Frictional Assignment

This paper examines the time-consuming process of matching the two sides of a market each having diverse characteristics. This is cast in a labor market setting where workers of di®erent skills need be matched with di®erent machine qualities to produce output. I characterize the e±cient allocation and then show that it can be decentralized by a competitive framework. A prominent feature of the frictional assignment is that each skill level is associated with a market tightness in addition to a machine quality. The di®erential market tightness as an additional allocative device implies that the assignment is not always positively assortative, i.e., high quality machines are not necessarily assigned to high skills even though machine qualities and skills are complementary in production. The market mechanism that decentralizes the e±cient assignment has the feature that ̄rms post wages to attract workers in addition to choosing machine qualities. A steady state is established and numerical exercises are used to show that the di®erential market tightness for di®erent skills is also quantitatively important for the wage function and wage distribution. JEL classi ̄cation: D33, J31, L11.