On the optimal monetary policy response to noisy indicators

We describe a behavior of a central bank when its measures of current inflation and output are subject to measurement errors, in a framework of optimizing models with nominal price stickiness. In our model, a central bank sets the interest rate equal to its current estimate of the so-called Wicksellian natural rate of interest. This is shown to imply that the interest rate responds to the central bank's estimates of both current inflation and output gap, as advocated by Taylor (1993). It is also shown that the noise contained in the indicators justifies a degree of policy cautiousness. A reduced-form representation of optimal policy should exhibit interest-rate smoothing, which is often found in the empirical literature on monetary policy reaction functions.