This paper proposes an overidentifying restriction test for high-dimensional linear instrumental variable models. The novelty of the proposed test is that it allows the number of covariates and instruments to be larger than the sample size. The test is scale-invariant and is robust to heteroskedastic errors. To construct the final test statistic, we first introduce a test based on the maximum norm of multiple parameters that could be high-dimensional. The theoretical power based on the maximum norm is higher than that in the modified Cragg-Donald test (Koles\'{a}r, 2018), the only existing test allowing for large-dimensional covariates. Second, following the principle of power enhancement (Fan et al., 2015), we introduce the power-enhanced test, with an asymptotically zero component used to enhance the power to detect some extreme alternatives with many locally invalid instruments. Finally, an empirical example of the trade and economic growth nexus demonstrates the usefulness of the proposed test.

翻译：本文提出了一种针对高维线性工具变量模型的过度识别约束检验。该检验的创新之处在于允许协变量和工具变量的数量大于样本量。该检验具有尺度不变性，且对异方差误差具有稳健性。为构建最终检验统计量，我们首先引入基于多个参数最大范数的检验，这些参数可能是高维的。基于最大范数的理论检验功效高于修正的Cragg-Donald检验（Kolesár, 2018），后者是现有唯一允许大维协变量的检验方法。其次，遵循功效增强原则（Fan et al., 2015），我们引入增强功效检验，其渐近为零的分量用于增强检测存在许多局部无效工具变量的某些极端备择假设的能力。最后，一个关于贸易与经济增长关系的实证案例展示了所提检验的实用性。