Rethinking the labor matching function

The Mortensen-Pissarides matching function has been a standard ingredient of any labor market model interested in the transition in and out of unemployment. It is easy to use, appears to have the right properties, and can be founded on microfeatures, as documented by Ricardo Lagos. The use of the matching function in business cycle models has, however, recently come under assault following the work of Robert Shimer because these models to not yield some key properties of labor market transitions during the business cycles. Is it time to rethink such reduced forms, as the matching function ultimately is?

Melvyn Coles and Barbara Petrongolo go back to the roots and note that the matching function essentially assumes that there is a single bin of unemployeds that are potentially matched with vacancies. In reality, we need to think about two bins: the first is the newly unemployeds, who scan all available vacancies and may match quickly, and the second is the previously unemployeds, who scan only the new vacancies, having already looked at the old vacancies. One should therefore not confuse stocks and flows. The question here is whether the confusion is empirically relevant or not. Coles and Petrongolo find that the matching function is still OK in steady state, but it indeed stumbles on the labor market transition facts Shimer highlighted. Time to rethink those business cycle models.