Asymptotic Behavior of a t Test Robust to Cluster HeterogeneityEconomics Department, UC Santa Barbara (2013)
AbstractWe study the behavior of a cluster-robust t statistic and make two principle contributions. First, we relax the restriction of previous asymptotic theory that clusters have identical size, and establish that the cluster-robust t statistic continues to have a Gaussian asymptotic null distribution. Second, we determine how variation in cluster sizes, together with other sources of cluster heterogeneity, affect the behavior of the test statistic. To do so, we determine the sample specific 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 specific error covariance matrix and the actual value of the covariates. Because, in the absence of a fixed design, the third quantity will always vary over clusters, the vast majority of empirical analyses have test statistics whose finite sample behavior is impacted by cluster heterogeneity. To capture this impact, we develop the effective number of clusters, which scales down the actual number of clusters by the measure of cluster heterogeneity. Through simulation we demonstrate this effect and find 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.
- t test
Citation InformationDouglas G Steigerwald. "Asymptotic Behavior of a t Test Robust to Cluster Heterogeneity" Economics Department, UC Santa Barbara (2013)
Available at: http://works.bepress.com/douglas_steigerwald/26/