High-skilled workers are four times more likely to migrate than low-skilled workers. This skill bias in migration – often called brain drain – has been at the center of a heated debate about the welfare consequences of emigration from developing countries. In this paper, we provide a global perspective on the brain drain by jointly quantifying its impact on the sending and receiving countries. In a calibrated multi-country model, we compare the current world to a counterfactual with the same number of migrants, but those migrants are randomly selected from their country of origin. We find that the skill bias in migration significantly increases welfare in most receiving countries. Moreover, due to a more efficient global allocation of talent, the global welfare effect is positive, albeit some sending countries lose. Overall, our findings suggest that more – not less – high-skilled migration would increase world welfare.