SummaryThe 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.

中文翻译：

---

两阶段最小二乘最小距离

摘要显示了具有单个内生变量的线性模型中参数的两阶段最小二乘（2SLS）工具变量（IV）估计器与基于特定于特定工具的最优最小距离（MD）估计器相同IV估算器。2SLS估计量是各个估计量的线性组合，权重由它们在条件同方差下的方差和协方差确定。进一步表明，用于过度识别限制的Sargan测试统计量与MD标准测试统计量相同。这提供了对Sargan测试的直观解释。等价结果还适用于矩的有效两步广义方法以及鲁棒的最佳MD估计量和准则函数，从而允许采用一般形式的异方差。