In 1987 Fijians of Indian descent began to emigrate in large numbers. Spurred by a political coup they felt damaged relative prospects at home, they left for places like Canada, Australia, and New Zealand, all of which privilege skilled, educated immigrants. As smart Indian Fijians left for Sydney, observers lamented the "ominous," "crippling," even "horrific" loss of human capital. One population researcher charmingly compared the migration to a massive increase in the death rate.
Economist Michael Clemens decided to find out what, exactly, was going on. By using the (static) ethnic Fijian population as a control group, he and Satish Chand decided to test the effect of labor movement on human capital stocks.
They found that as the exodus accelerated, young Indian Fijians began investing in tertiary education at levels never seen before. (Today Indo-Fijian children are more likely to go to college than American children.) Many left for jobs and lives off the islands. But the shift was so large that attainment of tertiary education by the remaining Indian Fijians was higher--much higher-- after the migration than before. Although the Indians were leaving and the native Fijians were staying put, both the remaining Indians and the stationary Fijians became more educated over time:
Recall that roughly one fifth of the Indian population departed the country during the intercensal period 1986‐1996, this departure was heavily weighted toward the highly educated, and the entire Indian population was in rapid decline. But despite all of this... the number of Indians with tertiary schooling in Fiji did not decline or even remain constant. It increased enormously—by almost exactly as much as did the number of Fijians with tertiary schooling. We can assert... that even very large, sudden departures of the highly educated from a developing country to rich countries need not correlate with a decline in the stock of highly educated workers in the country of origin.
As it turns out, human beings do not seek education purely for the betterment of their eternal souls. People locked in poor countries do not fail to invest years studying theoretical physics because they lack the appropriate imaginative capacity. If no one can afford to hire a cardiologist, no sane person is going to waste a decade studying to be one. Mobility transforms a questionable investment into one worth making.
The paper, which will ably answer all of your what-ifs and causation/correlation questions, is available here.