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Figure 1 shows the results, under the standard assumption that the promises are fully credible.
As time passes, however, the benefits of the smaller recession become history, leaving only the cost of the overshoot.
This well-known ‘time-inconsistency’ effect is shown in the bottom right panel of Figure 1.
We can incorporate scepticism about the policymaker’s ability to commit into our simulations by assuming that the private sector attributes some probability to the policymaker reneging whenever they have an incentive to do so (as measured by welfare).
We assume that the probability is increasing in the size of the renege benefit. Relative to the perfect credibility case (Figure 1), the most striking difference is that the two forward guidance policies now have very similar economic effects.
At this point, the policymaker has an incentive to renege on their original promise.