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: 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 explore the additional identifying power of a positive selection assumption. We illustrate its usefulness by revisiting the findings of Kline and Walters (2016) on the Head Start Impact Study. We derive informative bounds that suggest less beneficial effects of Head Start expansions than their parametric estimates.

翻译：多值处理在应用研究中十分常见。本文探讨如何利用离散值工具变量来控制此类情境下的选择偏误。我们的讨论围绕"目标化"这一核心概念展开：即哪些工具变量针对哪些处理状态。这一框架使我们能够建立反事实均值与处理效应在复合依从者子群中点识别或部分识别的条件。我们进一步探讨了正向选择假设所带来的额外识别效力。通过重新审视Kline和Walters（2016）关于"启蒙计划"影响研究的结论，我们展示了该方法的实用价值。本文推导出的信息性边界表明，启蒙计划扩展的实际效果可能低于其参数估计结果。