The canonical new Keynesian Phillips curve has become a standard component of models designed for monetary policy analysis. However, in the basic new Keynesian model, there is no unemployment, all variation in labor input occurs along the intensive hours margin, and the driving variable for...

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...