Optimal monetary policy rules in a rational expectations model of the Phillips curve

Using a rational expectations model based on a Phillips curve with persistence in inflation, we derive optimal monetary policy rules under both commitment and discretion. We assume that the central bank targets the natural rate of output, so there is no incentive generating an average inflation bias. With commitment, inflation has less persistence but more conditional variability, whereas output has more persistence and less conditional variability than with discretion. As the commitment strategy stabilizes the systematic component of inflation, it is less responsive to random shocks to inflation.