The purpose of this essay us to discuss the core readings of the time inconsistency school of economic analysis. Accepting the coherent structure in which the theory is presented, the essay will then go on to analyse the power of the policy which it derives by considering four areas in which time inconsistency is observed to arise. The next section of the essay is a brief discussion of the seminal papers of Kydland & Prescott and Barro & Gordon. While the problem of time inconsistency is a general one in every day life, this literature was particularly concerned with the time inconsistency of monetary policy. Hence, while the author has tried to present this topic in as general a context as possible, this is an area of policy to which it is inextricably linked. Section two is divided into three subsections, each of which consider the problem of time inconsistency with respect to the particular economic issues of tax policy, wage bargaining and fiscal policy. In each case the problem is set up as a non-co-operative game between two independent parties. Exactly how the time inconsistency is arising is identified and the question of whether the theory can suggest a possible solution to the problem is addressed. The third and final section concludes the essay.
Theoretical Background
There are four equilibria associated with the time inconsistency literature. The first three were outlined by Kydland & Prescott in their 1977 seminal paper. The last outcome is nested within the first three and was introduced by Barro & Gordon in 1983. While the author has attempted to outline these equilibria in as general a context as possible, the reader can view them in terms of the time inconsistency of announced monetary policy. The problem is presented as a non-co-operative game between the wage setting private sector and the policy maker who administers monetary policy, i.e. the Central Bank (CB). The private sector's wage bargaining is contingent upon the inflation expectations it derives from the monetary announcements of the CB. When the wage contracts are subsequently agreed upon, there remains the incentive for the CB to exploit the short run Phillips curve trade off by creating surprise inflation.
The first best outcome is the time inconsistent equilibrium. Policy makers renege on their announced commitment due to its suboptimality after the private sector has made certain decisions on the basis that the announced policy will prevail indefinitely. The ex post suboptimality of the announced policy arises even though the information set has not changed. The policy maker's constrained maximum is reached by cheating on the private sector. This corresponds to the CB creating surprise inflation, and so reducing real wages. In the case of a policy maker acting with perfect discretion in the absence of commitment technology and with agents forming expectations rationally, the third best outcome occurs and is the time consistent equilibrium. Here, the private sector knows that the policy maker has an incentive to deviate (or 'cheat') from the policy to which it has announced a commitment and expects that this is what will happen. The private sector makes decisions such that the costs of being cheated are avoided and so the policy maker is denied the benefits derived from cheating. Returning to the monetary policy problem, the consistent outcome occurs where the private sector's inflation expectation is set at the level which it believes the government has no incentive to add to the inflation rate: this is likely to be at a relatively high rate. Moreover, there is no output gain associated with this inflation rate. However, if the appropriate commitment technology is available, then the second best outcome may be achieved. Although the policy maker could be placed on a lower value of its loss function by cheating, the private sector employs an enforcement mechanism which prevents it from doing so. This result is known as the optimal rule equilibrium. It would amount to the CB legislating the rate at which the money supply was to expand over the period of the wage agreement. However, strict rules such as these are suboptimal when monetary policy needs to be used with discretion to alleviate the adverse effects of unanticipated economic shocks. The main point is that given rational expectations and without the required commitment technology, the time consistent equilibrium is the worst equilibrium. This occurs because in attempting to reach the first best outcome the economy is pushed to the third best one.
The final equilibrium is arrived at when reputational factors are considered in the context of the same game played an indefinite number of times. This equilibrium exists somewhere between the second and third best outcomes. Even if the policy maker is allowed to cheat, this involves a reputational cost. This cost is measured in terms of the private sector's scepticism over future announcements. Wage setters would punish the CB by attaching no credibility to the next policy announcement. The policy maker discounts this loss and makes announcements such that the expected benefit of cheating is at least as big as the associated expected reputational cost. Given the private sector's ability to punish the policy maker, it is rational for it to expect policy announcements to be credible. The reputational outcome is one of multiple equilibria equal to the weighted average of the consistent (discretion) and optimal rule outcomes. The proximity of this outcome to the second best equilibrium is inversely related to the rate at which reputational costs and cheating benefits are discounted, and to the duration of the punishment interval.
Kydland & Prescott's solution to the inflationary bias of monetary policy is to impose strict rules on the rate of monetary expansion. This policy prescription is similar to that suggested by Milton Friedman in his presidential address to the American Economic Association in 1967. However, they stress that it has been arrived at for reasons very different to Friedman's: '... unlike Friedman's argument, it does not depend upon ignorance of the timing and magnitude of the effects of policy.' In Friedman's adaptive theory of expectations, agents would reduce their inflation expectations faster if the rate at which the money was contracting was fixed. The faster expectations are revised, the sooner the economy will return to its natural long run equilibrium where prices remain stable.
Barro & Gordon argue that an optimal punishment mechanism is in place and that no intervention is necessary. However these results only apply in a world of no shocks. In general, as is recognised in this literature, it is suboptimal for policy to remain unresponsive to shocks.
The most celebrated suggested solution to the problem of monetary policy time inconsistency combined with the need to respond to negative economic shocks with discretion is to make the CB independent of the government with the overriding objective of price stability. The CB's reputation as an inflation fighter would be bolstered by its independence as it would not be in its best interest to create surprise inflation. Hence, the private sector would attach a high degree of credibility to any announcements that the CB intended to reduce inflation. Rogoff proposed that a similar result would emerge by appointing a CB governor who does not share the social objective function, but instead places 'too large' a weight on inflation rate stabilisation relative to employment stabilisation. In the case of a small open economy, Giavazzi & Pagano (1988) point out that many inflation prone economies in the EU joined the EMS specifically to link their monetary policies to those of institutions such as the Bundesbank in the hope of improving their reputations as anti-inflationary strategists. These anchoring tactics eliminate part of the inefficiency that arise from the lack of credibility of the monetary authority. Finally, Minford (1995) shows that a modern democracy combined with the self-confessedly discretionary behaviour of monetary authorities, e.g. the Bundesbank in Germany, can reach an optimal outcome with discriminatory punishment. This requires only that the power of the median voter be revealed by the process of democracy. Thus voters are able to punish government by the withdrawal of support at the next election. In this model, the government's best strategy is to react purely to shocks. However, it also requires that the consequences of all relevant shocks be realised before an election, something which can never be guaranteed.
Economic Issues
Tax Policy
Setting tax policy is an area where time inconsistency can be a problem. It has been discussed in detail by Rogers (1987). Her analysis is interesting for two reasons. Firstly, the efficiency consequences of time inconsistent tax policy are very significant given the important role played by tax rates in so many decisions. Secondly, these consequences can be particularly acute if we consider how easily tax rates can be changed. The problem itself reads as follows in a two period framework.
In the first period, the government sets tax at an optimal rate. However, after households have made saving decisions on the basis that these rates will prevail indefinitely, the government realises it could raise more revenue by exploiting those decisions and increasing taxes. The government secures a higher level of revenue with what amounts to a lump sum tax. Thus, the optimality of taxation depends on the elasticity of savings with respect to the second period tax rate. While Rogers does not proffer a solution to this problem, she uses the power of the time inconsistency literature to good effect. While traditional analysis would show expenditure taxation to dominate income taxes by a welfare ranking, this domination is reversed in Rogers' analysis. However, this paper also highlights a significant weakness in the general approach of proving and solving problems of time inconsistency. The time inconsistency of taxation is highly sensitive to the function chosen as the government's objective. Because Rogers uses a Cobb Douglas utility function in her analysis, savings are found to be perfectly inelastic with respect to the second period rate of taxation. Thus there is no welfare gain to be earned by the government by deviating from its ex ante policy, hence the optimal tax is time consistent. This author believes the results of such theoretical surveys are so tenuous to the chosen assumptions as to be viewed as no more than a guide to the general problem of time inconsistency in everyday life.
While this example did not present a possible solution to the problem, the following case of time inconsistent wage bargaining fits in very well with the theories referred to in the previous section.
Monopoly Trade Union Bargaining
Workers are usually portrayed as the victims of policy makers' ex post deviations from bilateral agreements when there is a temptation to create surprise inflation. However, in the following example of a monopoly trade union, the incentive to deviate is in the worker's hands. This issue is presented as a non-co-operative game between a monopoly trade union and one of many atomistic firms.
The trade union commits itself to lower wages in the future. Believing this, the firm makes optimal capital investment which requires extra workers. After the fixed costs are sunk, the trade union threatens industrial action unless higher wages are granted. The firm has no alternative but to pay its workers - old and new - higher wages. This is a problem of time inconsistency in the absence of binding contracts. Adding the assumption of rational expectations brings the game to a consistent and worst equilibrium where the firm does not respond to the promise of low wages and so does not invest in capital. This accentuates the inefficiencies of monopoly trade unions and reduces output, capital and employment. It suggests that long term wage contracts are essential for weakening the unemployment consequences of a monopoly trade union.
In a dynamic context binding contracts may not be necessary. The importance of reputational effects means the firm (Stackleberg follower) can prevent the union (the leader) from cheating. The dynamic result differs depending on whether the game is played a definite or indefinite number of times. Played a definite number of times, backward induction shows how if there is an incentive to deviate in the final round of the game, that this incentive will permeate every round back to the first. Thus, the consistent and worst equilibrium in the case of no contracts in a one shot game holds. However if the game is played an indefinite number of times, it may be worthwhile for the union to develop a reputation for sticking to its announcements. The outcome is one of multiple equilibria as in the case of the Barro & Gordon model. Whether this result coincides with either the consistent (third best) or the optimal rule (second best) equilibrium in the one shot game again depends on the discount rate and the duration over which the firms punish the trade union. The best enforceable announcement arises when the punishment for deviating is at least as big as the benefits derived from cheating. It defines a rational equilibrium in which the union never reneges on announcements and expectations are never falsified.
This is a highly theoretical approach to analysing a situation in which time inconsistency may arise. Hence, its results are perfectly in line with the literature outlined in the first section. However, in practice situations are not as simple and results are certainly less clear-cut. The final example considers the credibility problem faced by governments who wish to reduce debt ratios by means of fiscal policy. While the time inconsistency aspect of this example is easily identified, the prescribed policy solution is quite different from the solution that the theory has led us to expect.
Fiscal Policy
The motivation in this instance is provided by the recent attempts at fiscal stabilisation of Ireland in 1982 which failed because it relied on an increase in future taxes. The time inconsistency of this policy is that it is unlikely that any government will deliver on the promise of higher taxes given the nature of the political business cycle. In contrast, the second Irish fiscal stabilisation of 1987-89 attempted to correct the fiscal deficit and reduce the debt/GNP ratio by reducing government spending. This policy was more credible as far as fiscal consolidation is concerned, as the cut in spending signalled to the private sector a permanent cut in government consumption. This meant lower future taxes and led to higher private consumption and investment. A recent model proposed by Fountas (1994) explains the time inconsistency of fiscal policy in relation to Ireland outlined below. The issue of fiscal policy time inconsistency is particularly poignant given the increasing impotency of monetary policy in a small open economy such as Ireland which is committing itself to a centrally controlled single currency mechanism like the EMU.
Time inconsistency arises due to the availability of only one policy instrument - fiscal policy - yet the desire to achieve two policy objectives - current account target and a fiscal deficit target. The government in the first period announces a reduction in the budget deficit. In the presence of precommitment, the private investors will consider it credible, thus depreciating the domestic currency which in turn will increase the current account. Ex ante it is optimal for the government to announce a reduction in the budget deficit to achieve a stronger current account balance. However, ex post there is an incentive for the government to improve upon the announced policy and exploit the decisions made by the private sector and not alter the size of the budget deficit. If the government maintains its commitment to lower the deficit it reaches an equilibrium which can be improved upon by ex ante deviation. The current account will still be strengthened given the expectations of the currency markets while the government allows itself to spend more money than it announced. Given the policy maker's temptation to reach the first best outcome, any attempts at doing so will be unsuccessful as private agents anticipate such behaviour and push the equilibrium towards the time inconsistent outcome, which is worse.
In Ireland's case fiscal policy was set to achieve a lower debt ratio, assuming a certain stability in the current account. After a shock to the current account, ex post the temptation to allow for fiscal policy changes to alleviate the adverse effects of the shock to the current account are at the expense of the fiscal policy target, thus leading to the time inconsistency of fiscal policy. Fountas does not offer a specific solution to the problem of fiscal policy time inconsistency, but rather uses his model merely to highlight its importance in the context of an emerging EMU.
However, Evans (1990) does suggest a possible solution in a similar model of fiscal policy. He considers the problem when a government promises to reduce debt by increasing taxes while maintaining a deficit which preserves current consumption levels. There is obviously the temptation for the government not to increase taxes when necessary and place the burden of higher debt on future generations and possibly a different government. The unspectacular solution suggested by Evans is to promise only moderate increases in taxes. He admits that any promise regardless of its moderation will be subject to the criticism that it is inflexible to shocks and meets this criticism with the following retort. While it may seem reasonable for the government to anticipate losing all credibility if a change in policy is engineered purely to delude the public, it may not be if the public can be convinced that the switch was desirable given an unanticipated change in circumstances - such as an exogenous shock to the economy. However, in view of the obvious incentive to mis-report, the public will view these 'explanations' with some scepticism unless the true impact of a change can be independently verified. The independence aspect of this analysis, is equivalent to the idea that an independent CB adds credibility to announced monetary policy. Finally, the author believes there is a need to find an appropriate punishment mechanism to incorporate into a model of fiscal policy credibility. Inspiration could be derived from Minford's model of monetary policy where the power of the median voter is enough to keep the actions of authorities in line with announced intentions by the threat of voter withdrawal.
Conclusion
This essay has analysed the topic of time inconsistency in both a theoretical and policy context. Time inconsistency arises when there is an incentive for an agent to deviate from a contract made with another agent even when no news has emerged. Three results were arrived at when examining the theoretical literature. First, in a static model policy rules are time inconsistent but if legislated may allow the economy to avoid the worst case scenario when policy is conducted with discretion. Second, a dynamic model reveals that the threat of punishment in the shape of a damaged reputation may be enough to dampen the incentive for an agent to deviate from an announced policy. Finally, these results only apply in a world of no shocks. Policy needs optimal discretion to respond to negative economic shocks. When applied to the areas of monetary policy, tax policy, wage bargaining and fiscal policy, the advised solutions seem no more than common sense.
The author has found this area of macroeconomics most stimulating. In particular the important role it has played in the development of the New Classical economic thought by incorporating the tools of game theory and rational expectations. In a modelling context, however, it suffers the usual criticism that its results are too sensitive to their assumptions. Nevertheless, given that articles on this topic are still being published, it seems an area that will continue to develop as long as economic issues requiring analysis within its framework arise.
Bibliography
Barro, R.J. & Gordon, D.B. Rules, Discretion and Reputation in a Model of Monetary Policy, Journal Of Monetary Economics (12), 1983, 101-121
Barro, R.J., Recent Developments in the Theory of Rules versus Discretion, Economic Journal Supplement, 1986
Cukierman, Webb & Neyapti, Measuring the Independence of Central Banks and its Effect on Policy Outcomes, World Bank Economic Review, Volume 6, No. 63, 1993
Evans, M.D.D., Optimal Precommitment in Macroeconomic Policy: A Game Theoretic Analysis of Fiscal Policy Oxford Economic Papers, 42(4) October 1990, 695- 714
Fountas, S., Interactions among Private Investors and Government Policies: Rules versus Discretion, Journal of Economic Studies, 21(2), 1994, 38-56
Friedman, M., The Role of Monetary Policy, American Economic Review, May 1968
Giavazzi & Pagano, The Advantage of Tying Ones' Hands, European Economic Review, March 1988
Kydland & Prescott, Rules rather than Discretion: The Inconsistency of Optimal Plans, Journal of Political Economy, June 1977
Minford, P., Time Inconsistency, Democracy and Optimal Contingent Rules, Oxford Economic Papers, April 1995
van der Ploeg, F., Trade Unions, Investment, and Employment: A Non Co-operative Approach European Economic Review, 31(7), October 1987, 1465-92
Rogers, C. A., Expenditure Taxes, Income Taxes, and Time Inconsistency, Journal of Public Economics, 32(2), March, 215-30
Rogoff, The Optimal Degree of Commitment to an Intermediate Monetary Target, Quarterly Journal of Economics, November 1985
Whynes D.K. (1989) The Political Business Cycle, in Current Issues in Macroeconomics, ed. Greenaway, D. MacMillan, Basingstoke