In the context of a binary outcome, treatment, and instrument, Balke and Pearl (1993, 1997) establish that adding monotonicity to the instrument exogeneity assumption does not decrease the identified sets for average potential outcomes and average treatment effect parameters when those assumptions are consistent with the distribution of the observable data. We show that the same results hold in the broader context of multi-valued outcome, treatment, and instrument. An important example of such a setting is a multi-arm randomized controlled trial with noncompliance.

翻译：在二元结果、处理和工具变量的背景下，Balke和Pearl（1993，1997）证明，当单调性与可观测数据分布一致时，在工具变量外生性假设基础上增加单调性假设，并不会缩小平均潜在结果和平均处理效应参数的识别集。本文证明，这一结论在多元结果、处理和工具变量的更广泛背景下依然成立。此类场景的一个重要实例是存在不依从性的多臂随机对照试验。