Approximate Distributions and Power of Test Statistics for Overidentifying Restrictions in a System of Simultaneous Equations
推导了联立方程组中过度识别约束检验统计量在原假设和备择假设下的渐近展开，比较了Basmann统计量和似然比检验的功效，发现扰动方差足够小时前者功效更大，但随样本量增大差异消失。
We derive asymptotic expansions of the distributions of test statistics for over-identifying restrictions in a system of simultaneous equations under the null and the non-null hypotheses. We investigate the effects of the normality assumption for disturbances on the test statistics based on their asymptotic expansions. We also study the power functions of test statistics based on their asymptotic expansions. After modifying their critical regions to the same significance level, the power function of Basmann's statistic is larger than that of the likelihood ratio test when the variance of disturbances is sufficiently small. However, the difference in powers of the two test statistics disappears as the sample size grows larger.