论文标题
当错误聚集时，OLS协方差矩阵的无偏估计
Unbiased estimation of the OLS covariance matrix when the errors are clustered
论文作者
论文摘要
当数据聚集时，共同的实践已经成为OLS并使用接近无偏见的OLS估计器的协方差矩阵的估计量。在本文中，我们得出了一个估计器，该估计量在随机效应模型成立时是公正的。我们为另外两个通用结构做同样的事情。我们通过模拟来研究这些估计器对他人的有用性，$ t $测试的大小是标准。我们的发现表明，当回归器在集群上具有相同的分布时，估算器的选择几乎无关紧要。但是，当回归器是一个特定于集群的治疗变量时，选择确实很重要，即使簇高度不平衡，我们对随机效应模型提出的无偏估计器也会显示出出色的性能。
When data are clustered, common practice has become to do OLS and use an estimator of the covariance matrix of the OLS estimator that comes close to unbiasedness. In this paper we derive an estimator that is unbiased when the random-effects model holds. We do the same for two more general structures. We study the usefulness of these estimators against others by simulation, the size of the $t$-test being the criterion. Our findings suggest that the choice of estimator hardly matters when the regressor has the same distribution over the clusters. But when the regressor is a cluster-specific treatment variable, the choice does matter and the unbiased estimator we propose for the random-effects model shows excellent performance, even when the clusters are highly unbalanced.
