Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression
提出一种新的统计量，用于工具变量回归中所有结构参数的联合检验，该统计量计算简单，渐近分布不依赖冗余参数，克服了安德森-鲁宾统计量和基于似然的统计量的缺陷，并通过实证数据验证了其有效性。
We propose a novel statistic for conducting joint tests on all the structural parameters in instrumental variables regression. The statistic is straightforward to compute and equals a quadratic form of the score of the concentrated log–likelihood. It therefore attains its minimal value equal to zero at the maximum likelihood estimator. The statistic has a χ2 limiting distribution with a degrees of freedom parameter equal to the number of structural parameters. The limiting distribution does not depend on nuisance parameters. The statistic overcomes the deficiencies of the Anderson–Rubin statistic, whose limiting distribution has a degrees of freedom parameter equal to the number of instruments, and the likelihood based, Wald, likelihood ratio, and Lagrange multiplier statistics, whose limiting distributions depend on nuisance parameters. Size and power comparisons reveal that the statistic is a (asymptotic) size–corrected likelihood ratio statistic. We apply the statistic to the Angrist–Krueger (1991) data and find similar results as in Staiger and Stock (1997).