A dynamic labor matching economy is presented, in which the unemployed are either entitled to unemployment insurance (UI) or unemployment assistance (UA), and the employees are either eligible for UI or UA upon future separations. Eligibility for UI requires a minimum duration of contributions and UI benefits are then paid for a limited duration. Workers are risk-averse and wages are determined in a bilateral Nash bargain. As eligibility for UI does not automatically follow from employment, the two types of unemployed workers have different threat points, which delivers equilibrium wage dispersion. Most of the variables and parameters of the model are estimated using the French sample of the European Community Household Panel (1994-2000). We show that extending the UI entitlement improves the situation of all groups of workers and slightly lowers unemployment, while raising UI benefits harms the unemployed on assistance and raises unemployment. Easier eligibility for UI also improves the situation of all groups of workers and favours relatively more the least well-off than longer entitlement. The re-entitlement effect in France lowers by 10% the rise in the wage and by 13% the rise in unemployment following a 10% increase in benefit levels.