Unemployment insurance design: inducing moving and retraining

Evidence suggests that unemployed individuals can sometimes affect their job prospects by undertaking a costly action like deciding to move or retrain. Realistically, such an opportunity only arises for some individuals and the identity of those may be unobservable ex-ante. The problem of characterizing constrained optimal unemployment insurance in this case has been neglected in previous literature. We construct a model of optimal unemployment insurance where multiple incentive constraints are easily handled. The model is used to analyze the case when an incentive constraint involving moving costs must be respected in addition to the standard constraint involving costly unobservable job-search. In particular, we derive closed-form solutions showing that when the moving/retraining incentive constraint binds, unemployment benefits should increase over the unemployment spell, with an initial period with low benefits and an increase after this period has expired