Barro and Gordon offer a different approach to the time inconsistency problem. They assume that policy-makers suffer a loss of reputation if they renege on earlier commitments. With this punishment mechanism in place, Barro and Gordon show that there exist policies superior to the time-consistent policy which are credible and sustainable.
The Barro-Gordon analysis is, however, model-specific and, in particular, applies only to static models. The main purpose of this paper is to show how their analysis can be generalized to any rational expectations model with structural dynamics and stochastic exogenous shocks.
Within this framework the paper analyses various forces which can help sustain the optimal but time-inconsistent (ideal) policy. These are a lengthening of the period for which policy- makers may lose their reputation, the existence of non-achievable long-run targets, persistent and/or stochastic rather than transitory, deterministic shocks, and a discount factor close to unity. An illustration of these effects in an inflation-inertia dynamic model is provided.

It is now standard practice in macroeconomic modelling to assume that expectations are, at least in part, model- consistent or rational. As a consequence the use of optimal control for policy design in such models is open to the criticism advanced by Kydland and Prescott; that in models with forward-looking rational expectations, optimal policies become, through the mere passage of time, sub-optimal. The term time inconsistency is used to describe this phenomenon. Such time inconsistency undermines the credibility of a policy in the eyes of the private sector: they will come to expect the policy- maker to reoptimize. The optimal policy, if it is to be credible, must therefore be constrained to be time-consistent. In many models (including the one examined in this paper) the time-consistent policy is significantly inferior to the unconstrained optimal policy.
Kydland and Prescott regard the issue of time inconsistency as a fundamental obstacle to the issue of optimal control methods for macroeconomic policy design. They suggest that instead of attempting to select policy optimally, economic theory be used to evaluate policy rules and that one with good operating characteristics be selected ... It is preferable that selected rules be simple and easily understood, so that it is obvious when a policy-maker deviates from the policy. There should be institutional arrangements which make it a difficult and time- consuming process to change the policy rules in all but emergency situations.
Barro and Gordon offer a different approach to the time inconsistency problem. They examine whether reputational considerations can restore credibility for policy-makers and allow them to avoid the inferior time-consistent policy. Barro and Gordon consider an economy described by a Lucas-Sargent- Wallace supply curve in which the policy-maker is able to control inflation, and analyse three possible policy regimes. If the policy-maker has a reputation for precommitment then the ideal policy of zero inflation is optimal. Reputation is necessary to sustain this policy because it is time- inconsistent: there exists an incentive or temptation to renege since a bout of surprise inflation can lower real wages and increase output, at least in the short-run.
If the authorities have no reputation then the optimal policy is one of non-zero inflation. This policy, which is a Nash non- cooperative equilibrium of the game between the government and the private sector, is time-consistent but inferior to the ideal policy. Finally, there is a third regime, which consists of announcing a policy of zero inflation but implementing non-zero inflation. This perfect cheating policy is superior to the ideal policy, but is obviously implausible because it ignores the private sector's response to reneging.
The question is therefore whether one can build into the model a mechanism which can, in some circumstances, ensure reputation for precommitment. Barro and Gordon achieve this by postulating a threat or punishment by the private sector. Following an act of reneging by the government the private sector will, for some punishment interval of P periods, believe only in the time-consistent or Nash non-cooperative inflation rate, from which there is no incentive to renege. After the punishment interval it believes in the ideal policy once again. Since the ideal policy is characterized as cooperation in the Barro-Gordon game, this amounts to saying that the threat by the private sector is to withdraw cooperation for some interval P. We describe this absence of cooperation as a loss of reputation.
With the punishment mechanism operating, the government must weigh any temptation to renege against the costs associated with a loss of reputation. If these costs exceed the temptation then no incentive to renege exists. The ideal policy then becomes credible and sustainable.
The main shortcoming of the Barro and Gordon analysis is that it is model-specific and applies only to an essentially static model. The main purpose of this paper is to show how the analysis can be generalized to any rational expectations model with structural dynamics and stochastic shocks. The first stage is to develop dynamic counterparts to Barro and Gordon's ideal, time- consistent, perfect cheating, and best sustainable policies. We then generalize the Barro-Gordon punishment mechanism. Along the ideal policy the policy-maker faces two choices: either continue with the ideal policy, or renege, in which case one period of cheating (during which the private sector's behaviour remains frozen) is followed by P periods of punishment during which a time-consistent non-reputational policy must be followed.
In dynamic models there are two sources of temptation. The first, discussed by Barro and Gordon, arises from the one period of cheating. The second originates from the time inconsistency of the ideal policy even where long-run targets are achievable in the long run. There are also two sources of punishment which the private sector can impose. One is the inferiority of the time- consistent policy compared to the ideal policy in its dynamic adjustment to equilibrium. The second source is the inferiority of the long-run equilibrium of the time-consistent policy when targets are not achievable in the long run or when shocks are permanent.
When random disturbances are introduced into the model, I propose two stochastic generalizations of the sustainability condition. The first is that on average the cost after reneging should exceed that without reneging. The second, stronger condition is that the cost after reneging for all possible realizations of the trajectories should exceed that without reneging. For the second, stronger condition, sustainability requires the disturbances to be bounded. For both conditions an extra stochastic term is introduced into enforcement, which becomes very large as the discount factor tends to unity and which can ensure sustainability. The intuition behind this result is that the inferior dynamics of the time-consistent policy becomes more serious when the policy-maker must respond to repeated rather than one-off shocks. Then the temptation to respond to a particular configuration of the economy by reneging must be weighed against the enforcement effects of future disturbances. As the policy-maker becomes more far-sighted, the enforcement effects dominate and sustainability is established.
It follows from the analysis that the forces which help the sustainability of the ideal policy are:
A long punishment interval Non-achievable targets in the long run Permanent rather than transitory shocks A stochastic environment A discount factor close to 1
Our analysis does not indicate whether having a more or less Keynesian policy-maker (i.e. a high or low relative weight on output in the welfare function) helps sustainability. As the relative weight on output increases, both temptation and enforcement increase as in the static Barro-Gordon model. The overall effect of this on sustainability must be investigated empirically. The analysis also indicates that even if the ideal policy is not sustainable, all is not lost: there may exist another sub-optimal simple rule, superior to the time- consistent policy, which is sustainable.
The paper provides an illustration of these effects in an inflation-inertia, dynamic model taken from Buiter and Miller (1983). We begin with the case where sustainability fails (an achievable long-run output target at the natural rate, a transitory shock to core inflation and no noise). Then it is shown that by introducing an output target above the natural rate, or a permanent shock, or a simplicity constraint, or noise (each separately), sustainability can be achieved for a sufficiently large punishment period, the crucial parameter. With noise in the core inflation equation the ideal rule is sustainable, under the strong condition, for a punishment period as low as 4 quarters, provided that the discount rate is low (2.5% per year) and provided that random shocks remain within about twice their standard deviation. Clearly if all effects are present simultaneously either the punishment period could be pushed lower or the maximum size of shocks and the discount rate pushed higher without undermining sustainability.
These results suggest that there are a number of quite plausible forces that will ensure that enforcement outweighs temptation. The tentative answer to the question posed by the title is then no. A more emphatic answer, however, must await an investigation using empirically based models. This will be the subject of future research.

Discussion Paper No. 227, February 1988 (IM)