Central bank learning and monetary policy

We analyze optimal monetary policy when a central bank has to learn about an unknown coefficient that determines the effect of surprise inflation on aggregate demand. We derive the optimal policy under active learning and compare it to two limiting cases-certainty equivalence policy and cautionary policy, in which learning takes place passively. Our novel result is that the two passive learning policies represent an upper and lower bound for the active learning policy, irrespective of the state of the economy.