Multiply Robust Learning of the Average Treatment Effect with an Invalid Instrumental Variable

Instrumental variable (IV) methods have been widely used to identify causal effects in the presence of unmeasured confounding. A key IV identification condition known as the exclusion restriction states that the IV cannot have a direct effect on the outcome which is not mediated by the exposure in view. In the health and social sciences, such an assumption is often not credible. As a result, possible violation of the exclusion restriction can seldom be ruled out in practice. To address this concern, we consider identification conditions of the population average treatment effect (ATE) without requiring the exclusion restriction. We also propose novel semiparametric estimators in multiple observed data models targeting the ATE, and a multiply robust locally efficient estimator that is consistent in the union of these models. We illustrate the proposed methods through simulations and an econometric application evaluating the causal effect of 401(k) participation on savings.