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：本文提供了一个在异质因果效应模型中检验工具变量有效性的通用框架。该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推论，我们提出了一种非参数检验方法，并证明了其渐近尺寸受控且具有一致性。与文献中的现有检验相比，我们的检验方法适用于更广泛的设定，并且可能实现功效改进。通过检验对工具变量有效性的反驳，有助于识别可能导致因果效应结果不合理的无效工具变量。通过模拟实验验证了该检验在有限样本中的良好表现。我们重新审视了教育回报率的实证研究，以展示所提方法在实际中的应用。为建立零假设下检验统计量的渐近分布，我们提供了扩展连续映射定理和扩展Delta方法，这些结果本身可能具有独立的研究价值。