In efficient global labour markets for very high wage workers one might expect wage differentials between migrant and domestic workers to reflect differences in labour productivity. However, using panel data on worker-firm matches in a single industry over a seven year period we find a substantial wage penalty for domestic workers which persists within firms and is only partially accounted for by individual labour productivity. We show that the differential partly reflects the superstar status of migrant workers. This superstar effect is also apparent in migrant effects on firm performance. But the wage differential also reflects domestic workers' preferences for working in their home region, an amenity for which they are prepared to take a compensating wage differential, or else are forced to accept in the face of employer monopsony power which does not affect migrant workers.