Snowdon & Vane Modern Macroeconomics

expectation of the rate of inflation subject to the information available up to the previous period (Ω t–1). Kydland and Prescott then specify that there is some social objective function (S) which rationalizes the policy choice and is of the form shown in equation (5.25):

The social objective function (5.25) indicates that inflation and unemployment are ‘bads’ since a reduction in either or both increases social welfare. A consistent policy will seek to maximize (5.25) subject to the Phillips curve constraint given by equation (5.23). Figure 5.4 illustrates the Phillips curve

social objective function are indicated by the indifference curves S1 S2 S3 and S4. Given that inflation and unemployment are ‘bads’, S1 > S2 > S3 > S4, and the form of the indifference curves implies that the ‘socially preferred’ rate of inflation is zero. In Figure 5.4, all points on the vertical axis are potential equilibrium positions, since at points O and C unemployment is at the natural

sistent equilibrium) is at point O where a combination of ˙ = zero and U =

Pt t

UNt prevails. While the monetary authorities in this model can determine the rate of inflation, the position of the Phillips curves in Figure 5.4 will depend on the inflationary expectations of private economic agents. In this situation a time-consistent equilibrium is achieved where the indifference curve S3 is at a tangent to the Phillips curve passing through point C. Since C lies on S3, it is clear that the time-consistent equilibrium is sub-optimal. Let us see how such a situation can arise in the context of a dynamic game played out between policy makers and private agents.

In a dynamic game, each player chooses a strategy which indicates how they will behave as information is received during the game. The strategy chosen by a particular player will depend on their perception of the strategies likely to be followed by the other participants, as well as how they expect other participants to be influenced by their own strategy. In a dynamic game, each player will seek to maximize their own objective function, subject to their perception of the strategies adopted by other players. The situation where the game is between the government (monetary authorities) and private agents is an example of a non-cooperative ‘Stackelberg’ game. Stackelberg games have a hierarchical structure, with the dominant player acting as leader and the remaining participants reacting to the strategy of the leader. In the

Figure 5.4 Consistent and optimal equilibrium

monetary policy game discussed by Kydland and Prescott, the government is the dominant player. When the government decides on its optimal policy it will take into account the likely reaction of the ‘followers’ (private agents). In a Stackelberg game, unless there is a precommitment from the leader with respect to the announced policy, the optimal policy will be dynamically inconsistent because the government can improve its own pay-off by cheating. Since the private sector players understand this, the time-consistent equilibrium will be a ‘Nash’ equilibrium. In such a situation each player correctly perceives that they are doing the best they can, given the actions of the other players, with the leader relinquishing the dominant role (for a nontechnical discussion of game theory, see Davis, 1983).

254 Modern macroeconomics

Suppose the economy is initially at the sub-optimal but time-consistent equilibrium indicated by point C in Figure 5.4. In order to move the economy to the optimal position indicated by point O, the monetary authorities announce a target of zero inflation which will be achieved by reducing the

growth rate of the money supply from ˙ to ˙ If such an announcement

Mc Mo .

is credible and believed by private economic agents, then they will revise

curve to shift downwards from C to O. But once agents have revised their expectations in response to the declared policy, what guarantee is there that the monetary authorities will not renege on their promise and engineer an inflationary surprise? As is clear from Figure 5.4, the optimal policy for the authorities to follow is time-inconsistent. If they exercise their discretionary powers and increase the rate of monetary growth in order to create an ‘inflation surprise’, the economy can reach point A on S1, which is clearly superior to point O. However, such a position is unsustainable, since at point A

soon realize they have been fooled and the economy will return to the timeconsistent equilibrium at point C. Note that there is no incentive for the authorities to try to expand the economy in order to reduce unemployment once position C is attained since such a policy will reduce welfare; that is, the economy would in this case move to an inferior social indifference curve.

To sum up, while position A > O > C in Figure 5.4, only C is timeconsistent. Position A is unsustainable since unemployment is below the natural rate, and at position O the authorities have an incentive to cheat in order to achieve a higher level of (temporary) social welfare. What this example illustrates is that, if the monetary authorities have discretionary powers, they will have an incentive to cheat. Hence announced policies which are time-inconsistent will not be credible. Because the other players in the inflation game know the authorities’ objective function, they will not adjust their inflationary expectations in response to announcements which lack credibility and in the absence of binding rules the economy will not be able to reach the optimal but time-inconsistent position indicated by point O. The non-cooperative Nash equilibrium indicated by point C demonstrates that discretionary policy produces a sub-optimal outcome exhibiting an inflationary bias. Because rational agents can anticipate the strategy of monetary authorities which possess discretionary powers, they will anticipate inflation

of ˙ e Hence policy makers must also supply inflation equal to that expected

Ptc .

by the private sector in order to prevent a squeeze on output. An optimal policy which lacks credibility because of time inconsistency will therefore be neither optimal nor feasible. Discretionary policies which emphasize selecting the best policy given the existing situation will lead to a consistent, but sub-optimal, outcome. The only way to achieve the optimal position, O, is for

Figure 5.5 Game played between the monetary authorities and wage negotiators

the monetary authorities to pre-commit to a non-contingent monetary rule consistent with price stability.

The various outcomes which can arise in the game played between the monetary authorities and wage negotiators has been neatly captured by Taylor (1985). Figure 5.5, which is adapted from Taylor (1985), shows the four possible outcomes in a non-cooperative game between private agents and the central bank. The time-consistent outcome is shown by C, whereas the optimal outcome of low inflation with unemployment at the natural rate is shown by O. The temptation for a government to stimulate the economy because of time inconsistency is indicated by outcome A, whereas the decision not to validate a high rate of expected inflation and high wage increases will produce a recession and is indicated by outcome B.

The credibility problem identified by Kydland and Prescott arises most clearly in the situation of a one-shot full information non-cooperative

Stackelberg game where the government has discretion with respect to monetary policy. However, in the situation of economic policy making, this is unrealistic since the game will be repeated. In the case of a repeated game (a super-game) the policy maker is forced to take a longer-term view since the future consequences of current policy decisions will influence the reputation of the policy maker. In this situation the government’s incentive to cheat is reduced because they face an intertemporal trade-off between the current gains from reneging and the future costs which inevitably arise from riding the Phillips curve.

This issue of reputation is taken up in their development and popularization of the time-inconsistency model by Barro and Gordon (1983a, 1983b). They explore the possibilities of substituting the policy maker’s reputation for more formal rules. The work of Barro and Gordon represents a significant contribution to the positive analysis of monetary policy which is concerned with the way policy makers do behave, rather than how they should behave. If economists can agree that inflation is primarily determined by monetary growth, why do governments allow excessive monetary growth? In the Barro– Gordon model an inflationary bias results because the monetary authorities are not bound by rules. However, even a government exercising discretion will be influenced by reputational considerations if it faces punishment from private agents, and it must consequently weigh up the gains from cheating on its announced policy against the future costs of the higher inflation which characterizes the discretionary equilibrium. In this scenario, ‘a different form of equilibrium may emerge in which the policymaker forgoes short-term gains for the sake of maintaining a long-term reputation’ (Barro and Gordon, 1983b). Given this intertemporal trade-off between current gains (in terms of lower unemployment and higher output) and the future costs, the equilibrium of this game will depend on the discount rate of the policy maker. The higher the discount rate, the closer the equilibrium solution is to the time-consistent equilibrium of the Kydland–Prescott model (point C in Figure 5.4). If the discount rate is low, the equilibrium position will be closer to the optimal zero inflation pre-commitment outcome. Note that it is the presence of precommitment that distinguishes a monetary regime based on rules compared to one based on discretion.

One problem with the above analysis is that private agents do not know what type of government behaviour they face since they have incomplete information (see Driffill, 1988). Given uncertainty with respect to government intentions, private agents will carefully analyse various signals in the form of policy actions and announcements. In this scenario it is difficult for private agents to distinguish ‘hard-nosed’ (zero-inflation) administrations from ‘wet’ (high-inflation) administrations, since ‘wets’ have an incentive to masquerade as ‘hard-nosed’. But as Blackburn (1992) has observed, agents ‘extract

information about the government’s identity by watching what it does, knowing full well that what they do observe may be nothing more than the dissembling actions of an impostor’. Backus and Driffill (1985) have extended the Barro and Gordon framework to take into account uncertainty on the part of the private sector with respect to the true intentions of the policy maker. Given this uncertainty, a dry, hard-nosed government will inevitably face a high sacrifice ratio if it initiates disinflationary policies and engages in a game of ‘chicken’ with wage negotiators. For detailed surveys of the issues discussed in this section, the reader should consult Barro (1986), Persson (1988), Blackburn and Christensen (1989) and Fischer (1990).

More recently Svensson (1997a) has shown how inflation targeting has emerged as a strategy designed to eliminate the inflation bias inherent in discretionary monetary policies. The time-inconsistency literature pioneered by Kydland and Prescott and Barro and Gordon assumes that monetary authorities with discretion will attempt to achieve an implicit employment target by reducing unemployment below the natural rate, which they deem to be inefficiently high. This problem has led economists to search for credible monetary frameworks to help solve the inflation bias problem. However, the ‘first-best’ solution is to correct the supply-side distortions that are causing the natural rate of unemployment to be higher than the monetary authorities desire, that is, tackle the problem at source. If this solution is for some reason politically infeasible (strong trade unions), a second-best solution involves a commitment to a monetary policy rule or assigning the monetary authorities an employment target equal to the natural rate. If none of these solutions is feasible, then policy will be discretionary and the economy will display an inflation bias relative to the second-best equilibrium. Svensson classes the discretionary (time-inconsistent) outcome as a fourth-best solution. Improvements on the fourth-best outcome can be achieved by ‘modifying central bank preferences’ via delegation of monetary policy to a ‘conservative central banker’ (Rogoff, 1985) or by adopting optimal central bank contracts (Walsh, 1993, 1995a). Svensson argues that inflation targeting can move an economy close to a second-best solution.

5.5.4 Central bank independence

The debate relating to central bank independence (CBI) has been very much influenced by new classical thinking, especially with respect to inflationary expectations, time inconsistency, reputation and credibility. If we accept the Kydland–Prescott argument that discretionary policies lead to an inflation bias, then it is clearly necessary to establish some institutional foundation that will constrain discretionary actions. Many economists are persuaded that some form of CBI will provide the necessary restraint. The theoretical case for CBI relates to the general acceptance of the natural rate hypothesis that in

the long run the rate of inflation is independent of the level of unemployment and that discretionary policies are likely to lead to an inflation bias. Hence with no long-run exploitable trade-off, far-sighted monetary authorities ought to select a position on the long-run Phillips curve consistent with a low sustainable rate of inflation (a point near to O in Figure 5.4). The dynamic inconsistency theories of inflation initiated by Kydland and Prescott and developed by Barro and Gordon, and Backus and Driffill, provide an explanation of why excessive (moderate) inflation will be the likely outcome of a monetary regime where long-term commitments are precluded. Such discretionary regimes contrast sharply with monetary regimes such as the Gold Standard, where the underlying rules of the game revolve around a precommitment to price stability. The emphasis of these models on the importance of institutions and rules for maintaining price stability provides a strong case for the establishment of independent central banks whose discretion is constrained by explicit anti-inflation objectives acting as a pre-commitment device. Since the problem of credibility has its source in the discretionary powers of the monetary authorities with respect to the conduct of monetary policy, this could be overcome by transferring the responsibility for anti-inflationary policy to a non-political independent central bank. In addition, an independent central bank will benefit from a ‘credibility bonus’, whereby disinflationary policies can be accomplished at a low ‘sacrifice ratio’ (Cukierman, 1992; Goodhart, 1994a, 1994b).

In the debate over CBI it is important to make a distinction between ‘goal independence’ and ‘instrument independence’ (see Fischer, 1995a, 1995b). The former implies that the central bank sets its own objectives (that is, political independence), while the latter refers to independence with respect to the various levers of monetary policy (that is, economic independence). The recently (May 1997) created ‘independent’ Bank of England has instrument independence only. Initially, an inflation target of 2.5 per cent was set by government, which formed the Bank’s explicitly stated monetary policy objective. Therefore, in the UK, the decisions relating to goals remain in the political sphere (Bean, 1998; Budd, 1998).

As noted above, Svensson (1997a) argues that the inflation bias associated with the time-inconsistency problem can be improved upon by ‘modifying central bank preferences’ via delegation of monetary policy to a ‘conservative central banker’ (for example Alan Greenspan) as suggested by Rogoff (1985) or by adopting optimal central bank contracts, as suggested by Walsh (1993, 1995a). Rogoff’s conservative central banker has both goal and instrument independence and is best represented by the German Bundesbank, which before European Monetary Union remained the most independent central bank in Europe (Tavelli et al., 1998). In Rogoff’s model an inflation-averse conservative central banker is appointed

who places a higher relative weight on the control of inflation than does society in general (for example President Jimmy Carter’s appointment of Paul Volcker as Chairman of the Fed in 1979). This is meant to ensure that the excessive inflation associated with the time-inconsistency problem is kept low in circumstances where it would otherwise be difficult to establish a pre-commitment to low inflation. Overall, lower average inflation and higher output variability are predicted from this model (Waller and Walsh, 1996). However, the research of Alesina and Summers (1993) shows that only the first of these two predictions appears in cross-sectional data. In contrast, Hutchison and Walsh (1998), in a recent study of the experience of New Zealand, find that central bank reform appears to have increased the short-run output–inflation trade-off. In Rogoff’s model the conservative central banker reacts less to supply shocks than someone who shared society’s preferences, indicating a potential trade-off between flexibility and commitment. In response to this problem Lohmann (1992) suggests that the design of the central bank institution should involve the granting of partial independence to a conservative central banker who places more weight on inflation than the policy maker, but ‘the policymaker retains the option to over-ride the central bank’s decisions at some strictly positive but finite cost’. Such a clause has been built into the Bank of England Act (1998), where the following reserve power is set out: ‘The Treasury, after consultation with the Governor of the Bank, may by order give the Bank directions with respect to monetary policy if they are satisfied that the directions are required in the public interest and by extreme economic circumstances.’ It remains to be seen if such powers are ever used.

The contracting model, associated with Walsh (1993, 1995a, 1998), utilizes a principal–agent framework and emphasizes the accountability of the central bank. In Walsh’s contracting approach the central bank has instrument independence but no goal independence. The central bank’s rewards and penalties are based on its achievements with respect to inflation control. The Reserve Bank of New Zealand resembles this principal–agent type model. An important issue in the contracting approach is the optimal length of contract for a central banker (Muscatelli, 1998). Long terms of appointment will reduce the role of electoral surprises as explained in Alesina’s partisan model (see Chapter 10). But terms of office that are too long may be costly if societal preferences are subject to frequent shifts. Waller and Walsh (1996) argue that the optimal term length ‘must balance the advantages in reducing election effects with the need to ensure that the preferences reflected in monetary policy are those of the voting public’.

The empirical case for CBI is linked to cross-country evidence which shows that for advanced industrial countries there is a negative relationship between CBI and inflation. During the last 15 years a considerable amount of research

Source: Alesina and Summers (1993).

Figure 5.6 The relationship between average inflation and central bank independence

The ‘near perfect’ negative correlation between inflation and central bank independence is clearly visible in Figure 5.6. However, as Alesina and Summers recognize, correlation does not prove causation, and the excellent anti-inflationary performance of Germany may have more to do with the public aversion to inflation following the disastrous experience of the hyperinflation in 1923 than the existence of an independent central bank. In this case the independent central bank could be an effect of the German public aversion to inflation rather than a cause of low inflation. Indeed, the reputation established by the German Bundesbank for maintaining low inflation was one important reason given by the UK government for joining the ERM in October 1990. The participation of the UK in such a regime, where monetary policy is determined by an anti-inflationary central bank which has an established reputation and credibility, was intended to tie the hands of domestic policy makers and help lower inflationary expectations (see Alogoskoufis et al., 1992).

Considerable research has also been conducted into the role played by politics in influencing economic performance. The ‘political business cycle’ or ‘monetary politics’ literature also suggests that CBI would help reduce the problem of political distortions in macroeconomic policy making. What is now known as the ‘new political macroeconomics’ has been heavily influ-