This paper quantitatively investigates the short- and long-run effects of liberalizing global migration on the world distribution of income. We develop and parametrize a dynamic model of the world economy with endogenous migration, fertility and education decisions. We identify bilateral migration costs and their legal component for each pair of countries and two classes of worker. Our analysis reveals that the effects of a liberalization on human capital accumulation, income and inequality are gradual and cumulative. In case of a complete liberalization, the world average level of GDP per worker increases by 20 percent in the short-run, and by more than 55 percent after 50 years. The world average index of inequality decreases and the liberalization path has stochastic dominance over the Baseline-As-Usual. These results are very robust to our identifying assumptions. We also analyze partial liberalization shocks : efficiency and inequality effects are roughly proportional to the «liberalization rate».