Pre-print, Working paper: An increasing literature encourages the use of selective immigration policies as a tool to promote incentives to education. It is argued that, since not everybody is allowed to migrate, under these policies a poor country may well turn out with more human capital than in autarchy. The implicit assumption is that migrations are permanent. However, this assumption has recently been dropped: a large literature studies the optimal migration duration in an intertemporal framework. In our work we study how selective immigration policies affect the human capital accumulation and the migration duration. Unlike most of the existing literature, the probability of entering abroad is endogenous and our analisys is not limited to two periods: there is no reason to consider a single migration spell, and our infinite-horizon model includes an aggregate shock as a source of constrained migration. Contrary to the "brain gain with a brain drain" reasoning, we show that selective policies may be harmful for human capital accumulation. As a consequence, their effectiveness is questionable, and they may produce a "brain loss" rather than a brain gain. Besides, borders closure backfires on migration duration especially for unskilled workers.