I don't necessarily agree with the criticisms of the current metric of unemployment rate (which generally revolves around the idea that people who stop looking for work are not counted in the labor force, which "artificially" increases or decreases the unemployment rate), and here's why.
The clasical economic discussion is the labor-leisure tradeoff, where an individual makes a decision to work or not to work. However, you could see a different choice framework, which is the decision to look for a job or not to look for a job. Under an assumption of complete information, you could argue that an individual who has stopped looking for a job has weighed the expected benefits from the job search (a function of the probability of getting the job and the expected payment from that job) versus the expected costs (lost leisure time from a fruitless job search). Under this type of model, an individual could exit the labor force in a rational manner. This type of individual most certainly should not be counted in the unemployment rate, because he has rationally made the choice not to look for the job.
Of course, the main criticism of this model is from an information perspective, in that a person might not correctly assess the expected benefits (or expected costs) of the job search. This criticism likely has merit from the standpoint of individuals who spend time searching for a job and then drop out of the labor force (although this is confounded by things like unemployment benefits), suggesting that they had incomplete information when they began their search, and updated that information as the job search continued (another possible explanation, of course, is that for some reason their expected benefits vs expected costs actually changed during the course of the job search).
So this simple model is far from perfect, although it does suggest a reason not to include those who stopped looking for work in the unemployment figures.
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