The standard Mortensen and Pissarides (1994) search and matching model of equilibrium unemployment has been argued in many places to be inconsistent with key business cycle facts. In particular, it cannot explain the high volatilities of unemployment, vacancies and market tightness (Shimer, 2005), nor the persistence in the adjustment of these variables to exogenous shocks (Fujita and Ramey, 2007). Subsequent research has focused on whether the lack of internal propagation, both in terms of amplification and persistence, stems from the structure of the model itself or whether it is a question of setting an appropriate calibration.
Firms in these models must expend resources to fill job vacancies, a time-consuming process in the presence of search frictions on labor markets. Under Nash bargaining as a wage mechanism, wages absorb much of the change in the expected benefit to a new worker induced by fluctuations in labor productivity. As a result, Shimer (2005) argues, the incentive to post vacancies changes little over the business cycle. Quite naturally, subsequent research has focused on the dynamics of wages as a means of generating amplification of exogenous innovations. Such studies have either altered the particulars of the wage determination mechanism (e.g. Shimer 2004), or as in Hagedorn and Manovskii (2008), followed an alternative calibration strategy that results in a rigid wage. In order to address the second empirical shortcoming, the persistence in labor market adjustments to productivity shocks, a second strand of research has focused on the structure of vacancy costs. Fujita and Ramey (2007), for example, develop a story about sunk costs to vacancy creation such that the strongest change in market tightness occurs several periods after the original shock. Their approach, however, does not generate any additional amplification.