A new specification test for the validity of instrumental variables
A new specification test for the validity of instrumental variables
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DOI：
10.1111/1468-0262.00272
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发表时间：
2002-01-01
期刊：
影响因子：
6.1
通讯作者：
Hausman, J
中科院分区：
文献类型：
--
作者：
Hahn, J;Hausman, J
我们开发了一种新的规范测试，用于采用Bekker的特殊二阶近似的IV估计器。新的规范检验比较了当正规化改变时，右侧内生变量系数的正向(常规)2SLS估计与相同未知参数的反向2SLS估计的差异。在零假设下，传统的一阶渐近性提供了可靠的推断指南，这两个估计应该非常相似。检验两种估计结果的差异是否满足二阶渐近理论的结果。本质上，同样的想法被用来开发另一种新的规范检验，使用由Nagar最先提出的类型的二阶无偏估计。如果正向和反向Nagar型估计没有显著不同，我们推荐使用LIML估计，我们证明了LIML是Nagar型估计(二阶)的最优线性组合。我们还证明了Bekker方法和Rothenberg的Edgeworth展开方法对于k类估计具有高度的相似性。通过实证分析和蒙特卡罗检验，验证了新规范检验的有效性。
We develop a new specification test for IV estimators adopting a particular second order approximation of Bekker. The new specification test compares the difference of the forward (conventional) 2SLS estimator of the coefficient of the right-hand side endogenous variable with the reverse 2SLS estimator of the same unknown parameter when the normalization is changed. Under the null hypothesis that conventional first order asymptotics provide a reliable guide to inference, the two estimates should be very similar. Our test sees whether tire resulting difference in the two estimates satisfies the results of second order asymptotic theory. Essentially the same idea is applied to develop another new specification test using second-order unbiased estimators of the type first proposed by Nagar. If the forward and reverse Nagar-type estimators are not significantly different we recommend estimation by LIML, which we demonstrate is the optimal linear combination of the Nagar-type estimators (to second order). We also demonstrate the high degree of similarity for k-class estimators between the approach of Bekker and the Edgeworth expansion approach of Rothenberg. An empirical example and Monte Carlo evidence demonstrate the operation of the new specification test.