Setting up a good unemployment insurance system is awfully difficult. You need to take into account that there may be significant moral hazard, as workers may shirk their effort to find a new job or hide job rejections. But you still want to provide some level of insurance. Hugo Hopenhayn and Juan Pablo Nicolini have realized in 1997 that "one dimension" is not sufficient to get closer to first best. In addition to benefits that decline with unemployment duration, they devise a tax and subsidy scheme once you have a job, a scheme that depends on your unemployment duration.
Ofer Setty adds a third dimension, monitoring. Specifically, the idea is to monitor the job-search effort with a probability that depends on some observables. Monitoring is costly, by provides a somewhat informative signal, on which insurance benefits depend. In other words, if a case worker thinks you are lazy, he can spy on you and depending on what he observes, he may penalize or supplement you. Knowing this, you provide more effort to look good. The result: significantly better insurance, measured by the variance of consumption that is divided by three, and half the cost of insurance. Not bad.