Abstract Unemployment differentials are greater between countries in the euro area than between U.S. states. In both regions, net migration responds to unemployment differentials, though the response is smaller in the euro area compared to the U.S. We use a multi-country DSGE model with cross-border migration to quantify Mundell’s hypothesis that labour mobility could substitute for independent monetary policy in a currency union. While not as effective as independent monetary policy, increased labour mobility reduces business cycle fluctuations for most countries in the euro area. However, Mundell’s conjecture does not hold uniformly. For countries that primarily face demand shocks, labour mobility stabilizes inflation and unemployment and improves welfare. If supply shocks are dominant however, labour mobility increases the cost of being in a currency union by magnifying inflation volatility.