Should unemployment insurance cover partial unemployment?

A considerable share of the labor force consists of underemployed part-time workers: employed workers who, for various reasons, are unable to work as much as they would like to. Offering unemployment benefits to part-time unemployed workers is controversial. On the one hand, such benefits can strengthen incentives to take a part-time job rather than remain fully unemployed, thus raising the probability of obtaining at least some employment. On the other hand, these benefits weaken incentives for part-time workers to look for full-time employment. It is also difficult to distinguish people who work part-time by choice from those who do so involuntarily.