For subvector inference in the linear instrumental variables model under homoskedasticity but allowing for weak instruments, Guggenberger, Kleibergen, and Mavroeidis (2019) (GKM) propose a conditional subvector Anderson and Rubin (1949) (AR) test that uses data-dependent critical values that adapt to the strength of the parameters not under test. This test has correct size and strictly higher power than the test that uses standard asymptotic chi-square critical values. The subvector AR test is the minimum eigenvalue of a data dependent matrix. The GKM critical value function conditions on the largest eigenvalue of this matrix. We consider instead the data dependent critical value function conditioning on the second-smallest eigenvalue, as this eigenvalue is the appropriate indicator for weak identification. We find that the data dependent critical value function of GKM also applies to this conditioning and show that this test has correct size and power strictly higher than the GKM test when the number of parameters not under test is larger than one. Our proposed procedure further applies to the subvector AR test statistic that is robust to an approximate kronecker product structure of conditional heteroskedasticity as proposed by Guggenberger, Kleibergen, and Mavroeidis (2024), carrying over its power advantage to this setting as well.

翻译：在满足同方差性但允许弱工具变量的线性工具变量模型中，针对子向量推断问题，Guggenberger、Kleibergen与Mavroeidis（2019）（GKM）提出了一种条件子向量Anderson和Rubin（1949）（AR）检验。该检验采用数据依赖型临界值，能够根据非待检参数的强度进行自适应调整。此检验不仅具有正确的检验水平，其功效也严格高于使用标准渐近卡方临界值的检验。子向量AR检验统计量是某个数据依赖型矩阵的最小特征值，而GKM临界值函数以该矩阵的最大特征值为条件。本文提出改以第二小特征值为条件构建数据依赖型临界值函数，因为该特征值是弱识别的更恰当指标。研究发现GKM的数据依赖型临界值函数同样适用于此种条件设定，并证明当非待检参数数量大于一时，该检验在保持正确检验水平的同时，其功效严格优于GKM检验。我们提出的方法还可进一步推广至Guggenberger、Kleibergen与Mavroeidis（2024）提出的、对近似Kronecker积结构条件异方差具有稳健性的子向量AR检验统计量，从而将其功效优势延续至该设定中。