In the brain drain literature models with heterogeneous agents typically predict that all agents who get tertiary education will try to migrate. Hence, the skill composition of the migration flow is the same as that of the skilled population left behind. This result, however, may not represent the migration pattern of some source countries. In this paper I present and analyze a model of heterogeneous agents where immigrants go through an assimilation process upon arriving to the host country. I start by studying the skill composition of the migration flow of a less advanced country. Then, I characterize conditions that lead a benevolent government to promote migration among the skilled population. I show that the government may promote skilled migration despite the fact that the brain drain decreases per capita income.
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