Recent research has related characteristics of cities to differences in the distribution of wages across workers with different skill levels. We demonstrate that these differences in wage differentials arise naturally as a compensating variation in Rosen’s theoretical model of inter-city wages. For example, if the income elasticity of demand for housing services is less than unity, cities with higher house prices will have smaller money wage differentials between low and high skill workers. This result has no implications for differences in either absolute or relative real productivity or welfare of unskilled workers. Similarly, changes in the amenity of an urban area may result in changes in relative wages of skilled and unskilled workers with no implications for real productivity or welfare differentials.
Empirical tests in which housing cost differentials are added as a determinant of inter-city differences in an intra-urban wage differential model provide empirical confirmation of the theoretical expectations. It appears that intra-urban money wage differentials, differences in the quality of life, and variation in the cost of living in each city are jointly determined variables just as Rosen’s model of inter-city wage differentials predicts.