Also look up some less well-known names like Allengheny Technologies. You're trafficking in the usual truisms about what the US economy has evolved into. The reality (which I don't pretend to have a full handle on) is much more complex.

You may be aware of that business about how the US share of world manufacturing "value added" is still the highest and has in fact been quite stable since WWII.

As a start, for the US data alone, I found it, of all places, at http://www.census.gov/mcd/. I'm still trying to make sense of it all, but one thing I think I've determined is that the largest industry in the US in terms of 'value added' is ... Chemicals.

The industry classifications to be found in the Annual Survey of Manufactures (ASM) are an international standard and so those are comparable.

The thing that makes me most uncomfortable is exchange rates. But recently, I've developed the theory that while PPP is all the rage, it, in fact, applies only to domestic economies and that Nominal values are in fact the best current way to measure international trade. And therefore, in some sense, comparative advantage.