When it comes to unemployment insurance, it is well recognized that it suffers from moral hazard, as insured unemployeds may not do enough to search for a job or may turn down job offers. But quantifying how much of this happens is very difficult, as it is the undetected moral hazard that is the problem, and the undetected is not measurable. One can try to assess it indirectly with a well-controlled randomized experiment. Some people are randomly subject to tighter control about their job searching, and they know about it.
John Micklewright and Gyula Nagy performed such an experiment in Hungary. The result: the treatment had a strong effect (as measured by the hazard of the unemployment) only on one category, women over 30, which are the ones who have low attachment to the labor market anyway. Men and young women were unaffected. And for those "older" women, being married with a working husband is a clear determinant of moral hazard. Theory would tell use that is this is true, then unemployment insurance benefits should be lower for married women, but not married men. Try implementing that.