Economic models typically study the long-term effects of migration, and hence emphasise their impact on a country's endowment of skills using net migration rates. This approach however does not take into account the contribution of short-term movements of skilled labour on a country's stock of knowledge and ability to innovate. This paper develops a theoretical approach to extend the analysis to gross migration flows, which captures the volume of interactions and the potential for knowledge exchanges between a country's skilled labour and workers living elsewhere. One implication of the approach developed is that higher growth can be achieved through higher international labour mobility, even if there is no net migration. Countries that find it difficult or impossible to attract skilled labour on a permanent basis may therefore enjoy the growth effect brought by skilled temporary migrants.