We develop an equilibrium search-matching model with risk-neutral agents and two-sided ex-ante heterogeneity. Unemployment insurance has the standard e ect of reducing employment, but also helps workers to get a suitable job. The predictions of our simple model are consistent with the contrasting performance of the labor market in Europe and US in terms of unemployment, productivity g r o wth and wage inequality. T o s h o w this, we construct two ctitious economies with calibrated parameters which only di er by the degree of unemployment insurance and assume that they are hit by a common technological shock which enhances the importance of mismatch. This shock reduces the proportion of jobs which w orkers regards as acceptable in the economy with unemployment insurance (Europe). As a result, unemployment doubles in this economy. In the laissez-faire economy ( US), unemployment r emains constant, but wage inequality increases more and productivity grows less due to larger mismatch. The model can be used to address a number of normative issues.

We obtain a recursive formulation for a general class of optimization problems with forward-looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle-point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner's problem. The recursive formulation is obtained after adding a co-state variable μ t summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with μ t playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems.