Multivalued treatments are commonplace in applications. We explore the use of discrete-valued instruments to control for selection bias in this setting. Our discussion stresses the role of assumptions on targeting (which instruments target which treatments) and filtering (limits on the analyst's knowledge of the treatment assigned to a given observation). It allows us to establish conditions under which counterfactual averages and treatment effects are identified for composite complier groups. We illustrate the usefulness of our framework by applying it to data from the Head Start Impact Study and the Student Achievement and Retention Project.

翻译：多值处理在应用中十分常见。本文探索使用离散值工具变量来控制此类情境下的选择偏差。我们的讨论侧重于关于目标设定（哪些工具变量针对哪些处理）和过滤（分析者对给定观测所分配处理的知识限制）的假设所发挥的作用。这使我们能够确立在复合依从者群体中，反事实均值和处理效应可被识别的条件。我们通过将分析框架应用于“启智计划影响研究”和“学生成就与保留项目”的数据，说明了该框架的实用性。