Instrumental variables are widely used in econometrics and epidemiology for identifying and estimating causal effects when an exposure of interest is confounded by unmeasured factors. Despite this popularity, the assumptions invoked to justify the use of instruments differ substantially across the literature. Similarly, statistical approaches for estimating the resulting causal quantities vary considerably, and often rely on strong parametric assumptions. In this work, we compile and organize structural conditions that nonparametrically identify conditional average treatment effects, average treatment effects among the treated, and local average treatment effects, with a focus on identification formulae invoking the conditional Wald estimand. Moreover, we build upon existing work and propose nonparametric efficient estimators of functionals corresponding to marginal and conditional causal contrasts resulting from the various identification paradigms. We illustrate the proposed methods on an observational study examining the effects of operative care on adverse events for cholecystitis patients, and a randomized trial assessing the effects of market participation on political views.

翻译：工具变量在计量经济学和流行病学中被广泛用于识别和估计因果效应，当关注的暴露因素受到未测量因素的混杂影响时。尽管工具变量方法应用广泛，但文献中为证明其使用合理性所依据的假设存在显著差异。同样，用于估计由此产生的因果量的统计方法也大相径庭，且常常依赖于强参数假设。本文系统整理了非参数识别条件平均处理效应、处理组平均处理效应和局部平均处理效应的结构条件，重点关注基于条件瓦尔德估计量的识别公式。此外，我们在现有研究基础上，为不同识别范式下对应的边际和条件因果对比的函数提出了非参数高效估计方法。我们通过一项关于手术护理对胆囊炎患者不良事件影响的观察性研究，以及一项评估市场参与对政治观点影响的随机试验，对所提方法进行了实证验证。