# Bashing and coercion in monetary policy.

BASHING AND COERCION IN MONETARY POLICY

I. INTRODUCTION

"We've got excess plant capacity...I don't think that growth is excessive" ..." I have not been overly concerned with inflation." (President Bush in a February 14, 1989 interview with the Wall Street Journal, p. A8.)

"With the economy running close to potential, the risks seem to be on the side of a further strengthening of price pressure." (Chairman Greenspan in testimony before Congress on February 21, 1989, reprinted from the Wall Street Journal, February 22, 1989, p. A2.)

"Many investors appeared to be confused by conflicting statements by Bush, Greenspan and other U.S. officials." Wall Street Journal, February 22, 1989, p. A1.)

"If the Fed pushes interest rates significantly higher, Bush may go public with critism." (Wall Street Journal, March 24, 1989, p. A1.)

Recent research in macroeconomic policy games by Rogoff [1985!, Alesina [1988!, Tabellini [1987! and Waller [1989a! has concentrated on the importance of an "independent" central bank in a discretionary policymaking environment. In the original work on policy games by Barro and Gordon [1983a 1983b!, no distinction was made between the monetary authority and the fiscal authority. But these researchers argue that because the fiscal authority may have incentives to create excessive inflation, giving the powers of money creation to an independent monetary authority, whose inflation preferences differ from the current fiscal authority, may enable society to reduce the equilibrium inflation rate. This results holds even though monetary policy is still chosen in a discretionary fashion. Therefore, Backus and Driffill [1985a, 537! conclude "autonomous central banks thus act as a precommitment device which may help to make noninflationary policies more credible and less costly."

Implicit in the term "independent" is the belief that the central bank is free to choose monetary policy without interference from the fiscal authority (administration). However, this is not generally the case. The appointment of central bankers by the legislative or executive branch of the government, governmental oversight of policy decisions, or political pressure on the central bank by these branches will tend to influence the setting of monetary policy and, subsequently, the extent to which the central bank is truly "independent." (1)

Kane [1984! argues that, even if it is not able to directly choose monetary policy, the current administration still may be able to achieve its preferred monetary growth path by putting pressure on the monetary authority to do its bidding. Restricting the powers of the central bank, public criticism of central bank performance (here after referred to as "bashing" (2)), exclusion from fiscal policy planning (which hurts the egos of central bankers), or undertaking actions which damage the post-central-bank income or opportunities of the central bankers are ways, he suggests, in which the administration can coerce "cooperation" from the central bank in creating excessive money growth.

Such arguments have given rise to the view that the administration is engaged in a reputation building game with the central bank. Although the central bank has control of the money supply, the administration can threaten to impose a welfare loss by bashing the central bank if it does not generate the monetary policy preferred by the administration. The success of this strategy depends on the size of the "bashing" costs imposed on the central bank and also on the extent to which these threats are credible. Credibility, in turn, depends on the benefits and costs incurred by the administration in carrying out its threats. As a result, the administration may choose to bash the central bank if it does not produce the administration's preferred money/inflation outcome. By establishing a reputation for bashing, the administration may be able to obtain its desired policy outcome in the future.

An important side effect of this type of pressure is that it creates uncertainty in the private sector about future policy actions and, thus, expected future inflation rates. Even if it is known the central bank would like to follow a low inflation policy, private agents are not sure if the central bank will maintain a low inflation policy or, because of political pressure, give in to the administration's money growth demands which will create excessive inflation. If this uncertainty leads to errors in inflation expectations, then real output will be affected. Such politically-generated uncertainty is much different from the political uncertainty that arises in partisan models of monetary policy, such as Alesina [1988! and Waller [1989a!. In these models, electoral competition between parties with differing economic objectives generates uncertainty about future economic outcomes since private agents do not know who will be elected and, as a result, which policy will be enacted. Hence, these models are basically concerned with pre-election uncertainty, whereas this paper concentrates on post-election uncertainty.

The purpose of this paper is to develop a game theoretic model of the politics of monetary policy. Using the reputation building model of Kreps and Wilson [1982!, I analyze the interactions between the central bank and the administration over the setting and monetary policy and show that cooperation by the central bank will tend to occur early in the administration's term of office and that any episodes of noncooperation occuring early in the game will be met with "bashing" by the administration. Furthermore, the model gives substance to the notion of a "strong" administration/central bank and provides an explanation of why there are periods in which the central bank appears to be cooperating with the administration, while at other times it appears to be acting independently.

Although this reputation building model has been used before by Backus and Driffill [1985a 1985b!, Barro [1986!, and Tabellini [1988! to analyze monetary policy games, this paper extends the model by including three players: the administration, the central bank, and the private sector. This extension leads to the possibility of multiple expansions of the economy, whereas in these previous papers only one expansion could occur during the tenure of a single administration. The reason for this was alluded to above: if the central bank chooses to cooperate according to a mixed strategy, private agents will use this information when forming inflation expectations. As a result, inflation expectations may differ from the actual inflation outcome. Hence, if the central bank gives in to the administration, it produces a higher-than-expected inflation rate and real output increases. Since this outcome can occur more than once, the model is able to generate multiple expansions of the economy.

The paper is structured as follows. The basic model is presented in section II. In section III the model is solved to determine the equilibrium decision rules for the administration, the central bank and the private sector. In section IV, these equilibrium decision rules are analyzed and their implications for monetary policy and the path of real output are discussed. Section V is the conclusion.

II. THE STRUCTURE OF THE GAME

The Basic Model

There are three players in the model: the private sector, the central bank, and the administration. Following Gray [1976! and Fisher [1977!, private agents are wage setters who sign nominal wage contracts prior to the start of period t based on their expectations on inflation in period t. Wage setters are concerned with minimizing employment deviations, which depend on inflation expectations errors. Given these assumptions, aggregate output and the utility function for private agents can be written as

(1) [Y.sub.t! = [y.sup.N! + ([[pi!.sub.t! - [[pi!.sup.e.sub.t!)

(2) [uw.sub.t! = - [([[pi!.sub.t! - [[pi!.sup.e.sub.t!.sup.2!

where [y.sub.t! is aggregate output, [y.sup.N! is the natural level of output, [[pi!.sub.t! is the period t inflation rate, and [[pi!.sup.e.sub.t! is the expected rate of inflation.

With regards to the policymakers, I assume that the central bank has complete control of the money supply and is able to pursue any policy it wants, and that its money growth preferences differ from the administration's. Furthermore, for independence to have any meaning, the central bank is assumed to be free to choose its monetary policy without fear of being replaced if it fails to produce the monetary growth rate desired by the administration. Although the central bank is free to follow whatever policy it wants, the administration can put pressure on the central bank to "cooperate" and produce the monetary growth rate preferred by the administration. This pressure will be referred to as "bashing," and it is only mechanism by which the administration can influence the setting of monetary policy. (3) Hence, the only policy instrument in the model is the money growth rate, and for simplicity it is assumed that the inflation rate is proportional to the money growth rate, which essentially makes it the policy instrument.

The timing of decisions in this model is as follows. Wage setters sign contracts prior to the start of the period based on the inflation rate they expect the central bank to choose in the ensuing time period. After wage contracts are signed, the central bank chooses the inflation rate (money growth rate) for the current period. In doing so, the central bank decides whether to pursue a policy consistent with its own inflation preferences or to "cooperate" and choose an inflation rate preferred by the administration. Once the policy is enacted, the administration decides whether or not to bash the central bank. This sequence of actions is then repeated in the next period.

This decision making sequence implies that bashing by the administration can only influence future inflation rates and not the current inflation rate. As a result, the administration's decision to bash involves building a reputation for bashing in order to deter future defections by the central bank. Bashing imposes a welfare loss on the central bank this period, and the possibility of incurring this again may deter the central bank from defectng next period. But bashing can also create external costs or benefits for the administration in addition to any benefits that result from reputation building.

The reasons why bashing imposes costs on the central bank were described in the introduction. But what are the exogenous costs or benefits incurred by the administration? Bashing may be costly if public criticism by the administration of the central bank's policies creates a perception of internal dissent, which may damage its relationships with other agencies within the government. Furthermore, if the central bank has developed a base of support from the financial sector, the administration may subject itself to a loss of contributions or intense lobbying pressure by supporters of the central bank. In addition, the central bank may respond by publicly criticizing the administration's fiscal policy (although a strategic decision by the central bank to do this will not be considered here). (4)

Bashing noncooperative behavior by the central bank can also be beneficial. The administration may simply bash as a matter of principle. A more important reason is that if the administration is involved in power games with other agencies within the government, it may choose to bash noncooperative acts by the central bank to set an example for other agencies. However, bashing the central bank when it cooperates will be counterproductive and produce a welfare loss rather than a welfare gain. (5) The key point is that bashing by the administration, on net, can produce costs or benefits in addition to any reputation benefits it achieves. Whether bashing produces a net benefit or a net cost depends on the characteristics of the current administration.

The Policymakers' Objectives

The loss functions for the administration and the monetary authority are

(3) [Mathetematical Expression Omitted!

(3b) [Mathematical Expression Omitted!

where the subscript A denotes the administration and the subscript M denotes the monetary authority.

Equation (3) is a time-separable, intertemporal loss function which is common to both authorities. Equation (3a) is the one-period loss function for the administration. The administration suffers as welfare loss from deviations of inflation from its desired rate, c, which is greater than zero and reflects its desired rate of seigniorage. Equation (3b) is the one-period loss function for the central bank. The central bank is much more "conservarive" in that it prefers to maintain price stability and is thus not concerned with creating seigniorage for the administration. (6) The functions [phi![(B.sub.t'n)! and K[(B.sub.t)! represent, respectively, the costs of bashing by the administration and the loss to the central bank from being bashed. These will be discussed in more detail below. Finally, the time horizon for this game, T, is envisioned to be the lenght of the current administrations's term of office.

Preferred Inflation Rate Policies and

Expectation Formation

In an environment free of political pressure, the central bank will choose an inflation rate that minimizez the loss function (3b). This inflation rate is the central bank's preferred policy choice and is given by

(4) [Mathematical Expression Omitted!

On the other hand, if the administration controls the inflation rate, or the central bank adopts the inflation rate policy preferred by the administration, it will choose [[pi!.sub.t! such that (3a) is minimized. The administration's preferred inflation rate is given by

(5) [Mathematical Expression Omitted!

The administration's inflation rate choice reflects its desired level of seigniorage, c.

However, in a political environment the central bank must decide whether to cooperate with the administration or act independently (defect). If the central bank chooses not to cooporate (defects), it sets the inflation rate according to equation (4) and runs the risk of being bashed by the administration. If it cooporates, it sets the inflation rate according to equation (5), which gives the administration what it wants, thereby allowing the central bank to avoid the costs of being bashed. For convenience, I characterize the central bank's decision to cooparate as a mixed strategy. Consequently, define [f.sub.t! as the probability that the central bank cooperates with the administration in perio t by setting the inflation rate according to equation (5).

Given the central bank's cooperation straregy, wage setters from their inflation expectations according to

(6) [Mathematical Expression Omitted!

From (6) we can see that, for 0 [f.sub.t! [is less than! 1, there is uncertainty on the part of the private sector regarding the inflation outcome in period t. As a result, there will be an expansion of the economy if the central bank does cooperate. If not, then a contraction will occur. Furthermore, announcements by the central bank that it will follow a low inflation rate policy in the coming period will not be believed. [7!

Bashing Costs

If the central bank chooses not to cooperate with the administration it runs the risk of being bashed, which creates a welfare loss for the central bank. This welfare loss is captured by the fucntion K[(B.sub.t)!, where [B.sub.t! is an indicator function set equal to zero if the administration does not bash the central bank's policy choice and equal to one if bashing occurs. Hence, 5(0)=0 and K(1)= [k is greater than 0.!

As was mentioned above, bashing can generate benefits or costs unrelated to reputation effects, and these costs or benefits can vary from one type of administration to another. Let [phi![(B.sub.t'n)! represent the exogenous bashing cost or benefit to an administration of type n. For simplicity, suppose there are two types of administrations, a strong administration (n=s) and a weak adminstration (n=w). A strong administration receives a net welfare gain by bashing noncooperative behavior by the central bank, whereas a week administration receives a net welfare loss. However, both types of administrations receive a net welfare loss from bashing cooperative behavior. Thus, if the central bank cooperates, [phi!(1,n) = Q 0 for each type of administration. If the central bank does not cooperate, then [phi!(1,s) = -q

0 and [phi!(1,w) = q 0, where q is the cost of bashing and negative q is a benefit received from bashing. The paramater q will be assumed to the constant, which reflects the implicit assumption that the intensity of bashing is constant. Finally, if no bashing occurs, [phi!(0,n) = 0.

The period t loss matrix for the administration is

Since bashing cannot affect the period t inflation outcome, the weak administration minimizes period t losses by choosing not to bash regardless of whether the central bank cooperates or not. The strong administration minimizes period t losses by choosing to bash only if a defection occurs.

Given these bashing decisions by the two types of administrations, the central bank's losses in period t will be

The cental bank will never choose to cooperate with a weak administration since its threats to bash are not credible. As a result, reputation building by the weak administration can not occur. (8) Furthermore, if the cost of defection, k, is less than the loss from cooperating, (1/2)[sup.2!, the central bank would never cooperate with a strong administration and a zero inflation rate would prevail in all periods of the game. In this case, the central bank is "strong" since it is never influenced by threats of bashing by the administration. For bashing to have any chance of succeeding, it must be the case that

K (1/2)[c.sup.2!. This will be assumed for the remainder of the paper.

Central Bank Uncertainty and Beliefs

If the central bank knew the administration's type with perfect certainty, then we would observe either complete cooperation or noncooperation by the central bank. While these extreme cases are of some interest, a more interesting (and plausible) world is one in which there is some uncertainty regarding the administration's type.

One way of incorporating uncertainty is to assume that at the beginning of the game a new administration is elected and the central bank does not know this new administration's type. The only way for the central bank to infer the administration's type is to act independently and see if the administration responds by bashing. Given this assumption, a weak administration now can pose as a strong administration by bashing the central bank when it acts noncooperatively. This leads the central bank to believe it is dealing with a strong administration, thereby influencing future decisions to cooperate with the administration. Thus, in this world, the weak administration can engage in reputation building.

However, simply bashing a defection is not enough to convince the central bank that it is dealing with a strong administration since it is aware of the weak administration's incentive to act strong. As was done for the central bank, the weak administration's decision to bash is modelled as a mixed strategy. Let [g.sub.t! be the probability that a weak administration bashes a defection by the central bank. By construction, a strong administration bashes a defection with probability one.

When deciding whether or not to cooperate with the administration in period t, the central bank must determine the probability that it is dealing with a strong administration. This probability estimate measures the administration's reputation. The central bank updates its probability estimate that it is dealing with a strong administration according to Bayes' rule:

(7) [Mathematical Expression Omitted!

Since a strong administration always bashes a defection, if previous episodes of noncooperation by the central bank were not bashed, then the administration reveals itself as weak and [p.sub.t!=0. If the central bank cooperates in period t-1, then nothing new is learned and [p.sub.t!=[p.sub.t-1!. At the start of the game, the central bank has an initial prior (determined by nature) [p.sub.1! of dealing with a strong administration.

III. SOLUTION OF THE MODEL

Once reputation building is introduced, the model becomes dynamic. Since a strong administration always bashes a defection, the analysis below will concentrate on the bashing strategy of the weak administration. In period t, the weak administration and the central bank choose [g.sub.t! and [f.sub.t! to minimize expected intertemporal losses, given by

(8) [Mathematical Expression Omitted!

(9) [Mathematical Expression Omitted!

where [h.sub.t! equals one if the central bank cooperates in period t, and equals zero if the central bank defects. From (8), the central bank's decision to cooperate depends on the administration's reputation at time t as well as the weak administration's strategy for acting in period t. The term [p.sub.t! + (1-[p.sub.t!)[g.sub.t! is the central bank's probability estimate that a period t defection will be met with bashing.

From equation (9) we see that if the central bank cooperates, then the weak administration does not bash and the game proceeds to stage t+1. [Z.sub.A+1! is the value of the inter-temporal loss function at time t+1 given that the administration's true type is not revealed prior to t+1.

If [h.sub.t!=0, the weak administration must decide whether or not to bash the defection. In doing so, it compares the benefit of maintaining or improving its reputation versus the cost of revealing its true type. This benefit/cost tradeoff is measured by the square/bracket term in (9). If it bashes the defection, the weak administration incurs the bashing cost q but does not reveal its type. Bashing this period affects the central bank's probability estimate that the administration is strong, and thus its decision to cooperate in period t+1. This, in turn, affects the weak administration's period t+1 losses. If the administration does not bash the defection this period, it avoids the bashing cost q but, revealing its true type, it suffers the loss (1/2)[c.sub.2! for the remainder of the game.

Period T Strategies

The strategies for the weak administration and the central bank are determined by solving the game backwards from period T. At time T it is easy to see that, regardless of its reputation doing into period T, the weak administration will never bash a defection since there are no reputation benefits to be reaped by doing so. Hence [g.sub.T!=0, and from equation (8) [f.sub.T! becomes

(10) [Mathematical Expression Omitted!

The central bank will decide to cooperate in the last period if the probability that the administration is strong is sufficient large. As a result, announcements by the central nbank that it will follow a low inflation rate policy in the coming period will not be credible. This occurs in spite of the fact that the central bank is technically independent. Alternatively, if the administration's reputation is not sufficiently high, the central bank asserts its independence and sets the inflation rate equal to zero. The necessary reputation for the central bank to cooperate in period T is a function of the central bank's loss from cooperation, (1/2)[c.sub.2!, relative to the loss from being bashed, k. If bashing is relatively costly, then a smaller reputation is needed to induce cooperation by the central bank in the past period, and vice versa.

For the case in which [c.sub.2!/2k=[P.sub.T!, it would appear that any value of [f.sub.T! is consistent with loss minimization for the central bank. This freedom to define the strategy is characteristic of the Kreps-Wilson [1982! model. (9) As shown in the appendix, dynamic consistency requires 2q/[c.sub.2! [is less than or equal to! [f.sub.t! [is less than or equal to! 1 but does not lead to a unique expression for [f.sub.t!. (10) As long as [f.sub.t' is less than one, the central bank will randomize its decision to

cooperate with the administration. This implies that tehre is private sector uncertainty regarding the inflation outcome in period t and inflation expectations will be between zero and c. Since there is anecdotal evidence that the presence of administrative pressure leaves the private sector unsure of the monetary policy outcome, I will assume that the central bank sets f = 2q/[c.sup.2! when [c.sup.2!/2k = [p.sub.T!.

Given this assumption, if the central bank cooperates with the administration in period T, it sets the inflation rate equal to c. Since this is greater than expected, an expansion of output occurs. If the central bank acts independently and sets the inflation rate equal to zero, then expected inflation is too high and a recession occurs in the last period. Thus, political interference in the money creation process can create uncertainty about policy outcomes, thereby reducing the credibility of central bank policy announcements, which can cause undesired fluctuations in real output.

The period T looses for the weak administration and the central bank are

(11) [Mathematical Expression Omitted!

(12) [Mathematical Expression Omitted!

If [P.sub.T! = 0, the weak administration's payoff is (1/2)[c.sup.2!.

Period T-1 Strategies

As shown in the appendix, equations (8), (9), (10), (11) and (12) lead to the following bashing and cooperation strategies in period T-1:

(13) [Mathematical Expression Omitted!

(14) [Mathematical Expression Omitted!

The first line of equation (13) shows that if its reputation is sufficiently large, the weak administration will choose to maintain its reputation by bashing a defection with probability one. From Bayes' rule, this implies that [Mathematical Expressions Omitted! which means, by equation (10), that the central bank will cooperate in period T with probability one if this condition holds as a strict inequality. If it holds with equality, the central bank cooperates in period T with probability [f.sub.T! = 2q/[c.sup.2!. In either case, the weak administration reduces its period T losses by at least q if it bashes a defection in period T-1.

The second line of equation (13) shows that if the administration's T-1 reputation is such that setting [g.sub.T-1! = 1 generates a period T reputation that is insufficient to induce cooperation in the last period, then it will randomize its decision to bash the central bank if a defection occurs in period T-1. If it bashes the defection, its period T reputation rises enough to get the central bank to randomize its decision to cooperate in period T. Thus, bashing is beneficial since it increases the likelihood of cooperation next period. (11) If it does not bash the defection, it reveals itself as weak and the central bank defects with probability one in the last period.

The key point of equation (13) is that as long as its reputation is not zero, the weak administration will bash with some positive probability in period T-1 if a defection occurs. As a result, a smaller reputation is needed in period T-1, relative to period T, in order to induce the central bank to cooperate. Thus, comparing (13) and (14), for [Mathematical Expression Omitted!, even though there is a small probability that, if tested, a weak administration would reveal itself, the central bank decides to avoid the bashing cost by cooperating.

IV. EQUILIBRIUM STRATEGIES AND

IMPLICATIONS

The period t decision rules for the weak administration, the central bank and private agents are

(15) [Mathematical Expression Omitted!

(16) [Mathematical Expression Omitted!

(17) [Mathematical Expression Omitted!

for t=1,2,...,T-1.

Inspection of equation (15) reveals that, for a sufficiently long time horizon, in the early periods of the administration's term a relatively small reputation for being strong will be enough to induce the central bank to cooperate. This "spirit of cooperation" between the administration and the central bank could be characterized as a "honeymoon" effect that frequently occurs when there is a leadership change in a bureaucracy. However, as the game proceeds, a larger reputation for being strong is required to keep the central bank from defecting. This is because the central bank knows that, as the administration's term draws to a close, a weak administration has fewer and fewer incentives to masquerade as a strong administration by bashing defections. Eventually, a weak administration will start to randomize its decision to bash a defection by the central bank. It ie actually does bash a defection, then its reputation increases otherwise, it reveals itself as being weak and the zero inflation outcome prevails from there on.

As the weak administration's incentive to bash a defection decreases, the central bank starts to randomize its decision to cooperate. Once the central bank starts to do this there will be fluctuations in aggregate output. Whenever the central bank randomizes its decision to cooperate, wage setters expect an inflation rate between zero and c to prevail in the forthcoming period. If the central bank cooperates, actual inflation exceeds expected and real output expands. Non-cooperation leads to unexpectedly low inflation and a recession occurs. A key result of this model is that more than one expansion can occur over the course of this game, whereas in previous research using the Kreps-Wilson [1982! model only one expansion could occur. Thus, this model is able to produce output paths which more closely resemble a stochastic business cycle.

Although it is possible to have multiple expansions during this game, it is not possible to have back-to-back expansions. Basically, if the administration's reputation is just sufficient to induce the central bank to randomize in period t and cooperation results (expansion occurs), then no new information is obtained concerning the administration's type and [p.sub.t+1! = [p.sub.t!. Since an increased reputation is required in t+1 to induce the central bank to randomize once again, it necessarily follows that an expansion will be followed by a defection (zero inflation) by the central bank. Since private agents are aware of the central bank's cooperation strategy, they anticipate this defection (zero inflation) in the next period, and so there are no inflation surprises and output is stable. Consequently, expansions cannot be back-to-back.

On the other hand, a recession can be followed by either a recession or an expansion. Given that the central bank randomizes its inflation decision, expectations will be between zero and c. If the central bank actually defects, then a recession occurs. If the administration bashes this defection, then its reputation increases enough going into the next period to induce the central bank to randomize once again, and subsequently a recession or expansion can occur in the period following a recession.

A key feature of central bank's equilibrium strategy is that it is characterized by periodic episodes of cooperation and defection. If one views these defections as the central bank asserting its independence, then the model provides a well-defined notion of an independent central bank. Hence, this model is able to explain why the central bank often appears to be in "cahoots" with the administration and why, at other times, it appears to be acting independently by ignoring the administration's policy wishes.

As was mentioned in the introduction, Backus and Driffill [1985A! assert that the existence of an independent central bank would lead to a lower equilibrium inflation rate. Their assertion will most likely be supported in this model when (1) the central bank is strong (a small value of k), (2)the costs to the weak administration from bashing the central bank are large (large value of q), and (3) the initial probability that the administration is strong is very small. If these conditions are reversed then the central bank will appear to be nothing more than a monetary "puppet" for the administration.

It is interesting to note that the central bank's decision to cooperate is inversely related to the administration's preferred inflation rate. Consequently, the larger is the administration's desire for inflation, the larger the administration's reputation must be to induce cooperation by the central bank. This suggests that, in a multiple-party political system, we should observe varying degrees of cooperation between the central bank and the administration depending on which party is in power. As a result, in order to build a sufficient reputation for being strong, a liberal inflation party will have to make more threats and carry them out more often than an administration whose inflationary preferences are more conservative. This would appear to be an empirically testable hypothesis and may be an avenue for further research.

V. CONCLUSION

This paper has used recent developments in game theory to construct a model of monetary policy politics. Whereas many previous monetary policy game models have relied on the assumption that the central bank is indistinguishable from the administration, this paper incorporates a central bank that is technically independent but not immune to political influence. This has produced a framework that appears to be very rich in explaining the relationship between the administration and the central bank, and what it means to have an "independent" central bank.

APPENDIX

T-1 Strategies: Reputation Building

Given that all defections by the central bank prior to period T-1 have been bashed, the weak administration chooses [q.sub.T.-1! to minize

(A1) [Mathematical Expression Omitted!

If [p.sub.T! [c.sup.2!/2k, then the bracketed term in the last line of equation (A1) becomes q - [(1/2)c.sup.2!. If this term is positive, the bashing costs this period outweigh the cooperation benefits next period. Hence, the administration would never engage in bashing. Hence, it is assumed to be negative, and, as a result, a weak administration will play [q.sub.T-1! " 1.

If [p.sub.T! is less than [c.sup.2/2k then the bracketed term in the last line of equation term is equal to q. The weak administration could set [g.sub.T-1! = 0 thereby revealing itself as weak. This allows the weak administration to avoid incurring the bashing costs this period, but it gives up any change of increasing its reputation going into the last period.

However, if the weak administration exploits the central bank's use of Bayes' rule for updating its probability estimate of playing against a strong administration, it can choose [g.sub.T-1! such that it increases its reputation going into the last period. This is accomplished by setting

(A2) [Mathematical Expression Omitted! which is between zero and one for [p.sub.T-1! [c.sup.2'/2k. If [p.sub.T-1! = [c.sup.2!/2k, then (A2), [g.sub.T-1! = 1. In order for this to be loss minimizing behavior, and thus dynamically consistent, the bracketed term in the last line of equation (A1) must be less than or equal to zero, or q - [f.sub.T.(1/2)c.sup.2! [is less than or equal to! 0. This expression will be negative for all values of [f.sub.T' between one and 2q/[c.sup.2!. Setting [f.sub.t! = 2q/[c.sup.2! yields the central bank strategy given in equation (10). If a defection occurs in period T-1, randomizing the decision to bash according to (A2) allows the weak administratio to raise its reputation, if it actually bashes the defection, just enough to ensure that [p.sub.T! = [c.sup.2!/2k, thereby lowering expected period T losses by q. Equation (13) follows from this analysis.

In period T-1, the central bank will minimize

(A3) [Mathematical Expression Omitted!

Given the weak administration's strategy for

T-1, if [p.sub.t! [c.sup.2/2k then [q.sub.T-1! = 1 and [p.sub.T! = [p.sub.T-1!

[c.sup.202k. From this it follows that the bracketed term in the last line of equation (A3) is negative, so [f.sub.T-1! = 1. If [p.sub.T! [c.sup.2/2k then the weak administration sets [g.sub.T-1! according to equation (A3). Use of (A3) in (A2) yields equation (14).

(*1) Assistant Professor of Economics, Indiana University-Bloomington. I would like to thank Roy Gardner, Richard Sweeney and two anonymous referees for their comments on this paper.

(1.) Havrilesky [1988!, Stein [1985!, Weintraub [1978! and Woolley [1984! provide discussions and evidence concerning the impact of political pressure on the Fed.

(2.) In this paper, bashing will refer to political pressure put on the central bank by the administration. This notion is consistent with the press's use of the phrase but does not correspond to Kane's use of the term in explaining the "scapegoat hypothesis" of central bank behavior.

(3.) This model differs from previous models of games between the monetary authority and the fiscal authority considered by Waller [1987!, Tabellini [1987!, Alesina and Tabellini [1987!, and Loewy [1988!. In these papers, the monetary authority is concerned with the size of the deficit or variables that are affected by the deficit such as the interest rate or the level of the national debt. Thus, the fiscal authority can induce the monetary authority to create more seigniorage by increasing the size of the deficit. In this paper it is assumed that either there is a balanced budget net of seigniorage or the monetary authority is not concerned with variables that are a function of the government's deficit. Hence, the only "tool" the fiscal authority has to influence monetary policy is political pressure.

(4.) In a recent, well-publicized incident of Fed-bashing, Assistant Treasury Secretary Michael Darby sent a letter criticizing recent Fed policy to the Board prior to a policy meeting. This letter was met by "threats" by Alan Greenspan concerning future economic policy or by counter-bashing the administration's fiscal policy. Furthermore, Senator Proxmire also criticized this action by the Treasury. This anecdotal evidence suggests that bashing by the administration is not costless. (See "Treasury's Baker Reveals Agreement With Greenspan to Halt Criticism," Washington Post, Thursday, March 10, 1988. Also see, "Baker Says Fed, Administration Need to Consult," Wall Street Journal, p. 52, Thursday, March 10, 1988.)

(5.) If the administration bashes regardless of whether the central bank cooperates or not, then the central bank gains nothing by cooperating and so it would not cooperate. Hence, bashing cooperative behavior is counterproductive.

(6.) In many macroeconomic policy game models, the policymaker also attempts to exploit an inflation/output tradeoff by creating unexpected inflation. This could be incorporated into the administration's loss function, thereby capturing a common belief that the administration cares more about output than the monetary authority. This would be one explanation why the administration is willing to accept a higher inflation rate. However, since rational agents are aware of this incentive to inflate, they adjust expectations to compensate for it and the end result is an inflation bias with no output gain. Consequently, the administration would be happy to let the monetary authority choose a lower inflation rate in order to avoid this inflation bias. The real source of conflict between the two authorities is the optimal amount of seigniorage, and thus the output term is ignored for notational convenience.

(7.) This paper concentrates on the output effects of politically induced policy uncertainty. However, political disputes between the administration and the central bank may be more important to financial market participants than to labor market participants. Consequently, in my [1989b! paper, I examined how this type of uncertainty affects shortterm asset prices. In particular, I examined how this type of political uncertainty affects the slope of the term structure of interest rates and the efficiency of forward exchange rates as predictors of future spot rates. This type of uncertainty is capable of generating a "peso problem."

(8.) This follows from backward induction starting with period T.

(9.) See p. 264 of their paper for a discussion of this point.

(10.) For [f.sub.T! to be less than or equal to one, 2q/[c.sup.2! must be less than or equal to one. Rewriting this yields q - (1/2)[c.sup.2! [is less than or equal to! 0. This simply means that the cost to the weak administration of bashing a defection in period T-1 is less than the benefit of inducing cooperation by the central bank in period T. The reason for this condition is discussed more fully in the appendix.

(11.) After the Darby Fedbashing incident, Treasury Secretary James Baker reemphasized a previous statement he had made that bashing by either side was "counterproductive." ("Treasury's Baker Reveals Agreement With Greenspan to Halt Criticism." Washington Post, Thursday, March 10, 1988.) However, as this model shows, bashing may be very productive.

REFERENCES

Alesina, Alberto. "Macroeconomic Policy in a Two-Party System as a Repeated Game." Quarterly Journal of Economics, August 1987, 651-78.

_____. "Macroeconomics and Politics." NBER Annual, 1988, 13-52.

Alesina, Alberto and G. Tabellini. "Rules and Discretion With Noncoordinated Monetary and Fiscal Policy." Economic Inquiry, October 1987, 619-30.

Backus, D. and J. Driffill. "Inflation and Reputation." American Economic Review, June 1985a, 530-38.

_____. "Rational Expectations and Policy Credibility Following a Change in Regime." Review of Economic Studies, 52(2), April 1985b, 211-21.

Barro, Robert. "Reputation in a Model of Monetary Policy with Incomplete Information." Journal of Monetary Economics, January 1986, 3-20.

Barro, Robert and David Gordon. "A Positive Theory of Monetary Policy in a Natural Rate Model." Journal of Political Economy, August 1983, 589-610.

_____. "Rules, Discretion and Reputation in a Model of Monetary Policy." Journal of Monetary Economics, July 1983, 101-22.

Fischer, Stanley. "Long Term Contracts, Rational Expectations, and the Optimal Money Supply Rule." Journal of Political Economy, February 1977, 191-206.

Gray, Jo Anna. "Wage Indexation: A Macroeconomic Approach." Journal of Monetary Economics, April 1976, 221-35.

Havrilesky, Thomas. "Monetary Policy Signaling from the Administration to the Federal Reserve." Journal of Money, Credit and Banking, February 1988, 83-101.

Kane, Edward J. "External Pressure and the Operations of the Fed," in Political Economy of International and Domestic Monetary Relations, edited by R. E. Lombra and W. E. Witte. Ames: Iowa State University Press, 1982, 211-32.

Kreps, David and Robert Wilson. "Reputation and Imperfect Information." Journal of Economic Theory, August 1982, 253-79.

Loewy, Michael. "Reaganomics and Reputation Revisited." Economic Inquiry, April 1988, 253-64.

Stein, Herbert. Presidential Economics. New York: Simon and Schuster, 1985.

Rogoff, Kenneth. "The Optimal Degree of Commitment to an Intermediate Target." Quarterly Journal of Economics, November 1985, 1169-90.

Tabellini, Guido. "Centralized Wage Setting and Monetary Policy in a Reputational Equilibrium," Journal of Money, Credit and Banking, February 1988, 102-18.

_____. "Central Bank Reputation and the Monetization of Deficits: The 1981 Italian Monetary Reform." Economic Inquiry, April 1987, 185-200.

Waller, Christopher J. "Monetary Policy Games and Central Bank Politics." Journal of Money, Credit and Banking, November 1989a, 422-31.

_____. "Monetary Politics and Asset Prices." Unpublished working paper, 1989b.

_____. "Deficit Financing and the Role of the Central Bank--A Game Theoretic Approach." Atlantic Economic Journal, July 1987, 25-32.

Weintraub, Robert. "Congressional Supervision of Monetary Policy." Journal of Monetary Economics, April 1978, 341-62.

Woolley, John T. Monetary Politics: The Federal Reserve and the Politics of Monetary Policy. Cambridge: Cambridge University Press, 1984.

I. INTRODUCTION

"We've got excess plant capacity...I don't think that growth is excessive" ..." I have not been overly concerned with inflation." (President Bush in a February 14, 1989 interview with the Wall Street Journal, p. A8.)

"With the economy running close to potential, the risks seem to be on the side of a further strengthening of price pressure." (Chairman Greenspan in testimony before Congress on February 21, 1989, reprinted from the Wall Street Journal, February 22, 1989, p. A2.)

"Many investors appeared to be confused by conflicting statements by Bush, Greenspan and other U.S. officials." Wall Street Journal, February 22, 1989, p. A1.)

"If the Fed pushes interest rates significantly higher, Bush may go public with critism." (Wall Street Journal, March 24, 1989, p. A1.)

Recent research in macroeconomic policy games by Rogoff [1985!, Alesina [1988!, Tabellini [1987! and Waller [1989a! has concentrated on the importance of an "independent" central bank in a discretionary policymaking environment. In the original work on policy games by Barro and Gordon [1983a 1983b!, no distinction was made between the monetary authority and the fiscal authority. But these researchers argue that because the fiscal authority may have incentives to create excessive inflation, giving the powers of money creation to an independent monetary authority, whose inflation preferences differ from the current fiscal authority, may enable society to reduce the equilibrium inflation rate. This results holds even though monetary policy is still chosen in a discretionary fashion. Therefore, Backus and Driffill [1985a, 537! conclude "autonomous central banks thus act as a precommitment device which may help to make noninflationary policies more credible and less costly."

Implicit in the term "independent" is the belief that the central bank is free to choose monetary policy without interference from the fiscal authority (administration). However, this is not generally the case. The appointment of central bankers by the legislative or executive branch of the government, governmental oversight of policy decisions, or political pressure on the central bank by these branches will tend to influence the setting of monetary policy and, subsequently, the extent to which the central bank is truly "independent." (1)

Kane [1984! argues that, even if it is not able to directly choose monetary policy, the current administration still may be able to achieve its preferred monetary growth path by putting pressure on the monetary authority to do its bidding. Restricting the powers of the central bank, public criticism of central bank performance (here after referred to as "bashing" (2)), exclusion from fiscal policy planning (which hurts the egos of central bankers), or undertaking actions which damage the post-central-bank income or opportunities of the central bankers are ways, he suggests, in which the administration can coerce "cooperation" from the central bank in creating excessive money growth.

Such arguments have given rise to the view that the administration is engaged in a reputation building game with the central bank. Although the central bank has control of the money supply, the administration can threaten to impose a welfare loss by bashing the central bank if it does not generate the monetary policy preferred by the administration. The success of this strategy depends on the size of the "bashing" costs imposed on the central bank and also on the extent to which these threats are credible. Credibility, in turn, depends on the benefits and costs incurred by the administration in carrying out its threats. As a result, the administration may choose to bash the central bank if it does not produce the administration's preferred money/inflation outcome. By establishing a reputation for bashing, the administration may be able to obtain its desired policy outcome in the future.

An important side effect of this type of pressure is that it creates uncertainty in the private sector about future policy actions and, thus, expected future inflation rates. Even if it is known the central bank would like to follow a low inflation policy, private agents are not sure if the central bank will maintain a low inflation policy or, because of political pressure, give in to the administration's money growth demands which will create excessive inflation. If this uncertainty leads to errors in inflation expectations, then real output will be affected. Such politically-generated uncertainty is much different from the political uncertainty that arises in partisan models of monetary policy, such as Alesina [1988! and Waller [1989a!. In these models, electoral competition between parties with differing economic objectives generates uncertainty about future economic outcomes since private agents do not know who will be elected and, as a result, which policy will be enacted. Hence, these models are basically concerned with pre-election uncertainty, whereas this paper concentrates on post-election uncertainty.

The purpose of this paper is to develop a game theoretic model of the politics of monetary policy. Using the reputation building model of Kreps and Wilson [1982!, I analyze the interactions between the central bank and the administration over the setting and monetary policy and show that cooperation by the central bank will tend to occur early in the administration's term of office and that any episodes of noncooperation occuring early in the game will be met with "bashing" by the administration. Furthermore, the model gives substance to the notion of a "strong" administration/central bank and provides an explanation of why there are periods in which the central bank appears to be cooperating with the administration, while at other times it appears to be acting independently.

Although this reputation building model has been used before by Backus and Driffill [1985a 1985b!, Barro [1986!, and Tabellini [1988! to analyze monetary policy games, this paper extends the model by including three players: the administration, the central bank, and the private sector. This extension leads to the possibility of multiple expansions of the economy, whereas in these previous papers only one expansion could occur during the tenure of a single administration. The reason for this was alluded to above: if the central bank chooses to cooperate according to a mixed strategy, private agents will use this information when forming inflation expectations. As a result, inflation expectations may differ from the actual inflation outcome. Hence, if the central bank gives in to the administration, it produces a higher-than-expected inflation rate and real output increases. Since this outcome can occur more than once, the model is able to generate multiple expansions of the economy.

The paper is structured as follows. The basic model is presented in section II. In section III the model is solved to determine the equilibrium decision rules for the administration, the central bank and the private sector. In section IV, these equilibrium decision rules are analyzed and their implications for monetary policy and the path of real output are discussed. Section V is the conclusion.

II. THE STRUCTURE OF THE GAME

The Basic Model

There are three players in the model: the private sector, the central bank, and the administration. Following Gray [1976! and Fisher [1977!, private agents are wage setters who sign nominal wage contracts prior to the start of period t based on their expectations on inflation in period t. Wage setters are concerned with minimizing employment deviations, which depend on inflation expectations errors. Given these assumptions, aggregate output and the utility function for private agents can be written as

(1) [Y.sub.t! = [y.sup.N! + ([[pi!.sub.t! - [[pi!.sup.e.sub.t!)

(2) [uw.sub.t! = - [([[pi!.sub.t! - [[pi!.sup.e.sub.t!.sup.2!

where [y.sub.t! is aggregate output, [y.sup.N! is the natural level of output, [[pi!.sub.t! is the period t inflation rate, and [[pi!.sup.e.sub.t! is the expected rate of inflation.

With regards to the policymakers, I assume that the central bank has complete control of the money supply and is able to pursue any policy it wants, and that its money growth preferences differ from the administration's. Furthermore, for independence to have any meaning, the central bank is assumed to be free to choose its monetary policy without fear of being replaced if it fails to produce the monetary growth rate desired by the administration. Although the central bank is free to follow whatever policy it wants, the administration can put pressure on the central bank to "cooperate" and produce the monetary growth rate preferred by the administration. This pressure will be referred to as "bashing," and it is only mechanism by which the administration can influence the setting of monetary policy. (3) Hence, the only policy instrument in the model is the money growth rate, and for simplicity it is assumed that the inflation rate is proportional to the money growth rate, which essentially makes it the policy instrument.

The timing of decisions in this model is as follows. Wage setters sign contracts prior to the start of the period based on the inflation rate they expect the central bank to choose in the ensuing time period. After wage contracts are signed, the central bank chooses the inflation rate (money growth rate) for the current period. In doing so, the central bank decides whether to pursue a policy consistent with its own inflation preferences or to "cooperate" and choose an inflation rate preferred by the administration. Once the policy is enacted, the administration decides whether or not to bash the central bank. This sequence of actions is then repeated in the next period.

This decision making sequence implies that bashing by the administration can only influence future inflation rates and not the current inflation rate. As a result, the administration's decision to bash involves building a reputation for bashing in order to deter future defections by the central bank. Bashing imposes a welfare loss on the central bank this period, and the possibility of incurring this again may deter the central bank from defectng next period. But bashing can also create external costs or benefits for the administration in addition to any benefits that result from reputation building.

The reasons why bashing imposes costs on the central bank were described in the introduction. But what are the exogenous costs or benefits incurred by the administration? Bashing may be costly if public criticism by the administration of the central bank's policies creates a perception of internal dissent, which may damage its relationships with other agencies within the government. Furthermore, if the central bank has developed a base of support from the financial sector, the administration may subject itself to a loss of contributions or intense lobbying pressure by supporters of the central bank. In addition, the central bank may respond by publicly criticizing the administration's fiscal policy (although a strategic decision by the central bank to do this will not be considered here). (4)

Bashing noncooperative behavior by the central bank can also be beneficial. The administration may simply bash as a matter of principle. A more important reason is that if the administration is involved in power games with other agencies within the government, it may choose to bash noncooperative acts by the central bank to set an example for other agencies. However, bashing the central bank when it cooperates will be counterproductive and produce a welfare loss rather than a welfare gain. (5) The key point is that bashing by the administration, on net, can produce costs or benefits in addition to any reputation benefits it achieves. Whether bashing produces a net benefit or a net cost depends on the characteristics of the current administration.

The Policymakers' Objectives

The loss functions for the administration and the monetary authority are

(3) [Mathetematical Expression Omitted!

(3b) [Mathematical Expression Omitted!

where the subscript A denotes the administration and the subscript M denotes the monetary authority.

Equation (3) is a time-separable, intertemporal loss function which is common to both authorities. Equation (3a) is the one-period loss function for the administration. The administration suffers as welfare loss from deviations of inflation from its desired rate, c, which is greater than zero and reflects its desired rate of seigniorage. Equation (3b) is the one-period loss function for the central bank. The central bank is much more "conservarive" in that it prefers to maintain price stability and is thus not concerned with creating seigniorage for the administration. (6) The functions [phi![(B.sub.t'n)! and K[(B.sub.t)! represent, respectively, the costs of bashing by the administration and the loss to the central bank from being bashed. These will be discussed in more detail below. Finally, the time horizon for this game, T, is envisioned to be the lenght of the current administrations's term of office.

Preferred Inflation Rate Policies and

Expectation Formation

In an environment free of political pressure, the central bank will choose an inflation rate that minimizez the loss function (3b). This inflation rate is the central bank's preferred policy choice and is given by

(4) [Mathematical Expression Omitted!

On the other hand, if the administration controls the inflation rate, or the central bank adopts the inflation rate policy preferred by the administration, it will choose [[pi!.sub.t! such that (3a) is minimized. The administration's preferred inflation rate is given by

(5) [Mathematical Expression Omitted!

The administration's inflation rate choice reflects its desired level of seigniorage, c.

However, in a political environment the central bank must decide whether to cooperate with the administration or act independently (defect). If the central bank chooses not to cooporate (defects), it sets the inflation rate according to equation (4) and runs the risk of being bashed by the administration. If it cooporates, it sets the inflation rate according to equation (5), which gives the administration what it wants, thereby allowing the central bank to avoid the costs of being bashed. For convenience, I characterize the central bank's decision to cooparate as a mixed strategy. Consequently, define [f.sub.t! as the probability that the central bank cooperates with the administration in perio t by setting the inflation rate according to equation (5).

Given the central bank's cooperation straregy, wage setters from their inflation expectations according to

(6) [Mathematical Expression Omitted!

From (6) we can see that, for 0 [f.sub.t! [is less than! 1, there is uncertainty on the part of the private sector regarding the inflation outcome in period t. As a result, there will be an expansion of the economy if the central bank does cooperate. If not, then a contraction will occur. Furthermore, announcements by the central bank that it will follow a low inflation rate policy in the coming period will not be believed. [7!

Bashing Costs

If the central bank chooses not to cooperate with the administration it runs the risk of being bashed, which creates a welfare loss for the central bank. This welfare loss is captured by the fucntion K[(B.sub.t)!, where [B.sub.t! is an indicator function set equal to zero if the administration does not bash the central bank's policy choice and equal to one if bashing occurs. Hence, 5(0)=0 and K(1)= [k is greater than 0.!

As was mentioned above, bashing can generate benefits or costs unrelated to reputation effects, and these costs or benefits can vary from one type of administration to another. Let [phi![(B.sub.t'n)! represent the exogenous bashing cost or benefit to an administration of type n. For simplicity, suppose there are two types of administrations, a strong administration (n=s) and a weak adminstration (n=w). A strong administration receives a net welfare gain by bashing noncooperative behavior by the central bank, whereas a week administration receives a net welfare loss. However, both types of administrations receive a net welfare loss from bashing cooperative behavior. Thus, if the central bank cooperates, [phi!(1,n) = Q 0 for each type of administration. If the central bank does not cooperate, then [phi!(1,s) = -q

0 and [phi!(1,w) = q 0, where q is the cost of bashing and negative q is a benefit received from bashing. The paramater q will be assumed to the constant, which reflects the implicit assumption that the intensity of bashing is constant. Finally, if no bashing occurs, [phi!(0,n) = 0.

The period t loss matrix for the administration is

Since bashing cannot affect the period t inflation outcome, the weak administration minimizes period t losses by choosing not to bash regardless of whether the central bank cooperates or not. The strong administration minimizes period t losses by choosing to bash only if a defection occurs.

Given these bashing decisions by the two types of administrations, the central bank's losses in period t will be

The cental bank will never choose to cooperate with a weak administration since its threats to bash are not credible. As a result, reputation building by the weak administration can not occur. (8) Furthermore, if the cost of defection, k, is less than the loss from cooperating, (1/2)[sup.2!, the central bank would never cooperate with a strong administration and a zero inflation rate would prevail in all periods of the game. In this case, the central bank is "strong" since it is never influenced by threats of bashing by the administration. For bashing to have any chance of succeeding, it must be the case that

K (1/2)[c.sup.2!. This will be assumed for the remainder of the paper.

Central Bank Uncertainty and Beliefs

If the central bank knew the administration's type with perfect certainty, then we would observe either complete cooperation or noncooperation by the central bank. While these extreme cases are of some interest, a more interesting (and plausible) world is one in which there is some uncertainty regarding the administration's type.

One way of incorporating uncertainty is to assume that at the beginning of the game a new administration is elected and the central bank does not know this new administration's type. The only way for the central bank to infer the administration's type is to act independently and see if the administration responds by bashing. Given this assumption, a weak administration now can pose as a strong administration by bashing the central bank when it acts noncooperatively. This leads the central bank to believe it is dealing with a strong administration, thereby influencing future decisions to cooperate with the administration. Thus, in this world, the weak administration can engage in reputation building.

However, simply bashing a defection is not enough to convince the central bank that it is dealing with a strong administration since it is aware of the weak administration's incentive to act strong. As was done for the central bank, the weak administration's decision to bash is modelled as a mixed strategy. Let [g.sub.t! be the probability that a weak administration bashes a defection by the central bank. By construction, a strong administration bashes a defection with probability one.

When deciding whether or not to cooperate with the administration in period t, the central bank must determine the probability that it is dealing with a strong administration. This probability estimate measures the administration's reputation. The central bank updates its probability estimate that it is dealing with a strong administration according to Bayes' rule:

(7) [Mathematical Expression Omitted!

Since a strong administration always bashes a defection, if previous episodes of noncooperation by the central bank were not bashed, then the administration reveals itself as weak and [p.sub.t!=0. If the central bank cooperates in period t-1, then nothing new is learned and [p.sub.t!=[p.sub.t-1!. At the start of the game, the central bank has an initial prior (determined by nature) [p.sub.1! of dealing with a strong administration.

III. SOLUTION OF THE MODEL

Once reputation building is introduced, the model becomes dynamic. Since a strong administration always bashes a defection, the analysis below will concentrate on the bashing strategy of the weak administration. In period t, the weak administration and the central bank choose [g.sub.t! and [f.sub.t! to minimize expected intertemporal losses, given by

(8) [Mathematical Expression Omitted!

(9) [Mathematical Expression Omitted!

where [h.sub.t! equals one if the central bank cooperates in period t, and equals zero if the central bank defects. From (8), the central bank's decision to cooperate depends on the administration's reputation at time t as well as the weak administration's strategy for acting in period t. The term [p.sub.t! + (1-[p.sub.t!)[g.sub.t! is the central bank's probability estimate that a period t defection will be met with bashing.

From equation (9) we see that if the central bank cooperates, then the weak administration does not bash and the game proceeds to stage t+1. [Z.sub.A+1! is the value of the inter-temporal loss function at time t+1 given that the administration's true type is not revealed prior to t+1.

If [h.sub.t!=0, the weak administration must decide whether or not to bash the defection. In doing so, it compares the benefit of maintaining or improving its reputation versus the cost of revealing its true type. This benefit/cost tradeoff is measured by the square/bracket term in (9). If it bashes the defection, the weak administration incurs the bashing cost q but does not reveal its type. Bashing this period affects the central bank's probability estimate that the administration is strong, and thus its decision to cooperate in period t+1. This, in turn, affects the weak administration's period t+1 losses. If the administration does not bash the defection this period, it avoids the bashing cost q but, revealing its true type, it suffers the loss (1/2)[c.sub.2! for the remainder of the game.

Period T Strategies

The strategies for the weak administration and the central bank are determined by solving the game backwards from period T. At time T it is easy to see that, regardless of its reputation doing into period T, the weak administration will never bash a defection since there are no reputation benefits to be reaped by doing so. Hence [g.sub.T!=0, and from equation (8) [f.sub.T! becomes

(10) [Mathematical Expression Omitted!

The central bank will decide to cooperate in the last period if the probability that the administration is strong is sufficient large. As a result, announcements by the central nbank that it will follow a low inflation rate policy in the coming period will not be credible. This occurs in spite of the fact that the central bank is technically independent. Alternatively, if the administration's reputation is not sufficiently high, the central bank asserts its independence and sets the inflation rate equal to zero. The necessary reputation for the central bank to cooperate in period T is a function of the central bank's loss from cooperation, (1/2)[c.sub.2!, relative to the loss from being bashed, k. If bashing is relatively costly, then a smaller reputation is needed to induce cooperation by the central bank in the past period, and vice versa.

For the case in which [c.sub.2!/2k=[P.sub.T!, it would appear that any value of [f.sub.T! is consistent with loss minimization for the central bank. This freedom to define the strategy is characteristic of the Kreps-Wilson [1982! model. (9) As shown in the appendix, dynamic consistency requires 2q/[c.sub.2! [is less than or equal to! [f.sub.t! [is less than or equal to! 1 but does not lead to a unique expression for [f.sub.t!. (10) As long as [f.sub.t' is less than one, the central bank will randomize its decision to

cooperate with the administration. This implies that tehre is private sector uncertainty regarding the inflation outcome in period t and inflation expectations will be between zero and c. Since there is anecdotal evidence that the presence of administrative pressure leaves the private sector unsure of the monetary policy outcome, I will assume that the central bank sets f = 2q/[c.sup.2! when [c.sup.2!/2k = [p.sub.T!.

Given this assumption, if the central bank cooperates with the administration in period T, it sets the inflation rate equal to c. Since this is greater than expected, an expansion of output occurs. If the central bank acts independently and sets the inflation rate equal to zero, then expected inflation is too high and a recession occurs in the last period. Thus, political interference in the money creation process can create uncertainty about policy outcomes, thereby reducing the credibility of central bank policy announcements, which can cause undesired fluctuations in real output.

The period T looses for the weak administration and the central bank are

(11) [Mathematical Expression Omitted!

(12) [Mathematical Expression Omitted!

If [P.sub.T! = 0, the weak administration's payoff is (1/2)[c.sup.2!.

Period T-1 Strategies

As shown in the appendix, equations (8), (9), (10), (11) and (12) lead to the following bashing and cooperation strategies in period T-1:

(13) [Mathematical Expression Omitted!

(14) [Mathematical Expression Omitted!

The first line of equation (13) shows that if its reputation is sufficiently large, the weak administration will choose to maintain its reputation by bashing a defection with probability one. From Bayes' rule, this implies that [Mathematical Expressions Omitted! which means, by equation (10), that the central bank will cooperate in period T with probability one if this condition holds as a strict inequality. If it holds with equality, the central bank cooperates in period T with probability [f.sub.T! = 2q/[c.sup.2!. In either case, the weak administration reduces its period T losses by at least q if it bashes a defection in period T-1.

The second line of equation (13) shows that if the administration's T-1 reputation is such that setting [g.sub.T-1! = 1 generates a period T reputation that is insufficient to induce cooperation in the last period, then it will randomize its decision to bash the central bank if a defection occurs in period T-1. If it bashes the defection, its period T reputation rises enough to get the central bank to randomize its decision to cooperate in period T. Thus, bashing is beneficial since it increases the likelihood of cooperation next period. (11) If it does not bash the defection, it reveals itself as weak and the central bank defects with probability one in the last period.

The key point of equation (13) is that as long as its reputation is not zero, the weak administration will bash with some positive probability in period T-1 if a defection occurs. As a result, a smaller reputation is needed in period T-1, relative to period T, in order to induce the central bank to cooperate. Thus, comparing (13) and (14), for [Mathematical Expression Omitted!, even though there is a small probability that, if tested, a weak administration would reveal itself, the central bank decides to avoid the bashing cost by cooperating.

IV. EQUILIBRIUM STRATEGIES AND

IMPLICATIONS

The period t decision rules for the weak administration, the central bank and private agents are

(15) [Mathematical Expression Omitted!

(16) [Mathematical Expression Omitted!

(17) [Mathematical Expression Omitted!

for t=1,2,...,T-1.

Inspection of equation (15) reveals that, for a sufficiently long time horizon, in the early periods of the administration's term a relatively small reputation for being strong will be enough to induce the central bank to cooperate. This "spirit of cooperation" between the administration and the central bank could be characterized as a "honeymoon" effect that frequently occurs when there is a leadership change in a bureaucracy. However, as the game proceeds, a larger reputation for being strong is required to keep the central bank from defecting. This is because the central bank knows that, as the administration's term draws to a close, a weak administration has fewer and fewer incentives to masquerade as a strong administration by bashing defections. Eventually, a weak administration will start to randomize its decision to bash a defection by the central bank. It ie actually does bash a defection, then its reputation increases otherwise, it reveals itself as being weak and the zero inflation outcome prevails from there on.

As the weak administration's incentive to bash a defection decreases, the central bank starts to randomize its decision to cooperate. Once the central bank starts to do this there will be fluctuations in aggregate output. Whenever the central bank randomizes its decision to cooperate, wage setters expect an inflation rate between zero and c to prevail in the forthcoming period. If the central bank cooperates, actual inflation exceeds expected and real output expands. Non-cooperation leads to unexpectedly low inflation and a recession occurs. A key result of this model is that more than one expansion can occur over the course of this game, whereas in previous research using the Kreps-Wilson [1982! model only one expansion could occur. Thus, this model is able to produce output paths which more closely resemble a stochastic business cycle.

Although it is possible to have multiple expansions during this game, it is not possible to have back-to-back expansions. Basically, if the administration's reputation is just sufficient to induce the central bank to randomize in period t and cooperation results (expansion occurs), then no new information is obtained concerning the administration's type and [p.sub.t+1! = [p.sub.t!. Since an increased reputation is required in t+1 to induce the central bank to randomize once again, it necessarily follows that an expansion will be followed by a defection (zero inflation) by the central bank. Since private agents are aware of the central bank's cooperation strategy, they anticipate this defection (zero inflation) in the next period, and so there are no inflation surprises and output is stable. Consequently, expansions cannot be back-to-back.

On the other hand, a recession can be followed by either a recession or an expansion. Given that the central bank randomizes its inflation decision, expectations will be between zero and c. If the central bank actually defects, then a recession occurs. If the administration bashes this defection, then its reputation increases enough going into the next period to induce the central bank to randomize once again, and subsequently a recession or expansion can occur in the period following a recession.

A key feature of central bank's equilibrium strategy is that it is characterized by periodic episodes of cooperation and defection. If one views these defections as the central bank asserting its independence, then the model provides a well-defined notion of an independent central bank. Hence, this model is able to explain why the central bank often appears to be in "cahoots" with the administration and why, at other times, it appears to be acting independently by ignoring the administration's policy wishes.

As was mentioned in the introduction, Backus and Driffill [1985A! assert that the existence of an independent central bank would lead to a lower equilibrium inflation rate. Their assertion will most likely be supported in this model when (1) the central bank is strong (a small value of k), (2)the costs to the weak administration from bashing the central bank are large (large value of q), and (3) the initial probability that the administration is strong is very small. If these conditions are reversed then the central bank will appear to be nothing more than a monetary "puppet" for the administration.

It is interesting to note that the central bank's decision to cooperate is inversely related to the administration's preferred inflation rate. Consequently, the larger is the administration's desire for inflation, the larger the administration's reputation must be to induce cooperation by the central bank. This suggests that, in a multiple-party political system, we should observe varying degrees of cooperation between the central bank and the administration depending on which party is in power. As a result, in order to build a sufficient reputation for being strong, a liberal inflation party will have to make more threats and carry them out more often than an administration whose inflationary preferences are more conservative. This would appear to be an empirically testable hypothesis and may be an avenue for further research.

V. CONCLUSION

This paper has used recent developments in game theory to construct a model of monetary policy politics. Whereas many previous monetary policy game models have relied on the assumption that the central bank is indistinguishable from the administration, this paper incorporates a central bank that is technically independent but not immune to political influence. This has produced a framework that appears to be very rich in explaining the relationship between the administration and the central bank, and what it means to have an "independent" central bank.

APPENDIX

T-1 Strategies: Reputation Building

Given that all defections by the central bank prior to period T-1 have been bashed, the weak administration chooses [q.sub.T.-1! to minize

(A1) [Mathematical Expression Omitted!

If [p.sub.T! [c.sup.2!/2k, then the bracketed term in the last line of equation (A1) becomes q - [(1/2)c.sup.2!. If this term is positive, the bashing costs this period outweigh the cooperation benefits next period. Hence, the administration would never engage in bashing. Hence, it is assumed to be negative, and, as a result, a weak administration will play [q.sub.T-1! " 1.

If [p.sub.T! is less than [c.sup.2/2k then the bracketed term in the last line of equation term is equal to q. The weak administration could set [g.sub.T-1! = 0 thereby revealing itself as weak. This allows the weak administration to avoid incurring the bashing costs this period, but it gives up any change of increasing its reputation going into the last period.

However, if the weak administration exploits the central bank's use of Bayes' rule for updating its probability estimate of playing against a strong administration, it can choose [g.sub.T-1! such that it increases its reputation going into the last period. This is accomplished by setting

(A2) [Mathematical Expression Omitted! which is between zero and one for [p.sub.T-1! [c.sup.2'/2k. If [p.sub.T-1! = [c.sup.2!/2k, then (A2), [g.sub.T-1! = 1. In order for this to be loss minimizing behavior, and thus dynamically consistent, the bracketed term in the last line of equation (A1) must be less than or equal to zero, or q - [f.sub.T.(1/2)c.sup.2! [is less than or equal to! 0. This expression will be negative for all values of [f.sub.T' between one and 2q/[c.sup.2!. Setting [f.sub.t! = 2q/[c.sup.2! yields the central bank strategy given in equation (10). If a defection occurs in period T-1, randomizing the decision to bash according to (A2) allows the weak administratio to raise its reputation, if it actually bashes the defection, just enough to ensure that [p.sub.T! = [c.sup.2!/2k, thereby lowering expected period T losses by q. Equation (13) follows from this analysis.

In period T-1, the central bank will minimize

(A3) [Mathematical Expression Omitted!

Given the weak administration's strategy for

T-1, if [p.sub.t! [c.sup.2/2k then [q.sub.T-1! = 1 and [p.sub.T! = [p.sub.T-1!

[c.sup.202k. From this it follows that the bracketed term in the last line of equation (A3) is negative, so [f.sub.T-1! = 1. If [p.sub.T! [c.sup.2/2k then the weak administration sets [g.sub.T-1! according to equation (A3). Use of (A3) in (A2) yields equation (14).

(*1) Assistant Professor of Economics, Indiana University-Bloomington. I would like to thank Roy Gardner, Richard Sweeney and two anonymous referees for their comments on this paper.

(1.) Havrilesky [1988!, Stein [1985!, Weintraub [1978! and Woolley [1984! provide discussions and evidence concerning the impact of political pressure on the Fed.

(2.) In this paper, bashing will refer to political pressure put on the central bank by the administration. This notion is consistent with the press's use of the phrase but does not correspond to Kane's use of the term in explaining the "scapegoat hypothesis" of central bank behavior.

(3.) This model differs from previous models of games between the monetary authority and the fiscal authority considered by Waller [1987!, Tabellini [1987!, Alesina and Tabellini [1987!, and Loewy [1988!. In these papers, the monetary authority is concerned with the size of the deficit or variables that are affected by the deficit such as the interest rate or the level of the national debt. Thus, the fiscal authority can induce the monetary authority to create more seigniorage by increasing the size of the deficit. In this paper it is assumed that either there is a balanced budget net of seigniorage or the monetary authority is not concerned with variables that are a function of the government's deficit. Hence, the only "tool" the fiscal authority has to influence monetary policy is political pressure.

(4.) In a recent, well-publicized incident of Fed-bashing, Assistant Treasury Secretary Michael Darby sent a letter criticizing recent Fed policy to the Board prior to a policy meeting. This letter was met by "threats" by Alan Greenspan concerning future economic policy or by counter-bashing the administration's fiscal policy. Furthermore, Senator Proxmire also criticized this action by the Treasury. This anecdotal evidence suggests that bashing by the administration is not costless. (See "Treasury's Baker Reveals Agreement With Greenspan to Halt Criticism," Washington Post, Thursday, March 10, 1988. Also see, "Baker Says Fed, Administration Need to Consult," Wall Street Journal, p. 52, Thursday, March 10, 1988.)

(5.) If the administration bashes regardless of whether the central bank cooperates or not, then the central bank gains nothing by cooperating and so it would not cooperate. Hence, bashing cooperative behavior is counterproductive.

(6.) In many macroeconomic policy game models, the policymaker also attempts to exploit an inflation/output tradeoff by creating unexpected inflation. This could be incorporated into the administration's loss function, thereby capturing a common belief that the administration cares more about output than the monetary authority. This would be one explanation why the administration is willing to accept a higher inflation rate. However, since rational agents are aware of this incentive to inflate, they adjust expectations to compensate for it and the end result is an inflation bias with no output gain. Consequently, the administration would be happy to let the monetary authority choose a lower inflation rate in order to avoid this inflation bias. The real source of conflict between the two authorities is the optimal amount of seigniorage, and thus the output term is ignored for notational convenience.

(7.) This paper concentrates on the output effects of politically induced policy uncertainty. However, political disputes between the administration and the central bank may be more important to financial market participants than to labor market participants. Consequently, in my [1989b! paper, I examined how this type of uncertainty affects shortterm asset prices. In particular, I examined how this type of political uncertainty affects the slope of the term structure of interest rates and the efficiency of forward exchange rates as predictors of future spot rates. This type of uncertainty is capable of generating a "peso problem."

(8.) This follows from backward induction starting with period T.

(9.) See p. 264 of their paper for a discussion of this point.

(10.) For [f.sub.T! to be less than or equal to one, 2q/[c.sup.2! must be less than or equal to one. Rewriting this yields q - (1/2)[c.sup.2! [is less than or equal to! 0. This simply means that the cost to the weak administration of bashing a defection in period T-1 is less than the benefit of inducing cooperation by the central bank in period T. The reason for this condition is discussed more fully in the appendix.

(11.) After the Darby Fedbashing incident, Treasury Secretary James Baker reemphasized a previous statement he had made that bashing by either side was "counterproductive." ("Treasury's Baker Reveals Agreement With Greenspan to Halt Criticism." Washington Post, Thursday, March 10, 1988.) However, as this model shows, bashing may be very productive.

REFERENCES

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Tabellini, Guido. "Centralized Wage Setting and Monetary Policy in a Reputational Equilibrium," Journal of Money, Credit and Banking, February 1988, 102-18.

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Title Annotation: | political intervention in central banking |
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Author: | Waller, Christopher J. |

Publication: | Economic Inquiry |

Date: | Jan 1, 1991 |

Words: | 7077 |

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