Time Inconsistency
My word is my bond

One of the longest-running debates in the theory of economic policy has concerned the time inconsistency of policies. The problem arises particularly in an economy characterized by forward-looking rational expectations. The policy-maker can compute a set of policies which optimize his objective function over several periods. By announcing future as well as current policy actions, he will influence expectations of the future and induce a response by the private sector in the current period. The government will then discover that it can further improve its position in the second period by re-computing the optimal policy taking into account the private sector's response, even when nothing on which the first-period decision was based has changed. The recalculated optimal policy is time-inconsistent, and the private sector has been 'fooled'.

The temptation to renege on earlier promises is a common feature of agreements where one party is locked into a course of future actions on the promise of future action by another party. The second party then has both the incentive and the power to 'renegotiate' the agreement in its favour. A variety of devices are typically employed to prevent this, which foresee the incentive to renege on earlier promises and stipulate financial penalties for doing so which are agreed in advance.

In Discussion Paper No. 138, Research Fellow Andrew Hughes Hallett contends that analyses of time inconsistency are themselves inconsistent: agents are presumed to form rational expectations about future states of the economy but not about the future policies which determine those states. Hughes Hallett allows private sector agents to predict policy on the same basis as other economic variables. Under this more plausible assumption, they would not be 'fooled' by policy announcements that are not credible. This would deprive the policy-maker of the first-period private sector response which creates the incentive for the second-period policy switch. Once agents foresee that switch, the incentive to renege vanishes. This will force policy-makers to revert to a period-by-period choice of optimal policies, which presents no incentive to renege. Policy is therefore time-consistent, but inferior to the time- inconsistent set of policies calculated in the initial period so as to be optimal over the entire period.

How could the policy-maker persuade agents to believe the original announcements? Hughes Hallett notes that if the difference between the benefits to the policy-maker of the optimal (but time-inconsistent) policy and the benefits from the period-by-period (time-consistent) policy exceeds the gains from subsequently reneging, it will pay the policy-maker to put up a bond (such as a deposit or a penalty clause) which at least matches, in value, the incentive to renege. It will also pay the private sector to accept that bond since it commits the policy- maker to the time-consistent policy: the government will lose more by forfeiting the bond than it will gain by reneging. Such a guarantee will always be offered; the policy-maker gains if it is accepted, but loses nothing if it is not. The private sector, on the other hand, will accept that guarantee only if it at least matches the incentive to renege.

Hughes Hallett concludes that the possibility of such a bond implies that the policy-maker will always be precommitted to the best (time-consistent) strategy that can actually be reached: to the 'inferior' period-by-period policy if the best guarantee on offer is insufficient to match the gains from reneging, or to the 'superior' one when a sufficient guarantee can be offered. The time-inconsistent fully optimal policy is never an exploitable option, although it is important in evaluating the guarantee needed to make the 'superior' strategy operational. These conclusions are similar to those of earlier work on precommitment (e.g. by Backus and Driffill and by Currie and Levine), which have considered the cost of a lost reputation, incomplete information or the threat of retaliatory actions.


Is Time Inconsistent Behaviour Really Possible?
Andrew Hughes Hallett

Discussion Paper No. 138, October 1986 (IM)