This numerical regularity [of digit ordered frequency] is known as Benford's Law, and specifically, it says that the probability of the first digit from a set of numbers is d is given by [equation]....In fact, Benford's law has been used in legal cases to detect corporate fraud, because deviations from the law can indicate that a company's books have been manipulated. Naturally, I was keen to see whether it applies to the large public firms that we commonly study in finance,Deviations from Benford's law have increased substantially over time, such that today the empirical distribution of each digit is about 3 percentage points off from what Benford's law would predict. The deviation increased sharply between 1982-1986 before leveling off, then zoomed up again from 1998 to 2002. Notably, the deviation from Benford dropped off very slightly in 2003-2004 after the enactment of Sarbanes-Oxley accounting reform act in 2002, but this was very tiny and the deviation resumed its increase up to an all-time peak in 2009.So according to Benford's law, accounting statements are getting less and less representative of what's really going on inside of companies. The major reform that was passed after Enron and other major accounting standards barely made a dent.
Read the whole post at Studies in Everyday Life, Benford's Law and the Decreasing Reliability of Accounting Data for US Firms by Jialan Wang
(h/t Mark Thoma)
