Optimal unemployment insurance with monitoring

I model job-search monitoring in the optimal unemployment insurance framework, in which job-search effort is the worker's private information. In the model, monitoring provides costly information upon which the government conditions unemployment benefits. Using a simple one-period model with two effort levels, I show analytically that the monitoring precision increases and the utility spread decreases if and only if the inverse of the worker's utility in consumption has a convex derivative. The quantitative analysis that follows extends the model by allowing a continuous effort and separations from employment. That analysis highlights two conflicting economic forces affecting the optimal precision of monitoring with respect to the generosity of the welfare system: higher promised utility is associated not only with a higher cost of moral hazard, but also with lower effort and lower value of employment. The result is an inverse U-shaped precision profile with respect to promised utility.