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

We derive a linear-quadratic model that is consistent with sticky prices and search and matching frictions in the labor market. We show that the second-order approximation to the welfare of the representative agent depends on inflation and "gaps" that involve current and lagged unemployment. Our approximation makes explicit how welfare costs are generated by the presence of search frictions. These costs are distinct from the costs associated with relative price dispersion and fluctuations in consumption that appear in standard new Keynesian models. We show the labor market structure has important implications for optimal monetary policy. (JEL E24, E31, E52)