We develop an equilibrium search-matching model with risk-neutral agents and two-sided ex-ante heterogeneity. Unemployment insurance has the standard effect 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 growth and wage inequality. To show this, we construct two fictitious economies with calibrated parameters which only differ 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 workers 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 remains 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.