Optimal Unemployment Insurance in a Search Model with Variable Human Capital

The framework of a general equilibrium heterogeneous agents model is used to study the optimal design of an unemployment insurance scheme and the voting behaviour on unemployment policy reforms. Agents, who have a limited lifetime and participate in the labour market until they reach the retirement age, can either be employed or unemployed in each period of their working life. Unemployed agents receive job offers of different (match) qualities. Moreover, unemployed agents suffer a decline of their individual productivity during unemployment, whereas the productivity of employed agents increases over time. Any form of unemployment insurance must take into account an important trade-off. On the one hand, generous benefits are desirable as they provide good insurance of the risk-averse agents against unforeseen income fluctuations (caused by layoffs and the randomness of individual job offers). On the other hand, high benefits induce a moral-hazard problem, as certain groups of agents choose to decline job offers that, while not being as attractive as the unemployment benefit from an individual point of view, a central planner would make them accept. An optimal unemployment insurance scheme is one that maximizes the expected lifetime utility of a newly born agent. Two types of unemployment insurance are considered, one with defined benefits and one with defined replacement ratios. A numerical version of the model is calibrated to the West German economy and simulated at ½-monthly frequency, resulting in an agent’s life-span of 1440 periods. The welfare maximising unemployment insurance scheme is determined in simulations. Under this optimal system, no payments are made to short-term unemployed agents. Long-term unemployed receive rather low (social assistance level) benefits, the optimal level of which depends on the assumed degree of risk aversion. Defined benefit systems provide a higher welfare than defined replacement ratios. I then address the question whether the majority of population would support the optimal system given the status quo. It turns out that older or unemployed agents tend vote in favour of the status quo, whereas young employed agents would approve the reform. If voters can choose between keeping their current unemployment system and jumping to the equilibrium associated with the optimal policy, there is a slight majority of just above 50% for the optimal policy. Finally, a more realistic case is considered, in which voters do not choose between the long-rung equilibria associated with policy changes, but take into account the transition process to the new equilibrium. The adjustment process of the macro environment after the policy reform is computed for a time span of sixty years. As some of the relevant variables adjust very slowly to their new long-run equilibrium values, the effect of the transition process on voting behaviour cannot be neglected