Benford's law and the limits of digit analysis

Abstract

We use panel data that consists of aggregated annual bank account balances and analyze the first two digits of each observation to evaluate conformity to Benford's Law. The data spans a period of 14 years, is naturally generated, and meets the “drawing from a sequence” criterion. We conduct a full battery of null hypothesis significance testing, and we also calculate annual mean absolute deviation and excess mean absolute deviation. The results range from marginal conformity to marginal non-conformity to Benford's Law. We concur with previous research and urge caution when approaching auditing and fraud detection using these analytic tools. This finding illustrates the concept of usual level of conformity, that is, a data-specific signature, driven by the idiosyncrasies of the process that generated it. We also examine the time series of annual mean absolute deviation and excess mean absolute deviation. In a couple of cases, the Dickey-Fuller tests suggest trend-stationarity, although the small number of observations renders the reliability of these results questionable.