Multivalued treatments are commonplace in applications. We explore the use of discrete-valued instruments to control for selection bias in this setting. Our discussion revolves around the concept of targeting instruments: which instruments target which treatments. It allows us to establish conditions under which counterfactual averages and treatment effects are point- or partially-identified for composite complier groups. We illustrate the usefulness of our framework by applying it to data from the Head Start Impact Study. Under a plausible positive selection assumption, we derive informative bounds that suggest less beneficial effects of Head Start expansions than the parametric estimates of Kline and Walters (2016).

翻译：多值处理在应用中普遍存在。本文探讨在此背景下利用离散值工具变量控制选择偏差的方法。我们的讨论围绕"目标工具"这一概念展开：即哪些工具变量针对哪些处理。这一概念使我们能够建立条件，在复合依从者群体中实现对反事实平均值和处理效应的点识别或部分识别。通过将分析框架应用于"开端计划影响研究"数据，我们展示了其实用价值。在合理的正向选择假设下，我们推导出的信息性边界表明，"开端计划"扩展的效益低于Kline和Walters（2016）的参数估计值。