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5.5.3 Dynamic time inconsistency, credibility and monetary rules

The ‘hard core’ monetarist case for a constant monetary growth rate rule was

well articulated by Milton Friedman during the 1950s and 1960s. Friedman’s

case is based on a number of arguments, including the informational constraints

facing policy makers; problems associated with time lags and

forecasting; uncertainty with respect to the size of fiscal and monetary policy

multipliers; the inflationary consequences of reducing unemployment below

the natural rate; and a basic distrust of the political process compared to

market forces. The Lucas–Sargent–Wallace policy ineffectiveness proposition

calls into question the power of anticipated monetary policy to influence

real variables, adding further weight to Friedman’s attack on discretionary

policies. While the Walrasian theoretical framework of the new classical

economists differed markedly from Friedman’s Marshallian approach, the

policy conclusions of Lucas, Sargent and Wallace were ‘monetarist’ in that

their models provided further ammunition against the Keynesian case for

activist discretionary stabilization policies. For example, in his highly theoretical

paper, ‘Expectations and the Neutrality of Money’, Lucas (1972a)

demonstrates the optimality of Friedman’s k per cent rule.

In 1977, Kydland and Prescott provided a reformulation of the case against

discretionary policies by developing an analytically rigorous new classical

model where the policy maker is engaged in a strategic dynamic game with

sophisticated forward-looking private sector agents. In this setting, discretionary

monetary policy leads to an equilibrium outcome involving an ‘inflation

bias’. As Ball (1995) notes, models based on dynamic consistency problems

have now become the leading theories of moderate inflation.

The theory of economic policy which Kydland and Prescott attack in their

paper is that which evolved during the 1950s and 1960s. The conventional

approach, inspired by Tinbergen (1952), consists of three crucial steps. First,

the policy maker must specify the targets or goals of economic policy (for

example, low inflation and unemployment). Second, given this social welfare

function which the policy maker is attempting to maximize, a set of instruments

(monetary and fiscal) is chosen which will be used to achieve the

targets. Finally, the policy maker must make use of an economic model so

that the instruments may be set at their optimal values. This normative approach

to economic policy is concerned with how policy makers should act

and, within the context of optimal control theory, economists sought to identify

the optimal policy in order to reach the best outcome, given the decision

takers’ preferences (see Chow, 1975). Kydland and Prescott argue that there

is ‘no way’ that ‘optimal control theory can be made applicable to economic

planning when expectations are rational’. Although optimal control theory

had proved to be very useful in the physical sciences, Kydland and Prescott

deny that the control of social systems can be viewed in the same way. Within

social systems there are intelligent agents who will attempt to anticipate

policy actions. As a result, in dynamic economic systems where policy makers

are involved with a sequence of actions over a period of time, ‘discretionary

policy, namely the selection of that decision which is best, given the current

situation, does not result in the social objective function being maximised’

(Kydland and Prescott, 1977, p. 463). This apparent paradox results because

‘economic planning is not a game against nature but, rather, a game against

rational economic agents’. This argument has very important implications

both for the conduct of monetary policy and for the institutional structure

most likely to generate credibility with respect to the stated objective of low

inflation.

The fundamental insight provided by Kydland and Prescott relating to the

evaluation of macroeconomic policy is that when economic agents are forward-

looking the policy problem emerges as a dynamic game between

intelligent players – the government (or monetary authorities) and the private

sector (see Blackburn, 1987). Suppose a government formulates what it considers

to be an optimal policy which is then announced to private agents. If

this policy is believed, then in subsequent periods sticking to the announced

policy may not remain optimal since, in the new situation, the government

finds that it has an incentive to renege or cheat on its previously announced

optimal policy. The difference between ex ante and ex post optimality is

known as ‘time inconsistency’. As Blackburn (1992) notes, an optimal policy

computed at time t is time-inconsistent if reoptimization at t + n implies a

different optimal policy. Kydland and Prescott demonstrate how time-inconsistent

policies will significantly weaken the credibility of announced policies.

The demonstration that optimal plans are time-inconsistent is best illustrated

in the macroeconomic context by examining a strategic game played

between the monetary authorities and private economic agents, utilizing the

Lucas monetary surprise version of the Phillips curve trade-off between

inflation and unemployment to show how a consistent equilibrium will involve

an inflationary bias. In the Kydland and Prescott model discretionary

policies are incapable of achieving an optimal equilibrium. In what follows

we assume that the monetary authorities can control the rate of inflation

perfectly, that markets clear continuously and that economic agents have

rational expectations. Equation (5.23) indicates that unemployment can be

reduced by a positive inflation surprise:

U U P P t N t

e

t t ( ˙ −˙ ) (5.23)

Equation (5.23) represents the constraint facing the policy maker. Here, as

before, Ut is unemployment in time period t, UNt is the natural rate of unemployment,

is a positive constant, ˙Pt

e is the expected and ˙Pt the actual rate

of inflation in time period t. Kydland and Prescott assume that expectations

are rational as given by equation (5.24):

where, as before, ˙Pt is the actual rate of inflation; E(Pt t ˙ |−1) is the rational

expectation of the rate of inflation subject to the information available up to

the previous period (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):

S S(P˙t ,Ut ), where S(P˙t ) 0, and S(Ut ) 0 (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

trade-off for two expected rates of inflation, ˙Pto

e and P˙ . tc

e The contours of the

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

rate (that is, Ut = UNt) and agents are correctly forecasting inflation (that

is, ˙Pt

e = P˙ ). t The indifference curves indicate that the optimal position (consistent

equilibrium) is at point O where a combination of ˙Pt = zero and Ut =

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).

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 ˙Mc to M˙ o . If such an announcement

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

downwards their inflationary expectations from ˙Ptc

e to P˙ , to

e causing the Phillips

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

unemployment is below the natural rate and ˙Pt > P˙t .

e Rational agents will

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 P˙tc .

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

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.