A dynamic generalization of Becker's assortative matching result

This paper considers a dynamic matching model in which each agent's future productivity depends in part on their current match, as in labor markets, schooling, intergenerational marriage markets, and other environments. The Planner's endogenous rankings of human distributions are characterized. These Planner rankings are then used to develop sufficient conditions for positive assortative matching to be dynamically efficient. One lesson that emerges is that complementarity assumptions alone are insufficient for a robust sorting theory — the curvature of the static production function is also critical to determine optimal sorting patterns. In addition, the Planner's ranking of distributions over human capital yield characterizations of individual attitudes toward human capital gambles in an associated market equilibrium. Finally, the implied dynamics for (1) individual wages and (2) wage distributions across age cohorts are characterized.