Optimal Unemployment Insurance with Variable Skill Levels

I study the consequences of heterogeneity of skills for the design of an optimal unemployment insurance, using a principal-agent set-up with a risk neutral insurer and infinitely lived risk averse agents. Agents, who are characterised by different productivities or skills, are employed by firms offering wages that depend both on the agents’ individual skill level and the quality of the worker-firm-match. Agents face the risk of losing their job and, while unemployed, are offered jobs with different match qualities. No search effort by the agent is needed to receive offers. Individual productivity declines during unemployment due to depreciation of skills and increases on the job because of learning by doing. Any insurance offered must take into account the moral hazard problem created by the fact that job offers are private information to the agent. A further complication is due to the unobservability of an agent’s productivity. I find that under an optimal contract, periods of unemployment are characterised by declining benefits. Agents are further punished for long unemployment by reducing expected future utility. A new result obtained from this approach is the observation that under an efficient contract, agents whose productivity is relatively high tend to have a shorter unemployment duration and a higher productivity growth in the future. Unemployment benefits do not only depend on an agent’s employment history, but also on the skills reported by the agent. Agents are punished for accepting jobs that do not seem to be in line with their reported skills.