Optimal monetary policy inertia

I consider the desirability of the observed tendency of central banks to adjust interest rates only gradually in response to changes in economic conditions. I show, in the context of a simple model of optimizing private sector behaviour, that such inertial behaviour on the part of the central bank may indeed be optimal, in the sense of minimizing a loss function that penalizes inflation variations, deviations of output from potential and interest rate variability. Sluggish adjustment chatacterizes an optimal policy commitment, even though no such inertia would be present in the case of discretionary optimization.