Everyone has heard of the Big Mac Index, the Misery Index, even the Shoe Thrower Index. But the Book Cooking Index? This latest addition to the compendium of oddly named yet extremely fascinating "indices" is based around the statistical irregularity known as Benford's law, according to which within sets of numbers that span orders of magnitude, the distribution of first digits is strikingly regular: numbers beginning in 1 occur about 30% of the time, those beginning in 2 about 18% of the time, falling to roughly 5% of the time for the number 9. Specifically, as noted by the keenly observant Jialan Wang of Washington University in St. Louis, "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 any number of other categories." The most curious application of this law resides in the field of corporate fraud, "because deviations from the law can indicate that a company's books have been manipulated." Here is where things get interesting for fraudulent corporate America: the inquisitive Wang "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" and "used a standard set of 43 variables that comprise the basic components of corporate balance sheets and income statements." Her results were, in a word, startling.

As she observes, "here are the distribution of first digits vs. Benford's law's prediction for total assets and total revenues."





In other words, corporate numbers behaving precisely as predicted by a purely statistical law!

But here is where it gets truly strange. In her words, "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."

Said otherwise, the chronological change in this parameter allows some starting conclusions. As the Economist notes, "This regularity has been used to identify cases of fraud in public documents. Someone cooking books is likely to choose numbers somewhat randomly, generating a distribution of digits far more uniform than Benford's law would predict. Any divergence that shows up sets off alarm bells in those looking for funny business."

Visually presented, it looks as follows:



Yes, book-cooking, in the purest statistical "correlation does not imply causation" has hit an all time high! Granted we doubt any regulator, least of all the corrupt criminal SEC, whose own Benford's law chart would look like a lie detector test hooked up to Jamie Dimon during a conference all, would admit this evidence in a court of law, but deluded investors who believe that corporation are being always truthful with data and reporting should probably be aware that that is certainly not the case. Per the Economist: "As Ms Wang notes, this isn't decisive proof of misbehaviour. It is suggestive, however, of the possibility that systematic number-fudging has been on the upswing in recent decades. Moreover, it's an excellent use of clever statistical analysis to provide a new perspective on an economic question."

Considering the surge in white collar criminality over the past 3 decades, especially among financial firms, and the fact that this "index" is now at all time highs, we would hardly be as politically correct about the issue as the Economist.

But that's us.

As for next steps, "What types of firms, and what kind of executives drive the greatest deviations from Benford's law? Does this measure do well in predicting known instances of fraud? How much of these deviations are driven by government deregulation, changes in accounting standards, and traditional measures of corporate governance?" All these are fascinating questions that Wang will answer in the immediate future and we will advise readers when she does.

For now, the take home message is this: if it appears that "they" are lying to you, "they" probably are. Just run a numerical regression analysis to prove it.

Iniciado por sirpask

Muy interesante el articulo y de muy facil aplicacion por hacienda para hacer estadisticas.

Pero si en las empresas Españolas usaramos un detector de irregularidades... el programa estaria todo el dia pitando como mi coche cuando te quitas el cinturon de seguridad en marcha, seria un incordio, y acabarias por desconectarlo.

Euro Trillions

Earlier this year Bernhard Rauch, Max Göttsche, Gernot Brähler and Stefan Engel published an eye-opening paper entitled Fact and Fiction in EU-Governmental Economic Data. Unfortunately this is only available from behind a paywall, but it’s a fascinating read, if you’re into horror stories. Unsuprisingly Greece was the biggest culprit. Of course the deviation of Greece from Benford’s law was pretty much guaranteed: the scale of Greece’s problems is staggering. Michael Lewis in his new book, Boomerang: Travels in the New Third World, puts the problem into context. The Greeks owe:

“About $1.2 trillion, or more than a quarter-million dollars for every working Greek.”

If you read on, preferably from behind the sofa, through your fingers, you get to:

“In just the past twelve years the wage bill of the Greek public sector has doubled in real terms – and that number doesn’t take into account the bribes collected by public officials. The average government job pays almost three times the average private-sector job. The national railroad has annual revenues of 100 million euros against an average wage bill of 400 million, plus 300 million euros in other expenses”.

Birling Pigs

Given that the original research confirmed what was expected about the prime suspect, what looks even more worrying is who else the researchers fingered:

“We established a robust ranking of the EU member states according to the extent of the deviation from Benford’s law. The countries with the greatest deviations are Greece, Romania, Latvia, and Belgium. In the case of Greece, the suspicion of manipulating data has officially been confirmed by the European Commission.”

You’ll note that the remainder of the so-called PIIGS – the main focus of the world’s concerns – Italy, Ireland, Portugal and Spain – don’t appear on that list. Quite what sort of acronym we’ll get if you add Romania, Latvia and Belgium to the list of euro denominated black holes one dreads to think: PIGS BIRL, might be appropriate, though (yeah, I had to look it up, too).

Of course, if this data is correct, the real issue is why would these countries do this? In Greece’s case the answer seems fairly straightforward: as a nation it’s been in default for half of its independent history. For much of the rest of it, it’s been funded by the British as a defence against the Ottoman Empire and the Americans as protection against the Soviets. Like a fading movie star it needs external funding to maintain its lifestyle. Presumably something similar applies to the other countries, although quite what core Eurozone member Belgium is doing on the list is hard to say: probably the fact it’s not had a ********ing government for a while isn't helping.

Portugal, Italy and Spain have a clean bill of health.

Iniciado por nemo4

La ley de Benford es una puta mierda psicologoide pseudomatematica.

Groupon has struggled more than Zynga. Groupon filed for an I.P.O. in early June. The filing revealed some extraordinary numbers. In two and a half years, Groupon had grown from nothing to $645 million in revenue in the first quarter of 2011. This was amazing growth, but Groupon’s costs were also astronomical. In 2010, Groupon spent $263 million on marketing and lost $456 million. In the first quarter of 2011, Groupon disclosed that it spent roughly $208 million on marketing and lost $146.5 million. Apparently, it takes a lot of money to make a deal.

In the filing, Groupon’s chief executive, Andrew Mason, asked prospective shareholders to put these numbers into perspective by using a novel accounting metric: adjusted consolidated segment operating income. This measure subtracted hundreds of millions from online marketing and acquisition costs from operating performance. If used, Groupon’s results were strongly positive. With this metric, Groupon had income of $81.6 million in the first quarter of 2011.

While the accounting metric seemed to turn lead into gold, the response was negative. A number of commentators called the metric “income before expenses.” Groupon was polishing its numbers by simply taking out things that cost a lot. How could that be a valuable measure of the company’s worth?

Groupon’s revenue numbers also raised questions. In its initial filing, Groupon included payments to third-party merchants for the goods purchased. The result was to double Groupon’s revenue. But this appeared to count as revenue something that Groupon never earned.

The deal involved about €1.5 billion in loans by Dexia to its two largest institutional shareholders, part of which (certainly more than half based on statements in Pignal’s FT article), were used by the investors to buy more shares of Dexia. The security pledged by the borrowers? Existing shares of Dexia stock were the security. Thus the capital position of Dexia was made to appear stronger by borrowing money from itself to finance a capital increase, an obvious case of “double dip” accounting.