We develop an empirical search-matching model with productivity shocks so as to analyze policy interventions in a labor market with heterogeneous agents. To achieve this we develop an equilibrium model of wage determination and employment, which is consistent with key empirical facts. As such our model extends the current literature on equilibrium wage determination with matching and provides a bridge between some of the most prominent macro models and microeconometric research. The model incorporates long-term contracts, on-the-job search and counter-offers, and a vacancy creation and destruction process linked to productivity shocks. Importantly, the model allows for the possibility of assortative matching between workers and jobs, a feature that had been ruled out by assumption in the empirical equilibrium search literature to date. We use the model to estimate the potential gain from an optimal unemployment insurance scheme, as well as the redistributive effects of such a policy