Divergence from Benford’s law fails to measure financial statement accuracy

Abstract

The Financial Statement Divergence (FSD) score, a metric of the deviation of figures from Benford’s Distribution, has become increasingly popular in assessing financial information quality at the firm-year level. We test the validity of this metric by analyzing (1) if error-free financial statements conform to Benford and (2) if the FSD score increases with the presence of accounting errors or manipulations. Regarding the first analysis, firm-year financial statements’ conformity to Benford is much lower than previously reported in the literature; this implies that the assumption of error-free financial statements conforming to Benford would hold only if an exceptionally high proportion of companies report financial statements with a substantial number of line items affected by errors or manipulations. Regarding the second analysis, we theoretically show that the relationship between accounting errors or manipulations and divergence from Benford is inconsistent: FSD score variations are independent of the size of the error or manipulation, and errors or manipulations may increase, decrease, or have no effect on the FSD score. Empirically, we show that various subsamples with a priori lower accounting quality do not exhibit a higher FSD score and, using simulated values, we verify that manipulations can increase, decrease, or have no effect on the FSD depending on the value of the pre-managed FSD. Taken together, our results cast doubts on the FSD score’s validity in assessing financial information quality at the firm-year level.