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Two-stage least squares as minimum distance

机译：两个阶段最小二乘作为最小距离

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摘要

The two-stage least-squares (2SLS) instrumental-variables (IV) estimator for the parameters in linear models with a single endogenous variable is shown to be identical to an optimal minimum-distance (MD) estimator based on the individual instrument-specific IV estimators. The 2SLS estimator is a linear combination of the individual estimators, with the weights determined by their variances and covariances under conditional homoskedasticity. It is further shown that the Sargan test statistic for overidentifying restrictions is the same as the MD criterion test statistic. This provides an intuitive interpretation of the Sargan test. The equivalence results also apply to the efficient two-step generalized method of moments and robust optimal MD estimators and criterion functions, allowing for general forms of heteroskedasticity. It is further shown how these results extend to the linear overidentified IV model with multiple endogenous variables.
机译：具有单个内源变量的线性模型中参数的两级最小二乘（2SL）仪器变量（IV）估计值显示与基于各个仪器特定的最佳最小距离（MD）估计值相同IV估计。 2SLS估计器是各个估计器的线性组合，其重量由其差异和协方差根据条件性质的差异确定。进一步表明，用于过度凝视限制的Sargan测试统计与MD标准测试统计数据相同。这提供了对Sargan测试的直观解释。等效结果也适用于有效的两步通用方法和鲁棒优化MD估计器和标准功能，允许一般形式的异源性。进一步示出了这些结果如何扩展到具有多个内源变量的线性过度识别的IV模型。

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