A growing number of OECD countries are leaning toward the adoption of selective immigration policies, which are expected to raise the quality (or education level) of migrants. This view neglects two important dynamic effects: the role of migration networks, which could reduce the quality of migrants, and the responsiveness of education decisions to the prospect of migration. We propose a model of self-selection into migration with endogenous education choices, which predicts that migration networks and the quality of migrants can be positively associated when destination countries adopt sufficiently selective immigration policies. Empirical evidence, presented as background motivation, suggests that this is indeed the case.