Small-Sample Methods for Cluster-Robust Variance Estimation and Hypothesis Testing in Fixed Effects Models
Small-Sample Methods for Cluster-Robust Variance Estimation and Hypothesis Testing in Fixed Effects Models
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DOI：
10.1080/07350015.2016.1247004
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发表时间：
2018-01-01
影响因子：
3
通讯作者：
Tipton, Elizabeth
中科院分区：
文献类型：
--
作者：
Pustejovsky, James E.;Tipton, Elizabeth
在面板数据模型和其他具有未观测效应的回归模型中，固定效应估计通常与聚类稳健方差估计（CRVE）配对，以考虑误差之间的异方差性和未建模相关性。虽然CRVE是渐近一致的，但当聚类数较少时，CRVE可能会向下偏置，导致假设检验的拒绝率过高。更准确的测试可以使用偏差减少线性化（BRL），它纠正了CRVE的基础上的工作模型，结合Satterthwaite近似的t检验。我们提出了一个泛化的BRL，可以应用于模型与任意组的固定效应，原始的BRL方法是未定义的，并描述如何应用的方法时，估计吸收固定效应后的回归。我们还提出了多参数假设的小样本检验，它推广了t检验的Satterthwaite近似。在模拟覆盖范围广泛的情况下，我们发现，传统的集群鲁棒Wald测试可以严重过度拒绝，而建议的小样本测试保持I型误差接近标称水平。所提出的方法在一个名为clubSandwich的R包中实现。这篇文章有在线补充材料。
In panel data models and other regressions with unobserved effects, fixed effects estimation is often paired with cluster-robust variance estimation (CRVE) to account for heteroscedasticity and un-modeled dependence among the errors. Although asymptotically consistent, CRVE can be biased downward when the number of clusters is small, leading to hypothesis tests with rejection rates that are too high. More accurate tests can be constructed using bias-reduced linearization (BRL), which corrects the CRVE based on a working model, in conjunction with a Satterthwaite approximation for t-tests. We propose a generalization of BRL that can be applied in models with arbitrary sets of fixed effects, where the original BRL method is undefined, and describe how to apply the method when the regression is estimated after absorbing the fixed effects. We also propose a small-sample test for multiple-parameter hypotheses, which generalizes the Satterthwaite approximation for t-tests. In simulations covering a wide range of scenarios, we find that the conventional cluster-robust Wald test can severely over-reject while the proposed small-sample test maintains Type I error close to nominal levels. The proposed methods are implemented in an R package called clubSandwich. This article has online supplementary materials.