Auditor, and very soon to be CPA, here. The author "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." Quarterly reports are unaudited by an independent CPA firm (most often KPMG, PWC, EY, Deloitte), while annual reports (10-K) are audited. I would be curious if the the sum of squares analysis is as significant in the latter set.
The figures could be still be reliable if this reflects an actual change in distribution of business.
Speculation: Perhaps in 1960 businesses were really distributed according to a power law but have reapportioned a bit over time. Trends like consolidation and dominance of a few large firms might skew things.
He studied 43 different variables on 20,000 firms.
That's like measuring the heart rate, LDL, HDL, blood sugar level, systolic and diastolic blood pressure, height, weight, hair length, number of children, salary, home value, and total miles driven on all of the cars... of an entire football stadium worth of people.
And it's not like he's correlating these numbers, that your salary is proportional to your home value, or your weight is proportional to your blood pressure.
No, these are statistical properties of the numbers themselves.
The hypothesis of the paper is that statistical deviations correlate with financial crises. You doubt that correlation, but you think all of thousands of other numbers can credibly show a statistical correlation? :)
Not all measurements are subject to Benford's law. For example, a list of people's heights isn't going to follow the distribution. You can't just arbitrarily take values and expect them to fit into this mold.
Basically, Benford's Law works where the values are an open-ended count of something. When it's a measurement within a bounded domain, all bets are off.
And to tie this back into the financial domain, company stock prices are also not open-ended but a bounded domain. Below $1 gets you delisted from the exchanges; above $500 or so starts to impact the stock's liquidity.* Companies make stock splits to stay within that range intentionally, departing from Benford's law. And it follows that any other numbers tied to the stock price - say the value of 100,000 options - will also depart from Benford's law. The effect doesn't necessarily imply chicanery or wrongdoing. (It does imply manipulation but that is not necessarily evil, and there may be many layers of indirection between the manipulation and observed numbers)
*(of course some companies like Berkshire Hathaway are famously okay with that.)
As a soon to be CPA, these recent articles on Benford's Law fascinating. But it's funny that there's extreme skepticism around Moore's Law, but Benford's Law seems to get a free pass. Just like Moore's Law it's a law matched to empirical observations - meaning it works until it doesn't.
Benfords Law works as long as those that would mess with numbers aren't too much aware of it.
Moore's law works until you hit the limits of physics.
Benfords Law also works for the observation of various phenomena totally unrelated to human activity, so my guess is that it is here to stay. One day we will run into what we will probably call 'Moore's Wall' and then that will be that.
