Statistical and data mining techniques have been used to detect fraud in elections and financial statements.

http://www.economist.com/node/8733747?story_id=8733747

https://en.wikipedia.org/wiki/Data_Analysis_Techniques_for_F...

The NY Times reported last month that

Studies by Goldman Sachs and other institutions over the years have strongly suggested that Chinese statisticians smooth out the quarterly growth figures, underreporting growth during boom years and overstating growth during economic downturns.

http://www.nytimes.com/2012/06/23/business/global/chinese-da...

So private corporations (who granted have their own agenda and biases) make assessments of economic numbers reported.

It would be surprising that there is not publicly available studies that report the general reliability of economic statistics reported by a country. It would even be interesting to reported statistics aggregated in a way that allows for easy comparison between numbers reported by different countries. Something like the Index of Economic freedom: http://www.heritage.org/index/default

(I am not an economist - so can't say I have done an extensive analysis of available sources...)