>there is more to an economy than manufacturing.
Not really. Most developed economies are basically 70% Baumol's cost disease[1]. The 20% of the American GDP that goes to healthcare, half of the military budget that goes into salaries, public services, the police isn't billed on productivity. Those are non-tradeable services whose compensation inflates with growth in the productivity gaining sectors of the economy.
That's why you can go not to a wealthy Tier 1 city in China, but to a Tier 2 or 3 city and it has better public services despite having like 10% of the per capita budget of a US city. Most compensation is.. fake. If you want to know what an economy does look at the stuff they make.