Optimal Unemployment Insurance over the Business Cycle
This paper analyzes optimal unemployment insurance (UI) over the business cycle. We obtain an optimal UI formula that resolves the trade-off between insurance and job-search incentives in a broad class of models in which the job-finding rate depends on UI. Our formula generalizes the standard Baily-Chetty formula, only valid when the job-finding rate is a constant. The formula relates the optimal replacement rate of UI to the usual sufficient statistics (risk aversion, consumption-smoothing benefits of UI, and microelasticity of unemployment with respect to UI) and a new sufficient statistic (macroelasticity of unemployment with respect to UI). While the microelasticity accounts only for the response of job search to UI, the macroelasticity also accounts for the response of the job-finding rate to UI. We calibrate the formula using available empirical estimates of the sufficient statistics. The wedge between micro- and macroelasticity is positive and countercyclical in empirical studies, capturing negative job-search externalities that are more acute in recessions. An implication is that the Baily-Chetty formula underestimates optimal UI, especially in recessions. We show that the standard search-and-matching model with Nash bargaining generates a negative wedge between micro- and macroelasticity. To generate a wedge that is positive and countercyclical, we construct an alternative search-and-matching model with rigid wages and diminishing marginal returns to labor. Using our formula, we prove that optimal UI is countercyclical in this model. We also show that the calibrated model generates realistic fluctuations in unemployment and the elasticity wedge.
You may purchase this paper on-line in .pdf format from SSRN.com ($5) for electronic delivery.
This paper was revised on January 11, 2013