Two-Way Cluster-Robust Standard Errors—A Methodological Note on What Has Been Done and What Has Not Been Done in Accounting and Finance Research

Abstract

There is a widely application of panel data estimation in accounting and finance research. The approach is well accepted, because the pooled panel data provide rich information as compared to either cross-sections or time series data structure. However, within panel data structure, variables of interest are often cross-sectionally and serially correlated and as a result, OLS standard errors would be biased when panel data are used in the regression analysis. Several techniques, for example firm dummy variables, one-way cluster-robust standard errors, Fama-MacBeth procedure, and Newey-West procedure, are documented as a solution in analyzing panel data. These techniques to some extent correct either cross-sectional correlation or serial correlation. None is designed to deal with correlations in two dimensions (across firms and across time). With panel data structure, correlations are more likely to appear in two dimensions with both firm effects and time effects. This study suggests that two-way cluster-robust standard errors approach can correct both cross-sectional correlation and serial correlation and therefore should be considered as a better alternative in handling panel data. Nonetheless, two-way cluster-robust standard errors approach could be biased when applying to a finite sample. This study uses a real data set and constructs an empirical application of the estimation procedures of two-way cluster-robust regression estimation with and without finite-sample adjustment and the results show that finite-sample adjusted estimates are superior to unadjusted asymptotic estimates.