Imagine a series of one-shot random meetings between central banks and publics that know nothing about each other. The problem results from the central bankers' preferences combined with policy discretion- but leads to results even the central bankers don't like. It is then possible to solve for the critical value of b . If b is large enough, then a reputational solution is possible - though hardly necessary. Time consistency problem can be solved by giving independent authority to a person who dislikes inflation more than most people dislike it.
Data actually seem fairly consistent with simple model without supply shocks.
If more CB independence eventually makes real performance worse, then it seems hard to find examples of countries that have that much CB independence. Then , so , and with RE . With the right incentive scheme, discretion leads CB to first-best result. The gold standard provided the primary solution to the time consistency problem in earlier periods. Note Bordo and Kydland's revisionist concept of rules.