标题： 当误差聚类时OLS协方差矩阵的无偏估计 显示英文标题

标题： Unbiased estimation of the OLS covariance matrix when the errors are clustered

摘要： 当数据存在聚类时，通常的做法是进行OLS，并使用一个接近无偏的OLS估计量协方差矩阵的估计器。 在本文中，我们推导了一个在随机效应模型成立时无偏的估计器。 我们对另外两种更一般的结构也做了同样的处理。 我们通过模拟研究了这些估计器相对于其他估计器的有用性，$t$-检验的大小作为标准。 我们的研究结果表明，当回归变量在聚类中具有相同的分布时，估计器的选择几乎无关紧要。 但当回归变量是一个聚类特定的处理变量时，估计器的选择就变得重要，我们为随机效应模型提出的无偏估计器表现出色，即使聚类高度不平衡。 显示英文摘要

摘要： 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.