This paper provides a general framework for testing instrument validity in heterogeneous causal effect models. The generalization includes the cases where the treatment can be multivalued ordered or unordered. Based on a series of testable implications, we propose a nonparametric test which is proved to be asymptotically size controlled and consistent. Compared to the tests in the literature, our test can be applied in more general settings and may achieve power improvement. Refutation of instrument validity by the test helps detect invalid instruments that may yield implausible results on causal effects. Evidence that the test performs well on finite samples is provided via simulations. We revisit the empirical study on return to schooling to demonstrate application of the proposed test in practice. An extended continuous mapping theorem and an extended delta method, which may be of independent interest, are provided to establish the asymptotic distribution of the test statistic under null.

翻译：本文提出一个在异质性因果效应模型中检验工具变量有效性的通用框架。该框架的推广涵盖处理变量为有序或多分类无序的情形。基于一系列可检验的蕴含关系，我们构建了一个非参数检验方法，并证明该方法在渐近意义上具有尺寸控制性和一致性。相较于现有文献中的检验方法，本文提出的检验适用于更广泛的设定，且可能实现功效改进。通过该检验对工具变量有效性的反驳，有助于识别可能产生不合理因果效应估计结果的无效工具变量。模拟研究证明了该方法在有限样本中的优良表现。我们重新审视了教育回报率的实证研究，以展示所提检验在实际中的应用。为建立原假设下检验统计量的渐近分布，本文证明了拓展的连续映射定理和拓展的Delta方法，这些成果本身可能具有独立的研究价值。