This paper proposes novel inference procedures for instrumental variable models in the presence of many, potentially weak instruments that are robust to the presence of heteroskedasticity. First, we provide an Anderson–Rubin-type test for the entire parameter vector that is valid under assumptions weaker than previously proposed Anderson–Rubin-type tests. Second, we consider the case of testing a subset of parameters under the assumption that a consistent estimator for the parameters not under test exists. We show that under the null, the proposed statistics have Gaussian limiting distributions and derive alternative chi-square approximations. An extensive simulation study shows the competitive finite sample properties in terms of size and power of our procedures. Finally, we provide an empirical application using college proximity instruments to estimate the returns to education.

中文翻译：

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具有异方差和多种仪器的仪器变量模型的推理

本文提出了新的工具变量模型推理程序，其中存在许多对异方差的存在具有鲁棒性的潜在弱工具。首先，我们为整个参数向量提供了一个 Anderson-Rubin 型检验，该检验在比先前提出的 Anderson-Rubin 型检验弱的假设下有效。其次，我们考虑在假设存在未测试参数的一致估计量的情况下测试参数子集的情况。我们表明，在零值下，所提出的统计数据具有高斯极限分布，并得出替代卡方近似值。一项广泛的模拟研究显示了在我们程序的大小和功率方面具有竞争力的有限样本特性。最后，