Are We Really Doing What We Think We Are Doing? A Note on Finite-Sample Estimates of Two-Way Cluster-Robust Standard Errors

Archival researchers heavily rely on statistics software to deliver large sample analyses. To provide valid empirical analyses, an author needs to know the best statistical solution to the research issue and also the correct computer language that exactly carries out such statistical tests. However, unfortunately, researchers rarely explain what they exactly do in empirical analyses. Consequently, it is difficult for a reader to figure out the validity of the empirical results. This note uses two-way cluster-robust standard errors as an example to explain these points.Two-way cluster-robust standard errors are getting widely used in the accounting and finance literature. There are multiple different alternative specifications of two-way cluster-robust standard errors, which could result in very different significance levels than unadjusted asymptotic estimates. However, researchers rarely explain which estimate of two-way cluster-robust standard errors they use, though they may all call their standard errors “two-way cluster-robust standard errors”. Specifically, I first provide a short-discussion on alternative estimates of two-way cluster-robust standard errors. Second, I discuss two common mistakes in calculating two-way cluster-robust standard errors. Third, I show that popular statistics software (SAS and STATA) have options that could generate several alternative estimates of two-way cluster-robust standard errors. Therefore, if not explained, no reader would know which estimate is used. Finally, I suggest that future empirical research should carefully explain how it implements estimates of two-way cluster-robust standard errors in finite samples. In addition, a SAS macro code for two-way clustered standard errors is available at my website. If you use this code, please add the following footnote “To obtain unbiased estimates, the clustered standard errors are adjusted by (N-1)/ (N-P) × G/(G-1), where N is the sample size, P is the number of independent variables, and G is the number of clusters.”