Economic outcomes in dynamic economies with forward-looking agents depend crucially on whether or not the central bank can precommit, even in the absence of the traditional "inflation bias." This paper quantifies the welfare differential between precommitment and discretionary policy in both a stylized theoretical framework and in estimated data-consistent models. From the precommitment and discretionary solutions we calculate the permanent deviation of inflation from target that in welfare terms is equivalent to moving from discretion to precommitment, the "inflation equivalent." In the estimated models, using a range of reasonable central bank preference parameters, the "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.