Matthew Yglesias Comes up with a really tough Challenge.
"I'd love for somebody to write up a model for me in which the optimal level of US investment in math and science education is increased by an increase in the number of Asian scientists and engineers." -- Matthew Yglesias
"Isn't there some existence theorem that there is a second best argument for all policies ?" -- Robert Barro
I can think of two ways to make it work.
One is Marshallian spillovers imply increasing returns to engineers world wide. Basically we might benefit twice from our engineers if they invent stuff and China and India have enough engineers to adapt that stuff to labor abundant economies and we get more cool stuff from them (I mean what would be the point of inventing the internal combustion engine without Toyota to make decent cheap cars).
I don't think this is what Newtie had in mind.
The other is subsidizing education of engineers is a way to subsidize tehcnology intensive industries which might make sense as strategic trade policy. This is clearly what he has in mind (why is it that Republicans can be counted on to be against free markets ?). This would mean that we have to keep ahead so as to keep all of the high wage high profit margin production in the USA (except bit late for that eh). It can be made to work if we are at a sweet spot of the grabbing rents with subsidies curve and should stay there. As the amount of subsidies needed to keep that share of the good jobs industries in the USA increases in the number of Chinese and Indian engineers the desired result obtains.
Actually to get closer to a semi serious model, the claim must be that the elasticity of market share with respect to subsidies decreases in current market share. Thus the better other countries are at making the goods associated with rents (high profits or high wages given worker characteristics) the higher is the optimal subsidy.
In this neo-mercantalist model it doesn't matter whether the subsidy is of the form of paying to train engineers or cash later provided that engineer intensive industries generate high rents.
It is possible to write models in which mercantalists are right (see "Industry Rents: Evidence and Implications" by Larry Katz and Larry Summers Brookings Papers on Economic Activity:Microeconomics 1989 209-75 which I think is the same as "Can inter-Industry Wage Differentials Justify Strategic Trade Policy" in a book except Summers was advising Dukakis and said the phrase "Strategic Trade Policy" was a no no). You will noticed that Summers was not convinced by Katz and Summers.
Much theory due to Krugman (who was not convinced by Krugman).