This paper studies the impact of migration over the business cycle focusing on origin countries. According to conventional wisdom, cross-border labour mobility acts as an important adjustment mechanism during recessions; it is a way to reduce unemployment pressures and to smooth consumption via remittances. I argue that there is an important factor that previous research on cyclical migration has overlooked: skill heterogeneity. With recent migration flows becoming increasingly more concentrated in skilled labour an important trade-off arises. On the one hand, migration releases unemployment pressures and it creates beneficial risk-sharing channels for the origin countries. On the other hand, it generates negative compositional effects (the so called “brain-drain” effects) and skill imbalances which deepen and prolong rather than dampen recessions in the origin countries. I analyse quantitatively the impact of cyclical migration in an open-economy DSGE model with endogenous migration flows, trade linkages, search and matching frictions, and skill heterogeneity. I apply this framework to the case of the Greek emigration wave following the European Debt Crisis. I find that emigration flows imply negative dynamic effects for capital formation. Rather than stabilising the Greek business cycle, labour mobility had a destabilising effect leading to a deeper and more protracted recession.