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This paper studies optimal monetary policy rules in a framework with sticky prices, matching frictions and real wage rigidities. Optimal policy is given by a constrained Ramsey plan in which the monetary authority maximizes the agents’ welfare subject to the competitive economy relations and the assumed monetary policy rule. I find that the optimal rule should respond to unemployment alongside with inflation. This is so since models with matching frictions (unlike standard new Keynesian models) feature a congestion externality that makes unemployment inefficiently high. A strong response to inflation remains optimal while a response to output is always welfare detrimental.

Nowadays most central banks follow (or at least so they state) inflation targeting or price stability rules with little weight assigned to output stabilization and almost no attention devoted to other economic indicators such as unemployment. One common argument for such choice is that stabilizing prices optimizes the output-inflation volatility trade-off which implies that inflation stabilization can be achieved with a relatively small output cost. Theoretically this hypothesis is true in models with nominal rigidities and walrasian labor markets. This paper assesses the importance of responding to other real economic variables in a model with sticky prices, non-walrasian labor markets and real wage rigidities. To conduct such an analysis I employ a unitary framework which combines nominal and real rigidities and which has become common in the recent new Keynesian literature. More specifically the model economy is characterized by monopolistic competition, adjustment costs on pricing, matching frictions in the labor market and real wage rigidity.1 The assumption of monopolistic competition and adjustment cost on pricing a’ la Rotemberg (1982) is needed to obtain non-neutral effects of monetary policy and to make a meaningful comparison across different monetary policy rules. Introducing matching frictions a’ la Mortensen and Pissarides (1999) in the labor market allows to consider frictional unemployment in the steady state and provides a rich dynamics for the formation and dissolution of employment relations. The introduction of this congestion externality helps to recover a trade-off between the cost of volatile inflation and the cost of inefficient unemployment fluctuations

This paper derives a constrained Ramsey policy in a model with monopolistic competition and sticky prices, matching frictions and real wage rigidity in the labor market. Furthermore, it compares welfare under different monetary policy rules. It concludes that the introduction of labor market rigidities implies that the optimal rule should feature some response to unemployment. This is so since the introduction of matching frictions adds a congestion externality for which an excessive number of searching workers or vacancies might reduce the probability of forming matches. In those cases unemployment is inefficiently high and the policy maker faces an unemployment/inflation trade-off that calls for responding to unemployment along with inflation. In this paper it is assumed that households are able to insure the unemployment risk. An interesting extension would be to consider the impact of imperfect risk sharing arrangements on the optimal monetary policy. Incomplete risk sharing arrangements would probably increase the cost of unemployment and reinforce the incentive of the policy maker to stabilize labor market variables.