GDP equals C+I+G+X-M. It also equals national income, at least in theory. But estimates differs widely, even for the United States, which is rather disturbing. How do you conduct proper economic policy when estimates of GDP, even after revisions can differ by more than 2% points and their growth rates have a correlation coefficients of only 0.63 (see the work of Jeremy Nalewaik)?
Boragan Aruoba, Francis Diebold, Jeremy Nalewaik, Frank Schorfheide and Dongho Song make the old diversification of risk argument: why not combine both estimates? After all, this is often done with forecasts, and the two estimates can be treated like forecasts of the true GDP. And consistently with this literature, the weights on each should depend on the variance of the errors. Of course, they are not observed, but the authors have some guesstimates, based on correlations with variables not used to construct either GDP measure that are supposed to be correlated with the true GDP. They then show that measurement matters, for example in dating business cycles. We'll see whether the US will adopt such averaging, as some other countries already do.
Addendum: I wonder how the recent major revisions to US GDP would have fared with this scheme.