Still, the critique inspired me to get a bit more formal about the analytics, and there is a small clarification I think I should make.
So here’s how I think about it (which is actually a fairly standard trade model approach): approximate the economy as consisting of two sectors, traded and nontraded, with traded goods being basically manufacturing. Assume full employment for the sake of argument; then production is always on the production possibility frontier, which is the downward-sloping line in the figure.
With balanced trade, production = consumption (plus investment, but lump them together); that’s point A. When the economy runs a trade deficit, however financed, consumption lies outside the PPF, at a point like B; this point normally involves moving out an expansion path along which consumption of both nontraded and traded goods rises. However, the increase in nontraded consumption must be met out of domestic production, which means that traded production falls.
So a trade deficit in manufacturing does correspond to a fall in manufacturing production.
Now, one slight twist is that because a trade deficit also corresponds to a rise in overall spending, part of that trade deficit reflects increased consumption of manufactures rather than reduced production; you can see this in the figure, where the fall in traded production is smaller than the deficit. Quantitatively, however, this effect should be fairly small, since value-added in manufacturing is less than 12 percent of GDP.
Bottom line: yes, trade deficits reduce manufacturing production and jobs. They played a significant although far from dominant role in manufacturing job losses after 2000.