A Heteroscedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates
针对高维线性工具变量模型，提出一种允许协变量和工具变量数量超过样本量的过度识别约束检验，该检验具有尺度不变性和异方差稳健性，并通过贸易与经济增长关系的实证例子展示其应用。
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 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 (Kolesár, 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.