Humans are natural lie detectors. We are endowed with the ability to judge the credibility of what others say by listening to tonal inflections, noting facial expressions and watching body movements to see if all are consistent. When they are not, our suspicion is aroused. Determining whether numbers are credible is a more difficult task, but possible using Benford’s law.
Dr. Frank Benford, a physicist at General Electric, developed a system for predicting the frequency of the numbers 0 through 9 in certain positions of real numbers occurring naturally. Dr. Benford tested his system using actual numbers of certain disparate measures such as the areas of rivers, street addresses, baseball statistics and a host of other actual measures. To illustrate, Benford’s law states that the first digit of any number will begin with a 1, 30.10% of the time; further, the number 2 will be the first digit 17.61% of the time, and so on. Benford’s law states that when the patterns of numbers do not comply with the natural frequencies, there is a good chance they are not credible.
Benford’s law is beginning to receive increased attention from accounting and fraud detection professionals and is increasingly used to test the validity of numbers on financial statements and tax returns. A recent article by Dr. Charles Jordan and Dr. Stanley Clark (February 2011, The CPA Journal) illustrates how Benford’s law can be used to detect cosmetic earnings management in financial statements. Perhaps of more concern, is what empirical analysis may reveal about the current state of financial reporting.
Jialan Wang, a professor of finance at Washington University, performed an analysis of Benford’s law using quarterly financial data from Compustat, one of the largest databases of financial information from public companies in the US. Included in Wang’s analysis was a measurement of the trend of deviation from Benford’s law from the 1960’s to 2010. The upward trend is cause for concern.
Deviation from Benford’s law took a dramatic increase in the early 1980’s that coincides with the savings and loan crisis and again in the late 1990’s and early-2000’s that coincides with the dot-com bubble and accounting scandals. Wang admits, “While these time series don’t prove anything decisively, deviations from Benford’s law are compellingly correlated with known financial crises, bubbles and fraud waves.” More concerning is that the deviation trend is higher than ever and the upward trend was disturbed only twice since 1980—once in the 2003/2004 timeframe that immediately followed the implementation of Sarbanes-Oxley, and once in 2010 after reaching an all-time high in 2009.