This paper analyses a new-Keynesian model incorporating hysteresis in output. Specifically, we assume that the natural rate of output sluggishly adjusts towards current output. We also assume that the natural rate has an upper bound and that, in addition to having standard objectives, the policymaker seeks to minimise deviations of actual output from this upper bound. We then solve for optimal monetary policy under a range of Phillips curve specifications. Our results suggest that despite increasing inflation temporarily, gradual demand expansions are usually desirable when the natural rate is low. Our model also offers a new explanation for inflation persistence.
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