We derive the shape of optimal unemployment insurance (UI) contracts when agents can
exert search effort but face different search costs and have private information about their
type. We derive a recursive solution of our dynamic adverse selection problem with repeated
moral hazard. Conditions under which the UI agency should always offer separating
contracts are identified. We show that the good searcher receives an information rent and
that the bad searcher receives the minimal entitlement. From a methodological point of view,
we achieve a precise characterization of the sets of jointly feasible entitlements. This allows
us to map our analytical results one-to one to a numerical algorithm. According to our results
the contract for the good searcher has a decreasing benefit profile, as the one he would be
offered in a pure moral hazard environment. In contrast, the contract of the bad searcher is
distorted by an adverse selection effect, so that it tends to have an upward-sloping benefit
profile. We provide a comparative static analysis of changes in various parameters of our
model.