Prudent monetary policy and prediction of the output gap

Risk-adjusted LQG optimal control with perfect and imperfect observation of the economy is used to obtain prudent Taylor rules for monetary policies and cautious Kalman filters. A prudent central bank adjusts the nominal interest rate more aggressively to changes in the inflation gap, especially if the volatility of cost-push shocks is large. If the interest rate impacts the output gap after a lag, the interest also responds to the output gap, especially with strong persistence in aggregate demand. Prudence pushes up this reaction coefficient as well. If data are poor and appear with a lag, a prudent central bank responds less strongly to new measurements of the output gap. However, prudence attenuates this policy reaction and biases the prediction of the output gap upwards, particularly if output targeting is important. Finally, prudence requires an extra upward (downward) bias in its estimate of the output gap before it feeds into the policy rule if inflation is above (below) target. This reinforces nominal interest rate reactions. A general lesson is that prudent predictions are neither efficient nor unbiased.