We propose a new overidentifying restriction test for linear instrumental variable models. The novelty of the proposed test is that it allows the number of covariates and/or instruments to be larger than the sample size and is robust to heteroskedastic errors. We show that the test has the desired theoretical properties under sparse high-dimensional models and is more powerful than existing overidentification tests. First, we 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 shown to be higher than that in the modified Cragg-Donald test (Koles\'{a}r, 2018), which is 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 empirical power against some extreme alternatives with many locally invalid instruments. Focusing on hypothesis testing, we also provide a feasible estimator of endogenous effects for practitioners when instrument validity is not rejected. The simulation results show the superior performance of the proposed test, and the empirical power enhancement is clear. Finally, an empirical example of the trade and economic growth nexus demonstrates the usefulness of the proposed tests.

翻译：本文提出了一种针对线性工具变量模型的新型过度识别约束检验方法。该方法的创新之处在于允许协变量和/或工具变量的数量大于样本量，并且对异方差误差具有稳健性。我们证明了该检验在稀疏高维模型下具有理想的理论性质，且比现有过度识别检验更具统计功效。首先，我们引入了一种基于多个可能高维参数最大范数的检验方法。基于最大范数的理论功效表明，该检验优于允许大维度协变量的唯一现有检验——修正的Cragg-Donald检验（Kolesár, 2018）。其次，遵循功效增强原理（Fan等, 2015），我们引入了功效增强型检验，其渐近为零的分量可用于提升对某些包含大量局部无效工具变量的极端备择假设的经验功效。在假设检验框架下，我们还为实践中工具变量有效性未被拒绝时提供了内生效应参数的可估计算法。模拟结果表明所提检验具有优越性能，且经验功效增强效果显著。最后，通过贸易与经济增长关系的实证案例展示了所提检验方法的实用性。