论文标题
Kronecker产品结构协方差矩阵的测试
A Test for Kronecker Product Structure Covariance Matrix
论文作者
论文摘要
我们提出了协方差矩阵的测试，以具有Kronecker产品结构（KPS）。 KPS意味着对协方差矩阵的一定转换的等级限制减少，而新程序是Kleibergen and Paap（2006）的改编，降低了等级测试。得出WALD类型测试统计量的限制分布被证明是具有挑战性的部分是因为出现在加权矩阵中的协方差矩阵估计器的奇异性。我们表明，测试统计量具有Chi Square限制为无效分布，其自由度等于测试的限制数量。得出了局部渐近功率结果。蒙特卡洛模拟揭示了测试的尺寸和功率良好。重新审视了进行仪器变量回归的15篇高度引用的论文，我们发现在5％的名义规模的118个规格中，KPS并未拒绝KPS。
We propose a test for a covariance matrix to have Kronecker Product Structure (KPS). KPS implies a reduced rank restriction on a certain transformation of the covariance matrix and the new procedure is an adaptation of the Kleibergen and Paap (2006) reduced rank test. To derive the limiting distribution of the Wald type test statistic proves challenging partly because of the singularity of the covariance matrix estimator that appears in the weighting matrix. We show that the test statistic has a chi square limiting null distribution with degrees of freedom equal to the number of restrictions tested. Local asymptotic power results are derived. Monte Carlo simulations reveal good size and power properties of the test. Re-examining fifteen highly cited papers conducting instrumental variable regressions, we find that KPS is not rejected in 56 out of 118 specifications at the 5% nominal size.
