The recent literature on monetary policy has questioned the use of linear Phillips curves and the assumption of a constant NAIRU. In this paper we explore monetary policy considering different shapes of the Phillips curve and an endogenous NAIRU. The NAIRU is, as recent papers suggest, made endogenous in the sense that it depends on monetary policy actions. We first study monetary policy with different shapes of the Phillips curve: Linear, convex and convex-concave. As is demonstrated the optimal monetary policy changes with the shape of the Phillips curve, but there always exists a unique equilibrium no matter whether the Phillips curve is linear or nonlinear. Then, following recent research, for example Blanchard (2003), Graham and Snower et al (2002) we demonstrate how the NAIRU may be influenced by monetary policy. We provide empirical evidence using the Kalman filter to show that that monetary policy indeed has influenced the NAIRU in the US and Euro-area countries. We explore the implications for monetary policy facing such a moving target. We find that there may exist multiple equilibria, different from the results of models presuming a constant NAIRU. The model is analytically solved and the and further explored by way of a dynamic programming algorithm with flexible grid size
