Jialan Wang of Washington University in St. Louis has written a fascinating post about Benford’s Law. Benford’s Law relates to numerical regularity; more numbers begin with 1 than 2, 2 than 3, 3 than 4, and so on. It postulates that the first digit of a number is 1 almost one-third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty.
This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). Accordingly, Benford’s law is used to detect corporate fraud, in that deviations from it may indicate that a company’s books have been cooked. Prof. Wang’s post provides fodder for three particularly interesting inferences.
- Deviations from Benford’s law have increased substantially over time, suggesting that accounting statements and thus company reporting are becoming less and less reliable;
- Deviations from Benford’s law are compellingly correlated with known financial crises, bubbles, and fraud waves, suggesting that bad data may be a bigger cause of such events than generally assumed; and
- There is currently a high level of deviations from Benford’s law within finance, suggesting that those of us who are suspicious of bank balance sheet problems well in excess of what is claimed within the industry (those with a “trust deficit“) may be onto something.