Optimal unemployment insurance: Consumption versus expenditure

• We study optimal unemployment insurance if the unemployed pay lower prices.
• We derive a sufficient statistics formula in terms of observable variables.
• We compare our results to the standard Baily–Chetty formula.
• Lower insurance is optimal if relative risk aversion is greater than one.
• We calculate optimal replacement ratios for the United States.

We study the optimal provision of unemployment insurance (UI) in a framework that distinguishes between consumption and expenditure. We derive a “sufficient statistics” formula for optimal UI that is expressed in terms of observable variables and can therefore be used in applied work. Recent research has shown that unemployed households pay less per unit of consumption than employed households. This finding has two counteracting effects on the optimal level of UI. On the one hand, consumption smoothing benefits identified from expenditure data overestimate the true marginal benefits of UI. On the other hand, UI benefits become more valuable because they buy more consumption when unemployed. In an optimal design, which effect dominates depends on the curvature of the utility function. We show that for relative risk aversion larger than one the first effect dominates, leading to lower levels of optimal UI.