There used to be a time where the discussion of unemployment over the business cycle was limited to disputes over the level of NAIRU and how monetary policy would influence it. How much progress we have made since. A first step has been the Mortensen-Pissarides matching function, which has considerably refocused the discussion on micro-foundations on unemployment with the use of explicit labor search models.
After Robert Shimer showed some serious doubts about some of the critical business cycle properties of the matching function models, considerable effort has been made to either salvage the matching function models by augmenting or modifying them in some ways, or to come up with more micro-founded ways to understand the matching process.
One such avenue is the directed search model, where job seekers purposely decide to apply to certain positions on the basis of some signal (say, a posted wage). Guido Menzio and Shouyong Shi just wrote a paper that should be a trend setter for this class of models. The particular appeal here is that they are able to find a solution for a search model with aggregate fluctuation that is easy to compute, quite a feat for any model with heterogeneity across agents.
It is incredible how much such modeling has progressed in recent years. In this model, firms endogenously choose whether to open vacancies and how much to offer for each. Workers, unemployed or employed, decide where to apply and how much to ask. Each match has idiosyncratic productivity. In equilibrium, unemployed workers are less discriminating as to where they apply, as they want to make sure they are the only ones applying. Employment matches are also dissolved endogenously.
Aggregate fluctuations are triggered by the standard productivity shocks. For example, a positive shock lets firms open more vacancies with different terms, and workers look for better terms and better application success rates. In addition, fewer matches are dissolved. Once calibrated, the model can explain 40% of the fluctuations in the unemployment-employment transition and all of the reverse transition. In addition, 80& of changes in unemployment and 30% of those in vacancies can be accounted just by productivity shocks.
Firms and workers are ex-ante identical here. They are all in the same sector. Once even more complexity can be added to the model, it looks very promising what could be achieved in terms of understanding fluctuation of employment and, eventually, what policies could impact it.