A Linear Quadratic Approach to Optimal Monetary Policy with Unemployment and Sticky Prices: The Case of a Distorted Steady State

Ravenna and Walsh (2010) develop a linear quadratic framework for optimal monetary policy analysis in a New Keynesian model featuring search and matching frictions and show that maximization of expected utility of the representative household is equivalent to minimizing a quadratic loss function that consists of inflation, and two appropriately defined gaps involving unemployment and labor market tightness. This paper generalizes their analysis, most importantly by relaxing the Hosios (1990) condition which eliminates the distortions resulting from labor market inefficiencies, such that the equilibrium level of unemployment under flexible prices would not necessarily be optimal. I take account of steady-state distortions using the methodology of Benigno and Woodford (2005) and derive a quadratic loss function that involves the same three terms, albeit with different relative weights and definitions for unemployment- and labor market tightness gaps. I evaluate the resulting loss function subject to a simple set of log-linearized equilibrium relationships and perform policy analysis. The key result of the paper is that search externalities give rise to an endogenous cost push term in the new Keynesian Phillips curve, suggesting a case against complete price stability as the only goal of monetary policy, because there is now a trade-off between stabilizing inflation and reducing inefficient unemployment fluctuations. Transitory movements of inflation in this environment helps job creation and hence prevents excessive volatility of unemployment.