference population that does not have access to the exposure, and a stability condition on the confounderoutcome association between reference and target populations. Building on recent identification results of Richardson and Tchetgen Tchetgen (2021), we develop the semiparametric efficiency theory for a general bespoke instrumental variable model, and obtain a multiply robust locally efficient estimator of the average treatment effect in the treated. The utility of the estimators is demonstrated in simulation studies and an analysis of the Life Span Study, concerning atomic bomb survivors in Japan.