Benford's Law Raises New Doubts About Chinese Economic Data

Many have already questioned the reliability of Chinese economic data. Now, Benford's Law, a 1930s' mathematical tool named after former GE physicist Frank Benford, has been used to raise new concerns about data, according to research by the Australia & New Zealand Banking Group.

Benford's Law refers the to rate at which certain digits are distributed across data. It argues that the number 1 is the first digit about 30 percent of the time, while larger numbers will be the first digit fewer times.

From Bloomberg:

"The ANZ economists studied China’s annual nominal gross domestic product data from 1952 to 2011 to measure how frequently numbers from one to nine appeared as the first digit. While the 24 occurrences of “one” is higher than the 18 suggested by the rule, the economists said the statistics largely abide by what Benford’s Law allows. The same is true of industrial production data.

Suspicions emerged when the data was probed more deeply and reported in percentage terms, the ANZ report said, adding that the guilty party was often the second digit. An examination of the quarterly GDP growth rate from December 1991 to September 2012 shows zero occurred as the second digit 21 times, much higher than what Benford would calculate and suggesting a rounding-up to achieve a bigger leading digit. One through four also appeared more regularly than the law reckons, while seven through nine featured less.

Inflation reported on a percentage basis also failed to fit the law.

Non-conformity to the Benford’s law does not always indicate data manipulation, but nevertheless it raises doubts about the quality of Chinese data,” the authors said. “Our statistical analysis seems to have confirmed the long-rooted suspicion on quality and reliability of Chinese data."

Bloomberg says Benford's Law has previously shown that Greece and ponzi-schemer Bernard Madoff's numbers were manipulated.