Bad Test for Phony Data ?

Just over a year ago came the news that researchers applied "Benford's Law" to show that GDP data from China is likely fraudulent.  That's a huge finding!

                            BUT WE FIND THIS TEST TO BE UNRELIABLE

See above a graph that demonstrates BOTH the USA and China fail "Benford's Law" for GDP data from 1961 through 2012.  A conventional "Chi Square" test shows that both the USA and China data fail to obey Benford's Law at a confidence level higher than 95%.

What we call Benford's Law states that the first digits of a collection of numerical data will follow a known and non-intuitive pattern UNDER THE RIGHT CIRCUMSTANCES.  (See this link for a good discussion.)

But GDP % Change over time is not a data collection that typically satisfies criteria for Benford's Law to be relevant.  In fact, Benford's Law is often mis-used.

LINK TO WORLD BANK DATA SOURCE