econerdfood.blogspot.com, Jialan Wang, Oct 9, 2011
Benford's Law and the Decreasing Reliability of Accounting Data for US Firms
... there are more numbers in the universe that begin with the digit 1 than 2, or 3, or 4, or 5, or 6, or 7, or 8, or 9. And more numbers that begin with 2 than 3, or 4, and so on. This relationship holds for the lengths of rivers, the populations of cities, molecular weights of chemicals, and other categories (Gregory PS: where the numbers grow exponentially).
This numerical regularity is known as Benford's Law ... 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.
... I downloaded quarterly accounting data for all firms in Compustat, the most widely-used dataset in corporate finance that contains data on over 20,000 firms from SEC filings. I used a standard set of 43 variables that comprise the basic components of corporate balance sheets and income statements (revenues, expenses, assets, liabilities, etc.). ...
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.
This story was also covered in the Economist