Chinn quotes Fox: "the different components of real GDP can no longer be added together. That is, they can be added together but, except in the base year, they don't add up to real GDP." Pretty clear.
Fox also says:
The BEA's remedy to the problem is to put up warnings against doing share-of-real-GDP calculations all over its website.That's pretty funny. Also true, as even I have noticed those warnings.
But I'm having an awful lot of trouble understanding the problem. To use the example both Chinn and Fox use, consider manufacturing as a share of GDP. If you figure Nominal Value Added (for manufacturing only ) relative to Nominal Value Added (for all of GDP) you are okay. But maybe you think your result is unsatisfactory because prices have gone up more slowly for manufacturing than for all of GDP ("think health care", Justin Fox says). The nominals don't give you a good picture of manufacturing's share of real output over time. But that's not the error.
The error comes in when you switch to inflation-adjusted data. Since the mid-1990s, inflation-adjusted values have been figured by the "chain-weighted" method. Because they use this new method, when you take the inflation-adjusted components of GDP and add them up, the total doesn't come out equal to inflation-adjusted GDP. Here's Whelan:
A crucial feature of this chain aggregation methodology is that the real aggregate of X and Y will generally not equal the arithmetic sum of the real series for X and Y.For chain-weighted values, the whole is not equal to the sum of its parts. That's the problem. That much I get, but that's where I lose it.
It just doesn't make any sense to me. Y=C+I+G+NX, but only if they're nominal values? I have to ruminate on this for a while.
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