Central Banking as a Political Principal-Agent Problem

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CENTRAL BANKING AS A POLITICAL PRINCIPAL-AGENT PROBLEM MICHELE FRATIANNI, JORGEN VON HAGEN,

and CHRISTOPHER WALLER’

Due to their ties with elected leaders, central bankers may pursue policies that are not in society S best interests. Consequently, the relationship between the public and the central bank can be characterized as a principal-agent problem. An inflation and stabilization bias arise as a result of this agency problem and the magnitudes of these biases depend on the political environment. Various institutional proposals for eliminating these biases are examined, and wefind that central bank independence and performance contracts work best. However, we argue that central bank independence is preferable for resolving the agency problem. (JEL E3 1, E32, E58)

I. INTRODUCTION

Conventional wisdom holds that during election periods political leaders have incentives to misuse policy instruments to enhance their chances of reelection. Rogoff and Sibert [ 19881 construct a rational political economy model of monetary policy based on this theme.’ The results of their model can be interpreted in the following way.2 Society elects

* We are indebted for comments and suggestions received from Tom Willett, anonymous referees, Carl Walsh, Roy Gardner, Susanne Lohmann, Kevin Grier, Guido Tabellini, Roger Waud and seminar participants at the University of California-Santa Cruz, University of Oregon, Stanford Business School and Purdue University. All errors are our own. Frutianni: Professor, Indiana University Graduate School of Business, Bloomington, and Catholic University of Louvain, Phone 1-812-855-8679, Fax 1-812-855-3354 E-mail [email protected] von Hugen: Professor, University of Mannheim, Germany 68 131 and Indiana University Graduate School of Business and CEPR, Bloomington, Phone 49-228-739199 Fax 49-228-739199 E-mail [email protected] Wuller: Associate Professor, Department of Economics, Indiana University, Bloomington Phone 1-812-855-8453, Fax 1-812-855-3736 E-mail [email protected] 1. The incentive for political manipulation of the money supply is an old idea and recent research in this area has focused on incorporating rational decision making by private agents. While we focus on a rational expectationshmperfect information approach here, others have focused on the concept of “rational ignorance” to explain how rational agents can be “fooled” into attributing policy-induced output gains to the competence of the incumbent administration. 2. Their interpretation is somewhat different but the basic idea is the same in both cases. See Rogoff [I9901 for another variation on this same theme.

a leader every other period whose competence affects the level of output in the economy and private agents will tend to vote for the incumbent if the level of output is expected to be higher than that which can be provided by an unknown challenger. Voters have imperfect information regarding the politician’s true impact on output and exogenous shocks to output and consequently cannot disentangle the effects of one from the other. In an election period, this asymmetry of information gives the incumbent an incentive ‘to expand output through the use of inflationary monetary policy in order to appear more competent than he really is. However, rational voters are aware of this incentive to inflate and adjust their expectations such that, in equilibrium, no gain in output occurs and the economy suffers from excessive inflation. An implication of the Rogoff-Sibert model is that, unless a society does away with elections as a way to choose policymakers, excessive inflation and a political inflation cycle will be an unavoidable cost of democracy. However, societies can try, and have tried, to avoid these ill-effects by taking the power of money creation away from the elected officials and giving it to an appointed “independent” central banker who will presumably pursue the public good. But can this approach actually work? The problem with this proposal is that the central bankers’ well-being in many respects-reappointment, post-central bank employment opportunities, avoidance of public criticism, etc.-often hinges on pleasing their political benefactors, giving the central bankers incentives to act in the interest of

378 Economic Inquiry (ISSN 0095-2583) Vol. XXXV, April 1997, 378-393

BWestern Economic Association International

FRATIANNI, von HAGEN & WALLER: CENTRAL BANKING

elected official^.^ As a result, the central banker could pursue objectives different from society’s and may actually function as a “veil” for the elected policymaker. In the real world, this veil is not complete but partial and, hence, we can characterize the relationship between the monetary authority and society as a principal-agent problem. The advantage of delegating power to an appointed central banker and then erecting appropriate institutions is that the inflation problems may be resolved without abandoning the electoral process. In this paper we develop a rational political business cycle model that starts from the foundations laid down by Rogoff and Sibert. We depart from their model by having monetary policy delegated to a central banker who is appointed by the elected leader. The concern about reappointment is what motivates the agency problem-the central banker would like to be reappointed and this desire leads her to partially accommodate the wishes of the current administration which, in turn, may not coincide with the desires of the electorate. We then analyze the problem faced by a central banker who is concerned about her own selfinterest as well as social well-being. It is this feature that turns the setting of monetary policy into a political principal-agent problem. The contributions of our approach to modelling the agency problem of central banking are (1) it explicitly incorporates reappointment concerns into the decision process of the central banker, which heretofore has not been done in the literature, and (2) we explicitly model the source of the agency problem, unlike previous research that simply assumes an agency problem exists. Our key results are as follows. In equilibrium, the pursuit of her own self-interest leads the central banker to create a socially inefficient inflation bias. While Rogoff and Sibert also obtain this result, our explicit functionalform model allows us to analyze this bias in more detail and tie it directly to the strength of the relationship between the central banker and the current administration. The advantage of our model is that it allows us to investigate 3. It has been argued that “bashing” the central bank by blaming them for “bad” outcomes or to influence the central bank to pursue policies desired by the Administration and Congress creates costs for the central bank. See Kane 119881 and Waller [1991].

379

how particular institutional structures aimed at making the central bank “independent” affect the magnitude of this inflationary bias and how our results relate to the empirical findings of Alesina and Summers [ 19931, AlMarhubi and Willett [19951 and many others. It also allows us to see how modelling the source of the agency problem affects the implementation of a variety of monetary institutions ranging from the “simple” policy rules analyzed by Lohmann [ 19921 to the adoption of central bank “performance contracts” of the type studied by Walsh [1995a; 1995bl and Persson and Tabellini [1993]. In addition to the inflationary bias, we also derive a new result which shows that the central banker will also create a stabilization bias. The stabilization bias reflects the election-risk preferences of the incumbent administration. An incumbent with a strong chance of reelection is more risk averse to output shocks than is an incumbent with a weak chance of reelection. In short, a strong incumbent has more to lose and less to gain from output shocks. In equilibrium, these attitudes towards electoral risk influence the central banker’s decision to stabilize shocks. From this analysis we conclude that both the independence and performance contract approach are effective in eliminating the inflation and stabilization biases. We show that an interesting insight regarding the performance contract approach is that society may actually be made better off by appointing a central banker who is motivated purely by self-interest as opposed to one who partly worries about social welfare. However, we argue that, due to the source of the agency problem, central bank performance contracts will be very difficult to implement in practice. Consequently, we advocate the approach of making the central banker personally independent of the current administration as the ideal way of dealing with the inflation and stabilization biases that arise. In the end, the most appealing aspect of the work in this paper is the insight that excessive inflation and political inflation cycles need not be an inevitable consequence of representative democracy. As is often the case, effective institution building can often reduce the costs of socially desirable activities. Monetary policy appears to be no exception.

380

ECONOMIC INQUIRY

After deriving the basic results in section 11, we explore in section I11 various institutional arrangements proposed to resolve this principal-agent problem, including simple monetary rules, the appointment of “conservative” central bankers, central bank independence, and optimal incentive contracts for the central bankers, and discuss their advantages and disadvantages. Section IV closes with a summary and some conclusions.

But transactions costs and costs of collective decision making are involved in the wage setting process, and so nominal wage contracts are written fixing the nominal wage for a period. While this saves contracting and coordination costs, it generates undesired fluctuations in employment and output from shocks once contracts are signed. We describe the public’s interest in price and output stability by the following preference function:

II. THEMODEL

The Structure of the Economy Consider the following, log-linear model of monetary policymaking: (1)

Y,=

~ +f (nt - ~3+ ur, Y: =fl + UY,

nt=g+ ($5)

(x, - g

+Vt-

(2)

US =y: - (’/?)0.;-yf)’ - (b / 2)~:.

Society benefits from a higher level of fillinformation output but suffers from variability around that level of output. Inflation is assumed to impose costs on society as does variability of inflation around the socially optimal level, which is set to zero for convenience.

UJ,

where yt is real output, nt the rate of inflation, ne the expected inflation rate, v, an aggregate demand shock, U, an aggregate supply shock, xt the money growth rate, and xy its expectation. The aggregate demand and supply shocks are serially uncorrelated. All expectations are formed rationally on the basis of information available at the end of the previous period. Labor markets in this economy are characterized by Gray [ 1976EFischer [ 19771 type one-period nominal wage contracts; therefore, output rises with an unexpected increase in inflation. The variable y* is the fillinformation level of output that would prevail in the absence of wage contracts and fl is the “natural” level of output in period t. We assume that the monetary authority selects a monetary growth rate after private sector inflation expectations have been formed; therefore, it has the ability to create temporary deviations of output through inflation surprises. Furthermore, the authority observes the current shocks before setting policy, which allows it to undertake stabilization policies even though expectations are formed rationally. The Publicb Preferences. In a perfect, frictionless world, nominal wages would be set instantaneously in a spot labor market and fully reflect any exogenous shocks to the economy. No policymaker would be needed.

The Political Environment The Leader’s Competence. In this model, a leader is elected every other period to carry out a specified set of duties, one of which could be determining monetary policy. The leader’s competence is assumed to affect the level of output and inflation in the economy. This is because more efficient governance smooths the operation of private markets and leads to more efficient use of society’s resources. We model this competence as a “supply shock” that affects the aggregate production function. The leader’s competence is assumed to be a random variable that displays some degree of persistence. Thus, yesterday’s observed realization of the leader’s competence shock provides a signal of what his competence level will be today. We model competence as an MA(1) process: (3 )

%=‘%+%-I,

where E , is today’s level of competence and q, is today’s innovation to the leader’s competence, assumed to be a zero mean i.i.d. random variable with variance $, and qt-, is yesterday’s innovation to competence. As in Rogoff and Sibert, we assume that the current innovation to competence, qr is not observable by the public until next period. All they know about the leader’s competence level today is that qt-l carries over to today. Given

FRATIANNI, von HAGEN & WALLER: CENTRAL BANKING

these assumptions, we can further specify the natural rate of output and the supply shock of equation (1) as (4)

Y: =Y” + tlt-1,

ut= %+ PP

where y” is a constant and pr is an i.i.d., exogenous, transitory supply shock with mean zero and variance 0”p.

The Leader’s Preference Function. T h e elected policymaker wants to maximize T

(5)

UGt = Et [

C (k+ ust+j)l, j=O

where k is the payoff from holding office and T is an arbitrary finite time horizon assumed to be sufficiently long (greater than two periods). Discounting is ignored for parsimony. According to this preference function, the policymaker benefits from being in office and enjoys the same macroeconomic benefits from being a citizen as everyone else. Voting Behavior. In an election period t , the median voter will vote for the incumbent if his welfare is expected to be higher in the next two periods with the incumbent in office as opposed to an unknown challenger, or if

(6)

E (US:+* +

w+,I

YtY %I)

+

v

where Z denotes welfare if the incumbent is returned to office and C denotes welfare if the challenger is elected to office. The parameter denotes all information dated t-1 or earlier available to voters in period t . The term A? measures the income-equivalent payoff to the median voter of non-economic factors from reelecting the incumbent. This term reflects things like “look~,’~ philosophy, family values, etc. which matter to the voter but are unrelated to economic perfo~mance.~ Agents observe the level of output but not the inflation rate before voting. This assump4. From (6),voters are rational in their voting behavior and are “forward” looking. However, due to imperfect information and persistence of the competence shocks, it will be rational to look “backwards” at current and past output when voting. Thus, retrospective voting is rational in this model.

381

tion is also made by Rogoff and Sibert and is a fundamental assumption in most political business cycle model^.^ The observation of output is important because it provides a noisy signal about the incumbent’s competence. But without observing inflation, voters cannot break down output into the current competence innovation, the current supply shock, or monetary surprises. If inflation were known, then voters could use the observations of output and inflation to break output down into the sum of real shocks and nominal shocks. Hence, while voters could not distinguish the shock to output from the competence shock, they would not confuse monetary surprises with competence shocks. The timing of events in our model is as follows: 1. At the start of period r, last period’s shocks and inflation are observed by the public, expectations are formed and contracts are signed. 2. The shocks vt, qt, and pt hit the economy. 3. The non-economic payoff from reelecting the incumbent, At, is observed. 4. Monetary policy is determined. 5. Output is observed by voters. 6. Elections are held at t, t + 2 , etc. While the value of current output provides a signal about the incumbent’s expected competence level, it provides no information about the challenger’s expected competence, which is zero by assumption. Since output and inflation deviations in t + 1 and t + 2 only depend on time t + 1 and t + 2 policy and transitory innovations, and all potential leaders have the same preferences, the only difference between the incumbent and the challenger is the expected level of future output and non-economic payoffs, yal and A;“. Thus, the median voter votes for the incumbent if

5. It is also consistent with the empirical result that money generates inflation but with a substantial lag.

ECONOMIC INQUIRY

382

where p is the signal extraction parameter and .’,is the variance of inflatiom6 The parameter hy, representing the noneconomic factors that appeal to voters, is a random variable unknown to the incumbent or the challenger. However, through polling, all contestants can obtain an unbiased estimate of hy. Let this estimate be such that

The probability that the median voter votes for the incumbent, p g p is then

From (10) we can see that, for p > 0, if the incumbent can get output to increase above its natural level through the use of monetary surprises, he can increase the probability that he gets reelected. This occurs because the median voter attributes some part of this increase in output to an increase in the competence of the incumbent, which is expected to carry over to the period after the election as well. However, the larger is the variance of inflation, the less likely voters are to attribute a monetary-induced rise in output to a positive competence shock. Hence, significant monetary instability will be detrimental to the incumbent’s reelection. For analytical convenience, we assume that pf has a logit distribution. Hence, we can write Pgt as (11)

Pgr = exp”.Yt -

XI + I t 1

Furthermore, in order to derive closed-form solutions below, we take a second-order Taylor approximation of this function around the point At. This yields 6. Note that in so far as t + 2 is concerned the competence shocks are irrelevant because they are exhausted at the end ofqeriod t + 1 (cf. eq. (3)). To simplify the analysis, we treat ox as a parameter, although it is endogenous in our model. While implicit solutions for this variance and the necessary partial derivatives can be derived, incorporating them would make the model highly non-linear without changing the qualitative results derived below.

a = exp(h) / [1+ exp(h)], c = exp(h)P / [I + exp(h)l2,

d = exp(h)[(exp(A) - 1]p2/2[l + exp(h)I3,

where the time subscript on h has been dropped for notational sim~licity.~ Note that the non-economic factors, h,, determine the magnitudes of the parameters a, c and d. Given the temporal nature of h, these parameters will be time and state dependent as well. For h = 0 , a = b9, c = p/4,and d = 0 , which for yr =y,’ - up yields pgt= M . This essentially means that in the absence of a positive competence shock, a positive supply shock, or “help” from the central bank, the incumbent is perceived as being no different than the challenger. For h > 0 , I h < a < 1, O < c < 1, d>O, and pgt> M at yt =yf - ut‘Here, the incumbent is viewed positively by the public and, hence, as having more than a 50-50 chance of being reelected even without any current shocks. We will refer to such an incumbent as being “strong.” Similarly, for h < 0 , O < a < M, O < c < 1, d < 0, and p p g < M around the point yt =y,’ - ut. The incumbent is viewed negatively by the public and, in the absence of any shocks, as having less than a 50-50 chance of being reelected; that is, the incumbent is “weak.” Finally, as h approaches positive or negative infinity, c and d approach zero. It is important to remember that, while the parameters a, c and d are state-dependent, they are known at the time policy actions are taken in time t. Since c > 0 for all values of h, the linear term in (12) shows that the incumbent’s reelection probability increases when output is above the natural rate and vice versa. This is consistent with the observation that incum-

7. Throughout this paper we will only consider “pooling” equilibria--e.g., equilibria in which the weak incumbent chooses to masquerade as a strong incumbent by inflating. In a separating equilibria this would not be true. For more on this point see Rogoff and Sibert’s paper.

FRATIANNI, yon HAGEN 8~WALLER: CENTRAL BANKING

383

FIGURE 1 CDFs for Incumbents

..................................................

Strong

h>O

...........................................

Challenger h=O

bents do well in good economic times and do poorly in bad economic times. More interestingly, the fact that the parameter d changes sign as h changes sign means that output variability can have either a positive or negative effect on the incumbent’s reelection probability. The reason for this can be seen by looking at Figure 1 which shows the relationship between the probability of voting for the incumbent, pgr and output, yt, from (11). As a probability measure, pgt is monotonically increasing in yt; it is concave when h, + -fl) > 0 and is convex when the inequality is reversed. Therefore, if h > 0, pgt k concave at the point yt =fland a positive output shock causes a smaller marginal increase in pgt than the marginal decrease caused by a negative shock. Symmetric deviations of output from its expectation then have a negative effect on the expected probability of reelec-

pot

B

Probability of Reelection

Weak Incumbent hO corresponds to a “strong” government, this means that negative transitory shocks hurt strong incumbents more than positive shocks help them. The opposite holds if h < 0 and pgt is convex at y, =)$, i.e., positive output shocks increase the marginal reelection probability of a weak incumbent more than negative shocks reduce it. As a result, strong and weak incumbents have different views on output stabilization. The basic reason for this finding is that the elected leader’s utility is a function of his reelection probability. Hence, the curvature of the reelection probability corresponds to the incumbent’s attitude towards electoral risk. Strong incumbents are “risk averse” and want shocks to be stabilized. In contrast, weak incumbents are

8. This feature will arise for any S-shaped cumulative distribution function and is not unique to the logit function.

ECONOMIC INQUIRY

384

“risk loving” and prefer shocks not to be stabilized. The Leader’s Preferences Revisited. T h e leader’s preference function can be written as

( 1 3 ) UG,, = 2k + US,,

+ Et-i( us,+ uGt+J

for t-1 = a non-election period,

UG,= (1 + 2pg3k+ US,

This incentive to create excessive inflation leads to the problem outlined in the introduction of this paper: in a democracy prone to asymmetric information about the true abilities of its leaders, excessive inflation and a political inflation cycle are the unavoidable costs of the election process. The question then becomes: Can we design an institution that would overcome this problem without abandoning the electoral process? To this question we now turn. Ill. MONETARY POLICY REGIMES

for t = an election period. Since there are no inter-temporal economic linkages, by design, and the competence shock only lasts two periods, the leader has no influence over terms more than one period ahead. Similarly, since the variability of output and inflation depend only on the transitory shocks and monetary surprises in that period, any expectation of future variability losses is independent of the leader’s current actions or competence. Thus, for purposes of analysis, we can collapse the leader’s utility function down to:

The Monetary Authority As an Artijkially Intelligent Computer If the public had a perfectly informed, benevolent computer to conduct monetary policy, it would program it to maximize US (the public’s preference hnction) upon observing the realized values of the shocks. This would give rise to the following solutions:

x, = [2b/ ( 1

(15)

7ct=-[1/(1

7c;

(14)

UG,, = 2k + US,, for t-1 = a non-election period,

UG,= (1 + 2pg3k+ US,

+ b)]u, - v,, +b)]u,,

= 0, yt =y; + [b/ ( 1

+ b)]u p

Expected inflation is zero, and output demand and supply shocks are stabilized in an “optimal” way. The solutions in equation (1 5) will be referred to subsequently as the socially optimal outcome.

for t = an election period. We can now see the source of the problem outlined by Rogoff and Sibert. If the elected leader has control of the money supply in the non-election period, setting the money stock to maximize his own welfare is equivalent to maximizing social welfare since k is constant. However, i n the election period, the incumbent’s welfare depends on the expected payoff from being in office tomorrow. Because the probability of receiving a vote is a function of monetary surprises, the incumbent has an incentive to create an inflation surprise today in order to increase output, thereby appearing to be more competent than his challenger, which increases the probability of getting reelected and receiving k, the payoff from holding office, for two more periods.

Policy under a Benevolent But LimitedIntelligence Computer

The problem with ( 1 5 ) is that it would be difficult in reality to program a computer to respond “correctly” to the shocks. In some sense, human judgement is needed to properly use available information to stabilize shocks in the appropriate manner. The need for human judgement motivates the use of discretionary policymaking. Nevertheless, we can consider the outcome of using a computer with limited abilities. An imperfect but benevolent computer could be programmed to follow simple policy “rules,yyfor example a constant (zero-) money growth rule. The computer would simply set the expected value of inflation equal to zero (or, set x, = $ = 0) and

FRATIANNI, von HAGEN & WALLER CENTRAL BANKING

would not respond to shocks. The relevant solutions are

(16)

X,

(17)

385

UMt =At +Pt+lEtAt+,

= 0, R, = V t - u,,

g=o, y t = y : + v , . Obviously, such a policy regime forgoes the gains from stabilizing output and, thus, lowers the level of social welfare. A Discretionary Central Banker

The problem with a computer is that it lacks the ‘?judgement” to make the right decisions regarding stabilization policy. An alternative to the computer is to charge a monetary authority with the task of acquiring the necessary stabilization know-how. The risk of such a strategy is that one cannot be sure that the authority will always be benevolent. Situations arise in which the interest of the central banker may not match the preferences of society, just as is true for the elected policymaker. Nevertheless, society may still be better off with an imperfectly benevolent but discretionary central banker than with a computer. We will assume that a central banker is appointed in the non-election period, takes office at the start of the election period and serves two periods. The appointment process itself is assumed to be a “black box,” but we give the elected leader considerable influence in selecting the central banker. This is consistent with most appointment processes around the world and is the only salient feature needed for our a n a l y ~ i s The . ~ set of possible central bankers includes, on the one hand, quasi-benevolent individuals whose preferences are a combination of their own self-interest and the public interest, and on the other hand, selfish individuals who are only concerned about their own welfare. The central bankers’ preferences at the start of the election period are given by 9. For a formal analysis of central bank appointments, readers interested in this issue should see Waller [1992b]. Furthermore, Waller [1991] develops a dynamic garne-theory model that shows how an administration will engage in strategic “bashing” of the central bank in order to coerce the monetary authorities to produce the administration’s desired policy. We simply assume this type of behavior is subsumed in the central banker’s reappointment probability.

Here, A, is the central banker’s payoff from being in office in period t, pt+l is the probability of being reappointed to office in period t + 1, and the parameter z, whose values range from zero to one, is a measure of the central banker’s independence indicating to what extent her reappointment is conditional on the incumbent’s reelection. When z = 0, the central banker views the incumbent’s reelection chances as having no impact on her own reappointment probability; in that case p?+, = p o I 1 and the central banker’s decisions are unaffected by the political fate of the incumbent. In contrast, when z > 0, the central banker’s probability of being reappointed depends partly on the reelection chances of the incumbent, and the central banker has an incentive to choose monetary policy actions that improve the incumbent’s probability of being reelected. The parameter i is a binary variable which is set to 1 if the central banker is quasibenevolent and 0 if the central banker is selfish. We can now see how an agency problem arises in central bank policymaking. Once nominal wage contracts have been written, the central banker has the opportunity to counteract exogenous demand and supply shocks. Yet, she can also use her discretionary power to attempt to expand output above its expected full-information level to raise the incumbent government’s and, thereby, her own chances for reappointment. Obviously, her incentives to do so depend critically on the nature of the relationship between the central bank and the incumbent government. At first glance, one would think that the quasi-benevolent central banker is the lesser of the two evils so society should select from this pool, hence we will consider this case first. Then we will investigate whether, counter to our intuition, society might be better off with the selfish central banker if the proper institutional structure is erected. Consider the central banker’s choice of X, during an election period. Letting A,l = A for

386

ECONOMIC INQUIRY

now, substituting equation (12) into p,+],maximizing UM with respect to xr and imposing rational expectations yields the following equilibrium solutions: (18)

Xt

= (Acz / 2b) - v,

+ [2(b - Azd) /( 1 + b +Adz)] u,, 7c, = (Acz/2b)

- [(1 + U d z )

/(1 + b + A d z ) ] u, y t =y;

+ [b- Adz) / (1 + b + Adz)] U p

There are two main differences between the public’s optimal solution and the outcome chosen by the central banker. First, the conflict between private and social interest leads to an inflation bias without any additional output gains (y, is systematically no larger in (1 8) than it is in (15)). This bias is positive and is given by expected inflation, namely x e = A c z / 2 b . It results from the standard timeconsistency problem: the central banker is tempted to expand the economy and improve the incumbent’s reelection chances, yet the public realizes this incentive and adjusts nominal wage demands ex ante to eliminate any output gain in equilibrium. The magnitude of the inflation bias depends on the strength of the incumbent’s reelection chances in the absence of interventions by the central bank.1° It is maximized at h = 0, which corresponds to an ex ante reelection probability of 1/2. As h approaches positive or negative infinity, c goes to zero and the inflation bias disappears, because the marginal benefit from a monetary expansion on output is so small for both very strong and very weak incumbent governments that the central bank opts to pursue the public “good” instead. It should be recalled that since c is time dependent, the inflation bias will fluctuate over time as the government and popular support changes. The bias is also a positive function of z, suggesting that central banks whose appointments are more strongly controlled by elected officials are prone to a higher inflation bias than independent central banks. 10. Empirical evidence compatible with this result is shown for the U.S. in Davidson et al. [1990; 19921.

Second, the central banker stabilizes output more than is socially desired if the incumbent is strong and understabilizes output if the incumbent is weak. The reason is that strong incumbents are risk averse and weak incumbents are risk loving. Bad output shocks can cost a strong incumbent the election while good output shocks add very little to a strong incumbent’s reelection chances. Consequently, a strong incumbent wants the central bank to overstabilize the economy to maintain his current electoral advantage. The opposite is true for a weak incumbent-ood shocks can “snatch victory from the jaws of defeat” while bad output shocks just confirm the obvious. As a result, weak incumbents are willing to “roll the dice” and let the shocks hit the economy.‘’ In the non-election period, again due to the lack of a dynamic structure, the central banker’s current policy actions have no effect on next period’s values (cf. (14)) and all that matters is maximizing welfare in the current period. Since the current reward for being in office is a fixed value, the central banker will choose monetary growth x, to maximize the public’s utility US,.Hence, in non-election periods, the central banker acts like the perfectly informed, benevolent computer. These actions lead to a political inflation or monetary policy cycle. This analysis illustrates an important point: the problem is not that the central banker will never pursue the public interest, it is just that she cannot be expected to do so in every period, and this is the crux of the problem. l 2 IV.

INSTITUTIONAL DESIGN

The literature on discretionary monetary policy has stimulated an important discussion on the appropriate institutional design that would reduce the inflation bias. The range of solutions goes from Friedman’s [ 19601 fixed money growth rule to Thompson’s [1981] and Rogoff‘s [ 19851 proposal to delegate monetary policy to a conservative central banker, i.e., one whose preference weight against in11. Stabilizing good output shocks is desirable since workers end up working too much given the contracted wage. So an asymmetric stabilization response (stabilize bad shocks more than you stabilize an equal-sized positive shock) is not optimal. 12. Rogoff and Sibert’s model generates the same outcome.

FRATIANNI, von HAGEN & WALLER: CENTRAL BANKING

flation is larger than the public’s, and to recent proposals by Walsh [ 1995al and Persson and Tabellini [ 19931 to delegate monetary policy to a central banker whose remuneration depends explicitly on her policy performance. Our principal-agent paradigm allows us to evaluate these proposals within a unified framework. In this section, we compare a monetary rule and the appointment of a conservative central banker with two alternatives: one that makes the central banker independent from government and the other that ties her compensation to policy performance. l 3 Policy Rules The inflation bias arises because the central banker cannot precommit herself to a zero-inflation policy and is tempted to expand GNP out of self-interest. This has led to calls for eliminating discretionary policymaking and imposing policy rules. As argued above, a policy rule is equivalent to a limited-intelligent computer that is unable to achieve the desired degree of output stability. While average inflation is zero, output is more volatile. It may be the case that the loss from this additional output variability may exceed the gain from zero average inflation. Under discretion, the monetary authority completely offsets the demand shock but creates an inflation bias, whereas under the inflation rule, no bias occurs but the demand shock makes output and inflation more variable. For ease of analysis, consider d = 0 , and compare the expected value of the public’s preference function with discretionary policy and the zero-inflation rule. The public will prefer discretion over the inflation rule if

( 1 9)

g(1+ b)b + 4 [ 4 b 2/ ( 1 + b)]2 (Acz)~.

Inspection of expression (19) reveals that, the stronger is the public’s aversion to inflation (the larger is b), the more likely the public will prefer to retain discretion over excessive restraint. The reason is that the stronger is the public’s aversion to inflation, the smaller is 13. There is a question as to what degree of independence is needed for the performance contracting approach. Clearly there needs to be instrument independence but with regards to personal independence, such as the reappointment issues considered here, it is not clear whether or not it is necessary. Interested readers should see Walsh [ 1995bl. In this paper, he analyzes the design of performance contracts when reappointment is the form of “compensation.”

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the inflation bias which leads to an increased willingness to have the central bank stabilize output. The other point to consider from (19) is that the preference for rules versus discretion will change over time since the parameter c is time dependent. As was mentioned above, as h goes to positive or negative infinity, c goes to zero, whereas c is maximized at h = 0 . This implies that with very strong or very weak incumbents, the inflation bias will be small and there is less incentive to opt for monetary rules. The opposite is true when h equals zero. In this case, the incumbent is observationally equivalent to the challenger and would benefit greatly from a monetary surprise. The public recognizes such incentives and would prefer the rule over discretion. In practice, swings in h can create a highly uncertain environment, one in which a stable institutional design cannot easily emerge. Conservative Central Bankers Regardless of the public’s degree of inflation aversion, discretion can always be made preferable to a simple inflation rule by following Thompson’s and Rogoff‘s advice to appoint a sufficiently “conservative” central banker. To evaluate this proposal, we now assume that the government appoints a central banker with the preference function:

Recall that b is the weight that the public puts on inflation relative to output stabilization; 6 indicates the divergence between the public’s and the central banker’s preferences. With 6 = 1, the central banker has the same preference weights a s the public; with 6 > ( 1) improves socia1 welfare, and the optimal value of 6 is found by setting the marginal benefit of reducing the inflation bias equal to the marginal loss from increased output variability. Within the context of a Barro-Gordon model, this choice of the optimal degree of conservatism is not too difficult since the inflation bias and the variance of output are not time-dependent. But in our model, both the bias and the variability of output are time-dependent because of the temporal nature of the parameters a, c , and d. In times of political instability (A = 0) the inflation bias will be large but there will be very little stabilization bias. When the incumbent is relatively strong or weak, the inflation bias will be small but the stabilization bias could be large. So choosing a conservative central banker will not be easy in this model for two reasons. First, choosing the optimal degree of conservatism will require very accurate knowledge of the incumbent’s reelection probability and the strength of the relationship between the central banker and the incumbent. Second, in non-election periods the central banker does not create either bias. So appointing a conservative central banker will create excessive output variability in non-election periods without any corresponding benefit. This suggests that the optimal degree of conservatism requires inter-temporal tradeoff-his problem has not been identified in previous research. These problems lead us to the conclusion that choosing a conservative central banker may be much more difficult in practice than has been recognized heretofore. Personal Independence of a Benevolent Central Banker

A better way of attacking the inflation bias is to reduce the central banker’s payoff from using monetary policy for personal gain, which is the source of the principal-agent problem. This can be achieved by appointing a quasi-benevolent central banker and making this central banker independent from government.

Neumann [1991] argues that central bank independence from government involves two aspects, institutional independence and personal independence. Institutional independence means the ability of the central bank to pursue a course of monetary policy without being overruled by the govemment. Personal independence means that the central banker is not subservient to the government. Here, we assume that institutional independence is achieved and that the govemment cannot simply dismiss a central banker from office in the current period if it dislikes her policy. The question then is, how can the parameters of the central banker’s loss function determining the relationship between her and the incumbent government be chosen to achieve the socially optimal monetary policy? A comparison of the solutions in (1 8) and (15) reveals two critical parameters, namely the expected remuneration from being in office i n the next period, Edt+,,and t h e government’s influence on the re-appointment probability pt+,,expressed in the parameter z. With a benevolent central banker, the socially optimal results can be obtained by setting EA,, = 0 or z = 0. The first can be interpreted as stipulating that the central banker’s term in office is not renewable. Fratianni, von Hagen and WaIler l19921 point out that this is the approach recently taken in the Maastricht Agreement among the 12 members of the European Community for the European Central Bank. The latter means that the government’s political future has no consequences for the central banker’s future benefits; that is, the central banker’s reappointment is not linked to the incumbent government being reelected. This is the solution adopted in Germany, where central bank appointments are automatically renewed after the first term. Our model shows, then, that central bank independence is preferable to the appointment of a conservative central banker since it eliminates both the inflation bias and the stabilization bias. Furthermore, institutional structures promoting central bank independence can be implemented in a simple, time-invariant fashion. The analysis above also helps explain Alesina and Summers’s [1993] findings that the degree of central bank independence is negatively correlated with average inflation rates

FRATIANNI, von HAGEN & WALLER: CENTRAL BANKING

but there appears to be no correlation between the degree of central bank independence and output variability. Our model predicts that, as the central banker becomes increasingly independent, she is less concerned with using monetary policy to enhance the incumbent government’s reelection chances and the inflation bias decreases. However, it is not obvious what happens to output stability if the central banker is made more independent. A higher level of central bank independence lowers output variability if the incumbent government is sufficiently strong, but raises output variability if the incumbent government is sufficiently weak. Therefore, a move towards an independent central bank may lead to more or less output variability. If there is a mixture of “weak” and “strong” incumbents in the data set, then it is likely that no correlation will be uncovered between central bank independence and output variability. Perfonnance-based Compensation for a Serfish Central Banker According to the mechanism design literature the principal-agent problem can be solved by tying the agent’s compensation to observed outcomes. In our case, the inflation bias could be eliminated by appointing a “selfish” central banker (someone who is only interested in maximizing her self-interest) and offer her a perfonnance-based ~ o n t r a c t . This ‘ ~ theme has been investigated, albeit along different lines, by Walsh [ 1995al and Persson and Tabellini’s [1993] extension of Walsh’s early work.15 Such a contract would stipulate the following payment, A,, at the end of period t:

where the base income, w,is set such that the expected compensation is no smaller than the central banker’s opportunity cost (lost private sector income) of being in office. The central banker’s income would thus be a function of the rate of inflation, the Variability of inflation, and the variability of output and, there-

fore, depend on her own actions. The key feature of such a contract is that it explicitly states what the central banker will be held accountable for and makes the setting of policy more “transparent.”’6 It is this aspect of performance contracts, not the actual functional form or macro aggregates, that is innovative. The payment to the central banker should also be interpreted as a vector of compensation items such as salary, budgets, fewer public hearings, etc., rather than the salary of the central banker per se. The central banker will then choose the money growth rate to maximize = A, +Pf+lE,A f+l .

The first-order condition for this problem is (24) a ~ ~ / d=xa , ~/ax, , + (ap,+’ aXf)Ep,+, +P,+,[ W A + l )1%I = 0.

Since there are no intertemporal linkages in the economic structure of the model, the money growth rate has no impact on the following period’s output or inflation and consequently, no impact on the central banker’s compensation. Therefore, the last term of equation (13) is zero. Making the appropriate substitutions into (24) yields

(25)

Xf = (CZAe,,

- a1)/ 2 a , - v,

+ [2(a2 - dzA&,)/(a2+ a3 + dzA&l)lut, where AL1 =Ed,+l. Through appropriate choice of the parameters al,a2,and a3of the contract, the central banker can be induced to act in the socially optimal way. Comparing (15 ) with (25), this can be accomplished by setting

a2= arbitrary but CL= ~ [a2- dzA;+,(l

14. The first reference to our knowledge of this type of compensation scheme is Havrilesky [1972]. 15. The problem with Walsh’s model, and Persson and Tabellini’s extensions to it, is why the principal-agent problem arises in the first place. Hence, one key contribution of our paper is providing a foundation for these models.

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f

0,

+ 2 b ) ] /b.

16. We should note that accountability can be achieved in other ways. Targeting procedures and public disclosure of the policy decisions are two commonly used methods for holding the central bank accountable for its actions.

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While a2is a free parameter it must be different from zero to achieve optimal stabilization policies. For example, it might be set equal to by the corresponding weight on price stability in the public’s preference f u n ~ t i o n . ‘ ~ According to ( 2 6 ) , the central banker’s compensation should be decreasing in the level and (with a, = b) the variability of inflation. However, its relation to output variability is ambiguous, since d can be less than, greater than, or equal to zero. When d = 0, only the inflation bias exists, and the optimal weights on inflation and output variability in the central banker’s compensation scheme match the public’s preference weights (a2= b, a3= 1). The central banker takes a pay cut for any inflation rate greater than zero. The inflation bias is eliminated by making the marginal benefit of increasing t h e incumbent’s reelection probability less than the marginal compensation loss for creating excess inflation. Things get more complicated when d is greater or less than zero. To eliminate the ensuing stabilization bias, the optimal a3may be greater than or less than one or may even be negative depending on the incumbent government’s reelection strength. Nevertheless, the point is that it is possible to construct a compensation contract that is consistent with the socially optimal solution even though the weights in the performance contract are time and state contingent. Even more surprising is that society may be made better off by choosing a central banker motivated by self-interest than to rely on the benevolence of the central banker to generate the appropriate policy. In short, this approach lets the central banker essentially do what she wants-but she will pay the consequences of those actions. Additional results can be obtained by solving for the reduced-form solutions, which requires determining A;+,. Under the optimal contract the inflation bias will be zero and the variance of inflation will be 0: = [ 1 / (1 + b)I2 o;,where cr; is the variance of real shocks. Consequently,

Substituting equation (27) into (25) and solving yields (2 8)

a1 = (1 + b ) 2 ~ ~ ~+/ b)’ [(1

+ (1 + 2b)dz4] a2= (1 + b)2(1 -+ 2b)dzw / [(1 + b), + (1 + 2b)dz. The reduced-form solutions for a1 and a3 are the fixed points of equation (27).

18. The increase in the variance of ut also reduces the value of @, the signal extraction parameter, which reduces the value of c. This merely reinforces the results described in the text.

FRATIANNI, von HAGEN & WALLER: CENTRAL BANKING

institutional design would reduce worries about the optimal degree of central bank independence, as an optimal, performance-oriented contract can be designed for any degree of central bank independence. Consequently, the contract approach is a promising alternative particularly for those countries where political and legal traditions make it hard to accept the notion of a central bank that is independent from government. The contract approach is attractive, therefore, in that the optimal monetary policy can be implemented without requiring legislation making the central bank independent. Nevertheless, the contract approach has its difficulties. The parameters of the optimal contract derived above are not, in general, constant over time. Since the optimal weights a1and ag,through c and d, depend on h, they would change over time as the incumbent’s political support changes. Thus, the optimal contract would have to be revised on a periodby-period basis, which would be extremely difficult to do in practice. Making the quasibenevolent central banker independent has the advantage of requiring only a once-and-for-all adjustment of the central bank law. This suggests that performance-oriented contracts are more appropriate in a stable political environment, while an independent central bank is more appropriate in an environment of large swings in the political climate. Furthermore, we have derived the optimal contract for a central banker who is assumed to be completely selfish (i = 0 in (17)). In practice, however, candidates for central bank appointments are likely to give at least some weight i > 0 to society’s concerns in their own preferences. The optimal contract then depends on the preference weight i. While it is still possible to derive an optimal contract for a given weight i under such circumstances, it will be difficult, in practice, to determine a candidate’s true preferences. Making the central banker independent from government and paying her a fixed salary eliminates concerns about the central banker’s degree of benevolence. This suggests that the latter approach is more appropriate if there is a large degree of preference-heterogeneity among potential candidates for central bank office. Finally, one has to ask: Who is it that actually negotiates the contract with the central banker? In reality, it would have to be the

39 1

elected leaders but, in our view, these are the people who are responsible for creating the problem in the first place! Consequently, there is a serious problem with relying on these contracts as a type of commitment device. We suspect that this is probably the reason why we do not observe compensation contracts for central bankers. Given the time- and statecontingent nature of the contract weights, elected Ieaders need legal flexibility to adjust the contract as circumstances change. But flexibility invites political abuse by giving the elected leaders an opportunity to reset the weights in a socially non-optimal way. Even in New Zealand, the one country where something like a performance contract exists, there is concern about the government allowing the central bank to wriggle out of its contract if sufficiently large supply shocks hit. Identifying these shocks, in particular, ones of sufficient magnitude, is likely to be very difficult and fraught with political uncertainty. Elected officials will be tempted to cry “Big Supply Shock Hits” when it is politically convenient thereby undermining the credibility of the contract. All of these problems lead one to question the political feasibility of performance contracts. Thus, only time will tell if the New Zealand approach will be a watershed in central bank design or merely a historical footnote. V.

SUMMARY AND CONCLUSIONS

In this paper we argue that an inflation bias and a stabilization bias may arise as a result of the principal-agent nature of monetary policy. A major contribution of this paper has been to tie together two important strands of the literature on monetary policy institutions: the political economy model of Rogoff and Sibert [I9881 and the contracting approach of Walsh [1995a] and Persson and Tabellini [19931. We show how inflation and stabilization biases can arise because of the nature of the relationship between the central banker and the elected policymakers. Furthermore, we have demonstrated that there are several institutional designs which can alleviate one or both of the biases associated with discretionary monetary policy. The basic results of this analysis suggest that, in contrast to Friedman-type policy rules or the appointment of “conservative” central bankers, personal inde-

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pendence of the central banker from government or performance-oriented compensation packages can achieve both optimal stabilization and the elimination of the inflation bias. Our model suggests that electoral uncertainty translates to high inflation rates. This is consistent with the empirical observation made by Cukierman, Edwards, and Tabellini [1992] that unstable political systems tend to rely more heavily on seignorage to finance expenditures than do stable systems. Furthermore, our model accounts for the “odd man” in empirical studies of central bank independence, namely the result that long-run inflation is relatively low in Japan, although its central bank is very dependent on the government. With Japan’s political system being extremely stable in the post-war period, our model predicts a small inflation bias even for a very dependent central bank, since the marginal benefit from using monetary surprises to secure reelection is very small. Therefore, the model helps to understand the empirical relationship between inflation performance and political stability. The model also helps explain why we might observe an absence of correlation between the degree of central bank independence and the variance of GDP. Models that rely on the Barro-Gordon framework will not have a stabilization bias unless it comes out of institutional arrangements such as appointing conservative central bankers. But, if one follows our approach and recognizes that political interference can induce positive or negative stabilization biases by the central banker, then the absence of an empirical link between central bank independence and the variability of GDP is not s~rprising.‘~ To reiterate what we stated in the beginning of the paper, the most appealing aspect of the work in this paper is the insight that excessive inflation and political inflation cycles need not be an inevitable consequence of representative democracy. Effective institutional design works well in all aspects of governance and central banks are no exception.

19. Readers interested in the relationship between central bank independence and its effects on output variability should see Waller and Walsh [1996].

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FRATIANNI, von HAGEN & WALLER: CENTRAL BANKING Thompson, Earl. “Who Should Control the Money Supply?“ American Economic Review Papers and Proceedings, May 1981,356-61. Waller, Christopher. “Bashing and Coercion in Monetary Policy.” Economic Inquiry, January 1991, 1-13. . “A Bargaining Model of Partisan Appointments to the Central Bank.” Journal of Monetaly Economics, June 1992a, 411-28. .“The Choice of a Conservative Central Banker in a Multi-Sector Economy.” American Economic Review, September 1992b, 1006-12. Waller, Christopher, and Carl Walsh. “Central Bank Independence, Economic Behavior and Optimal Term Lengths.” American Economic Review, December 1996, 1139-53. Walsh, Carl. “Optimal Contracts for Central Bankers.” American Economic Review, March 1995a. 15067. . “Is New Zealand’s Reserve Bank Act of 1989 an Optimal Central Bank Contract?” Journal ofMoney, Credit and Banking, November 1995b, 1179-9 1. Willett, Thomas, ed. Political Business Cycles. Durham: Duke University Press, 1988.

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