Optimal Unemployment Insurance over the Business Cycle

By Camille Landais, Pascal Michaillat and Emmanuel Saez


This paper analyzes optimal unemployment insurance over the business cycle in a search model in which unemployment stems from matching frictions (in booms) and job rationing (in recessions). Job rationing during recessions introduces two novel effects ignored in previous studies of optimal unemployment insurance. First, job-search efforts have little effect on aggregate unemployment because the number of jobs available is limited, independently of matching frictions. Second, while job-search efforts increase the individual probability of finding a job, they create a negative externality by reducing other jobseekers’ probability of finding one of the few available jobs. Both effects are captured by the positive and countercyclical wedge between micro-elasticity and macro-elasticity of unemployment with respect to net rewards from work. We derive a simple optimal unemployment insurance formula expressed in terms of those two elasticities and risk aversion. The formula coincides with the classical Baily-Chetty formula only when unemployment is low, and macro- and micro-elasticity are (almost) equal. The formula implies that the generosity of unemployment insurance should be countercyclical. We illustrate this result by simulating the optimal unemployment insurance over the business cycle in a dynamic stochastic general equilibrium model calibrated with US data.

We have now a very good characterization of optimal unemployment insurance in steady-state. What ought to happen to it over a business cycle is less well established, and is subject to a vigorous debate in politics given the current surge in unemployment in the United States. The optimal policy follows the intuition that benefits should become more generous when it becomes more difficult to find jobs. In this respect, it follows the policy already in place in Canada, where generosity depends on the unemployment rate in the region, as I have analyzed in Pallage and Zimmermann (2006).

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