I propose a new identification-robust test for the structural parameter in a heteroskedastic linear instrumental variables model. The proposed test statistic is similar in spirit to a jackknife version of the K-statistic and the resulting test has exact asymptotic size so long as an auxiliary parameter can be consistently estimated. This is possible under approximate sparsity even when the number of instruments is much larger than the sample size. As the number of instruments is allowed, but not required, to be large, the limiting behavior of the test statistic is difficult to examine via existing central limit theorems. Instead, I derive the asymptotic chi-squared distribution of the test statistic using a direct Gaussian approximation technique. To improve power against certain alternatives, I propose a simple combination with the sup-score statistic of Belloni et al. (2012) based on a thresholding rule. I demonstrate favorable size control and power properties in a simulation study and apply the new methods to revisit the effect of social spillovers in movie consumption.

翻译：本文提出一种新的针对异方差线性工具变量模型中结构参数的识别鲁棒性检验。所提出的检验统计量在本质上类似于刀切法K统计量，只要辅助参数能被一致估计，该检验即可实现精确的渐近尺寸。当工具变量数量远大于样本量时，在近似稀疏性条件下仍可实现参数一致估计。由于允许（而非要求）工具变量数量较大，现有中心极限定理难以检验该统计量的极限行为。本文转而采用直接高斯逼近技术，推导出检验统计量的渐近卡方分布。为提升对特定备择假设的检验功效，本文基于阈值规则提出将该统计量与Belloni等(2012)的极大得分统计量进行简单组合。数值模拟验证了该方法在尺寸控制与检验功效方面的优越性，并将新方法应用于重新审视电影消费中的社会溢出效应。