Monday, November 19, 2007

Benford's Law... and Testing Economics Data

I earlier posted a link on Benford's law, the idea that most data series are likely to have many more observations starting with the digit "1" than "2", and more starting with "2" than "3", etc. The idea was that to get from "1" to "2" requires a 100% increase in magnitude, while getting from "2" to "3" requires only a 50% increase in magnitude.... and so on.

Well, the undercover economist has more... the same principle can be used to assess whether economic statistics are accurate.

Suspician of the accuracy of statistics has a long history. Benjamin Disraeli famously commented that there are three kinds of lies.... "lies, damned lies, and statistics." But maybe this is not fair. At a minimum, most statistics should satisfy Benford's law.

I can think of an excellent application. Many people are suspicious of the macroeconomic numbers generated by Mainland China, especially at the state level. A simple test of whether they're made-up or not would be to see whether the series satisfy Benford's Law.

Of course this would not be a fall-proof test. What if the numbers really were made up, but by statisticians who knew about Benford's law?

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