GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.96

Optimal Structure of Monetary Policy Committees

Keiichi Morimoto

October 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Optimal Structure of Monetary Policy Committees∗
Keiichi Morimoto†
October, 2009

Abstract
This paper explores an optimal personnel organization problem of monetary
policy committees. First, I construct an analytically tractable model for monetary
policy analysis which starts from decision-making in the monetary policy committee. Using the model, I investigate the relationship between preference heterogeneity among the committee members and the optimal structure of the monetary
policy committee. The result shows that it is optimal in general cases to appoint
not only inﬂation-minded (hawkish) persons but also output-minded (dovish) persons. This is a justiﬁcation for the fact that the actual monetary policy committees(e.g. MPC of Bank of England and FOMC) usually consist of both type members
as the empirical researches suggest.

Keywords: monetary policy, committee, delegation, imperfect information
JEL Classiﬁcation: D71; D84; E58∗

I am very grateful to Kazuo Mino and Koichi Futagami for their invaluable advice and encouragement. I also thank Masaki Aoyagi, Ryo Arawatari and the participants of the Fall Meeting (2009) ofJapanese Economic Association for their helpful comments. I acknowledge ﬁnancial support from the
Research Fellowships for Young Scientists of the Japan Society for the Promotion of Science (JSPS).
†
Graduate School of Economics, Osaka University, 1-7, Machikaneyama, Toyonaka, Osaka 560-0043,
Japan. E-mail address: gge014mk@mail2.econ.osaka-u.ac.jp

1

Introduction

How should the monetary policy committees be organized? This paper addresses thisproblem. Since about a decade ago, the central banks of many countries have establishedthe formal committees for decision-making on monetary policy one after another: England, Japan, Sweden, Brazil and so on. This trend of central banking by committees
brings some important problems on monetary policy design to macroeconomists. 1 The
next three are representative ones. Why have the committees replaced the single policy
makers in most central banks? How should the committees collect the members’ views
and adjust the diﬀerences of their opinions? Who should be chosen for members of thecommittees? In this paper, I focus on the third. 2
The question is signiﬁcant in terms of the actual institutions. In most countries,
the procedure for appointing members of the monetary policy committee is one of legal
mandates. The Monetary Policy Committee of Bank of England consists of nine members.
Five are from the inside of Bank of England and four from the outside. FOMC of theFederal Reserve System consists of twelve members. Five are district bank presidents, theinsiders, and seven are politically appointed governors, the outsiders. Thus, the optimal
personnel organization problem of monetary policy committees is one of the objects ofmonetary policy design. This paper analyze it in view of information imperfectness andcoordination behavior of the monetary policy committee.
There are empirical studies on a related topic which provide the interesting facts of
the actual monetary policy committees. The monetary policy committees often consistof the outsiders and insiders and the outsiders are apt to prefer more ﬂexible monetary
policy than the insiders. Bhattacharjee and Holly (2006) reports that in the Monetary
Policy Committee of Bank of England, the outsiders tend to be more output-minded than
the insiders according to the voting records of the meetings. Meade and Sheets (2005)
ﬁnd the empirical fact that in FOMC, the district bank presidents (the insiders) seems
more inﬂation-minded than the governors (the outsiders) on average.
Considering the facts above, this paper gives the next answer for the optimal personnel
organization problem. It is optimal in general cases to appoint not only inﬂation-minded(hawkish) persons but also output-minded (dovish) persons. The mechanism for this is asfollows. Under imperfect information, along with coordination behavior, the monetary
policy committee fails to set the optimal level of nominal interest rate corresponding
to the economic state. It causes ineﬃcient volatility of the demand side of the macro
economy. This also brings excessive volatility of inﬂation through the AS relation. The
1
2

Blinder (2004, 2007) provides a brief survey of this issue.
I will show that the answer for the third solves the ﬁrst.

1

output-minded committee members play the role of mitigating these eﬀects, while theinﬂation-minded members balance monetary policy by stabilizing expected and current
inﬂation.
This paper’s argument is related to another problem. Despite the facts above, thepopular belief, which may be based on the established theory, is that central bankers
should concern primarily with inﬂation stabilization. Since the seminal work by Rogoﬀ(1985), many theoretical studies focus on the optimal delegation of monetary policy tosingle policy makers. In various economic environments, they suggest that appointing
conservative central bankers, who place on higher weights on the real objectives (e.g.
output and unemployment) relative to inﬂation than society, improves social welfare under the discretionary policy regimes. 3 Adding to the theoretical studies, the discussions
on practice of central banking usually emphasis on importance of conservatism and it is
widely regarded as common sense on contemporary central banking.
So, why is the actual monetary policy not delegated to only (single) conservative
central bankers? This papers’ main result answers this. Under imperfect information,to accommodate control error of the demand side of the economy, it is desirable in viewof social welfare to include output-minded persons in the monetary policy committee tosome extent.
There is a few existing studies on the appointments of the monetary policy committees. Waller (1992) analyzes the endogenous appointment of the monetary policy committee by modeling the situation that the dovish and hawkish political parties bargain overdesignating the monetary policy committee. Faust (1996) tries to explain theoretically
why the FOMC is a compound of the district bank presidents and politically appointed
governors by showing that preference heterogeneity among the FOMC members lowers
ineﬃcient inﬂation under peculiar voting structure. However, as Blinder (2007) claims,
these existing literature does not clarify why the monetary policy committees replace
single policy makers and why the actual central banks do not just follow the Rogoﬀ’s(1985) suggestion and appoint only a single conservative central banker. This paper’s
result gives an answer for these questions by showing the merit of preference heterogeneity among the members and especially, the welfare-improving role of the output-mindedmembers.
In the methodological aspect, this paper provides a way to model monetary policy bycommittee easily. To conduct a simple welfare analysis, I construct a tractable forwardlooking model that starts from decision-making of monetary policy committees. The
model consists of two parts. One part is a macroeconomic model which gives macroe3

See, for examples, Adam and Billi (2008), Svensson (1997), Vestin (2006), Walsh (2003a) and etc.

2conomic consequences of decision-making by committees and their welfare evaluation. I
adopt a basic New Keynesian model as the underlying macroeconomic model since it
has a rigorous micro foundation and is used for a benchmark model for contemporarymonetary policy analysis. However, according to the analysis later, it will appear thatthe approach in this paper is applicable to a wide class of forward-looking macroeconomic models. The other part is a microeconomic model which describes the process ofdecision-making in the committee. I assume that the committee members play a variant of the beauty contest game, which was exploited by Morris and Shin (2002), in thedecision-making on setting nominal interest rate. This simple structure makes it possible to model a strategic situation in the monetary policy committee and shows that theframework of this paper applies to the class of the games that have linear equilibrium
strategies as in many applied game-theoretic studies.
In the literature, several works deal with monetary policy by committees. GelrachKristen (2006) uses a (backward-looking) traditional Keynesian model and compares themacroeconomic consequences of alternative aggregation rules of the committee members’
votes on economic conditions, which are honestly declared according to their information
without any strategic manipulations. Sibert (2003) and Mihov and Sibert (2006) use
a Lucas type Phillips curve and analyze the role of reputation for monetary policy bycommittees in view of communication with the private sector. Therefore, the technicalinnovation of this paper is that it gives the way to analyze the game structures in monetary
policy committees and connect it simply to various contemporary macroeconomic models.
The rest of this paper is organized as follows. Section 2 sets up a benchmark modeland describes equilibrium. As the benchmark, I treat the case of homogeneous committee
members. Section 3 analyzes the optimal delegation of monetary policy in the benchmark
model, which reveals the desirable type of central bankers in the economic environment
this paper assumes. Section 4 extends the benchmark model to the case of heterogeneouscommittee members which the empirical studies report. Based on the results in Section
3, I analyze the optimal personnel organization of monetary policy committees. Section
5 concludes.

2

Benchmark Model

This section provides a detail explanation of the benchmark model and the description ofequilibrium. The model can be partitioned into the two parts. One is a macroeconomic
model, which determines the consequences of monetary policy. The other is a microe3

conomic model that describes the process of decision-makings in the monetary policy
committee. By connecting the two models, we can discuss the welfare implication andthe design of the committee structure.

2.1

Macroeconomic Model

As the underlying macroeconomic model, I adopt a basic New Keynesian model. 4 The
model consists of the following two dynamic equations
1(it − Et πt+1 ) + ut ,σ
= βEt πt+1 + κxt + et ,xt = Et xt+1 −

(1)

πt

(2)

together with a monetary policy rule. Here, xt , it , πt , ut and et denote output gap, nominal interest rate, inﬂation rate, demand shock and cost shock in period t, respectively.
Parameters σ, β and κ are positive constants, where σ is the degree of constant relativerisk aversion, β is the discount factor and κ is the impact of one unit of output gap on
inﬂation. The symbol Et denotes a mathematical expectation conditioned on information∞
available to the private agents in period t. I assume that {ut }∞t=0 and {et }t=0 follow AR(1) processes such thatut = ρu ut−1 + ϕt ,et = ρe et−1 + ψt ,where ρu , ρe ∈ [0, 1) and ϕt and ψt follow independently the normal distributions withmean 0 and variance σϕ2 and σψ2 , respectively.
Equation (1), the dynamic IS curve, represents the AD relation that is derived fromthe Euler equation of household. Equation (2), the New Keynesian Phillips curve, is
the AS relation which is a linear approximation of the ﬁrms’ optimization condition andthe dynamic equation of average price under price-stickiness. The parameter κ depends
on the structural parameters which represent the technology of the ﬁrms, the degree of
price-stickiness and so on. If necessary, we specify the function form of the household
utility function and the micro structure behind the New Keynesian Phillips curve but for
the time being, we treat κ itself as one of the structural parameters for simplicity.
One of the reason why we use the New Keynesian model is that the model has goodand manageable property in view of modern central banking in that the macroeconomic
dynamics is determined once a setting rule of the central bank’s policy instrument, it ,is speciﬁed. Many central banks today, as widely known, adopt nominal interest rate
4

For detail of a micro foundation of New Keynesian models, see Ch.5 of Walsh (2003b).

4

as their policy instruments. So that, the most important part of decision-making in themonetary policy committee is determination of policy interest rate. The New Keynesianmodel is appropriate to incorporate it. The other reason is that welfare analysis ismeaningful in the New Keynesian framework because it has rigorous micro foundations
and thus clariﬁes the source of ineﬃciency in the market economy and the goal and roleof monetary policy.
Along the line of Woodford (2002), the social loss function is endogenously determinedas the second order approximation of household’s utility function and its function form
is proportional toE0∞∑

β t (πt2 + λx2t ),t=0where λ is the weight which society places on output gap relative to inﬂation as disutility.
The parameter λ depends on the structural parameters in the way that is determined
once we assume a particular micro foundation of the New Keynesian model. I treat,
however, λ as a structural parameter for analytical ease unless a speciﬁcation is needed.
5
Since the purpose of this paper is to analyze an optimal institution design problem ofmonetary policy committees, I focus on only the average performance of monetary policy.
Thus, I reset the social loss function to 6
L ≡ V [π] + λV [x],(3)where V [π] and V [x] are asymptotic variances of inﬂation rate and output gap respectively.

2.2

Monetary Policy Committee

Next, I set up the decision-making process of the monetary policy committee in thismodel. The committee consists of N ≥ 2 members. Here, assume that all member is(ex-ante) homogenous in this benchmark model. To make a decision on monetary policy,
they receive noisy signals on the economic condition. Given realizations of signals, any
5

The results of this paper are invariant as long as we specify a form of λ which depends on a usual
micro foundation of the New Keynesian model.
6
The average social loss L can be obtained by
L = lim (1 − β)E0

∞
∑

β→1

t=0

5

(
)
β t πt2 + λx2t .

committee member j votes a level of nominal interest rate, ij , to maximize his/her own
payoﬀ and then all votin rates are aggregated by a speciﬁc rule.
First, let us see the detail of the informational structure of the monetary policy
committee. As in the actual monetary policy procedure, I assume the situation thatdecision-making on policy instrument setting in each period must be done with noisy
information about the economic state in the concerned period before it reveals. In theend of period t − 1, each member receives the two kinds of noisy signals on innovations ofdemand shock and cost shock in period t. One is common and the other is idiosyncratic
signal. The common signals on innovations of demand shock and cost shock are of thestandard form such that
ϕct = ϕt + µt ,
ψtc = ψt + νt ,where µt and νt are independent and serially uncorrelated noises which are normally
distributed with mean zero and variance σµ2 and σν2 , respectively. Each member knows
the distribution of µt and νt and that realizations of ϕct and ψtc are common to everyone.
The common signals can be interpreted as well-balanced recognition among economists on
the future economic condition or the result of discussions in the committee which usuallydepend on suggestion of the report by the research staﬀ of the central bank. 7 In actual,
the monetary policy committees usually begin with staﬀ reports on economic conditions.
For example, every meeting of FOMC begins with a staﬀ report and discussion on theeconomic condition. 8
Besides, there is probably idiosyncrasy among the committee members’ assessments
on future economic developments. Each committee member j receives idiosyncratic signal
on innovations of demand shock and cost shock of the form such that
ϕjt = ϕt + εjt ,ψtj = ψt + ηtj ,where εjt and ηtj are independent and serially uncorrelated noises which are normally distributed with mean zero and variance σε2 and ση2 , respectively. They know the distributionof the noise terms and that these are common to them but do not know realizations of
the others’ idiosyncratic signals. That is, idiosyncratic signals are private information ofeach member. For simplicity, I assume that similar to the private agents, the central bank7
8

In this paper, to keep the model simple, I do not deal with the issues of communication.
Chappell, McGregor and Vermilyea (2005) explains this point precisely.

6can observe innovations of demand shock and cost shock in period t once they realize inthe beginning of period t. 9
Second, consider the behavior of the committee members. Assume that any member
j votes a level of nominal interest rate in period t, ijt , to minimize the following loss
function][(1 ∑ k )2
j
j
j
j
∗ 2
lt = Et−1 (1 − r)(it − it ) + r it −i,
N − 1 k6=j t
where r ∈ [0, 1], i∗t is the level of interest rate in period t which would be set in optimaljmonetary policy under perfect information and Et−1
is a mathematical expectation conditioned on information available to member j in the end of period t − 1. The meaningof this function form is that each member concerns with the weighted sum of accuracy of
his/her vote on interest rate (the ﬁrst term) and the distance between it and the averageof the others members’ votes (the second term). Therefore, using the available information, the committee members seek to balance the two objectives: to spot the genuine
optimal level of interest rate and to coordinate with the others. Thus, the parameter r isinterpreted as a measure of a motive for coordination or strategic complementarity. The
presence of the coordination motive among the committee members reﬂects that they
dislike standing out in the committee in that they care the position in the committee,
the relationship with the other members and the release of the voting record.
In this paper, I mean optimal policy for optimal discretionary policy. Indeed, it might
be natural to adopt optimal commitment policy but there is no analytical solution in thepolicy regime. Besides, the policy implication generated from introducing the decisionmaking of the monetary policy committee does not change in the both regimes. So, I
adopt optimal discretionary policy and keep the model analytically tractable. As usuallyseen in the New Keynesian literature, equilibrium interest rate in optimal discretionary
monetary policy under perfect information, i∗t , is the solution of the following linearquadratic problem
min πt2 + λc x2t ,1(it − Et πt+1 ) + ut ,σπt = βEt πt+1 + κxt + et ,s.t. xt = Et xt+1 −where the parameter λc > 0 is the relative weight that the committee members place on
output gap. Note that it is not necessarily identical to society’s weight. This preference
9Thus, except the process of decision-making on policy instrument setting, this paper’s model is amodel with perfect information.

7

parameter can be thought to represent the underlying preference of the committee members in that it determines their attitudes on desirable trade-oﬀ of monetary policy. The
solution of the problem above is 10i∗t = σut + Φet ,ce +(1−ρe )σκwhere Φ = λλcρ(1−βρ
2 .
e )+κ
The game described above is a variant of the beauty contest framework exploited
by Morris and Shin (2002). In this setting, unlike Morris and Shin (2002), the target
each member seeks is not the true state of the economy but a variable determined by it.
However, the framework of Morris and Shin (2002) is applicable to this paper’s model
because of linearity of the target, i∗t , with respect to the state, (ut , et ).
Finally, I set the aggregation rule of individual votes to the arithmetic mean:

1 ∑ j
it =
i.
N j=1 tN

(4)This rule is quite simple and not so realistic in terms of the actual institutions but caneasily grasp an aspect of compromise in the monetary policy committee. Since the goalof this paper is not to ﬁnd the optimal aggregation rule but to investigate the optimal
personnel organization of monetary policy committee, we use this simple aggregation rule
as a starting point of analysis of monetary policy committee. We may adopt the weighted
average rule for a generalization of the arithmetic mean but it does not change the resultsof this paper.

2.3

Equilibrium

To calculate the equilibrium of the whole model, I ﬁrst derive the equilibrium of thesubgame which describes the decision-making of the monetary policy committee. The
ﬁrst order condition of each committee member j’s problem is∑kk6=j it
j
j
j
∗
.
(5)
it = (1 − r)Et−1 it + rEt−1
N −1
Along the line of Morris and Shin (2002), consider the following linear strategy of eachcommittee member j’s voting on interest rate
]
]
[
[
(6)
ijt = σ ρu ut−1 + γu ϕjt + (1 − γu )ϕct + Φ ρe et−1 + γe ψtj + (1 − γe )ψtc ,10

See Ch.11 of Walsh (2003b) for a detail explanation on the issue.

8where γu ∈ [0, 1] and γe ∈ [0, 1] are undetermined coeﬃcients. 11 Let pµ = σµ−2 , pν =σν−2 , pε = σε−2 , pη = ση−2 . I interpret them as measures of the precision of the corresponding signals. Using pµ , pν , pε , pη , for each j,
]
]
[
[
pµ
pη
pν
pε
j
ϕjt +
ϕct + Φ ρe et−1 +
ψtj +
ψtc ,
Et−1
i∗t = σ ρu ut−1 +pε + pµpε + pµpη + pνpη + p ν
]
[
)
( p
pµ
ε
j
ϕjt +
ϕc + (1 − γu )ϕct
Et−1
ikt = σ ρu ut−1 + γu
pµ + pεpµ + p ε t
[
]
( p
)
pν
η
j
c
c
+Φ ρe et−1 + γeψ +
ψ + (1 − γe )ψt , for k 6= j.
p ν + pη t p ν + pη tThus, substituting these equations into the right-hand side of (5) and comparing thecoeﬃcients of (6), the undetermined coeﬃcients turn out to beγu =(1 − r)pε,
pµ + (1 − r)pεγe =(1 − r)pη,pν + (1 − r)pη

which give the solution of the subgame of the decision-making by the monetary policy
committee. Here, I investigate the properties of the response coeﬃcient above.
Remark 1
∂γu
< 0,
∂r

∂γe
< 0,
∂r

∂γu
> 0,
∂pε

∂γe
> 0,
∂pη

∂γu
< 0,
∂pµ

∂γe
< 0.
∂pν

This is parallel to the analysis of Morris and Shin (2002). Since the importance of common information rises when the motive for coordination becomes larger, each committee
member then places a higher weight on the common signals relative to the private signals:∂γue< 0, ∂γ< 0. Since private signals (common signals, resp.) become more informa∂r∂rtive relative to common signals (private signals) when the precisions of private signals(common signals) increase, each member is tend to depend on private signals (common
∂γe
∂γe
u
u
signals) more: ∂γ> 0, ∂p> 0, ∂γ< 0, ∂p
< 0.
∂pε
∂pµ
η
ν
Next, let us see equilibrium nominal interest rate and the consequent macroeconomic
dynamics. Using the solution of the subgame in the monetary policy committee, nominalinterest rate set in equilibrium is determined by the aggregation rule (4) as follows.
it = σ[ut + γu ε̃t + (1 − γu )µt ] + Φ[et + γe η̃t + (1 − γe )νt ]= i∗t + σ[γu ε̃t + (1 − γu )µt ] + Φ[γe η̃t + (1 − γe )νt ],11(7)

According to the setting of this paper, this is enough to ﬁnd equilibrium linear strategy. For a detailof the calculation of equilibrium in global games with ﬁnite players, see Calvó-Armengol and de Martı́
Beltran (2009).

9

∑
∑N j
j
1
where ε̃t = N1 N
ε
and
η̃
=
t
t
j=1
j=1 ηt are the average of private signals on innovationsNof demand shock and cost shock. The second and third terms of (7) represent the eﬀects
of imperfect information on interest rate setting in the monetary policy committee.
Now, macro dynamics of the model economy is given by AD relation, (1), AS relation,(2), and monetary policy rule, (7). By the method of undetermined coeﬃcients, we ﬁnd
the solution of the system above. Equilibrium output gap and inﬂation rate are 12
[
]
κ
γe Φ
(1 − γe )Φ
xt = − cet − γu ε̃t +η̃t + (1 − γu )µt +νt ,(8)
λ (1 − βρe ) + κ2
σ
σ
[
]
λc
γe Φ
(1 − γe )Φ
πt =et − κ γu ε̃t +η̃t + (1 − γu )µt +νt .
(9)
λc (1 − βρe ) + κ2σσ
Under perfect information, equilibrium output gap and inﬂation rate in the equations
above are identical to those of the basic New Keynesian model with discretionary monetary policy. The eﬀect of coordination vanishes if information is perfect since every
member shares the same information set with the others under perfect information. 13
Calculating asymptotic variances of output gap and inﬂation rate, social loss in equilibrium is obtained by (3). 14
Proposition 1 In the benchmark model, asymptotic variances of output gap and inﬂation rate and social loss are
]2 2
[
]
[
σψ
1 2 2 ( γe Φ )2 2
κ
+
γ σ +
ση
V [x] =λc (1 − βρe ) + κ2 1 − ρ2e N u ε
σ
[
(
)2 ]
(1 − γe )Φ
2 2
σν2 ,
(10)
+ (1 − γu ) σµ +
σ
[
]2 2
[
]
σψ
λc
κ2 2 2 ( γe Φ )2 2
V [π] =+γ σ +σηλc (1 − βρe ) + κ2 1 − ρ2e
N u ε
σ
[
(
)2 ]
(1 − γe )Φ
2
2 2
σν2 ,
(11)
+κ (1 − γu ) σµ +
σ
[(
)2
(
)2 ] σ 2
λc
κ
ψ
L =
+λ c
λc (1 − βρe ) + κ2
λ (1 − βρe ) + κ2
1 − ρ2e1213

For a detail of the calculation, see Appendix A.
In the case of perfect information, ε̃t = η̃t = µt = νt = 0 holds. Then, in (8) and (9),xt = −κet ,λc (1 − βρe ) + κ2

πt =

λc
et ,
λc (1 − βρe ) + κ2

which are equilibrium output gap and inﬂation rate in the basic New Keynesian model with discretionary
optimal policy. Ch.11 of Walsh (2003b) provides the derivation and an explanation of the issue.
14
Appendix A provides a derivation of asymptotic variances of output gap and inﬂation rate.

10

[
]
[
(
)2 ]
κ2 + λ 2 2 ( γe Φ )2 2
(1 − γe )Φ
2
2 2
+
σν2 .
γu σε +ση + (κ + λ) (1 − γu ) σµ +N
σσThis seems somewhat complicated but the meaning is clear. The macroeconomic
volatility presented in (10) and (11) is decomposed into the three parts as follows. The
ﬁrst term is due to cost shock, the second term is due to noisy common information andthe third term is due to noisy private information. Therefore, the cause of the ﬁrst term
is a fundamental element and those of the second and third term are non-fundamental
elements.
Immediately, we obtain the following assertion which provides a welfare implication
about the committee size N in this benchmark case.
Corollary 1 In this benchmark model, asymptotic variances of output gap and inﬂation
rate are decreasing in the size of the monetary policy committee. Thus social welfare isincreasing in it.
This is intuitively plausible. The larger the committee becomes, the more accurate
the averages of idiosyncratic information on the two shocks become since idiosyncratic
noises of information among the members are absorbed by averaging. In fact, the second
term of (10) and (11) show that an increase of the committee size reduces the part ofmacroeconomic volatilities due to idiosyncratic noises in the same order as N . Since it
is not costly to enlarge the monetary policy committee in the setting of this section, aﬁnite optimal size of the monetary policy committee does not exist. This mechanism
for Corollary 1 is the same as Condorcet’s (1785) jury theorem. The part of social loss
which noisy private signals generate goes to 0 as the committee size goes to inﬁnity. It
indicates that the averages of private signals on demand shock and cost shock converge
to realizations of the two shocks in probability. In fact, in this model, the two important
assumptions of Condorcet’s jury theorem hold. First, the assumption that enlarging
the size of the monetary policy committee is costless means that so is getting more
information. Second, the aggregation of information is costless since private signals areused without strategic manipulations in this model.
Let us discuss the value of information. The next corollary shows the relationshipbetween the precision of private signals and social welfare.
Corollary 2
∂L
≤ 0,
∂pε

∂L
≤ 0.
∂pη

11

Corollary 2 indicates that an increase of the precisions of common signals always
improve social welfare. While precise common information stimulates the coordination
motive of the committee members, precise private information does not so. Hence, a risein the quality of private signal has only the positive eﬀect that it raises the accuracy ofthe members’ forecast on demand shock and cost shock. The relationship between the
precision of private signals and social welfare is as below.
Corollary 3
∂L
≤0
∂pµ
∂L
≤0
∂pν

iﬀ
iﬀ

[
]
pµ
2
≥ (1 − r) 1 − (1 − r) ,
pε
N
[
]
pν
2
≥ (1 − r) 1 − (1 − r) .
pηNCorollary 3 asserts that the marginal values of common signals are non-negative whencommon signals are suﬃciently precise relative to private signals and vice versa. It mightseem curious that the anti-transparency result holds but we can explain this as follows.
15
Raising the precisions of common signals has two eﬀects on the behavior of thecommittee members. One is a direct eﬀect such that the committee members can get
more precise information on economic developments and forecast more exactly the target
level of nominal interest rate, i∗t . The other is an indirect eﬀect such that the committee
members become more dependent on common signals as Remark 1 shows and it increases
the ineﬃciency of interest rate setting due to noisiness of common signals, which brings
larger macroeconomic volatility. Clearly, the former is positive one and the latter isnegative one. When the precisions of common signals are low, the marginal eﬀect of thelatter is relatively large and thus social welfare decreases as the common signals become
more precise.

3

Optimal Delegation Problem of Monetary Policy
Committees

This section deals with the optimal delegation problem of monetary policy, which has been
one of the most important issues of monetary policy analysis. Since the seminal work by
Rogoﬀ (1985), many researches on this topic support for optimality of conservative central
15

The mechanism for Corollary 2 presented below is similar to literature of global games, for example,
Morris and Shin (2002).

12

bankers under various environments. As shown later, introducing decision-makings bycommittees, however, makes a diﬀerence in this topic. We ﬁrst analyze two limiting cases
to understand it easily.

3.1

Optimality of Conservatism: Limiting Cases

3.1.1

The Case of Serial Uncorrelation

Next, we consider the case where cost shock is serially uncorrelated and information ofeach committee member is imperfect, i.e., et = ψt and σµ2 , σν2 , σε2 , ση2 > 0. In this case, thesocial loss function is[([]( Φ )2 ]σ − κΦ0 )2
κ2 + λ 2 2 ( γe Φ0 )2 2
0
2
L =
+λ
ση
σψ +
γu σε +
σ
σ
N
σ
[
(
)2 ]
(1 − γe )Φ0
2
2 2
σν2 ,
(12)
+(κ + λ) (1 − γu ) σµ +σ∂Lwhere Φ0 = λcσκ. As in the previous case, the ﬁrst order condition, ∂λc = 0, gives the+κ2∗
optimal weight λ such thatσ 2 (κ2 + λ)γe2 ση2λ∗ = λ + (1 − γe )2 (κ2 + λ) 2ν +
· 2.
σψ
N
σψ

(13)

We obtain the following proposition immediately from (15).
Proposition 2 In the benchmark model without serial correlation of cost shock, the optimal weight on output gap is higher than society’s weight. That is, it is optimal to appointa monetary policy committee which consists of more ﬂexible policy makers than society.
An elemental cause of this result is imperfectness of information. By ρe = 0, equilibrium output gap and inﬂation in this case are
[
]
γe Φ0
(1 − γe )Φ0Φ0η̃t + (1 − γu )µt +νt ,xt = − et − γu ε̃t +
σ
σ
σ
[
]
σ − κΦ0γe Φ0(1 − γe )Φ0πt =et − κ γu ε̃t +η̃t + (1 − γu )µt +
νt .
σ
σ
σ
The ﬁrst terms of equilibrium output gap and inﬂation rate in the expression above
are identical to those of the case of perfect information. The second terms of them are
generated from information imperfectness (and coordination motive) in the interest ratesetting. Note that the second term of inﬂation rate is as κ times as that of output gap
13and κ is the slope of the New Keynesian Phillips curve. Thus, we ﬁnd that the control
error of interest rate due to imperfect information aﬀects output gap directly in the AD
relation, (1), and then impacts inﬂation through the AS relation, (2).
The eﬀect mentioned above leads to non-fundamental macroeconomic volatility: thesecond and third terms of (12). So that, to reduce the volatility, it is beneﬁcial to appoint
central bankers who place higher weights on output gap. This appears the second andthird term in (13). The ﬁrst term of (13) reﬂects the famous result in the literature thatsharing the relative weight with society is optimal under perfect information. 16 To see
this, by (12), we have enough to solve the equation of λc{( Φ )2 }∂ ( σ − κΦ0 )2
0
+λ
= 0.
∂λc
σ
σ
The solution is λc = λ. Therefore, the optimal weight given by (13) balances the beneﬁtof heightening the weight to reduce the economic volatility due to common and crosssectional noise of the members’ information and its cost: excessive variance of inﬂation
which the accompanying weak response to cost shocks brings.
Remark that by the analysis above, information imperfectness require ﬂexible inﬂation
targeters for the committee members through the channel of control error of nominalinterest rate.
Let us investigate the relationships between the optimal weight and the parameters,
which help us analyze the general case.
Corollary 4 If the information of the committee members on the cost shock is imperfect,i.e., σν2 > 0, ση2 > 0, then
∂λ∗
> 0,
∂r

∂λ∗
> 0,
∂λ

∂λ∗
> 0,
∂κ

∂λ∗
< 0.
∂σψ2

When coordination motive among the committee members rises, their dependency oncommon information, 1 − γe , also rise and ineﬃciency due to the common noise increases.
∗> 0. When the society’s weight on output gap is high, the central bank is
So that, ∂λ∂r∗> 0. When an impact of output gap
required to place a correspondingly high weight: ∂λ∂λto inﬂation rises, control error of the demand side due to common and cross-sectional noise∗of information induces more excessive inﬂation. Thus, ∂λ> 0. When the innovation in∂κ
the cost shock becomes larger, the marginal cost of raising the weight on output gap (andthus weakening the response to the cost shock) increases, which leads to a lower optimal∂λ∗weight: ∂σ
2 < 0.
ψ16

I review the detail of this issue in the next subsection.

14

Next, let us see the relationships between the parameters on informational structure
and the optimal weight.
Corollary 5
∂λ∗
< 0,
∂pη
∂λ∗
≤ 0 iﬀ
∂pν

(14)
[
]
pν
2
≥ (1 − r) 1 − (1 − r) .
pη
N

(15)

According to (13), we ﬁnd that both of changes in the parameters pη and pν havethree eﬀects on the optimal weight λ∗ :[]∂γe p−1γe ∂γe p−1γe2 p−2∂λ∗ηην2= (κ + λ) − 2(1 − γe )
·
+2 ·
·
−
·
,
(16)
∂pη
∂pη σψ2N ∂pη σψ2
N σψ2
[
]
−2
∂λ∗
∂γe p−1γe ∂γe p−1
η
ν
2
2 pν
= (κ + λ) − 2(1 − γe )·− (1 − γe ) 2 + 2 ··. (17)∂pν
∂pν σψ2σψN ∂pν σψ2∂γeConsider the meaning of (16). Note that ∂p> 0. The ﬁrst term of the bracketed part
ηis the indirect negative eﬀect which is made by the decrease of dependency of interest
rate setting on the common signal. The second term is the positive eﬀect which is madeby the increase of dependency of interest rate setting on the private signal. The third
term is the direct negative eﬀect due to the decrease of economic volatility generated
by noisiness of the private signal. We can easily ﬁnd that the third term dominates thesecond term as long as r < 1. 17 Thus, the optimal weight is always decreasing in the
precision of the private signal on cost shock.
∂γe
The second assertion of Corollary 5, (15), is also intuitive. Note that ∂p< 0. Theνﬁrst term of the bracketed part of (17) is a positive eﬀect owing to an increase of themembers’ dependency on common signals. As in (16), the second and third terms are thedirect and indirect negative eﬀects respectively. However, contrary to (16), the positiveeﬀect can dominate the two negative eﬀects when, for example, N is large and the third
eﬀect is small. Recall that Corollary 3 suggests that when the precision of the common
signal is suﬃciently small, an increase of dependency on it generates a dominantly large
volatility, which requires more ﬂexible monetary policy. This is because the optimal
weight can be increasing in the precision of the common signal on cost shock when it issuﬃciently noisy.
17

When r = 1, γe = 0 and thus the second and third term vanish. Even in this case, the result does
not change by the negativity of the ﬁrst term.

15

Corollary 6 The optimal weight on output gap is decreasing in the size of the committee.
The mechanism which generates this result is similar to that of Corollary 1. Whenthe size of the monetary policy committee becomes larger, the cross-sectional noise of
the members’ information is absorbed by averaging the individual votes. The marginal
beneﬁt of raising the relative weight on output gap then decreases, which makes the
optimal weight lower.
3.1.2

The Case of Perfect information

To begin with, consider the case of perfect information, i.e., σε2 = ση2 = σµ2 = σν2 = 0.
The coordination motive is irrelevant in this case, so that the model is identical to the
popular version of the New Keynesian model with perfect information. This case had
been analyzed in literature but let us review it brieﬂy for comparison with the result of
this paper.
The results of Clarida et al. (1999) indicate that in the basic New Keynesian modelwith perfect information, if the cost shock {et }∞t=0 is serially correlated, then the optimal
weight on output gap under discretionary monetary policy is smaller than the social
preference λ. In other words, it is optimal to appoint a central banker who dislikes
inﬂation more than society. In fact, by σε2 = ση2 = σµ2 = σν2 = 0, social loss is reduced to[()2)2 ] σ 2
(
λc
κ
ψ
.
+λ c
L =
λc (1 − βρe ) + κ2
λ (1 − βρe ) + κ2
1 − ρ2e∂L∗
18
The ﬁrst order condition ∂λc = 0 gives the optimal weight λ such thatλ∗ = (1 − βρe )λ,which implies that λ∗ = λ when ρe = 0 and λ∗ < λ when ρe > 0. The intuition for this∑result is as follows. Since et+j = ρje et + ji=0 ρie ψt+j−i , if ρe > 0, the future values of thecost shocks can be partially forecast by public. Noting that in the basic New Keynesianmodel, equilibrium inﬂation in inﬂation targeting under discretion is given by 19
πt+j =λc
et+j ,λc (1 − βρe ) + κ2

the response coeﬃcient is increasing in λc . Since the expected inﬂation rate in periodt + j at period t is
Et πt+j =1819

λc
ρj et ,λc (1 − βρe ) + κ2 e

Vestin (2006) also derives the optimal weight on output gap in the case of perfect information.
For the derivation, see Chapter 11 of Walsh (2003).

16

the role above of λc becomes larger as ρe increases. Hence, intuitively, the rational agents,
who know that a conservative central banker (i.e., one with lower λc ) will stabilize inﬂation
harder, expect stable future inﬂation. This behavior contributes to stabilizing current
inﬂation. Clearly, it disappears if ρe = 0.
Summing up, the existence of serial correlation of cost shock supports for appointing conservative committee members through the channel of stabilization of inﬂation
expectations.

3.2

Optimality of Conservatism: The General Case

The general case where information is imperfect and cost shock is serially correlated isquite complex but we can analyze it with help of the limiting cases presented above.
For simplicity, we assume that ρe κ < σ(1−ρe )(1−βρe ). 20 This condition is equivalent∂Φto ∂λc < 0. That is, we consider only the case where conservative central bankers react
to cost shock harder.
Proposition 3 Assume that the social loss function L is convex with respect to λc andits critical point is positive. 21 Then, the optimal weight on output gap is[σκ(1 − ρe ) + ρe λ]Λ − βρe κλ,κ − ρe Λ[ 2]
ση2(λ + κ2 )γeσν22where Λ =[σ(1 − βρe )(1 − ρe ) − ρe κ]·+ (1 − γe ) 2.
σ2
N σψ2 /(1 − ρ2e )σψ /(1 − ρ2e )λ∗ = λ +Besides, it is optimal to appoint more (less, resp.) ﬂexible inﬂation targeters when information about cost shock is suﬃciently noisy (accurate, resp.).
Proof.
The proof is so long but straightforward. It is available on request.
Proposition 3 asserts that the parameter λ∗ can be both lower and higher than λ.
Recall the two limiting cases. Serial correlation of cost shock brings expectations eﬀect
and lowers the optimal weight on output gap. Contrary, imperfectness of the members’
information generates extra economic volatility and requires ﬂexible monetary policy
makers. Since the optimal weight in the general case balances the both eﬀect, it is lower(higher, resp.) than society’s weight when the former (the latter) dominates the latter(the former). Since Λ is small (large) when ση2 and/or σν2 are small (large), I obtain thefollowing remark.
20
21This condition holds for usual calibrations of the New Keynesian literature.
The assumption is equivalent to that κ − ρe Λ > 0. The parameter Λ is presented below.

17Remark 2 Inﬂation-minded committee members improve social welfare if their information on economic shocks is accurate. Otherwise, appointing output-minded committee
members is optimal.

4

Optimal Structure of the Committee

This section studies optimal structure of the committee members. In practice of monetary
policy, it is often pointed out that there is preference heterogeneity among the membersof the monetary policy committees. This may be because each member has diﬀerent
background, career and thus principle for goal of monetary policy, especially on trade-oﬀ
between inﬂation and real objectives.
I abstract from serial correlation of demand shock and cost shock since it is notessential to understand the role of imperfect information. However, the approach I willtake is applicable to the case where demand shock and cost shock are serially correlated.
The qualitatively similar results will be obtained in the case where the shock is seriallycorrelated by a few modiﬁcation.

4.1

Preference Heterogeneity of the Members

Assume that L members of the monetary policy committee place more weight on inﬂation than the other members. Without loss of generality, we assume that the weighton output gap of every member j ∈ {1, 2, ..., L} is λh , that of the other member k ∈{L + 1, L + 2, ..., N } is λd and λh < λd . 22 I call {1, 2, ..., L} and {L + 1, L + 2, ..., N }”Hawk group” and ”Dove group” respectively. For convenience, put H = {1, 2, ..., L} andD = {L + 1, L + 2, ..., N }. For the time being, I assume that N ≥ 4 and 2 ≤ L ≤ N − 2,which ensure that both the groups have at least two members and the beauty contest
frame games described below make sense. To address why the monetary policy committees are usually amalgams of both the groups, this assumption will be relaxed later byconsidering a non-strategic situation where the coordination motive among the members
does not exist.
I set up a beauty contest game in which ex ante heterogeneity among the committee
members exists. The modiﬁcation of the members’ preference generates heterogeneity
22

Since I do not treat the issues of communication in this paper, this preference heterogeneity does
not cause Crawford and Sobel (1982) type strategic information transmission.

18

of the problem they face since the targets of the members are not homogenous. Byρu = ρe = 0, the levels of interest rate in period t in optimal policy under perfect
information for the hawkish and dovish members are respectively
ih∗= σut + Φh et ,
t

(18)

itd∗

(19)

d

= σut + Φ et ,where Φh = λhσκand Φd = λdσκ. 23 Equations (18) and (19) display the role of hetero+κ2+κ2
geneity of underlying preferences among the committee members. It makes a diﬀerence
between their responses to cost shock. The members of Hawk group react to cost shock
harder than the members of Dove group: Φh > Φd .
Since the target rates are diﬀerent, I set up the problems of the committee membersin the both groups separately. I reset the loss function of each member j ∈ H to
[
(
)2 ]
∑
1
j
j
j
j
h∗ 2
m
lt = Et−1 (1 − r)(it − it ) + r it −it
L−1m∈H\{j}and that of each member k ∈ D to[(kklt = Et−1 (1 − r)(ikt − itd∗ )2 + r ikt −1
N −L−1

∑

im
t

)2 ]
.

m∈D\{k}The parameter r represents the degree of coordination motive with the other membersin the same group. In this setting, I assume the situation that each members of bothgroups cares the position in the same group and the relationship with her fellows.
All committee members in the both groups are assumed to minimize their own loss
function above. The ﬁrst order conditions for both the problems are∑mm∈H\{j} itjjjh∗it = (1 − r)Et−1 it + rEt−1, for j ∈ H,
(20)
∑ L−1 mm∈D\{k} itkkikt = (1 − r)Et−1
itd∗ + rEt−1, for k ∈ D.
(21)
N −L−1
Note that the problems of the both groups are mutually independent since every
member does not pursue coordination with the others who belongs to the opponent
group. Thus, I consider the following linear strategy as in the benchmark model:
]
[
]
[
j
c
h
h j
h
c
h
h j
(22)
it = σ γu ϕt + (1 − γu )ϕt + Φ γe ψt + (1 − γe )ψt , for j ∈ H,
]
[
]
[
(23)
ikt = σ γud ϕkt + (1 − γud )ϕct + Φd γed ψtk + (1 − γed )ψtc , for k ∈ D,hde +(1−ρe )σκe +(1−ρe )σκOf course, we need to reset Φh and Φd to λλhρ(1−βρand λλdρ(1−βρrespectively when we
2
2
e )+κ
e )+κ
treats the case where the shock are serially correlated.

23

19

where γuh , γeh , γud , γed are undetermined coeﬃcients.
Substituting (22) and (23) into (20) and (21), by the method of undetermined coeﬃcients, we can ﬁnd γuh , γeh , γud , γed . We omit the detail of the calculation because it is longand similar to the benchmark model. The undetermined coeﬃcients turn out to be(1 − r)pε= γu ,
γuh = γud =pµ + (1 − r)pε(1 − r)pηγeh = γed == γe .
pν + (1 − r)pηNominal interest rate in period t set by the committee is determined by (22) and (23)
as follows.
1 ( ∑ j ∑ k)
it =
i +
i
N j∈H t k∈D t[] []= σ ut + γu ε̃t + (1 − γu )µt + qΦh + (1 − q)Φd et
]
[
]
[
h
d
h h
d d
(24)
+γe qΦ η̃t + (1 − q)Φ η̃t + (1 − γe ) qΦ + (1 − q)Φ νt ,
P

ηj

P

ηk

t
t
where η̃th = j∈H, η̃td = Nk∈D
and q = NL . The parameter q is the share of Hawk
L
−L
group in the monetary policy committee and plays the most important role in this section.
Note that the committee tends to response harder against the cost shock when q is large
and vice versa.
As in the benchmark model, macroeconomic dynamics is determined by the system(1),(2) and (24). Equilibrium output gap and inﬂation rate in period t are linear in the(relevant) state variables in period t. In this case, they are et , ε̃t , η̃th , η̃td , µt and νt . By
the method of undetermined coeﬃcients, we obtain equilibrium output gap and inﬂation
rate as follows. 24]]
γe [ h h1[ hdd dqΦ η̃t + (1 − q)Φ η̃t
xt = − qΦ + (1 − q)Φ et − γu ε̃t −σ
σ[]1 − γehd−(1 − γu )µt −qΦ + (1 − q)Φ νt ,
(25)
σ
]
)]
[
(
[
κγe
κ
πt = 1 −qΦh + (1 − q)Φd et − κγu ε̃t −qΦh η̃th + (1 − q)Φd η̃tdσσ]
κ(1 − γe ) [ hd−κ(1 − γu )µt −(26)qΦ + (1 − q)Φ νt .
σEquilibrium output gap and inﬂation rate in (25) and (26) nest those of the basic New
Keynesian model as the case where information is perfect and the members’ preference
are homogenous, i.e., λh = λd .

24

I omit the derivation because it is long but straightforward.

20

We can calculate asymptotic variances of output gap and inﬂation in the same way
in Proposition 2.
Proposition 4 In the presence of preference heterogeneity among the committee members, asymptotic variances of output gap and inﬂation rate are 25[ h]2[( ( h )2
( Φd )2 ) ]qΦ + (1 − q)Φd
1 2 2
Φ
2
2
V [x] =+ (1 − q)σψ +γ σ + γe q
ση2
σ
N u ε
σ
σ
[
) ]
( h
d 2
2 2
2 qΦ + (1 − q)Φ
+ (1 − γu ) σµ + (1 − γe )
σν2 ,
(27)
σ
[
[
( ( h )2
( qΦh + (1 − q)Φd )]2( Φ d )2 ) ]κ2 2 2Φ22
V [π] = 1 − κσψ +γ σ + γe q
+ (1 − q)
ση2
σ
N u ε
σ
σ
[
( h
) ]
d 2
2 2
2
2 qΦ + (1 − q)Φ
σν2 .
(28)
+κ (1 − γu ) σµ + (1 − γe )σBy (3), (27) and (28), we obtain the following result immediately.
Corollary 7 Given q, asymptotic variance of output gap and inﬂation rate are decreasingin N and thus so is social loss. That is, the larger the monetary policy committee is, thebetter social welfare is unless the ratio of the size of Hawk and Dove group changes.
This is a variant of Corollary 1. Note that the substantial diﬀerence of the modelin this section from that of section 2 is the existence of preference heterogeneity among
the committee members, or the existence of q. 26 Since the role of the ratio q is only
to determine the response of the monetary policy committee to cost shock, it does notmake a diﬀerence on the role of the committee size N . Thus, in this model, enlarging
the committee always improves social welfare by mitigating noisiness of private signalsof the committee members.

4.2

The Optimal Personnel Organization

In actual, the members of monetary policy committees are usually chosen from the insideand outside of the central banks subject to the legal mandates which mention the proportions explicitly. The empirical researches report preference heterogeneity between boththe types and the results of the previous section tell us that this is meaningful in view ofsocial welfare. So, how should the seats of the committees be allocated to both? The rest
25

σ2

ψ
We have to replace σψ2 by 1−ρ
2 when we analyze the case of serial correlation.
e
26
The abstraction of serial correlation of cost shock does not aﬀect this point.

21

of this section addresses this question, i.e., the optimal personnel organization problemof the monetary policy committee. The approach is to ﬁnd the ratio which minimizes
the social loss function L, given the values of λh and λd .
4.2.1

Analytical Results

The analysis of the optimal ratio is slightly diﬃcult but the most elemental results areavailable in the analytical way. Fist, I provide a characterization of the optimal ratio.
Proposition 5 Let the optimal ratio of the size of Hawk group to the whole committee
be q ∗ . Thenq ∗ = argmin |q 0 − q̃|,
q 0 ∈Q

where Q = { N2 , ..., NN−2 } 27 and
[
]
γe2 2
σκ − Φd (κ2 + λ) σψ2 − (Φh + Φd )(κ2 + λ) 2Nση − Φd (κ2 + λ)(1 − γe )2 σν2
[
]
q̃ =
.
(Φh − Φd )(κ2 + λ) σψ2 + (1 − γe )2 σν2(29)

Proof.
See Appendix B.
Proposition 5 asserts that the optimal ratio of the size of Hawk group to the wholeof the committee is the nearest one to some real number q̃. 28 This fact is important for
the analysis on optimal ratio q ∗ since it provides the following useful result.
Remark 3 The optimal ratio q ∗ is non-decreasing in q̃.
Remark 3 suggests that comparative statics about q̃ is enough to investigate therelationships between the optimal ratio q ∗ and the parameters. Indeed, quantitative
analyses of q ∗ face diﬃculty of discreteness of q but qualitative analyses of q ∗ is relatively
easily conducted by use of continuity of q̃.
I next provide a simple but important limiting result. In the discussion on Proposition 6 below, I treat the case of r = 0. Since there is no coordination motive among theLater, in the discussion on Proposition 6, Q is reset to {0, N1 , ..., NN−1 , 1}.
There is a possibility of multiple optima. Since the social loss function L is quadratic in q, there are
two optimal ratios when q̃ corresponds the middle point of some two grid points. That is, both of two
ratios q− and q+ (q− < q+ ) are optimal if q̃ = q− + N1 (or equivalently, q̃ = q+ − N1 ). Here, we neglectsuch a case.
27

28

22

members, I may assume that 0 ≤ L ≤ N . That is, we can consider the case where themonetary policy committee is occupied by only one group. The set Q in Proposition 5
is hence modiﬁed to {0, N1 , ..., NN−1 , 1}. This is an expedient setting to give a theoreticalexplanation to the fact that the actual monetary policy committees usually consist of heterogeneous members. However, the restriction above is not substantial and Proposition
6 below is true about the general case where r > 0.
hLet Θ = ΦΦd . Since heterogeneity of underlying preferences aﬀects only the responsesof the members’ target to cost shock as (18) and (19) show, I interpret Θ as a measureof the eﬀect of preference heterogeneity. This is a key element of the next proposition,
which provides a necessary condition for that it is optimal to organize the monetary
policy committee into a compound of hawkish and dovish persons.
Proposition 6
2

σ2

γe
1. q̃ ≥ 0 if and only if λd ≥ λ∗ + (Θ − 1)(λ + κ2 ) 2N
· σ2η .
ψ

2

σ2

γe
2. q̃ ≤ 1 if and only if λh ≤ λ∗ − (1 − Θ1 )(λ + κ2 ) 2N
· σ2η .
ψ

Proof.
See Appendix C.
To gain an intuition for Proposition 6, consider the case of perfect information: σν2 =ση2 = 0. We obtain the following corollary immediately from Proposition 6.
Corollary 8 Suppose that information of the committee members on cost shock is perfect,i.e., ση2 = σν2 = 0. Then the following statements hold.
1. q̃ ≥ 0 if and only if λd ≥ λ.
2. q̃ ≤ 1 if and only if λh ≤ λ.
Corollary 8 has a very simple background. Note that by (13), the optimal weight λ∗is equal to the social preference λ when the committee members’ information is perfect.
Consider the case of λd ≤ λ. All the committee members place lower or equal weights
on output gap than optimum in this case. Hence, to approximate interest rate setting
to optimum with respect to policy weight, it is suboptimal to appoint only the members
who belong to Dove group. We can understand similarly the case where λh ≥ λ.
The mechanism for the ﬁrst assertion of Proposition 6 is similar to this. However, theassertion indicates that the necessary condition for that appointing a hawkish member is23

valid is stricter than that of in the case of perfect information. This is because there is
extra social loss due to the hawkish members’ weak interest in stabilizing the volatilityof output gap from information imperfectness. So that, strong preference heterogeneity
pushes up the lower bound of λd for optimality of the compound committees. I interpretthe second assertion of Proposition 6 in the same way.
The results of the previous section and Proposition 6 reﬂects the merit of appointing liberal (i.e., output-minded) central bankers, while the literature on this topic largely
suggests the optimality of conservative central bankers. Proposition 6 asserts that a compound monetary policy committee is optimal unless the bias of the members’ preferenceis very small. It can be regarded as a justiﬁcation for that the actual monetary policy
committees consist of heterogeneous members with respect to preferences over the goalsof monetary policy. It also answer for why the committees have replaced the single policy
makers in recent years by showing the merit of preference heterogeneity. 29
Next, I investigate the relationships between the optimal ratio q ∗ and the parameters.
The results which can be analytically obtained are the following.
Proposition 7
1. The optimal ratio q ∗ is non-decreasing in N and σψ2 and non-increasing in λ.
2. Suppose that q̃ ≥ 0. Then, q ∗ is non-increasing in r if (1+Θ)(1−r)≤ 2.
N
3. Suppose that information of the committee members on the cost shock is perfect,i.e., ση2 = σν2 = 0. Then, q ∗ is non-decreasing in κ if λh ≤ λ ≤ λd .
Proof.
See Appendix D.
These are intuitively plausible in view of Corollary 4 and 6. Consider the ﬁrst assertion. Since enlarging the committee makes accommodates control error of interest
rate setting due to imperfect information, it lowers the value of adding output-mindedmembers. So that, q ∗ is non-decreasing in N .
Intuitively, q ∗ seems to be non-increasing in r unconditionally since the coordination behavior strengthens the volatility due to noisiness of common information. Thereexists, however, the possibility that an increase in r lowers the dependency of the committee members on their noisy individual information and it improves social welfare. The
full characterization of the relationship between r and q ∗ is somewhat complex but thesuﬃcient condition presented in the second assertion of Proposition 7 is simple and informative. Unless the size of the committee is extremely small, noisiness of individual
29

Heterogeneity of members’ tastes is one of substantial features of committee decision-making.

24

information is considerably absorbed by aggregation. 30 This removes the possibility
mentioned above.
To gain an intuition for the third assertion of Proposition 7, at ﬁrst, consider thecase where a single policy maker conducts monetary policy under perfect information.
Tillmann (2008) claims that too conservative central bankers are more harmful than too
liberal ones. This is because the optimization condition under discretionary policy by asingle policy makerκ
xt = − c π tλimplies that excessive conservatism (i.e. low λc relative to λ) leads to enormous volatility of output gap. Thus, excessive liberalism generates relatively small ineﬃciency toexcessive conservatism. This mechanism is true in this paper. By λh ≤ λ ≤ λd , thehawkish and dovish members are the too conservative and liberal central bankers respectively. To raise q means that the monetary policy committee becomes more conservative.
As the equation above indicates, a rise in κ reduces the safety of excessive liberalism(relative to excessive conservatism) by increasing volatility of output gap. Since the beneﬁt of appointing liberal central bankers in Proposition 2 vanishes in the case of perfect
information, an increase in κ makes the optimal ratio q ∗ larger monotonically.
4.2.2

Numerical Results

Let us investigate other important issues by a numerical approach. First, I set the baseline
parameter value. This paper does not aim to obtain quantitatively conclusive results andthe qualitative results are invariant with the baseline values. As the baseline value, set
β = 0.99, σ = 1, λ = 0.25, κ = 0.05. I follow Walsh (2003b) about β, λ and κ. The
value of σ is irrelevant as seen in the analytical results above. Even if it is incorporated
that λ is endogenously determined by particular micro foundations, it does not change
the following discussion basically. Since an empirically valid values of r, λh and λd are
not available, ﬁx r = 0.2, λh = 0.15 and λd = 0.35. These speciﬁcations do not make adiﬀerence in the qualitative results. I set σψ2 = 1 since the important factor is not theabsolute value of σψ2 but the ratios of σν2 and ση2 to it. Because the values of σν2 and ση2
aﬀects the results signiﬁcantly, I examined several cases about them. I use σν2 = 0.6 andση2 = 0.8 as a baseline value and report the results based on them because I obtained
the qualitatively same results. The size of the monetary policy committee varies among
the countries. For example, the numbers of committee members of FOMC, the MPC of30

The actual sizes of the monetary policy committees are about 10. I provide a few examples later.

25

Bank of England and the Policy Board of Bank of Japan are 12, 9 and 9, respectively. I
set N = 10 here, for it keeps q = NL numerically simple.
At ﬁrst, I analyze the relationship between the slope of the New Keynesian Phillips
curve, κ, and the optimal ratio, q̃.
[Figure 1 about here.]
Figure 1 illustrates it. The reason why q̃ is hump-shaped in κ is as follows. An increasein κ has three eﬀects on q̃. First, even in the case of imperfect information, the channelof the third assertion of Proposition 7 is eﬀectual. Second, a decrease in the ratio of
the response coeﬃcients on cost shock in target rates of Hawk group and Dove group, Θ,
reduces the relative beneﬁt of appointing the output-minded person rather than inﬂationminded person to stabilize output gap and eventually inﬂation. This is interpreted as
below. The larger the trade-oﬀ of monetary policy is, the closer the attitudes about
inﬂationary pressure of inﬂation-minded and output-minded group are. It reduces the
merit of Dove group members for accommodating the volatility due to ineﬃciency ofinterest rate setting. Third, an increase of impact of output gap in inﬂation enlarges theeﬀect of inaccurate and ineﬃcient interest rate setting on inﬂation as Corollary 4 shows.
The ﬁrst and second dominate the third for small κ and vice versa for large κ. 31 The
second and third do not exist under perfect information, which leads to the monotone
result, i.e., the third assertion of Proposition 7. This result is robust with respect toother parameters’ values.
Next, let us see the relationship between the degree of information imperfectness (ση2and σν2 ) and the optimal ratio, q ∗ .
[Figure 2 about here.]
Figure 2 shows the result. Broadly, the optimal ratio q ∗ decreases in ση2 and σν2 . It
is intuitively plausible since the merit of increasing dovish members is generally large
when the ineﬃciency of imperfect information is large. In detail, the optimal ratio ismonotonically decreasing in ση2 for a ﬁxed σν2 but it is not necessarily so in σν2 for a ﬁxed
ση2 . The background of this asymmetric result is the asymmetric results of Corollary 5.
While noisiness of the private signal always lowers the optimal weight on output gap and31

In this example, the range of κ in which the third dominates the ﬁrst and second is not so realistic
in view of the empirical evidences. However, this paper focus only on the mechanism that provides theresult above.

26

hence heightens the optimal ratio, noisiness of the common signal can make the converse
eﬀect when it is suﬃciently intense. Thus, for a given ση2 , the optimal ratio can decreases
in the intermediate values of σν2 in Figure 2.

5

Concluding Remark

Incorporating that monetary policy is conducted by committees brings various problems
about the institution design of monetary policy to macro economists. This paper deals
with one of them: optimal personnel organization problem of monetary policy committees. Through the analysis of this problem, I ﬁnd a way to model strategic situationsin the committees and its limitations. It also tell us that there is a merit of appointing
liberal central bankers when the central bank can not control the demand side of theeconomy perfectly because of imperfect information on economic shocks. This paper provides a theoretical justiﬁcation for that the actual monetary policy committees usuallyconsist of members with heterogeneous preferences.
One of the remaining problems along this paper’s direction is how large the monetary
policy committees should be. This is important for practice of monetary policy but is noteasy to solve in formal models. The key mechanism for determination of the optimal size
may be a harmful eﬀect of common information which is augmented by adding committee
members.
There is possibility of another extension. Riboni and Ruge-Murcia (2008) and GerlachKristen (2008) reports that the outsiders of the BOE’s MPC have, on average, the asymmetric preferences in that they are apt to avoid raising nominal interest rate harder thanlowering it. This fact is intuitive in a sense and should be incorporated into the optimalorganization problem of the monetary policy committees.

27

Appendices
Appendix A: Derivation of (8),(9),(10),(11)In the benchmark model, macroeconomic dynamics of the artiﬁcial economy is given by
the following system of stochastic diﬀerence equations.
1(it − Et πt+1 ) + ut ,σ
= βEt πt+1 + κxt + et ,xt = Et xt+1 −

(30)

πt

(31)

it = σ[ut + γu ε̃t + (1 − γu )µt ] + Φ[et + γe η̃t + (1 − γe )νt ].

(32)

Since the relevant state variables in period t are et , ε̃t , η̃t , µt and νt , the solution will beof the form
xt = Ax et + Bx ε̃t + Cx η̃t + Dx µt + Ex νt ,(33)

πt = Aπ et + Bπ ε̃t + Cπ η̃t + Dπ µt + Eπ νt ,(34)

where Ak , Bk , Ck , Dk and Ek (k = x, π) are undetermined coeﬃcients. Substituting(33),(34) into (30),(32) and then (32) into (30) and comparing the coeﬃcients of bothsides,γe ΦΦ − ρe Aπ, Bx = −γu , Cx = −,σσ(1 − γe )Φ
= −(1 − γu ), Ex = −.
σ

Ax = ρe Ax −
Dx

(35)

Substituting (33),(34) into (31) and comparing the coeﬃcients of both sides,Aπ = βρe Aπ + κAx + 1, Bπ = κBx , Cπ = κCx , Dπ = κDx , Eπ = κEx .

(36)

Solving the ﬁrst equations of (35) and (36), we getκ,
Ax = − cλ (1 − βρe ) + κ2

Aπ =

λc
.
λc (1 − βρe ) + κ2

Thus, we obtain equilibrium output gap and inﬂation rate in period t in the text.
Finally, we calculate asymptotic variances of output gap and inﬂation rate. By et =σ2ρe et−1 + ψt , asymptotic variance of et is 1−ρψ 2 . Besides, since et , εjt , ηtj , µt and νt areemutually independent, each covariance of them is zero. Noting the two facts above, we
ﬁnd asymptotic variance of output gap in the text. Similarly, we can calculate asymptotic
variance of inﬂation rate in the text.
28

Appendix B: Proof of Proposition 5
The optimal ratio q ∗ is deﬁned as
q∗ =

{
}
argminV [π] + λV [x] .
−22q 0 ∈{ N,..., NN}

Note that according to (31) and (33), social loss V [π] + λV [x] is a quadratic functionof q with a positive coeﬃcient of the second order term. Consider the continuation of∂ (V [π]+λV [x])V [π] + λV [x] with respect to q and let the solution of= 0 be q̃. Then, q̃∂qmust satisfy{ [( q̃Φh + (1 − q̃)Φd )][ κ]2 σ−κ− (Φh − Φd ) σψ2
σ
σ
[
}
]
(
)
)
(
( h
2
d )( hΦh 2
Φ − Φd ) 2
Φd 2 22
2 q̃Φ + (1 − q̃)Φ
2 γe
σν
+κ
−
ση + 2κ (1 − γe )
N
σ
σ
σ
σ
{ ( h
q̃Φ + (1 − q̃)Φd ) Φh − Φd 2
+ λ 2
σψ
σ
σ
}
( h
d )( hΦ − Φd ) 2
γe2 [( Φh )2 ( Φd )2 ] 2
2 q̃Φ + (1 − q̃)Φση + 2(1 − γe )
σν
+
−
N
σ
σ
σ
σ
= 0.
Solving this with respect to q̃, we obtain (29). 32 Since discrete convexity of V [π] + λV [x]with respect to q, the optimal ratio q ∗ must belong to the set
¯
{
} {
}
¯
L̃ + 12 N −2L̃¯q− , q+ ¯∃L̃ ∈ N, 2 ≤ L̃ ≤ N − 3,
= q− ≤ q̃ ≤ q+ =
∪
,
.
N
N
N
N
Moreover, since V [π] + λV [x] is quadratic in q and quadratic functions are symmetricwith respect to their axises, we ﬁnd that q ∗ is the nearest element of { N2 , ..., NN−2 } to q̃.
Q.E.D.

Appendix C: Proof of Proposition 6
Using (15), the numerator of (29) becomes[]γ2σκ − Φd (κ2 + λ) σψ2 − (Φh + Φd )(κ2 + λ) e ση2 − Φd (κ2 + λ)(1 − γe )2 σν2
2N
[
]
2
2
2
σψ2 d
σ
γe
η
2
2
2 σν
=
λ − λ − (Θ + 1)(κ + λ)·− (κ + λ)(1 − γe ) 2Φd2N σψ2σψ32

I omit the detail of the calculation since it is long but straightforward. It is available on request.

29

[
]
σψ2 d ( ∗γe2 ση2 )2=λ − λ + (Θ − 1)(κ + λ)·.
Φd2N σψ2This shows the ﬁrst assertion. Next, q̃ ≥ 1 if and only if[]γ2σκ − Φd (κ2 + λ) σψ2 − (Φh + Φd )(κ2 + λ) e ση2 − Φd (κ2 + λ)(1 − γe )2 σν2
2N
]
[
2 2
h
d
2
2
≥ (Φ − Φ )(κ + λ) σψ + (1 − γe ) σν .
Dividing the both sides by Φh σψ2 , we have(1) 2
γe2 ση2σ2λ +κ − 1+(κ + λ)· 2 ≥ λ + κ2 + (1 − γe )2 (κ2 + λ) 2ν ,
Θ
2N σψ
σψ
h

2

which is reduced to1) 2
γe2 σν2λ ≥λ − 1−(κ + λ)·.
Θ
2N σψ2h

It completes the proof.

∗(

Q.E.D.

Appendix D: Proof of Proposition 7
We can show the ﬁrst assertion as follows. It is immediately obtained from (29) that q ∗is non-decreasing in N and non-increasing in λ. By (29), we have
[
]
γe2 2
d
h
2
d
2
d 2
(Φ + Φ )(κ + λ) 2N ση + (σκ − Φ (λ + κ )) + Φ (κ + λ) (1 − γe )2 σν2
∂ q̃
=
.
∂σψ2
(Φh − Φd )(κ2 + λ)(σψ2 + (1 − γe )2 σν2 )2∂ q̃
Since Φh > Φd by Φd = λdσκ, Φh = λhσκand λd > λh , we obtain that ∂σ
2 ≥ 0.
+κ2+κ2
ψ
Next, I provide a proof of the second assertion. Since I assume that q̃ ≥ 0 here, it isa suﬃcient condition for the assertion that the numerator of (29) is decreasing in r. Put

f (r) = (Φh + Φd )γe2

ση2
+ Φd (1 − γe )2 σν2 .
2NThen, after some calculations, I obtainf 0 (r) = −

[
∂γe
Φd
(1 + Θ)(1 − r) ]·2−.
∂r pν + (1 − r)pηNe
Since ∂γis negative, this proves the second assertion.
∂r

30

Let us prove the third assertion. By (29), under perfect informationq̃ =dσκ − Φd (κ2 + λ)λd − λ=,(Φh − Φd )(κ2 + λ)(Θ − 1)(κ2 + λ)2

. Note that we may regard q̃ as a function of κ2 . Diﬀerentiating q̃ with
where Θ = λλh+κ+κ2respect to κ2 , we have
]
[
∂Θ
2
d
(λ − λ) ∂κ2 (κ + λ) + (Θ − 1)
∂ q̃
=
−
.
∂κ2
(Θ − 1)2 (κ2 + λ)2
λ −λ
∂Θ
By ∂κ
2 = (λh +κ2 )2 , we obtain
h

d

∂Θ 2
(λ − λh )(λd − λh )
(κ
+
λ)
+
(Θ
−
1)
=
−
.
∂κ2
(λh + κ2 )2∂ q̃hdThis implies that ∂κ
2 ≥ 0 as long as λ ≤ λ ≤ λ . The proof is ﬁnished.

31

Q.E.D.

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33

q~
.48

.46

.44

.42

.4

.38

.36
0

.1

.2

.3

.4

.5

κ

.6

.7

.8

Figure 1: The relationship between κ and q̃

34

.9

1

.5

.4

.3

0
.2
.4
.6

.2
.8

0
.2

1

.4
.6

1.2
.8

1.4

1

σ2η

1.2

σ

1.6

1.4
1.8

1.6
1.8
2

2

Figure 2: The relationship between (ση2 , σν2 ) and q ∗352ν