Consider Becker’s classic 1963 matching model, with unobserved ﬁxed types and stochastic publicly observed output. If types are complementary, then matching is assortative in the known Bayesian posteriors (the ‘reputations’). We discover a robust failure of Becker’s result in the simplest dynamic two type version of this world. Assortative matching is generally neither eﬀicient nor an equilibrium for high discount factors. In a labor theoretic rationale, we show that assortative matching fails around the highest (lowest) reputation agents for ‘low-skill (high-skill) concealing’ technologies. We then ﬁnd that as the number of production outcomes grows, almost all technologies are of either form. Our theory implies the dynamic result that high-skill matches eventually break up. It also reveals that the induced information rents create discontinuities in the wage proﬁle. This in turn produces life-cycle eﬀects: young workers are paid less than their static marginal product, and old workers more.
Anderson, Axel and Smith, Lones, "Assortative Matching and Repubation" (2006). Cowles Foundation Discussion Papers. 1841.