The instrumental variable method is widely used in the health and social sciences for identification and estimation of causal effects in the presence of potentially unmeasured confounding. In order to improve efficiency, multiple instruments are routinely used, leading to concerns about bias due to possible violation of the instrumental variable assumptions. To address this concern, we introduce a new class of g-estimators that are guaranteed to remain consistent and asymptotically normal for the causal effect of interest provided that a set of at least $\gamma$ out of $K$ candidate instruments are valid, for $\gamma\leq K$ set by the analyst ex ante, without necessarily knowing the identities of the valid and invalid instruments. We provide formal semiparametric efficiency theory supporting our results. Both simulation studies and applications to the UK Biobank data demonstrate the superior empirical performance of our estimators compared to competing methods.

翻译：为了提高效率,经常使用多种工具,从而引起对可能违反工具变量假设的偏见的关切。为了解决这一关切,我们引入了一种新的测算员类别,这些测算员在利益因果关系方面保证保持一贯性和无损正常性,但前提是,在分析员前期设定的一套至少为1美元(gamma\leq K)的候选工具中,至少有1美元(gomma$)是有效的,而分析员前期设定的1美元($\gamma\leq K)不一定知道有效和无效工具的身份。我们提供了正式的半对称效率理论来支持我们的结果。模拟研究和对英国生物库数据的应用都显示了我们的测算员相对于竞争方法的优异经验表现。