Waiting for the perfect job does not work

We usually think that one advantage of unemployment insurance is that it allows unemployed workers to take more time to find an appropriate job and not rush to the first available job for which they may not be qualified. As Acemoglu and Shimer have forcefully argued, the absence of unemployment insurance could lead to important mis-allocations for this reason, and thus losses of efficiency in the economy. This argument implies that workers with longer unemployment durations, after controlling for other characteristics, should be getting better jobs. Is this true?

Miki Kohara, Masaru Sasaki and Tomohiro Machikita test this for Japan using job tenure as a signal of job quality. It turns out the hypothesis above is easily rejected. Indeed, the longer the unemployment duration, the shorterthe subsequent employment duration. So it appears that other factors, like loss of skills and human capital during unemployment and stigma matter more than the search for the perfect job. Of course, it could also be due to some missing control variables, but the effect is so strong I doubt it can be overturned.