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The conventional cluster-robust (CR) standard errors may not be robust. Theyare vulnerable to data that contain a small number of large clusters. When aresearcher uses the 51 states in the U.S. as clusters, the largest cluster(California) consists of about 10% of the total sample. Such a case in factviolates the assumptions under which the widely used CR methods are guaranteedto work. We formally show that the conventional CR methods fail if thedistribution of cluster sizes follows a power law with exponent less than two.Besides the example of 51 state clusters, some examples are drawn from a listof recent original research articles published in a top journal. In light ofthese negative results about the existing CR methods, we propose a weighted CR(WCR) method as a simple fix. Simulation studies support our arguments that theWCR method is robust while the conventional CR methods are not.

Non-Robustness of the Cluster-Robust Inference: with a Proposal of a New Robust Method