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Long-term appointment of central bankers: costs and benefits
European Journal of Political Economy Vol. 16 Ž2000. 639–654
Long-term appointment of central bankers: costs and benefits Axel Lindner ) Department of Economics, Goethe-UniÕersitat, ¨ 60325 Frankfurt am Main, Germany Received 7 January 1999; received in revised form 4 August 1999; accepted 23 September 1999
Abstract Why do independent central bank boards have a reputation for more moderate policy than do elected governments, even if the board’s members have been appointed by the current or former government? This paper gives an explanation for the case of a political world with ‘zeitgeist shocks’ on the electorate’s preferences. If the median position of preferences inside the board determines the monetary policy, a trade-off concerning member term length arises: a longer term entails more moderation, while enhancing the likelihood of detachment from contact to the electorate’s current preferences. q 2000 Elsevier Science B.V. All rights reserved. JEL classification: D71; D72; E58 Keywords: Central banks; Boards; Elections; Becket effect
1. Introduction Central bank independence has a major role in modern economics of monetary policy. In order to enforce independence, it is common wisdom that some legal requirements such as irremovability of board members during the term of office have to be met. The danger of a partisan board by virtue of preferences of board members is rarely considered to be a serious problem. This view is based on empirical observations: central bank boards often seem to behave quite indepen)
Corresponding author. E-mail address: [email protected] ŽA. Lindner..
0176-2680r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 7 6 - 2 6 8 0 Ž 0 0 . 0 0 0 1 2 - 4
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A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
dently of the political forces responsible for the appointment of board members. In particular, a board’s policy tends to be more moderate and consensus-oriented than that of the governing parties. This appears to be the case even when members formerly close to one party are the majority in the committee. This finding is usually referred to as the ‘Becket effect’: apparently, people1 change their behaviour in line with their social position ŽNeumann, 1991.. This paper proposes that a systematic change of member behaviour is not necessary to explain these observations. Instead, it will be assumed that preferences of a single member coincide with the political positions of the appointing government and are fixed over time. The board’s policy will be determined by the preferences of its median member. In this case, moderation of boards with long-term appointments follows from a variant of the law of large numbers, if the political positions of the parties change according to a stationary stochastic process. The behavior of parties will be motivated in a simple public choice model. Moreover, if the polarization of party platforms — and thus of government policies — is inefficient, delegating political power can enhance efficiency. This is the case although every single board member continues to share preferences of the various former governments. The appointment process transforms polarization of partisan views into heterogeneity inside the board, which leads to moderation as long as the median position prevails. On the other hand, common sense suggests that a long-term appointment might result in wide differences between the preferences of the committee and the current electorate. This trade-off between costs and benefits of long-term appointment is the central subject of the paper. The task of modeling appointments of central bankers in a partisan political world has already been undertaken by Waller Ž1992.. Contrary to this paper, Waller’s analysis does not focus on decision making inside the board. Instead, he analyzes an appointment procedure similar to that in the United States: the administration has the right to nominate candidates, who then have to be confirmed by the opposition. The same approach applies to Waller Ž1998.. Aspects of the optimal term length of central bankers have been discussed in a paper by Waller and Walsh Ž1996.. While that paper views the central bank as a single homogenous decision maker and argues that long board member terms reduce uncertainty about monetary policy, I assume heterogeneity within central bank boards as a consequence of appointment of its members via a first-in, first-out system. Hence, I focus on the advantage of moderation in a polarized political world. Although the pioneering model of Downs Ž1957. suggests conÕerging platforms in modern democracies, a polarized environment can frequently be observed Žfor the USA, see Alesina and Rosenthal, 1995.. Such an environment can be easily explained within a public choice framework in the spirit of Palfrey Ž1984.: polarization of two incumbent parties deters entry of competitors at the
1
Like the former counselor to the English king and later Archbishop of Canterbury Thomas Becket.
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fringes of the political spectrum. In a world with linear costs of divergence between conducted policy and individual preferences, the rent maximizing position is the median, so that the board’s tendency to moderation enhances efficiency. The public choice framework is outlined in Section 2. Section 3 introduces the central bank board’s preferences as the result of a stochastic public choice process. This approach is used to assess costs and benefits of long-term appointments in Section 4. Section 5 concludes the paper. 2. The public choice framework The following is based on a simple, frequently used framework for monetary policy in the spirit of Barro and Gordon Ž1983.. There is a trade-off between price level stability and output stability, because monetary policy responding to random supply shocks is more flexible than nominal wage setting. The policy conducted by the central bank depends on the preferences of its board concerning this trade-off. Preferences can be described by f , which is the weight given to price stability relative to output stability. Below, I develop a simple public choice model determining f under the assumption that the monetary authority is subject to full control by the elected government. In general, costs due to the variation in inflation and output are not distributed equally across the electorate. If compensation is not feasible, different individuals will have different preferences with respect to the weight f on price stability. In real world, political preferences for a high f are usually regarded as ‘right wing’, those for a low f as ‘left wing’. This justifies reducing the political preference space to the dimension ‘weight given to price stability’. The assumption of a one-dimensional issue space is the basis of the classic model of a democratic political system of Downs Ž1957.. He found that two competing parties would concentrate at the position of the median voter, so that government policy becomes independent of the outcome of elections. Palfrey Ž1984. modified the Downs model to show that two vote-maximizing incumbent parties will take more polarized positions, if they expect entry of a new competitor. This will deter a candidate, if her objective is not, as Palfrey Ž1984. assumed, the absolute number of votes, but to finish among the most successful parties. For such an objective function, however, equilibrium might not exist Žsee Greenberg and Shepsle, 1987.. This problem is avoided by assuming entry costs for vote maximizing parties. Weber Ž1998. argues convincingly in favor of the importance of fixed entry costs for setting up a new party and running its campaign.2 The following simple model is a special case of Weber’s approach and will serve as the basis for the rest of the paper. 2
A different way of modeling entry deterrence by polarization can be found in Osborne Ž1997.. This approach rests on uncertainty about the voters’ preferences.
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In a world with complete information, two incumbent parties L and R maximize the number of votes for the coming election as their payoff. They do so by positioning their platforms in the issue space, the real closed interval wyH; H x Ž H ) 0.. Next, an outside party O decides whether to enter the election race and, if so, which position to take on. Finally, elections are held: voters give their ballot to that party whose position is closest to their own preferred point in the issue space. In the case of a draw, they randomize with equal probability for the two parties. For simplicity, we assume a uniform distribution of voter’s ideal points f v between yH and H: f Ž fv
°1 ¢0
. s~ 2 H
for yH F f v F H
Ž 1.
otherwise
Hence, the median position, f M , is 0. In addition to timing, the outsider O differs from the incumbent parties in another way: O has to incur fixed promotion costs if it chooses to enter. Entry takes place if there is expectation of a strictly positive payoff in the upcoming election Žestablishing a position for future elections is not an attractive strategy given a high discount rate..3 The assumption of a uniform distribution makes it possible to measure the payoff in form of the number of votes by simply taking the interval of points to which a party position is closer than that of competitors. Entry costs z are measured in the same units. Weber Ž1998. showed the existence of a unique equilibrium of pure strategies for any single-peaked distribution of voters’ ideal points such as the uniform distribution employed here. If entry costs are ‘intermediate’, the entry of the third party is deterred by the incumbents’ polarized positions. In this model, ‘intermediate’ entry costs mean H ) z G Hr2, which implies f L s yH q z, f R s H y z Žassuming that f L is the focus point for L, f R for R ., and no entry of O as equilibrium. The intuition is straightforward: For z G H, the unique equilibrium without consideration of a possible entry, which is both incumbents taking the median position, blocks entry by itself. For z - Hr2, entry cannot be deterred because to block entry at the fringes results in entry in the center. For H ) z G Hr2, however, entry is deterred by a symmetric polarization, which, in equilibrium, is just enough to block entry. It does not pay to enter the race if the highest payoff of votes O can achieve equals z. The optimal entry position would be either close to the left of f L or close to the right of f R . Therefore, in equilibrium, f L s yH q z and f R s H y z. It is easy to see that, ceteris paribus, the incumbents cannot gain by changing their positions: moving 3 Osborne Ž1997. derives the equilibrium without entry costs for a much broader concept, namely a symmetric, unimodal density function. This is not done here, as the public choice model is not the main focus of the paper.
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f R to the right by D, for example, would imply a loss of Dr2 votes to L or, if D is large enough to induce entry between f L and f R , of even more votes to O. Moving to the left would induce entry of O close to the right of f R , leading to a loss of about z votes for R. For the rest of the paper, I assume that H ) z G Hr2 and that the equilibrium strategies are played in every period t. The winning probability for the two incumbent polarized parties is P s 0.5. Let b s H y z Then the position of the government in power, fg t , is simply equal to the random variable bt with the density function: f Ž bt . s
½
0.5 0.5
for bt s yb for bt s b
Ž 2.
The degree of polarization Žas opposed to moderation. will be measured by the variance of the government’s position in t, fg t . This is sf2g t s b 2 if monetary policy is under direct control of the current government in period t.
3. Central bank preferences and policies This section introduces an independent central bank board responsible for monetary policy, which, by assumption, is determined by the median preferences, i.e. the preferences of the median board member fm . The question of interest is under what conditions the board can be expected to conduct a more moderate and, given linear costs of divergence between actual policy and individual preferences, a more efficient policy. The time between two elections is one period. At the end of each period, the central banker with the longest-term length retires. After the election, the new government will replace the banker by a person4 who has preferences identical to its own. This implies a large board if the terms of office are long. A board consisting of three members, for example, includes the appointees of the current and the two former governments. Note that strategic misrepresentation of one’s own preferences by appointing a central banker with more polarized preferences is not a sensible strategy, as the median position Žrather than some weighted average. determines the kind of policy implemented. According to Section 2, each central banker will belong to either the ‘left’ or the ‘right’ party with probability 0.5. Because either party will hold the majority of seats with ex ante probability 0.5, the same holds true for the median member.5 The variance is given by sf2m t s b 2 , as in the case if monetary policy is under direct control of the government. 4 5
The replacement of an entire group is equivalent to that of just one person. In order to exclude the situation of a tie, an odd number of members is assumed.
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Now suppose that election results are not the only random shocks. To avoid the formalization of a Becket effect, we keep the personal preferences of members fixed over time. Instead, the party positions are assumed to vary due to random shifts of the distribution of the electorate. Such unpredictable changes will be referred to as ‘zeitgeist shocks’. They occur at the end of each period before an election takes place. The incumbent parties observe these shocks with sufficient time left to adjust their relative positions to the new distribution of preferences, so that entry will continue to be blocked. Now, the position of the median central bank member is no longer trivial. In particular, it becomes dependent on the number of board members or, in this setting equivalently, of the term length of a single central banker. Section 4 will analyze this aspect for the case of stationary ‘zeitgeist shocks’.
4. Costs and benefits of long-term appointment 4.1. The stationary case The position of the median central banker is a function of the set of board members’ positions. The member appointed in period t takes on the position of the party in power in t. This position is determined by the random election result and the distribution of the electorate’s preferences at t, which depends on the ‘zeitgeist shock’ at t. Formally, the ‘zeitgeist shock’ is captured by the realization at t of the random variable a , with EŽ a . s 0 and sa , so that the density function in Eq. Ž1. becomes: f Ž fv t
°1 ¢0
. s~ 2 H
for e y H q a t F f v t F e q H q a t
Ž 3.
otherwise
with e as the median of the voters’ preferences for a t s 0. Or, put differently, as the stationary expected median of voters’ preferences Ž e has been assumed to be 0 so far.. The incumbent parties consider the ‘zeitgeist shock’ a t when choosing their respective positions. Following Eq. Ž2., the election result for period t can be represented by the random variable bt , so that the position of the board member appointed in t is:
f b t s e q a t q bt
Ž 4.
The shocks a t and bt are assumed to be uncorrelated, as are the time path observations in this subsection. Fig. 1 illustrates the position of the median banker for the cases of 3 and 9 period term lengths, respectively. The distribution of the random variable a is bounded by wya; ax. The median position fm t is encircled. The board with nine members takes on a more moderate position. This is not a coincidence: intuitively, the larger the board,
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Fig. 1. Random central bank preferences for term lengths 3 and 9.
the more probable is an almost equal number of AleftB and ArightB members, implying that the median position is at the inner side of one of the two groups. The inner side shifts to the center, as more and more members enter the board. This effect is closely related to the law of large numbers: by drawing a sample from a population with finite variance, the distribution of the sample mean becomes more and more concentrated near the population mean as the sample size increases. Since the emergence of new board members’ positions is a stationary stochastic process, it can be regarded as a repeated drawing from the population of all potential board members. What is of interest in this context, though, is the distribution of the median rather than that of the mean. The following lemma can be proven:
Lemma 1. Consider a random sample drawn from a one-dimensional numerical population. For the median of this sample, the probability of being outside an arbitrary range around the median of the population approaches 0 as the sample size approaches infinity. Proof. See Appendix A. In other words, it is always possible for the most moderate position to become the median position of the board almost with certainty, if the board becomes sufficiently large. But moderation comes at a cost. If the ‘zeitgeist shocks’ are very large, the moderate median position inside a long-term board, despite mitigating the collective choice inefficiency, might not closely reflect the electorate’s current preferences. This trade-off is central to assessing alternative term lengths. The criterion used in the following is the expected squared divergence between the board’s median position and the electorate’s current median, EŽ fm t y f M t . 2 . It will be applied to a one- and a three-member board, respectively. If the election period is taken to be 4 years long, this implies comparing term lengths of 4 and 12 years.6 6
Members of the FED’s board of governors regularly serve 14 years, which is by far the longest term of office for central bankers in any major central bank board.
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In order to simplify the calculations, the electorate’s current median will be normalized to 0: f M t s 0. This yields the following expression: 2
`
2
E Ž fm t y f M t . s E Ž fm t . s
Hy`f
2 mt
f Ž fm t . d fm t
Ž 5.
As stated above, the random shift of the electoral median happens prior to the election, allowing party positions to adapt. During the government’s term of office, the electorate’s preferences are assumed to be fixed. For a one-member board, EŽ fm t y f M t . 2 depends only on the uncertainty of the electoral results. This leads to the Žvery simple. first proposition. Proposition 1. In the model presented in Sections 2 and 3, if elections follow a stochastic process according to Eq. (2), the expected squared diÕergence between the board’s median position and the electorate’s current median is giÕen by: E(fm t y f M t ) 2 s b 2 . Proof. 2
E Ž fm t y f M t . s
b2
b2 q
2
2
s b2
I
Ž 6.
For a multiple-member board, the position of each board member relative to f M t depends on the electoral shock bt and, for all but the youngest members, on the random electoral shifts a . The distribution of a is assumed to be uniform:
° ¢
1 f Ž at . s 2 a 0
~
for ya F a t F a
,
Ž 7.
otherwise
with a ) 0. Under this assumption, EŽ fm t y f M t . 2 can be derived: Proposition 2. In the model presented in Sections 2 and 3, if elections follow a stochastic process according to Eq. (2) and the ‘ zeitgeist shocks’ to the distribution of Õoters’ preferences giÕen by Eq. (3) follow a stochastic process according to Eq. (7), the expected squared diÕergence between the board’s median position and the electorate’s current median, E(fm t y f M t ) 2 , for a three-member board is giÕen by:
2
°1
10b 2 a3 q 8 a 5 q 10 b 3 a 2 y b 5
~ 30
a3
E Ž fm t y f M t . s
¢
2
b q
2 5
2
a y
1 2
for a G b
Ž 8. ab
for a F b
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Proof. See Appendix B.7 Differentiation shows that EŽ fm t y f M t . 2 increases with a greater degree of polarization: EEŽ fm t y f M t . 2rEb ) 0. More interesting is the dependence of EŽ fm t y f M t . 2 on a:
EE Ž fm t y f M t . Ea
2
°) 0
for a )
~s 0
for a s
¢- 0
for a -
5 8 5 8 5 8
b b
Ž 9.
b
If the dispersion a of the ‘zeitgeist shock’ is sufficiently small relative to the political polarization, a marginal increase in dispersion reduces the expected squared divergence between the board’s median position and the electorate’s current median. The intuitive explanation follows from the above argument: party polarization has less impact if the dispersion between party supporters is larger, because the moderate positions are more likely to be the median than extreme ones for n ) 1. This is the argument in favor of longer term lengths, but it has to be qualified: a term of three election periods entails a lower expected squared divergence between the board’s median position and the electorate’s current median than does one of only one period, provided a is not too large relative to b Žnot larger than about 1.25b .. Proposition 3. For eÕery b, there exists a critical aˆ so that E(fm t y f M t ) 2 is larger (smaller) for a three-member board than for a one-member board, if a is larger (smaller) than a. ˆ Proof. See Appendix C. This result is due to the already mentioned trade-off between moderation and the importance of the latest ‘zeitgeist shock’: if a is very large, the benefits of the moderation effect of long-term membership are outweighed by the high probability of a large gap between the current electorate’s preferences and the median position of the board. A numeric illustration shows that for b s a, we have EŽ fm t y f M t . 2 s b 2 for the case n s 1, and EŽ fm t y f M t . 2 s Ž9r10. b 2 for n s 3.8 7
It is easy to check the result for some special cases: the two expressions coincide for bs a, EŽ fm t y f M t . 2 s b 2 for as 0, and EŽ fm t y f M t . 2 s Ž4r15. a 2 for bs 0. 8 The ‘zeitgeist shock’ minimizing EŽ fm t y f M t . 2 for ns 3 is a ) s Ž5r8. b. In this case, EŽ fm t y f M t . 2 f 0.84 b 2 .
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4.2. The random walk case The analysis in Section 4.1 was confined to the stationary case: the expected median of the electoral preferences e was constant in every period. This is a rather strong assumption. Alternatively, a high electoral median in one period might imply a high expected median in the following one. The simplest stochastic process formalizing this principle is the random walk. In this case, the electoral distribution is path-dependent: f Ž fv t
°1 ¢0
. s~ 2 H
for a t q a ty1 y H F f v t F a t q a ty1 q H
Ž 10 .
otherwise
The same is true for the position f b t of the board member appointed in period t Žnote that the election result bt does not influence future positions.:
f b t s f b ,ty1 y bty1 q a t q bt
Ž 11 .
Appointments of a new banker in each period can no longer be considered as repeated draws from the same population. The larger the board, the higher is the risk of board members with preferences very different from the median position f M of the actual electorate. But the collective choice distortion continues to be reduced for the reasons given above. Again this can be shown by comparing EŽ fm t y f M t . 2 for a one-and a three-member board. The positions of board members appointed in former periods t y 1 and t y 2 are determined by Eq. Ž11.. The following proposition can be derived. Proposition 4. In the model presented in Sections 2 and 3, if elections follow a stochastic process according to Eq. (2) and the ‘ zeitgeist shocks’ on the distribution of Õoter’s preferences giÕen by Eq. (10) follow a stochastic process according to Eq. (7), the expected squared diÕergence between the board’s median position and the electorate’s current median is giÕen by:
°1 2
12 b 2 a 2 q 5a 4 q 4 b 4
~ 24
a
E Ž fm t y f M t . s
¢
2
b q
29 96
2
2
a y
5 12
ab
for b F for b G
a 2 a
Ž 12 .
2
Proof. See Appendix D.9 In principle, EŽ fm t y f M t . 2 behaves as in Section 4.1: it increases with increasing polarization ŽEEŽ fm t y f M t . 2rEb ) 0.; if a is sufficiently small rela9
Again some limit cases are easily checked: the two expressions coincide for bs ar2, EŽ fm t y f M t . 2 s b 2 for as 0, and EŽ fm t y f M t . 2 s 5a2 r24 for bs 0.
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tive to the degree of political polarization, a marginal increase in dispersion reduces the variance of the central bank position:
EE Ž fm t y f M t . Ea
2
°) 0
for a )
~s 0
for a s
¢- 0
for a -
20
b 29 10
9 10 9
Ž 13 .
b
The intuitive explanation for Eq. Ž13. is the same as that given for Eq. Ž9.. Moreover, it is easy to see that a term of three electoral periods still entails a lower expected squared divergence than one of only one period Žwhen EŽ fm t y f M t . 2 s b 2 ., provided a is not larger than 40 br29. To give a numerical example, for b s a and 0 s 1, the expected squared divergence EŽ fm t y f M t . 2 is b 2 , while EŽ fm t y f M t . 2 f 0.88 b 2 for a three-member board.10
5. Conclusions This paper has shown that delegating authority to a central bank board with long terms of office that overlap for individual board members can moderate monetary policy in a polarized political world: if random shocks on the electorate’s preferences Žor on entry costs for political parties. entail shifting party positions, the median position of board members will tend to be more moderate than that of the government. This potential benefit comes, however, at a cost: independent boards can become detached from the current preferences of society. The trade-off depends, as was demonstrated for two special cases of random preference paths, on the intensity of political polarization relative to that of the ‘zeitgeist shocks’. Empirical testing is an obvious next step of further research. The results of two recent papers analyzing data on voting behaviour of central bankers are encouraging. Chappell et al. Ž1993. estimate Taylor reaction functions for single members of the Federal Open Market Committee at the Federal Reserve for 1960–1987, and Berger and Woitek Ž1998. test the dependence of the German Bundesbank’s responses to exogenous shocks on partisan majorities inside its board between 1950 and 1994. Both papers find that governments formed by parties generally considered as Alax on inflationB ŽDemocrats in the USA and Social Democrats in Germany. appoint central bankers who indeed tend to vote for a loose monetary 10
The minimum expected squared divergence for ns 3 is EŽ fm t y f M t . 2 f 0.85b 2 with a ) s 20 br29.
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policy, while the opposite is true for parties in favor of tight monetary policies ŽRepublicans in the USA and the CDU in Germany..11 Moreover, Berger and Woitek Ž1998. find that the Bundesbank’s monetary policy was the softer Žharder., the larger was the majority of the soft Žhard. appointees at the board. They argue that this fact points towards a bargaining mechanism behind the Bundesbank’s decisions, but it is also possible to interpret this result as the median position prevailing if partisan positions are heterogeneous due to ‘zeitgeist shocks’.12 The existence of such ‘zeitgeist shocks’ on monetary policy preferences should not be too controversial: for example, Chappell et al. Ž1993. identify the ‘supply side oriented’ policy of members appointed by the Reagan administration as distinct from the typical republican view on monetary policy. Yet, quantitative measurement of ‘zeitgeist shocks’ might be intricate. Weber Ž1998. has shown that unique equilibria of electoral spacial competition with entry deterrence can exist for more than two established parties.13 In such cases, with no party having an absolute majority, it is difficult to predict which policy will be undertaken Žsee Austen-Smith and Banks, 1988.. Nonetheless, as long as polarization exists, the main argument of this paper continues to hold. This approach also applies to other government committees that are characterized by high autonomy and long-term membership, such as constitutional courts. I have viewed time as a device that generates heterogeneity in the board committee. Other appointment systems might have similar effects. An important alternative is the federal principle that applies to both the US Federal Reserve Board and the European Central Bank. In a purely federal system, members represent diverse regions rather than diverse former and current governments. It is straightforward to apply the argument presented in this paper to the federal case, if ‘zeitgeist shocks’ are replaced by regional ones. Yet, there exists one obvious difference: as the regional distributions of the electorate’s preferences determine the nationwide distribution as well as the positions of the regional representatives in the board, detachment of the long serving representatives from the electorate is no longer an issue. From this point of view, a federal system appears to be more attractive than is a time-oriented one. Other institutional boards formed by regional principles do not appear to fit well into the concept of this paper. Consider parliaments consisting of regional representatives in a two-party system like the British one. Regional peculiarities might entail less polarization of members’ positions compared to a nationwide voting system. Nevertheless, such parliaments are frequently said to create the
11 Contrary to Vaubel Ž1997., Berger and Woitek Ž1997. show that the Bundesbank’s policy appears to be independent of whether or not it shares the partisan views of the government. 12 If partisan positions are homogenous, the prevalence of the median implies either a loose or a tight policy depending on which side has the majority with the relative size of this majority being irrelevant. 13 In this case, then, equilibrium only exists if entry costs are not too high.
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very problem of polarization, which can, as has been argued, be moderated by transmitting power to independent boards. The reason is that parliamentary parties deprive the median position of its power. Hence, a precondition for moderation of a board seems to be the absence of incentives to organize partisan voting. Such a potential incentive is the expectation of a party’s support for re-election. From this perspective, a legal prohibition of multiple terms should further moderation, but this is certainly not the whole story. Clearly, this paper has done no more than to highlight one possibly important aspect of the voting behavior in central bank boards.
Acknowledgements I thank Frank Heinemann, Gerhard Illing, Birgitta Weitz, and two anonymous referees for helpful comments. Any errors are my own.
Appendix A. Proof of the Lemma
Proof. The probability that some lower range f - fm y e Žwhere fm is the median position. contains a number of positions x, follows the binomial distribution f Ž x; n, u . with n being the number of all draws and u the probability that a particular position is inside the range. The probability P for this range to contain the median position is Ž n is any odd integer.: n
P Ž fm - e . s
Ý xs
f Ž x ; n, u .
Ž A.1 .
nq1 2
That is, at least half of the positions plus one have to fall into the defined range. The probability distribution for this event approaches the normal distribution N Ž x; m , s ., as n approaches infinity with m s nu and s 2 s nu Ž1 y u .. If we approximate the probability given in Eq. ŽA.1. by the standardized normal distribution, the lower limit z and the upper limit z of integration are given as: nq1
y nu 2 zs ; 1r2 Ž nu Ž 1 y u . .
™
zs
nŽ 1 y u .
Ž nu Ž 1 y u . .
1r2
™
Ž A.2 .
™
As can easily be seen, z- z Žfor n ) 1.; z, z ` so that N Ž x; 0, 1. 0 for n `. The argument is analogous for an upper preference range f ) fm q e . Both arguments together prove the lemma. I
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
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Appendix B. Proof of Proposition 2 Proof. Eq. ™ Ž5. can be™decomposed into the eight possible combinations of electoral results bt,ty1,ty2 s bi : ` ` 1 E Ž fm2 t . s fm2 f Ž fm . d fm s Ý f 2 f ™Ž f . d fm Ž B.1 . ™ 8 y` m b i m y`
žH
H
bi
/
Any of the eight terms can again be decomposed into the three cases of fm s f t , fm s f ty1 and fm s f ty2 , with f t , f ty1 f ty2 representing the position of the member appointed in t, in the previous election period, and in the one before that, respectively: `
Hy`f
`
2 ™ m fb i
Ž fm . d fm s H fm2 fb™i , f m s f tŽ fm . d fm y`
`
Hy`f
q
`
Hy`f
q
2 ™ m fb i , f m s f ty 1
Ž fm . d fm
2 ™ m fb i , f m s f ty 2
Ž fm . d fm
Ž B.2 .
Given f M s 0, the distribution of the long-run median of voter’s preferences e is: 1 for ya F e F a f Ž e. s 2 a Ž B.3 . 0 otherwise Using Eqs. Ž2. and ŽB.3., the 8 = 3 s 24 cases can be calculated. They differ only by different limits of integration. These ™ limits depend on the condition b c a. This will be shown for the example of b j s Ž bt s b, bty1 s b, bty2 s yb . and fm s f ty2 : the currently appointed central banker and the banker appointed one period before are chosen by a ‘right wing’ government, the banker appointed in t y 2 is ‘left wing’ and holds the median position. For b G a, the probability is 0, because MaxŽ f ty2 . s e q a y b F f t s b and also MaxŽ f ty2 . s e q a y b F MinŽ f ty1 . s e y a q b Žthe ‘zeitgeist shocks’ cannot outweigh the electoral shocks, so that f t - f t -2 cannot be fulfilled.. For b F a, we get:
° ¢
~
`
Hy`f s
2 ™ m fb j, f m s f ty 2
ž
Ž fm . d fm
a
eqay2 b
H2 byaH0 eqa
ž
2 bya
Ž a ty2 y b .
eqa
Heqay2 bH2 b
q
q
a 2q2 b
H2 b
Ž a ty2 y b .
eqay2 b
Hya Heya
2
1 2a
2
1 2a
d a ty2
1 2a
eqa
Ha
ty1 q2 b
d a ty2
Ž a ty2 y b .
2
1 2a
d a ty1 1
2a
d a ty1
1 2a
d a ty2
de 1
2a
/
d a ty1
1 2a
de
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654 a
0
2b
H2 bya HeyaHa
q
ty1 q2 b
Ž a ty2 y b .
2
1 2a
d a ty2
1 2a
d a ty1
1 2a
653
de
/
1 3b 5 y 5ab 4 q 5a 3 b 2 y 5a4 b q 2 a 5
Ž B.4 . 30 a3 The term inside the first large brackets relates to the case f t - f ty2 - f ty1. It integrates over all three random variables e Žwhich is random since f M is normalized to 0., a ty1 , a ty2 . Note the limits of integration: e ) 2 b y a because otherwise, f ty2 - f t cannot be fulfilled; a ty1 ) 0 because otherwise f ty1 - f t ; and a ty2 ) 2 b because otherwise f t ) f ty2 . The term inside the second brackets relates to the case f ty1 - f ty2 - f t . Computations of all 24 cases can be obtained from the author upon request. I s
Appendix C. Proof of Proposition 3 Proof. For n s 1, Eq. Ž6. yields EŽ fm t y f M t . 2 s b 2 . For n s 3 and for a F b, it follows from Eq. Ž8. that EŽ fm t y f M t . 2 - b 2 . For a G b and for any given b, EEŽ fm t y f M t . 2rEa ) 0 is a continuous function; for a s b, EŽ fm t y f M t . 2 - b 2 ; for sufficiently large a, EŽ fm t y f M t . 2 ) b 2 . Thus, for any given b, there exists one aˆ with E Ž fm t y f M t
°F b ~ . sb ¢G b 2
2 2 2
for a F aˆ for a s aˆ for a G aˆ
Ž C.1 . I
Appendix D. Proof of Proposition 4
Proof. The calculation is analogous to that in Appendix B. Again we normalize the median of the present electoral distribution f M to 0 Žand so the position of the recently appointed banker to bt .. All equations and comments up to Eq. ŽB.2. still hold. The limits of integration, however, are now path-dependent. As an example of the 24 cases, the term for bt s yb, bty1 s bty2 s b and b F ar2 is calculated: `
Hy`f
2 ™ m fb i , f m s f t
s Ž yb .
Ž fm . d fm
2
y2 b
žH
ya
a ty1 qa
Hy2 b
1 2a
d a ty2
1 2a
d a ty1
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
654
ay2 b
y2 b
Hy2 b Ha
q
s
ty1 ya
b 2 Ž a2 y 2 b 2 . 4 a2
1 2a
d a ty2
1 2a
d a ty1
/ Ž D.1 .
The first term inside the brackets in the second line depicts the case f ty1 - f t f ty2 , the second, the case f ty2 - f - f ty1. Note that the limits of integration ensure positive values for the density functions. Computations of all cases can be obtained from the author on request. I
References Alesina, A., Rosenthal, H., 1995. Partisan Politics, Divided Government, and the Economy. Cambridge Univ. Press, Cambridge, MA. Austen-Smith, D., Banks, J.S., 1998. Elections, coalitions, and legislative outcomes. American Political Science Review 82, 405–422. Barro, R., Gordon, D., 1983. Rules, discretion, and reputation in a model of monetary policy. Journal of Monetary Economics 12, 101–120. Berger, H., Woitek, U., 1997. How opportunistic are partisan German central bankers: evidence on the Vaubel hypothesis. European Journal of Political Economy 13, 807–821. Berger, H., Woitek, U., 1998. Does concervativism matter? A time series approach to central banking. University of Glasgow Discussion Paper in Economics 9814. Chappell, H., Havrilesky, Th., McGregor, R., 1993. Partisan monetary policies: presidential influence through the power of appointment. The Quarterly Journal of Economics 108, 185–218. Downs, A., 1957. An Economic Theory of Democracy. Harper and Row, New York. Greenberg, J., Shepsle, K., 1987. The effect of electoral rewards in multiparty competition with entry. American Political Science Review 81, 525–537. Neumann, M., 1991. Precommitment by central bank independence. Open Economics Review 2, 95–112. Osborne, M., 1997. Entry-deterring policy differentiation by electoral candidates. McMaster University Discussion Paper, Hamilton. Palfrey, Th., 1984. Spatial equilibrium with entry. Review of Economic Studies 51, 139–156. Vaubel, R., 1997. The bureaucratic and partisan behaviour of independent central banks: German and international evidence. European Journal of Political Economy 13, 201–224. Waller, Ch., 1992. A bargaining model of partisan appointments to the central bank. Journal of Monetary Economics 29, 411–428. Waller, Ch., 1998. Appointing the median voter of a policy board. Federal Reserve Bank of Cleveland Working 9802. Waller, Ch., Walsh, C., 1996. Central-bank independence, economic behaviour, and optimal term length. American Economic Review 86, 1139–1153. Weber, S., 1998. Entry deterrence in electoral spatial competition. Social Choice and Welfare 15, 31–56.
Long-term appointment of central bankers: costs and benefits Axel Lindner ) Department of Economics, Goethe-UniÕersitat, ¨ 60325 Frankfurt am Main, Germany Received 7 January 1999; received in revised form 4 August 1999; accepted 23 September 1999
Abstract Why do independent central bank boards have a reputation for more moderate policy than do elected governments, even if the board’s members have been appointed by the current or former government? This paper gives an explanation for the case of a political world with ‘zeitgeist shocks’ on the electorate’s preferences. If the median position of preferences inside the board determines the monetary policy, a trade-off concerning member term length arises: a longer term entails more moderation, while enhancing the likelihood of detachment from contact to the electorate’s current preferences. q 2000 Elsevier Science B.V. All rights reserved. JEL classification: D71; D72; E58 Keywords: Central banks; Boards; Elections; Becket effect
1. Introduction Central bank independence has a major role in modern economics of monetary policy. In order to enforce independence, it is common wisdom that some legal requirements such as irremovability of board members during the term of office have to be met. The danger of a partisan board by virtue of preferences of board members is rarely considered to be a serious problem. This view is based on empirical observations: central bank boards often seem to behave quite indepen)
Corresponding author. E-mail address: [email protected] ŽA. Lindner..
0176-2680r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 7 6 - 2 6 8 0 Ž 0 0 . 0 0 0 1 2 - 4
640
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
dently of the political forces responsible for the appointment of board members. In particular, a board’s policy tends to be more moderate and consensus-oriented than that of the governing parties. This appears to be the case even when members formerly close to one party are the majority in the committee. This finding is usually referred to as the ‘Becket effect’: apparently, people1 change their behaviour in line with their social position ŽNeumann, 1991.. This paper proposes that a systematic change of member behaviour is not necessary to explain these observations. Instead, it will be assumed that preferences of a single member coincide with the political positions of the appointing government and are fixed over time. The board’s policy will be determined by the preferences of its median member. In this case, moderation of boards with long-term appointments follows from a variant of the law of large numbers, if the political positions of the parties change according to a stationary stochastic process. The behavior of parties will be motivated in a simple public choice model. Moreover, if the polarization of party platforms — and thus of government policies — is inefficient, delegating political power can enhance efficiency. This is the case although every single board member continues to share preferences of the various former governments. The appointment process transforms polarization of partisan views into heterogeneity inside the board, which leads to moderation as long as the median position prevails. On the other hand, common sense suggests that a long-term appointment might result in wide differences between the preferences of the committee and the current electorate. This trade-off between costs and benefits of long-term appointment is the central subject of the paper. The task of modeling appointments of central bankers in a partisan political world has already been undertaken by Waller Ž1992.. Contrary to this paper, Waller’s analysis does not focus on decision making inside the board. Instead, he analyzes an appointment procedure similar to that in the United States: the administration has the right to nominate candidates, who then have to be confirmed by the opposition. The same approach applies to Waller Ž1998.. Aspects of the optimal term length of central bankers have been discussed in a paper by Waller and Walsh Ž1996.. While that paper views the central bank as a single homogenous decision maker and argues that long board member terms reduce uncertainty about monetary policy, I assume heterogeneity within central bank boards as a consequence of appointment of its members via a first-in, first-out system. Hence, I focus on the advantage of moderation in a polarized political world. Although the pioneering model of Downs Ž1957. suggests conÕerging platforms in modern democracies, a polarized environment can frequently be observed Žfor the USA, see Alesina and Rosenthal, 1995.. Such an environment can be easily explained within a public choice framework in the spirit of Palfrey Ž1984.: polarization of two incumbent parties deters entry of competitors at the
1
Like the former counselor to the English king and later Archbishop of Canterbury Thomas Becket.
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fringes of the political spectrum. In a world with linear costs of divergence between conducted policy and individual preferences, the rent maximizing position is the median, so that the board’s tendency to moderation enhances efficiency. The public choice framework is outlined in Section 2. Section 3 introduces the central bank board’s preferences as the result of a stochastic public choice process. This approach is used to assess costs and benefits of long-term appointments in Section 4. Section 5 concludes the paper. 2. The public choice framework The following is based on a simple, frequently used framework for monetary policy in the spirit of Barro and Gordon Ž1983.. There is a trade-off between price level stability and output stability, because monetary policy responding to random supply shocks is more flexible than nominal wage setting. The policy conducted by the central bank depends on the preferences of its board concerning this trade-off. Preferences can be described by f , which is the weight given to price stability relative to output stability. Below, I develop a simple public choice model determining f under the assumption that the monetary authority is subject to full control by the elected government. In general, costs due to the variation in inflation and output are not distributed equally across the electorate. If compensation is not feasible, different individuals will have different preferences with respect to the weight f on price stability. In real world, political preferences for a high f are usually regarded as ‘right wing’, those for a low f as ‘left wing’. This justifies reducing the political preference space to the dimension ‘weight given to price stability’. The assumption of a one-dimensional issue space is the basis of the classic model of a democratic political system of Downs Ž1957.. He found that two competing parties would concentrate at the position of the median voter, so that government policy becomes independent of the outcome of elections. Palfrey Ž1984. modified the Downs model to show that two vote-maximizing incumbent parties will take more polarized positions, if they expect entry of a new competitor. This will deter a candidate, if her objective is not, as Palfrey Ž1984. assumed, the absolute number of votes, but to finish among the most successful parties. For such an objective function, however, equilibrium might not exist Žsee Greenberg and Shepsle, 1987.. This problem is avoided by assuming entry costs for vote maximizing parties. Weber Ž1998. argues convincingly in favor of the importance of fixed entry costs for setting up a new party and running its campaign.2 The following simple model is a special case of Weber’s approach and will serve as the basis for the rest of the paper. 2
A different way of modeling entry deterrence by polarization can be found in Osborne Ž1997.. This approach rests on uncertainty about the voters’ preferences.
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In a world with complete information, two incumbent parties L and R maximize the number of votes for the coming election as their payoff. They do so by positioning their platforms in the issue space, the real closed interval wyH; H x Ž H ) 0.. Next, an outside party O decides whether to enter the election race and, if so, which position to take on. Finally, elections are held: voters give their ballot to that party whose position is closest to their own preferred point in the issue space. In the case of a draw, they randomize with equal probability for the two parties. For simplicity, we assume a uniform distribution of voter’s ideal points f v between yH and H: f Ž fv
°1 ¢0
. s~ 2 H
for yH F f v F H
Ž 1.
otherwise
Hence, the median position, f M , is 0. In addition to timing, the outsider O differs from the incumbent parties in another way: O has to incur fixed promotion costs if it chooses to enter. Entry takes place if there is expectation of a strictly positive payoff in the upcoming election Žestablishing a position for future elections is not an attractive strategy given a high discount rate..3 The assumption of a uniform distribution makes it possible to measure the payoff in form of the number of votes by simply taking the interval of points to which a party position is closer than that of competitors. Entry costs z are measured in the same units. Weber Ž1998. showed the existence of a unique equilibrium of pure strategies for any single-peaked distribution of voters’ ideal points such as the uniform distribution employed here. If entry costs are ‘intermediate’, the entry of the third party is deterred by the incumbents’ polarized positions. In this model, ‘intermediate’ entry costs mean H ) z G Hr2, which implies f L s yH q z, f R s H y z Žassuming that f L is the focus point for L, f R for R ., and no entry of O as equilibrium. The intuition is straightforward: For z G H, the unique equilibrium without consideration of a possible entry, which is both incumbents taking the median position, blocks entry by itself. For z - Hr2, entry cannot be deterred because to block entry at the fringes results in entry in the center. For H ) z G Hr2, however, entry is deterred by a symmetric polarization, which, in equilibrium, is just enough to block entry. It does not pay to enter the race if the highest payoff of votes O can achieve equals z. The optimal entry position would be either close to the left of f L or close to the right of f R . Therefore, in equilibrium, f L s yH q z and f R s H y z. It is easy to see that, ceteris paribus, the incumbents cannot gain by changing their positions: moving 3 Osborne Ž1997. derives the equilibrium without entry costs for a much broader concept, namely a symmetric, unimodal density function. This is not done here, as the public choice model is not the main focus of the paper.
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f R to the right by D, for example, would imply a loss of Dr2 votes to L or, if D is large enough to induce entry between f L and f R , of even more votes to O. Moving to the left would induce entry of O close to the right of f R , leading to a loss of about z votes for R. For the rest of the paper, I assume that H ) z G Hr2 and that the equilibrium strategies are played in every period t. The winning probability for the two incumbent polarized parties is P s 0.5. Let b s H y z Then the position of the government in power, fg t , is simply equal to the random variable bt with the density function: f Ž bt . s
½
0.5 0.5
for bt s yb for bt s b
Ž 2.
The degree of polarization Žas opposed to moderation. will be measured by the variance of the government’s position in t, fg t . This is sf2g t s b 2 if monetary policy is under direct control of the current government in period t.
3. Central bank preferences and policies This section introduces an independent central bank board responsible for monetary policy, which, by assumption, is determined by the median preferences, i.e. the preferences of the median board member fm . The question of interest is under what conditions the board can be expected to conduct a more moderate and, given linear costs of divergence between actual policy and individual preferences, a more efficient policy. The time between two elections is one period. At the end of each period, the central banker with the longest-term length retires. After the election, the new government will replace the banker by a person4 who has preferences identical to its own. This implies a large board if the terms of office are long. A board consisting of three members, for example, includes the appointees of the current and the two former governments. Note that strategic misrepresentation of one’s own preferences by appointing a central banker with more polarized preferences is not a sensible strategy, as the median position Žrather than some weighted average. determines the kind of policy implemented. According to Section 2, each central banker will belong to either the ‘left’ or the ‘right’ party with probability 0.5. Because either party will hold the majority of seats with ex ante probability 0.5, the same holds true for the median member.5 The variance is given by sf2m t s b 2 , as in the case if monetary policy is under direct control of the government. 4 5
The replacement of an entire group is equivalent to that of just one person. In order to exclude the situation of a tie, an odd number of members is assumed.
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Now suppose that election results are not the only random shocks. To avoid the formalization of a Becket effect, we keep the personal preferences of members fixed over time. Instead, the party positions are assumed to vary due to random shifts of the distribution of the electorate. Such unpredictable changes will be referred to as ‘zeitgeist shocks’. They occur at the end of each period before an election takes place. The incumbent parties observe these shocks with sufficient time left to adjust their relative positions to the new distribution of preferences, so that entry will continue to be blocked. Now, the position of the median central bank member is no longer trivial. In particular, it becomes dependent on the number of board members or, in this setting equivalently, of the term length of a single central banker. Section 4 will analyze this aspect for the case of stationary ‘zeitgeist shocks’.
4. Costs and benefits of long-term appointment 4.1. The stationary case The position of the median central banker is a function of the set of board members’ positions. The member appointed in period t takes on the position of the party in power in t. This position is determined by the random election result and the distribution of the electorate’s preferences at t, which depends on the ‘zeitgeist shock’ at t. Formally, the ‘zeitgeist shock’ is captured by the realization at t of the random variable a , with EŽ a . s 0 and sa , so that the density function in Eq. Ž1. becomes: f Ž fv t
°1 ¢0
. s~ 2 H
for e y H q a t F f v t F e q H q a t
Ž 3.
otherwise
with e as the median of the voters’ preferences for a t s 0. Or, put differently, as the stationary expected median of voters’ preferences Ž e has been assumed to be 0 so far.. The incumbent parties consider the ‘zeitgeist shock’ a t when choosing their respective positions. Following Eq. Ž2., the election result for period t can be represented by the random variable bt , so that the position of the board member appointed in t is:
f b t s e q a t q bt
Ž 4.
The shocks a t and bt are assumed to be uncorrelated, as are the time path observations in this subsection. Fig. 1 illustrates the position of the median banker for the cases of 3 and 9 period term lengths, respectively. The distribution of the random variable a is bounded by wya; ax. The median position fm t is encircled. The board with nine members takes on a more moderate position. This is not a coincidence: intuitively, the larger the board,
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
645
Fig. 1. Random central bank preferences for term lengths 3 and 9.
the more probable is an almost equal number of AleftB and ArightB members, implying that the median position is at the inner side of one of the two groups. The inner side shifts to the center, as more and more members enter the board. This effect is closely related to the law of large numbers: by drawing a sample from a population with finite variance, the distribution of the sample mean becomes more and more concentrated near the population mean as the sample size increases. Since the emergence of new board members’ positions is a stationary stochastic process, it can be regarded as a repeated drawing from the population of all potential board members. What is of interest in this context, though, is the distribution of the median rather than that of the mean. The following lemma can be proven:
Lemma 1. Consider a random sample drawn from a one-dimensional numerical population. For the median of this sample, the probability of being outside an arbitrary range around the median of the population approaches 0 as the sample size approaches infinity. Proof. See Appendix A. In other words, it is always possible for the most moderate position to become the median position of the board almost with certainty, if the board becomes sufficiently large. But moderation comes at a cost. If the ‘zeitgeist shocks’ are very large, the moderate median position inside a long-term board, despite mitigating the collective choice inefficiency, might not closely reflect the electorate’s current preferences. This trade-off is central to assessing alternative term lengths. The criterion used in the following is the expected squared divergence between the board’s median position and the electorate’s current median, EŽ fm t y f M t . 2 . It will be applied to a one- and a three-member board, respectively. If the election period is taken to be 4 years long, this implies comparing term lengths of 4 and 12 years.6 6
Members of the FED’s board of governors regularly serve 14 years, which is by far the longest term of office for central bankers in any major central bank board.
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In order to simplify the calculations, the electorate’s current median will be normalized to 0: f M t s 0. This yields the following expression: 2
`
2
E Ž fm t y f M t . s E Ž fm t . s
Hy`f
2 mt
f Ž fm t . d fm t
Ž 5.
As stated above, the random shift of the electoral median happens prior to the election, allowing party positions to adapt. During the government’s term of office, the electorate’s preferences are assumed to be fixed. For a one-member board, EŽ fm t y f M t . 2 depends only on the uncertainty of the electoral results. This leads to the Žvery simple. first proposition. Proposition 1. In the model presented in Sections 2 and 3, if elections follow a stochastic process according to Eq. (2), the expected squared diÕergence between the board’s median position and the electorate’s current median is giÕen by: E(fm t y f M t ) 2 s b 2 . Proof. 2
E Ž fm t y f M t . s
b2
b2 q
2
2
s b2
I
Ž 6.
For a multiple-member board, the position of each board member relative to f M t depends on the electoral shock bt and, for all but the youngest members, on the random electoral shifts a . The distribution of a is assumed to be uniform:
° ¢
1 f Ž at . s 2 a 0
~
for ya F a t F a
,
Ž 7.
otherwise
with a ) 0. Under this assumption, EŽ fm t y f M t . 2 can be derived: Proposition 2. In the model presented in Sections 2 and 3, if elections follow a stochastic process according to Eq. (2) and the ‘ zeitgeist shocks’ to the distribution of Õoters’ preferences giÕen by Eq. (3) follow a stochastic process according to Eq. (7), the expected squared diÕergence between the board’s median position and the electorate’s current median, E(fm t y f M t ) 2 , for a three-member board is giÕen by:
2
°1
10b 2 a3 q 8 a 5 q 10 b 3 a 2 y b 5
~ 30
a3
E Ž fm t y f M t . s
¢
2
b q
2 5
2
a y
1 2
for a G b
Ž 8. ab
for a F b
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
647
Proof. See Appendix B.7 Differentiation shows that EŽ fm t y f M t . 2 increases with a greater degree of polarization: EEŽ fm t y f M t . 2rEb ) 0. More interesting is the dependence of EŽ fm t y f M t . 2 on a:
EE Ž fm t y f M t . Ea
2
°) 0
for a )
~s 0
for a s
¢- 0
for a -
5 8 5 8 5 8
b b
Ž 9.
b
If the dispersion a of the ‘zeitgeist shock’ is sufficiently small relative to the political polarization, a marginal increase in dispersion reduces the expected squared divergence between the board’s median position and the electorate’s current median. The intuitive explanation follows from the above argument: party polarization has less impact if the dispersion between party supporters is larger, because the moderate positions are more likely to be the median than extreme ones for n ) 1. This is the argument in favor of longer term lengths, but it has to be qualified: a term of three election periods entails a lower expected squared divergence between the board’s median position and the electorate’s current median than does one of only one period, provided a is not too large relative to b Žnot larger than about 1.25b .. Proposition 3. For eÕery b, there exists a critical aˆ so that E(fm t y f M t ) 2 is larger (smaller) for a three-member board than for a one-member board, if a is larger (smaller) than a. ˆ Proof. See Appendix C. This result is due to the already mentioned trade-off between moderation and the importance of the latest ‘zeitgeist shock’: if a is very large, the benefits of the moderation effect of long-term membership are outweighed by the high probability of a large gap between the current electorate’s preferences and the median position of the board. A numeric illustration shows that for b s a, we have EŽ fm t y f M t . 2 s b 2 for the case n s 1, and EŽ fm t y f M t . 2 s Ž9r10. b 2 for n s 3.8 7
It is easy to check the result for some special cases: the two expressions coincide for bs a, EŽ fm t y f M t . 2 s b 2 for as 0, and EŽ fm t y f M t . 2 s Ž4r15. a 2 for bs 0. 8 The ‘zeitgeist shock’ minimizing EŽ fm t y f M t . 2 for ns 3 is a ) s Ž5r8. b. In this case, EŽ fm t y f M t . 2 f 0.84 b 2 .
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4.2. The random walk case The analysis in Section 4.1 was confined to the stationary case: the expected median of the electoral preferences e was constant in every period. This is a rather strong assumption. Alternatively, a high electoral median in one period might imply a high expected median in the following one. The simplest stochastic process formalizing this principle is the random walk. In this case, the electoral distribution is path-dependent: f Ž fv t
°1 ¢0
. s~ 2 H
for a t q a ty1 y H F f v t F a t q a ty1 q H
Ž 10 .
otherwise
The same is true for the position f b t of the board member appointed in period t Žnote that the election result bt does not influence future positions.:
f b t s f b ,ty1 y bty1 q a t q bt
Ž 11 .
Appointments of a new banker in each period can no longer be considered as repeated draws from the same population. The larger the board, the higher is the risk of board members with preferences very different from the median position f M of the actual electorate. But the collective choice distortion continues to be reduced for the reasons given above. Again this can be shown by comparing EŽ fm t y f M t . 2 for a one-and a three-member board. The positions of board members appointed in former periods t y 1 and t y 2 are determined by Eq. Ž11.. The following proposition can be derived. Proposition 4. In the model presented in Sections 2 and 3, if elections follow a stochastic process according to Eq. (2) and the ‘ zeitgeist shocks’ on the distribution of Õoter’s preferences giÕen by Eq. (10) follow a stochastic process according to Eq. (7), the expected squared diÕergence between the board’s median position and the electorate’s current median is giÕen by:
°1 2
12 b 2 a 2 q 5a 4 q 4 b 4
~ 24
a
E Ž fm t y f M t . s
¢
2
b q
29 96
2
2
a y
5 12
ab
for b F for b G
a 2 a
Ž 12 .
2
Proof. See Appendix D.9 In principle, EŽ fm t y f M t . 2 behaves as in Section 4.1: it increases with increasing polarization ŽEEŽ fm t y f M t . 2rEb ) 0.; if a is sufficiently small rela9
Again some limit cases are easily checked: the two expressions coincide for bs ar2, EŽ fm t y f M t . 2 s b 2 for as 0, and EŽ fm t y f M t . 2 s 5a2 r24 for bs 0.
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649
tive to the degree of political polarization, a marginal increase in dispersion reduces the variance of the central bank position:
EE Ž fm t y f M t . Ea
2
°) 0
for a )
~s 0
for a s
¢- 0
for a -
20
b 29 10
9 10 9
Ž 13 .
b
The intuitive explanation for Eq. Ž13. is the same as that given for Eq. Ž9.. Moreover, it is easy to see that a term of three electoral periods still entails a lower expected squared divergence than one of only one period Žwhen EŽ fm t y f M t . 2 s b 2 ., provided a is not larger than 40 br29. To give a numerical example, for b s a and 0 s 1, the expected squared divergence EŽ fm t y f M t . 2 is b 2 , while EŽ fm t y f M t . 2 f 0.88 b 2 for a three-member board.10
5. Conclusions This paper has shown that delegating authority to a central bank board with long terms of office that overlap for individual board members can moderate monetary policy in a polarized political world: if random shocks on the electorate’s preferences Žor on entry costs for political parties. entail shifting party positions, the median position of board members will tend to be more moderate than that of the government. This potential benefit comes, however, at a cost: independent boards can become detached from the current preferences of society. The trade-off depends, as was demonstrated for two special cases of random preference paths, on the intensity of political polarization relative to that of the ‘zeitgeist shocks’. Empirical testing is an obvious next step of further research. The results of two recent papers analyzing data on voting behaviour of central bankers are encouraging. Chappell et al. Ž1993. estimate Taylor reaction functions for single members of the Federal Open Market Committee at the Federal Reserve for 1960–1987, and Berger and Woitek Ž1998. test the dependence of the German Bundesbank’s responses to exogenous shocks on partisan majorities inside its board between 1950 and 1994. Both papers find that governments formed by parties generally considered as Alax on inflationB ŽDemocrats in the USA and Social Democrats in Germany. appoint central bankers who indeed tend to vote for a loose monetary 10
The minimum expected squared divergence for ns 3 is EŽ fm t y f M t . 2 f 0.85b 2 with a ) s 20 br29.
650
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
policy, while the opposite is true for parties in favor of tight monetary policies ŽRepublicans in the USA and the CDU in Germany..11 Moreover, Berger and Woitek Ž1998. find that the Bundesbank’s monetary policy was the softer Žharder., the larger was the majority of the soft Žhard. appointees at the board. They argue that this fact points towards a bargaining mechanism behind the Bundesbank’s decisions, but it is also possible to interpret this result as the median position prevailing if partisan positions are heterogeneous due to ‘zeitgeist shocks’.12 The existence of such ‘zeitgeist shocks’ on monetary policy preferences should not be too controversial: for example, Chappell et al. Ž1993. identify the ‘supply side oriented’ policy of members appointed by the Reagan administration as distinct from the typical republican view on monetary policy. Yet, quantitative measurement of ‘zeitgeist shocks’ might be intricate. Weber Ž1998. has shown that unique equilibria of electoral spacial competition with entry deterrence can exist for more than two established parties.13 In such cases, with no party having an absolute majority, it is difficult to predict which policy will be undertaken Žsee Austen-Smith and Banks, 1988.. Nonetheless, as long as polarization exists, the main argument of this paper continues to hold. This approach also applies to other government committees that are characterized by high autonomy and long-term membership, such as constitutional courts. I have viewed time as a device that generates heterogeneity in the board committee. Other appointment systems might have similar effects. An important alternative is the federal principle that applies to both the US Federal Reserve Board and the European Central Bank. In a purely federal system, members represent diverse regions rather than diverse former and current governments. It is straightforward to apply the argument presented in this paper to the federal case, if ‘zeitgeist shocks’ are replaced by regional ones. Yet, there exists one obvious difference: as the regional distributions of the electorate’s preferences determine the nationwide distribution as well as the positions of the regional representatives in the board, detachment of the long serving representatives from the electorate is no longer an issue. From this point of view, a federal system appears to be more attractive than is a time-oriented one. Other institutional boards formed by regional principles do not appear to fit well into the concept of this paper. Consider parliaments consisting of regional representatives in a two-party system like the British one. Regional peculiarities might entail less polarization of members’ positions compared to a nationwide voting system. Nevertheless, such parliaments are frequently said to create the
11 Contrary to Vaubel Ž1997., Berger and Woitek Ž1997. show that the Bundesbank’s policy appears to be independent of whether or not it shares the partisan views of the government. 12 If partisan positions are homogenous, the prevalence of the median implies either a loose or a tight policy depending on which side has the majority with the relative size of this majority being irrelevant. 13 In this case, then, equilibrium only exists if entry costs are not too high.
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
651
very problem of polarization, which can, as has been argued, be moderated by transmitting power to independent boards. The reason is that parliamentary parties deprive the median position of its power. Hence, a precondition for moderation of a board seems to be the absence of incentives to organize partisan voting. Such a potential incentive is the expectation of a party’s support for re-election. From this perspective, a legal prohibition of multiple terms should further moderation, but this is certainly not the whole story. Clearly, this paper has done no more than to highlight one possibly important aspect of the voting behavior in central bank boards.
Acknowledgements I thank Frank Heinemann, Gerhard Illing, Birgitta Weitz, and two anonymous referees for helpful comments. Any errors are my own.
Appendix A. Proof of the Lemma
Proof. The probability that some lower range f - fm y e Žwhere fm is the median position. contains a number of positions x, follows the binomial distribution f Ž x; n, u . with n being the number of all draws and u the probability that a particular position is inside the range. The probability P for this range to contain the median position is Ž n is any odd integer.: n
P Ž fm - e . s
Ý xs
f Ž x ; n, u .
Ž A.1 .
nq1 2
That is, at least half of the positions plus one have to fall into the defined range. The probability distribution for this event approaches the normal distribution N Ž x; m , s ., as n approaches infinity with m s nu and s 2 s nu Ž1 y u .. If we approximate the probability given in Eq. ŽA.1. by the standardized normal distribution, the lower limit z and the upper limit z of integration are given as: nq1
y nu 2 zs ; 1r2 Ž nu Ž 1 y u . .
™
zs
nŽ 1 y u .
Ž nu Ž 1 y u . .
1r2
™
Ž A.2 .
™
As can easily be seen, z- z Žfor n ) 1.; z, z ` so that N Ž x; 0, 1. 0 for n `. The argument is analogous for an upper preference range f ) fm q e . Both arguments together prove the lemma. I
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
652
Appendix B. Proof of Proposition 2 Proof. Eq. ™ Ž5. can be™decomposed into the eight possible combinations of electoral results bt,ty1,ty2 s bi : ` ` 1 E Ž fm2 t . s fm2 f Ž fm . d fm s Ý f 2 f ™Ž f . d fm Ž B.1 . ™ 8 y` m b i m y`
žH
H
bi
/
Any of the eight terms can again be decomposed into the three cases of fm s f t , fm s f ty1 and fm s f ty2 , with f t , f ty1 f ty2 representing the position of the member appointed in t, in the previous election period, and in the one before that, respectively: `
Hy`f
`
2 ™ m fb i
Ž fm . d fm s H fm2 fb™i , f m s f tŽ fm . d fm y`
`
Hy`f
q
`
Hy`f
q
2 ™ m fb i , f m s f ty 1
Ž fm . d fm
2 ™ m fb i , f m s f ty 2
Ž fm . d fm
Ž B.2 .
Given f M s 0, the distribution of the long-run median of voter’s preferences e is: 1 for ya F e F a f Ž e. s 2 a Ž B.3 . 0 otherwise Using Eqs. Ž2. and ŽB.3., the 8 = 3 s 24 cases can be calculated. They differ only by different limits of integration. These ™ limits depend on the condition b c a. This will be shown for the example of b j s Ž bt s b, bty1 s b, bty2 s yb . and fm s f ty2 : the currently appointed central banker and the banker appointed one period before are chosen by a ‘right wing’ government, the banker appointed in t y 2 is ‘left wing’ and holds the median position. For b G a, the probability is 0, because MaxŽ f ty2 . s e q a y b F f t s b and also MaxŽ f ty2 . s e q a y b F MinŽ f ty1 . s e y a q b Žthe ‘zeitgeist shocks’ cannot outweigh the electoral shocks, so that f t - f t -2 cannot be fulfilled.. For b F a, we get:
° ¢
~
`
Hy`f s
2 ™ m fb j, f m s f ty 2
ž
Ž fm . d fm
a
eqay2 b
H2 byaH0 eqa
ž
2 bya
Ž a ty2 y b .
eqa
Heqay2 bH2 b
q
q
a 2q2 b
H2 b
Ž a ty2 y b .
eqay2 b
Hya Heya
2
1 2a
2
1 2a
d a ty2
1 2a
eqa
Ha
ty1 q2 b
d a ty2
Ž a ty2 y b .
2
1 2a
d a ty1 1
2a
d a ty1
1 2a
d a ty2
de 1
2a
/
d a ty1
1 2a
de
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654 a
0
2b
H2 bya HeyaHa
q
ty1 q2 b
Ž a ty2 y b .
2
1 2a
d a ty2
1 2a
d a ty1
1 2a
653
de
/
1 3b 5 y 5ab 4 q 5a 3 b 2 y 5a4 b q 2 a 5
Ž B.4 . 30 a3 The term inside the first large brackets relates to the case f t - f ty2 - f ty1. It integrates over all three random variables e Žwhich is random since f M is normalized to 0., a ty1 , a ty2 . Note the limits of integration: e ) 2 b y a because otherwise, f ty2 - f t cannot be fulfilled; a ty1 ) 0 because otherwise f ty1 - f t ; and a ty2 ) 2 b because otherwise f t ) f ty2 . The term inside the second brackets relates to the case f ty1 - f ty2 - f t . Computations of all 24 cases can be obtained from the author upon request. I s
Appendix C. Proof of Proposition 3 Proof. For n s 1, Eq. Ž6. yields EŽ fm t y f M t . 2 s b 2 . For n s 3 and for a F b, it follows from Eq. Ž8. that EŽ fm t y f M t . 2 - b 2 . For a G b and for any given b, EEŽ fm t y f M t . 2rEa ) 0 is a continuous function; for a s b, EŽ fm t y f M t . 2 - b 2 ; for sufficiently large a, EŽ fm t y f M t . 2 ) b 2 . Thus, for any given b, there exists one aˆ with E Ž fm t y f M t
°F b ~ . sb ¢G b 2
2 2 2
for a F aˆ for a s aˆ for a G aˆ
Ž C.1 . I
Appendix D. Proof of Proposition 4
Proof. The calculation is analogous to that in Appendix B. Again we normalize the median of the present electoral distribution f M to 0 Žand so the position of the recently appointed banker to bt .. All equations and comments up to Eq. ŽB.2. still hold. The limits of integration, however, are now path-dependent. As an example of the 24 cases, the term for bt s yb, bty1 s bty2 s b and b F ar2 is calculated: `
Hy`f
2 ™ m fb i , f m s f t
s Ž yb .
Ž fm . d fm
2
y2 b
žH
ya
a ty1 qa
Hy2 b
1 2a
d a ty2
1 2a
d a ty1
A. Lindnerr European Journal of Political Economy 16 (2000) 639–654
654
ay2 b
y2 b
Hy2 b Ha
q
s
ty1 ya
b 2 Ž a2 y 2 b 2 . 4 a2
1 2a
d a ty2
1 2a
d a ty1
/ Ž D.1 .
The first term inside the brackets in the second line depicts the case f ty1 - f t f ty2 , the second, the case f ty2 - f - f ty1. Note that the limits of integration ensure positive values for the density functions. Computations of all cases can be obtained from the author on request. I
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