Lei de Benford e dados econômicos da China

Aplicação da Lei de Benford nas estatísticas econômicas oficiais do governo chinês:

A mathematical tool devised by an American physicist in the 1930s underscores doubts about the quality and reliability of Chinese economic data, according to research by Australia & New Zealand Banking Group Ltd. (ANZ)

The results are based on “Benford’s Law,” which holds that in any series of numbers, certain patterns will be found only if the statistics are naturally generated. The rule, created by former General Electric Co. (GE) engineer Frank Benford, suggests patterns for the first and second digits in a numeric series and can be used to detect phony data, Li-Gang Liu, ANZ’s chief economist for Greater China, and colleague Louis Lam said in a Jan. 8 report.

Benford’s work has already been adapted to show Greece should have been suspected of manipulating its data before the European debt crisis and that now-jailed financier Bernard Madoff was overstating investment returns.

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.”

Fonte: aqui