Inference with Few Heterogenous Clusters

Consider inference with a small number of potentially heterogeneous clusters. Suppose estimating the model on each cluster yields q asymptotically unbiased, independent Gaussian estimators with potentially heterogeneous variances. Following Ibragimov and Müller (2010), one can then conduct asymptotically valid inference with a standard t-test based on the q cluster estimators, since at conventional signi…cance levels, the small sample t-test remains valid under variance heterogeneity. This note makes two contributions. First, we establish the new corresponding small sample result for the two-sample t-test under variance heterogeneity. One can therefore apply t-statistic based inference also for comparisons of parameters between two populations, such as treatment and control groups, or preand post-structural break data. Second, we develop a test for the appropriate level of clustering, with the null hypothesis that clustered standard errors from a …ne partition are correct, against the alternative that only q clusters provide asymptotically independent information. JEL classi…cation: C12, C14, C32