Characterization of optimal durations of unemployment benefits in a nonstationary job search model

This paper studies the optimal duration of unemployment insurance (UI) benefits in a job search model where a risk neutral UI agency cannot monitor the search effort of risk-averse workers. Unemployment assistance benefits for noneligible unemployed are taken as exogenous by the unemployment agency which chooses optimally the constant level of UI benefits, the date of their exhaustion and the constant level of the financing tax. So, due to possible finite values of the duration of unemployment benefits, the resulting agency’s problem involves nonstationarities that appears somewhat difficult to solve from the analytical viewpoint. Based upon the geometric properties of the incentive and budget constraints, we successfully provide two explicit sufficient conditions regarding the parameters of the model for obtaining a positive and finite optimal duration of UI. We then give a theoretical rationale for most unemployment insurance systems.