Prudent Monetary Policy: Applications of Cautious LQG Control and Prediction

Risk-adjusted linear-quadratic-Gaussian (LQG) optimal control with perfect and imperfect observation of the economy gives prudent feedback policy rules and cautious Kalman filters. The reaction coefficients depend on the variances of the modelling errors, since precaution reduces the power of its instruments by these variances. Also, prudence implies less weight to new uncertain observations that are less important for welfare and introduces a bias in prediction. Prudent predictions are thus neither efficient nor unbiased. 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. Prudence attenuates this policy reaction and biases the prediction of the output gap upwards, however, 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.