It's well known that the Beveridge curve relationship (the negative correlation between the unemployment rate and the vacancy rate) shifted out as the unemployment rate began to come down from its peak of 10% in late 2009. The first chart shows the most recent update.
Suppose that we disaggregate, and look for Beveridge relationships in terms of duration of unemployment. The second chart is a scatter plot of the vacancy rate vs. the unemployment rate for those unemployed less than 5 weeks (those unemployed less than five weeks divided by the total labor force).
Finally, let's take a look at the number of those unemployed 27 weeks or more, as a fraction of total unemployed, since 1948.
So, where do these observations lead us? The unemployment rate is currently unusually high, and high in a way that does not appear to be consistent with posted vacancies. But if we disaggregate, it seems that the characteristics of the time series might have a lot to do with the fact that there are much more long-term unemployed now than is typically the case. But why has that happened? Especially since the phenomenon appears not to be new (going back to 1990 at least), it's hard to avoid thinking about mismatch. But in order to evaluate that story, we need more information about the long-term unemployed. How many of these are former construction workers? How many are David Autor's middle-skill people? Possibly the financial crisis merely increased the rate of structural change that was already occurring in labor markets? Are there other features of the long-term unemployed we need to be thinking about? The long-term unemployed may have depreciated skills; they may have been picked over as a group and be of perceived low average quality. Their search effort may be low. All of these things matter for policy, particularly for unemployment insurance programs.
What is clear is that conventional models typically have insufficient heterogeneity to explain these facts. In Mortensen-Pissarides models, for example, labor is homogeneous, and mismatch is embedded in reduced-form matching functions. I'm interested in learning about work you know about that either already captures this stuff, or could potentially do so.