Opening up to international trade raises the return to skills in advanced economies and reduces it in the less advanced ones, according to the standard factor-endowments story. If human capital accumulation in turn depends on these returns to skills, trade should enhance human capital accumulation in the rich countries, but slow it down in poor economies. In other words, trade could serve to accentuate over time an initial divergence in income levels. As a result of trade, already rich countries should end up growing faster, while poor countries remain poor.
Just a theoretical possibility? In an interesting paper, Oded Galor and Andrew Mountford argue that it is a lot more than that. This story may help account for the "Great Divergence" in economic history--i.e., why Britain took off while India, say, failed to industrialize (yes, yes, I know there are other reasons too...). It may also shed light on the failure of poor countries to converge to the living standards of the rich in the current era of globalization.
It's not that there are no gains from trade for both sides. But rich countries take the gains in the form of larger income per capita, while the poor take it in the form of larger population (higher fertility).
Aside from an interesting historical discussion, Galor and Mountford provide some striking evidence on the contemporary relationship between trade, on the one hand, and fertility and education, on the other. Controlling for endogeneity and other possible problems, they show that larger trade shares are associated with lower fertility and greater investment in education in the OECD economies, but with higher fertility and lower education in developing economies.
I am more convinced by the historical discussion than by the contemporary evidence (for one thing, the skill premium has generally risen--not fallen--in most developing economies opening up to trade in recent decades). But I do find these scatter plots intriguing.