When an exposure of interest is confounded by unmeasured factors, an instrumental variable (IV) can be used to identify and estimate certain causal contrasts. Identification of the marginal average treatment effect (ATE) from IVs relies on strong untestable structural assumptions. When one is unwilling to assert such structure, IVs can nonetheless be used to construct bounds on the ATE. Famously, Balke and Pearl (1997) proved tight bounds on the ATE for a binary outcome, in a randomized trial with noncompliance and no covariate information. We demonstrate how these bounds remain useful in observational settings with baseline confounders of the IV, as well as randomized trials with measured baseline covariates. The resulting bounds on the ATE are non-smooth functionals, and thus standard nonparametric efficiency theory is not immediately applicable. To remedy this, we propose (1) under a novel margin condition, influence function-based estimators of the bounds that can attain parametric convergence rates when the nuisance functions are modeled flexibly, and (2) estimators of smooth approximations of these bounds. We propose extensions to continuous outcomes, explore finite sample properties in simulations, and illustrate the proposed estimators in a randomized experiment studying the effects of vaccination encouragement on flu-related hospital visits.

翻译：当感兴趣的处理变量受未测量因素混杂影响时，工具变量可用于识别和估计特定因果对比。利用工具变量识别边际平均处理效应依赖于强不可检验的结构假设。当不愿施加此类结构时，工具变量仍可用于构建平均处理效应的界。著名的是，Balke和Pearl（1997）在无协变量信息的非依从随机试验中证明了二元结局下平均处理效应的紧界。我们展示了这些界如何在存在工具变量基线混杂因素的观察性研究及含测量基线协变量的随机试验中保持实用性。所得的平均处理效应界是非光滑泛函，因此标准非参数效率理论不能直接适用。为解决此问题，我们提出：（1）在新颖的边界条件下，基于影响函数的界估计量，该估计量在灵活建模干扰函数时能达到参数收敛速率；（2）这些界的光滑逼近估计量。我们提出扩展到连续结局的方案，通过模拟探索有限样本性质，并在研究疫苗接种鼓励对流感相关住院影响的随机实验中阐明所提出的估计量。