Consistent estimation with a large number of weak instruments
Consistent estimation with a large number of weak instruments
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DOI：
10.1111/j.1468-0262.2005.00632.x
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发表时间：
2005-09-01
期刊：
影响因子：
6.1
通讯作者：
Swanson, NR
中科院分区：
文献类型：
--
作者：
Chao, JC;Swanson, NR
本文分析了在工具变量（IV）回归中，当可用工具较弱且工具个数K-n随样本容量趋于无穷大时，一致估计的条件。我们表明，一致的估计重要地取决于由r（n），所谓的浓度参数的增长率测量的工具的强度，也对K-n。特别是，当K-n ->无穷大时，浓度参数可以增长，即使每个单独的工具与内生解释变量仅弱相关，并且某些估计量的一致性可以在比文献中先前假设的更弱的条件下建立。因此，许多弱工具的使用实际上可以提高某些点估计的性能。更具体地说，我们发现当根K-n/r（n）-> 0时，有限信息极大似然（LIML）估计和偏差校正两阶段最小二乘（B2 SLS）估计是相容的，而两阶段最小二乘（2SLS）估计只有当K-n/r（n）-> 0且n ->无穷大时才是相容的.这些一致性结果表明LIML和B2 SLS比2SLS对仪器弱点更鲁棒。
This paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables (IV) regression when the available instruments are weak and the number of instruments, K-n, goes to infinity with the sample size. We show that consistent estimation depends importantly on the strength of the instruments as measured by r(n), the rate of growth of the so-called concentration parameter, and also on K-n. In particular, when K-n -> infinity, the concentration parameter can grow, even if each individual instrument is only weakly correlated with the endogenous explanatory variables, and consistency of certain estimators can be established under weaker conditions than have previously been assumed in the literature. Hence, the use of many weak instruments may actually improve the performance of certain point estimators. More specifically, we find that the limited information maximum likelihood (LIML) estimator and the bias-corrected two-stage least squares (B2SLS) estimator are consistent when root K-n/r(n) -> 0, while the two-stage least squares (2SLS) estimator is consistent only if K-n/r(n) -> 0 as n -> infinity. These consistency results suggest that LIML and B2SLS are more robust to instrument weakness than 2SLS.