The Welfare Effect of Sorting in the Labor Market

We construct a labor-barter economy under search friction, introducing quality heterogeneity and information asymmetry into the economy. Under this environment, we examine the welfare effect of a sorting device. The main modifications to the standard sorting model are that i) an agent's type is endogenously determined by his optimal behavior and ii) rejecting trade is an option available for agents, so a ``lemon market'' problem may possibly emerge. Our findings are as follows: First, sorting can prevent the labor market from collapsing even under a serious information asymmetry by providing a more favorable condition for good-type workers. Second, sorting has a positive welfare effect, as opposed to the standard sorting models, by disciplining bad-type workers and encouraging trade. Finally, introducing a sorting device can significantly reduce the equilibrium unemployment rate by alleviating the informational friction and creating a positive externality, which prevents a possible coordination failure caused by that friction.