Valid Causal Inference with (Some) Invalid Instruments

Instrumental variable methods provide a powerful approach to estimating causal effects in the presence of unobserved confounding. But a key challenge when applying them is the reliance on untestable "exclusion" assumptions that rule out any relationship between the instrument variable and the response that is not mediated by the treatment. In this paper, we show how to perform consistent instrumental variable estimation despite violations of the exclusion assumption. In particular, we show that when one has multiple candidate instruments, only a majority of these candidates- or, more generally, the modal candidate-response relationship-needs to be valid to estimate the causal effect. Our approach uses an estimate of the modal prediction from an ensemble of instrumental variable estimators. The technique is simple to apply and is "black-box" in the sense that it may be used with any instrumental variable estimator as long as the treatment effect is identified for each valid instrument independently. As such, it is compatible with recent machine-learning based estimators that allow for the estimation of conditional average treatment effects (CAPE) on complex, high dimensional data. Experimentally, we achieve accurate estimates of conditional average treatment effects using an ensemble of deep network-based estimators, including on a challenging simulated Mendelian randomization problem.