Monday, October 17, 2011

Benford's Law in accounting

Tim Harford, Mark Thoma and Marginal Revolution have interesting posts on Benford's Law, which in essence states that in contrast to the statistically irregular manipulated data, "real" data in any type of data distribution have some statistical regularity.

Tim Harford writes,

"Benford’s Law was discovered in 1881 by the astronomer Simon Newcomb, and then again by Frank Benford, a physicist at General Electric, in 1938. The law is a curious one: it predicts the frequency of the first digits of a collection of numbers. For example, measure the lengths of the world’s rivers, and see how many of the digits begin with “one” (184 miles; 1,543 miles) versus “three” (3,022 miles) or “nine” (985 miles). Newcomb and Benford discovered that the first digit is usually a “one” – fully 30 per cent of the time, over six times more common than an initial “nine”. And the result is true whether one counts the numbers on the front page of The New York Times or leafs through baseball statistics."

And he gives an example of how manipulated data fails the Benford test,

"A manager who must submit receipts for expenses over £20 may end up filing claims for lots of £18 and £19 expenses – and the data will then contain too many ones, eights and nines. A forensic accountant can easily check this, and while not an infallible check, it’s an indicator of possible trouble."

Marginal Revolution draws attention to a post by Jialan Wang who shows how Benford's law reveals possible manipulation of corporate accounting statements.

"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... deviations from Benford's law are compellingly correlated with known financial crises, bubbles, and fraud waves... Accounting data seem to be less and less related to the natural data-generating process that governs everything from rivers to molecules to cities."

Can analytics software developed based on Benford's Law be of practical use in monitoring public policy? For example, can it be used to detect cheating in performance reporting among all types of officials, say, students academic performance reported by teachers?

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