How important is precommitment for monetary policy?

We quantify the welfare differential between precommitment and discretionary monetary policy in three estimated models of the U.S. economy by calculating the permanent deviation of inflation from target that in welfare terms is equivalent to moving from discretion to precommitment. Using a range of reasonable central bank preference parameters, this "inflation equivalent" ranges from 0.05 to 3.6 percentage points, with a mid-point of either 0.15 or 1-1.5 percentage points, depending on the model. In addition to the degree of forward-looking behavior, we show that the existence of transmission lags and/or information lags is crucial for determining the welfare gain from precommitment.