Optimal social insurance with endogenous health

This paper analyzes optimal insurance against unemployment and disability in a private information economy with endogenous health and search effort. Individuals can reduce the probability of becoming disabled by exerting, so-called, prevention effort, which is costly in terms of utility. A healthy, i.e., not disabled, individual either works or is unemployed. An unemployed individual can exert search effort in order to increase the probability of finding a new job. I show that the optimal sequence of consumption is increasing for a working individual and constant for a disabled individual. During unemployment, decreasing benefits are not necessarily optimal in this setting. The prevention constraint implies increasing benefits over time while the search constraint demands decreasing benefits while being unemployed. However, if individuals respond sufficiently much to search incentives, the latter effect dominates the former and the optimal consumption sequence is decreasing during unemployment.