Wage differentials, discrimination and efficiency

I analyze a large labor market where homogeneous firms post wages to direct the search of workers who differ in productivity. I show that the model has a unique equilibrium. The wage differential depends positively on the workers' productivity differential only when the latter is large. When the productivity differential is small, high-productivity workers get a lower wage than low-productivity workers. This reverse wage differential remains even when the productivity differential shrinks to zero. However, the equilibrium is socially efficient. High-productivity workers always get the employment priority and higher expected wages than low-productivity workers. Although discrimination in terms of expected wages does not exist, conventional measures are likely to incorrectly find discrimination in the model.