Credibility and Time Inconsistency in a Stochastic World

This paper re-examines the issue of the credibility and sustainability of optimal policies derived from Pontryagin's Maximum Principle and generally regarded as time-inconsistent, in models with forward-looking rational expectations. Specifically, it considers the behaviour of such models in the presence of continuing stochastic noise. This is shown to convert the policy problem from a one-shot dynamic policy game to a continuing game, giving governments an incentive to invest in a reputation for not reneging on the full optimal rule. This incentive may, in certain circumstances, render the full optimal rule credible and therefore sustainable. It is demonstrated that a sufficiently low degree of discounting on the part of government, or a sufficiently high variance of shocks (measured relative to the initial displacement) ensures the sustainability of the full optimal rule. Using a simple dynamic open economy model, these conditions are shown to be plausible unless the discount rate is very high.