On Using The Two-Way Cluster-Robust Standard Errors

Abstract: Thousands of papers have reported two-way cluster-robust (TWCR) standard errors. However, the recent econometrics literature points out the potential non-gaussianity of two-way cluster sample means, and thus invalidity of the inference based on the TWCR standard errors. Fortunately, simulation studies nonetheless show that the gaussianity is rather common than exceptional. This paper provides theoretical support for this encouraging observation. Specifically, we derive a novel central limit theorem for two-way clustered triangular arrays that justifies the use of the TWCR under very mild and interpretable conditions. We, therefore, hope that this paper will provide a theoretical justification for the legitimacy of most, if not all, of the thousands of those empirical papers that have used the TWCR standard errors. We provide a guide in practice as to when a researcher can employ the TWCR standard errors.