The law of numbers
I WONDER HOW many readers of this column are familiar with something called Benford’s Law? I must confess, I didn’t know what it was until I chanced upon a piece of research from ANZ that applied the law to China’s GDP numbers going all the way back to 1949. I don’t wish to go into the arcane mathematics underlying Benford’s Law, but states that in a recurring data series the first digit is much more likely to be a low number than a high number.
Apparently, the law forms a core modus operandi of forensic accountants in their search for cooked books, and has been instrumental in unearthing some major financial frauds. According to ANZ, while China’s GDP data conformed to Benford’s Law from 1949 to 2011, in the period since then, they have not.
The inference is that the data has been rounded up to achieve a higher first digit in the data. So, while Benford’s Law as applied to second digits predicts that the numbers 7, 8 and 9 are more likely to appear than zero or 1, 2, 3 or 4, when it comes to China’s GDP data, the lower second digits are more frequent. And improbably so, according to that law.
It’s become a piece of received wisdom that social unrest will ensue if China’s growth falls below 7%. I’m not sure where the science underlying that nugget comes from, but you get the idea. If the observations regarding China’s GDP data and conformity to Benford’s Law are sound, should growth look like it’s falling below that psychologically significant 7% level, we’re likely to get a 7.1% rather than 6.9%.
Perhaps unsurprisingly, recent research on economic data released by European Union member states points out that Greece’s data do not comply with Benford’s Law, and the European Commission suspects it may have been manipulated. Does any of this matter? Well, data move markets and comforting – but false – data can buy you breathing room from a day of reckoning.
I RECALL READING Gordon Chang’s The Coming Collapse of China about a decade ago. The author argued in the book that non-performing loans in China’s banking system would bring about the country’s financial collapse. If any of us – mainland Chinese included – had followed that advice we would have missed out on some of the juiciest investment returns available in global financial markets over that period.
Late last year, Chang claimed in an interview that China’s GDP growth rate in the third quarter had been overstated, and was closer to zero rather than the 7.4% that the Chinese authorities had reported. He based this view on weak China purchasing managers’ data and slow electricity production across the country. That was a bold claim and light years away from parsing the data using Benford’s Law. Who knows whether uber China bear Chang will eventually, like the proverbial stopped clock, be right?
But in his interview he also drew attention to something a Hong Kong-based banker mate of mine has been banging on about for years: civil unrest in the country. He says that there are about 500 serious incidents of civil unrest every day in China and they go unreported. Chang reckons there are 200,000 such incidents every year and that the Beijing central government has ceased to produce statistics on civil unrest due to the sheer number of the incidents.
CHINA’S NATIONAL BUREAU of Statistics last week released for the first time in over a decade the country’s Gini coefficient, a measure of the economic inequality between a country’s social groups. The higher the number, the higher the inequality. According to the NBS, the coefficient was 0.474 last year, down from 0.477 in 2011 and below the decade’s high of 0.491 registered in 2008. I’m tempted to invite a Benford’s Law analysis of this data, but I won’t.
I will, however, point to the official news release made by the Xinhua news agency early last month which signalled a move on the part of the Chinese authorities that had more than a whiff of North Korea about it. The agency announced that the country’s 34 satellite TV channels would have their entertainment programming reduced by two thirds.
Meanwhile each station would have to broadcast at least two hours of news programming a day. The State Administration of Radio, Film and Television decried programming that was deemed “excessive entertainment” or of “low taste”. The Xinhua release mentioned the promotion of “traditional virtues” and “core socialist values”.
I wonder if there is any connection between rising civil unrest in China and this new focus on virtues and values. Just as I wonder whether the country’s GDP data is any more reliable than the numbers trundled out of Greece and other weak EU states that help when it comes to accomplishing goals. In the latter case by facilitating the transfer of budgetary largess, in China’s by keeping the market sweet.
It might just be that the failure of China’s GDP data to conform to Benford’s Law is an indicator that the real numbers are rather different from the official numbers. Rising civil unrest might also indicate that they are, if the received wisdom is right.