In observational studies, treatments are typically not randomized and therefore estimated treatment effects may be subject to confounding bias. The instrumental variable (IV) design plays the role of a quasi-experimental handle since the IV is associated with the treatment and only affects the outcome through the treatment. In this paper, we present a novel framework for identification and inference using an IV for the marginal average treatment effect amongst the treated (ETT) in the presence of unmeasured confounding. For inference, we propose three different semiparametric approaches: (i) inverse probability weighting (IPW), (ii) outcome regression (OR), and (iii) doubly robust (DR) estimation, which is consistent if either (i) or (ii) is consistent, but not necessarily both. A closed-form locally semiparametric efficient estimator is obtained in the simple case of binary IV and outcome and the efficiency bound is derived for the more general case.

中文翻译：

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用工具变量处理的边际平均处理效果的识别和推断

在观察性研究中，治疗通常不是随机的，因此估计的治疗效果可能会受到混杂偏差的影响。工具变量 (IV) 设计起到了准实验手柄的作用，因为 IV 与治疗相关并且仅通过治疗影响结果。在本文中，我们提出了一种新的识别和推理框架，在存在未测量的混杂的情况下，使用 IV 来处理被治疗者（ETT）之间的边际平均治疗效果。对于推理，我们提出了三种不同的半参数方法：（i）逆概率加权（IPW），（ii）结果回归（OR）和（iii）双稳健（DR）估计，如果（i）或（ ii) 是一致的，但不一定两者都是。