Welfare-Based Optimal Monetary Policy with Unemployment and Sticky Prices: A Linear-Quadratic Framework

The steep increases in unemployment associated with the financial crisis and global recession of 2008–2009, and the widespread focus on unemployment in both the popular press and in policy debates, is in sharp contrast to the canonical new Keynesian model in which unemployment is noticeably absent. In that model, workers are never unemployed, and only hours worked per worker vary over the business cycle. As a consequence, the basic new Keynesian (NK) model cannot shed light on whether monetary policy should respond to the unemployment rate or whether there is a role for stabilizing unemployment fluctuations that is distinct from stabilizing fluctuations in inflation and the consumption gap as in standard NK models. Our objective in this paper is to explore the implications for monetary policy of a model with sticky prices and search-based unemployment. We first show how such a model can be reduced to a linear expectational-IS curve and a Phillips curve linking inflation and the gap between unemployment and its efficient level. The coefficients in these two relationships depend on the underlying structural parameters of the model that govern preferences, the degree of nominal price rigidity, and the search and bargaining processes in the labor market.