Asymptotic Behavior of a t-Test Robust to Cluster Heterogeneity

Autor: Douglas G. Steigerwald, Kevin T. Schnepel, Andrew V. Carter
Rok vydání: 2017
Předmět:
Zdroj: The Review of Economics and Statistics. 99:698-709
ISSN: 1530-9142
0034-6535
Popis: We study the behavior of a cluster-robust t statistic and make two principle contributions. First, we relax the restriction of pre- vious asymptotic theory that clusters have identical size, and establish that the cluster-robust t statistic continues to have a Gaussian asymp- totic null distribution. Second, we determine how variation in cluster sizes, together with other sources of cluster heterogeneity, aect the be- havior of the test statistic. To do so, we determine the sample speci…c measure of cluster heterogeneity that governs this behavior and show that the measure depends on how three quantities vary over clusters: cluster size, the cluster speci…c error covariance matrix and the actual value of the covariates. Because, in the absence of a …xed design, the third quan- tity will always vary over clusters, the vast majority of empirical analyses have test statistics whose …nite sample behavior is impacted by cluster heterogeneity. To capture this impact, we develop the eective number of clusters, which scales down the actual number of clusters by the mea- sure of cluster heterogeneity. Through simulation we demonstrate this eect and …nd rejection rates as high as 30 percent for a nominal size of 5 percent. We then apply our measure of cluster heterogeneity in several empirical settings to show how observable variation over clusters impacts the performance of a cluster-robust test.
Databáze: OpenAIRE
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