2017
DOI: 10.1162/rest_a_00639
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Asymptotic Behavior of a t-Test Robust to Cluster Heterogeneity

Abstract: For a cluster-robust t-statistic under cluster heterogeneity we establish that the cluster-robust t-statistic has a gaussian asymptotic null distribution and develop the effective number of clusters, which scales down the actual number of clusters, as a guide to the behavior of the test statistic. The implications for hypothesis testing in applied work are that the number of clusters, rather than the number of observations, should be reported as the sample size, and the effective number of clusters should be r… Show more

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Cited by 129 publications
(128 citation statements)
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“…Given the formula for , cluster heterogeneity ( ≠ 0) can arise for many reasons, including variation in , variation in and variation in Ω across clusters. In simulations using standard normal critical values, Carter et al (2013) find that test size distortion occurs for * < 20. In application they assume errors are perfectly correlated within cluster, so Ω = ′ where is an × 1 vector of ones.…”
Section: Effective Number Of Clustersmentioning
confidence: 93%
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“…Given the formula for , cluster heterogeneity ( ≠ 0) can arise for many reasons, including variation in , variation in and variation in Ω across clusters. In simulations using standard normal critical values, Carter et al (2013) find that test size distortion occurs for * < 20. In application they assume errors are perfectly correlated within cluster, so Ω = ′ where is an × 1 vector of ones.…”
Section: Effective Number Of Clustersmentioning
confidence: 93%
“…115 for balanced clusters of sizes, respectively, 10 and 100. Recent papers by Carter, Schnepel, and Steigerwald (2013) and Imbens and Kolesar (2012) provide theory that also indicates that the effective number of clusters is reduced when varies across clusters; see also the simulations in MacKinnon and Webb (2013). Similar issues may also arise if the clusters are balanced, but estimation is by weighted LS that places different weights on different clusters.…”
Section: A the Basic Problems With Few Clustersmentioning
confidence: 98%
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“…Then test the null hypothesis H 0 : β = β 0 with the usual t-test using the q observations {β j } q j=1 and q − 1 degrees of freedom. 3 Given the result of Bakirov and Székely (2005), this test is asymptotically valid as long as theβ j 's are asymptotically 1 See Imbens and Kolesár (2012), Carter, Schnepel, and Steigerwald (2013), Webb (2014), MacKinnon and Webb (2014), and Canay, Romano, and Shaikh (2014) for some recent alternative suggestions for inference with a small number of clusters.…”
mentioning
confidence: 99%