The classical tests in the instrumental variable model can behave arbitrarily if the data is contaminated. For instance, one outlying observation can be enough to change the outcome of a test. We develop a framework to construct testing procedures that are robust to weak instruments, outliers and heavy-tailed errors in the instrumental variable model. The framework is constructed upon M-estimators. By deriving the influence functions of the classical weak instrument robust tests, such as the Anderson-Rubin test, K-test and the conditional likelihood ratio (CLR) test, we prove their unbounded sensitivity to infinitesimal contamination. Therefore, we construct contamination resistant/robust alternatives. In particular, we show how to construct a robust CLR statistic based on Mallows type M-estimators and show that its asymptotic distribution is the same as that of the (classical) CLR statistic. The theoretical results are corroborated by a simulation study. Finally, we revisit three empirical studies affected by outliers and demonstrate how the new robust tests can be used in practice.

翻译：在工具变量模型中，如果数据受到污染，经典检验可能表现出任意性。例如，单个异常观测值就足以改变检验结果。我们构建了一个框架，用于设计在工具变量模型中对弱工具变量、异常值和重尾误差具有稳健性的检验程序。该框架基于M估计量构建。通过推导经典弱工具变量稳健检验（如安德森-鲁宾检验、K检验和条件似然比检验）的影响函数，我们证明了这些检验对无穷小污染具有无界敏感性。因此，我们构建了抗污染/稳健的替代方法。特别地，我们展示了如何基于马洛斯型M估计量构建稳健的CLR统计量，并证明了其渐近分布与经典CLR统计量相同。模拟研究验证了理论结果。最后，我们重新审视了三个受异常值影响的实证研究，并展示了如何在实践中应用新的稳健检验。