Department of Forensic Statistics: The Book-Cooking Index

How exciting is this? Statisticians can detect corporate accounting fraud just by looking at the first digits of the numerals in the accounting books!

The Economist Free Exchange blog reports on Jialan Wang’s fascinating application of statistics to corporate fraud. She has applied Benford’s Law to actual accounting numbers to judge if they are faked.

Benford’s Law states that within sets of numerals that span orders of magnitude, the distribution of first digits is strikingly regular: Numerals beginning with 1 occur about 30% of the time, those beginning with 2 about 18% of the time, falling to roughly 5% of the time for the number 9.

The actual formula for Benford’s Law: 

The probability of the first digit from a set of numbers is d is given by

Here's how this comes in handy for detecting corporate fraud. Someone who is faking data, as in cooking business account books, is more likely to choose numbers at random, rather than in accordance with Benford’s Law. Thus the deviation between what Benford’s predicts and what is observed in actual accounts can be taken as a measure of accounting fraud. 

Jialan Wang’s chart above shows the deviation from Benford’s Law since 1960. Note the drop off in 2003-2004 after the enactment of Sarbanes-Oxley. Ms. Wang goes on to break out the data for individual industries:

Be sure to read her discussion of how these curves reflect the Saving and Loan Crisis of the 1980s.

How much do you trust corporations now? Or, as Ms. Wang says: “...it's just one more reason for investors to beware.”

Here is the original analysis by Jialan Wang: “Benford's Law and the Decreasing Reliability of Accounting Data for US Firms.”

See also Tyler Durden’s discussion at Zero Hedge.  --WTP

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--Bill Paarlberg is editor of  The Measurement Standard blog and newsletter, and of Katie Paine's new book Measure What Matters. The Measurement Standard is a publication of KDPaine & Partners, a company that delivers custom research to measure brand image, public relationships, and engagement.

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