Uninsurable Individual Risk and the Cyclical Behavior of Unemployment and Vacancies

This paper is concerned with the business cycle dynamics in search and matching models of the labor market when agents are ex-post heterogeneous. We focus on wealth heterogeneity that comes as a result of imperfect opportunities to insure against idiosyncratic risk. We show that this heterogeneity implies wage rigidity relative to a complete insurance economy. The fraction of wealth poor agents pre- vents real wages from falling too much in recessions, since small decreases in income imply large losses in utility. Analogously, wages rise less in expansions compared to the standard model as small increases are enough for poor workers to accept job offers. This mechanism reduces the volatility of wages and increases the volatility of vacancies and unemployment. This channel can be relevant if the lack of insurance is large enough so that the fraction of agents close to the borrowing constraint is significant. However, discipline in the parameterization implies an earnings variance and a persistence in the unemployment state that results in a large degree of self insurance.