In recent years, monetary business cycle models with monopolistic competition and staggered price setting have been widely used to study the implications of alternative specifications of monetary policy. One shortcoming of these models, however, is that they typically do not include a very detailed description of the labor market, and are therefore not suited to discuss the relationship between monetary policy and unemployment. In the labor market literature, on the other hand, search and matching models with equilibrium unemployment have been fairly successful in explaining aggregate labor market fluctuations. Such labor market specifications have recently been extended to monetary business cycle models, originally by Trigari (2004, 2006) and Walsh (2005b), and thus present a natural alternative to the standard monetary framework.
Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2003) have demonstrated that nominal wage rigidities are a crucial ingredient when explaining U.S. business cycles, using monetary business cycle models without search and matching frictions. Within a similar model, Levin, Onatski, Williams, and Williams (2005) have shown that wage rigidities account for the main welfare cost of business cycle fluctuations, and that a monetary policy rule that responds only to nominal wage inflation performs almost as well as the welfare optimizing policy. However, these results are very sensitive to the precise form of wage rigidities, suggesting that the specification of the labor market has important consequences for monetary policy.