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 field experiment studying the effects of canvassing on resulting voter turnout.

翻译：当感兴趣的暴露因子受未测量因素混杂影响时，工具变量可用于识别和估计某些因果对比。从工具变量中识别边际平均处理效应依赖于强且不可检验的结构性假设。若不愿采用此类结构假设，工具变量仍可用于构建平均处理效应的边界。著名的Balke和Pearl（1997）研究证明，在无协变量信息的非依从性随机试验中，二元结局的平均处理效应存在紧边界。我们展示了这些边界如何在存在工具变量基线混杂因素的观察性研究以及存在测量基线协变量的随机试验中保持实用性。所得平均处理效应边界是非光滑泛函，因此标准非参数效率理论无法直接适用。为解决此问题，我们提出：（1）在新型边际条件下，基于影响函数的边界估计量，当干扰函数灵活建模时可达到参数收敛速度；（2）这些边界光滑逼近的估计量。我们提出连续结局的扩展方法，通过模拟研究探索有限样本性质，并在考察拉票活动对选民投票率影响的随机现场试验中演示所提估计量。