GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.106

Optimal Structure of Monetary Policy Committees

Keiichi Morimoto

December 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

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

Optimal Structure of Monetary Policy Committees∗
Keiichi Morimoto†‡
December, 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 theoretical justiﬁcation for the fact that the actual monetary policy committees (e.g., MPC of Bank of England and FOMC) usually consist of both typemembers as the empirical researches suggest. It also explains why the committees
have replaced the single policy makers in the actual central banks.

Keywords: monetary policy, committee, delegation, imperfect information, higher
order expectations
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 and the participants of the Fall Meeting (2009) of Japanese Economic
Association and 108th meeting of Kansai Macroeconomics workshop for their helpful comments. Allremaining errors are mine. I acknowledge ﬁnancial support from the Research Fellowships for Young
Scientists of the Japan Society for the Promotion of Science (JSPS).
†
Japan Society for the Promotion of Science.
‡
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 analyzes 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) report 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
as follows. 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 Aggregate Sup1
2

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

1

ply (AS) relation. The output-minded committee members play the role of mitigatingthese eﬀects, while the inﬂation-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 a higher weight on inﬂation relative to the real
objectives (e.g. output and unemployment) 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 over designating the monetary policy committee. Faust (1996) models the historicalargument that it was why FOMC was organized into a compound committee that thisstructure was a solution to the conﬂict between the farmers and creditors over the redistributive eﬀect of inﬂation. He shows that balancing these heterogeneous interests brings
a better performance of monetary policy even for the majority under the peculiar voting
structure. However, as Blinder (2007) claims, these existing literature does not clarify
why in general countries, the monetary policy committees replace single policy makers
and why the actual central banks do not just follow the Rogoﬀ’s (1985) suggestion andappoint 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-minded members.
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
3

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

2

model consists of two parts. One part is a macroeconomic model which gives macroeconomic 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 macroeconomic3

model, which determines the consequences of monetary policy. The other is a microeconomic 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 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 Aggregate Demand (AD) relationthat is derived from the Euler equation of household. Equation (2), the New KeynesianPhillips curve, is the AS relation which is a linear approximation of the ﬁrms’ optimization condition and the dynamic equation of average price under price-stickiness. The
parameter κ depends on the structural parameters which represent the technology ofthe 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 KeynesianPhillips 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 macroeconomic4

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

4

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
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 (2001), 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 only on 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, I assume that all the members
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 .

are (ex-ante) homogeneous in this benchmark model. To make a decision on monetary
policy, they receive noisy signals on the economic conditions. Given realizations of signals,
each committee member j votes a level of nominal interest rate, ij , to maximize his/herown payoﬀ and then all voting 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 research staﬀs of the central bank. 7 In actual, themonetary policy committees usually begin with staﬀ reports on economic conditions. For
example, every meeting of FOMC begins with a staﬀ report and discussion on economic
conditions. 8
Besides, there is probably idiosyncrasy among the committee members’ assessments
on future economic developments. Each committee member j receives idiosyncratic signals 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 of
7
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each member. For simplicity, I assume that similar to the private agents, the central bankcan 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. I assume that each 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
i
lt = Et−1 (1 − r)(it − it ) + r it −,N − 1 k=j t
where r ∈ [0, 1], i∗t is the level of interest rate in period t which would be set in optimalj
is a mathematical expectation conmonetary policy under perfect information and Et−1
ditioned 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. As usually seenin the New Keynesian literature, the 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
parameter can be thought to represent the underlying preference of the committee members in that it represents their attitudes on desirable trade-oﬀ of monetary policy. The
9Thus, except the process of decision-making on policy instrument setting, this paper’s model is amodel with perfect information.

7

solution of the problem above is 10i∗t = σut + Φet ,e +(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:
c

1  j
i.
it =
N j=1 tN

(4)

Although this rule is quite simple, it can easily grasp an aspect of compromise in themonetary policy committee. Since the goal of this paper is not to ﬁnd the optimal
aggregation rule but to investigate the optimal personnel organization of monetary policy
committee, I use this simple aggregation rule as a starting point of analysis of monetary
policy committee. I may adopt the weighted average rule for a generalization of thearithmetic mean but it does not change the results of this paper.

2.3

Equilibrium

To calculate the equilibrium of the whole model, I ﬁrst derive equilibrium of the subgame which describes decision-making of the monetary policy committee. The ﬁrst ordercondition of each committee member j’s problem isjji∗t + rEt−1
ijt = (1 − r)Et−1kk=j it

N −1

.

(5)

Along the line of Morris and Shin (2002), consider the following linear strategy of eachcommittee member j’s voting on the interest rate
ijt = σ ρu ut−1 + γu ϕjt + (1 − γu )ϕct + Φ ρe et−1 + γe ψtj + (1 − γe )ψtc ,(6)

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 precisions of the correspond10

See Ch.11 of Walsh (2003b) for a detail explanation on the issue.
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 Calvo-Armengol and de Marti
Beltran (2009).
11

8

ing signals. Using pμ , pν , pε , pη , for each j,
pε
pμ
pη
pν
j
i∗t = σ ρu ut−1 +ϕjt +ϕct + Φ ρe et−1 +
ψtj +
ψtc ,
Et−1
pε + pμpε + pμpη + pνpη + pν


 p

pμ
ε
j
Et−1
ikt = σ ρu ut−1 + γu
ϕjt +ϕc + (1 − γu )ϕct
pμ + pεpμ + pε t


 p

pν
η
j
c
c
ψ +
ψ + (1 − γe )ψt , for k = j.
+Φ ρe et−1 + γepν + pη t pν + 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 decision-making by the monetary policy committee. Here, I investigate the properties of the response coeﬃcients 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 tends to depend on private signals (common
∂γe
∂γe
u
u
> 0, ∂p> 0, ∂γ< 0, ∂p< 0.
signals) more: ∂γ
∂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, thenominal interest 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 ],

(7)

N
j
j
1
where ε̃t = N1 N
j=1 εt and η̃t = N
j=1 ηt . The second and third terms of (7) represent the eﬀects of imperfect information on interest rate setting in the monetary policy
committee.

9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, I ﬁnd
the solution of the system above. The equilibrium output gap and inﬂation rate are 12


κ
γe Φ
(1 − γe )Φ
η̃t + (1 − γu )μt +νt ,xt = − cet − γu ε̃t +(8)λ (1 − βρe ) + κ2
σ
σ


λc
γe Φ
(1 − γe )Φ
η̃t + (1 − γu )μt +νt .
et − κ γu ε̃t +
πt =(9)λc (1 − βρe ) + κ2σσ
Under perfect information, the equilibrium output gap and the inﬂation rate in the equations above are identical to those of the basic New Keynesian model with discretionary
monetary policy. The eﬀect of coordination behavior vanishes if information is perfectsince every member shares the same information set with the others under perfect information. 13
Calculating asymptotic variances of output gap and inﬂation rate, I obtain the social
loss in equilibrium by (3). 14
Proposition 1 In the benchmark model, the asymptotic variances of the output gap andthe inﬂation rate and the social loss are

2 2


σψ
κ
1 2 2  γe Φ 2 2+ση
V [x] =γ σ +λc (1 − βρe ) + κ2 1 − ρ2e N u εσ2(1 − γe )Φ
2 2
2+ (1 − γu ) σμ +
σν ,
(10)
σ
2 2



σψ
κ2 2 2  γe Φ 2 2
λc
+
ση
γ σ +
V [π] =λc (1 − βρe ) + κ2 1 − ρ2e
N u ε
σ


2
(1 − γe )Φ
22 2
2+κ (1 − γu ) σμ +
σν ,
(11)
σ


2
2  σ 2
κ
λc
ψ
+λ c
L =
λc (1 − βρe ) + κ2
λ (1 − βρe ) + κ2
1 − ρ2e
2(1 − γe )Φ
κ2 + λ 2 2  γe Φ 2 2
2
2 2
2
+
ση + (κ + λ) (1 − γu ) σμ +σν .
γu σε +
N
σ
σ
12
13

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 the 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 theissue.
14
Appendix A provides a derivation of asymptotic variances of output gap and inﬂation rate.

10This seems somewhat complicated but the meaning is clear. The macroeconomic
volatilities presented in (10) and (11) are 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 terms are non-fundamental
elements.
Immediately, I 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 the social welfare
is increasing 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
terms 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 the 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 the demand shock and the 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, I implicitly assume thatenlarging the size of the monetary policy committee is costless. This means that there isno information acquisition cost. Second, the aggregation of information is costless sinceprivate signals are used 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

Corollary 2 indicates that an increase of the precisions of common signals always improve the social welfare. While precise common information stimulates the coordination
motive of the committee members, precise private information does not so. Hence, a rise11

in 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 relationships between the
precisions of private signals and the social welfare are 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 can hold but I 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 the 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 thelatter is negative one. When the precisions of common signals are low, the marginal
eﬀect of the latter is relatively large and thus the 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 of monetary policy, which has been oneof 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
bankers under various environments. However, introducing decision-makings by committees under inperfect information makes a diﬀerence in this topic. I ﬁrst analyze twolimiting cases to understand it.
15

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

12

3.1

Optimality of Conservatism: Limiting Cases

3.1.1

The Case of Serial Uncorrelation

First, I consider the case where the cost shock is serially uncorrelated and the informationof each committee member is imperfect, i.e., et = ψt and σμ2 , σν2 , σε2 , ση2 > 0. In this case,the social loss function is κ 2 
λ c 2κ2 + λ 2 2  γe Φ0 2 2
2
L =
+λ c
ση
σψ +
γu σε +
λc + κ2
λ + κ2Nσ
2(1 − γe )Φ02
2 22+(κ + λ) (1 − γu ) σμ +
σν ,
(12)
σ
∂L
c
. Solving the ﬁrst order condition, ∂λwhere Φ0 = λcσκc = 0, with respect to λ , I obtain+κ2
the optimal weight λ∗ such thatσ 2 (κ2 + λ)γe2 ση2· 2.
λ∗ = λ + (1 − γe )2 (κ2 + λ) 2ν +
σψ
N
σψ

(13)

Equation (13) gives the following proposition.
Proposition 2 In the benchmark model without serial correlation of the cost shock, theoptimal weight on the output gap is higher than the society’s weight. That is, it is optimal
to appoint a monetary policy committee which consists of more output-minded members
than society.
An elemental cause of this result is imperfectness of the information. Because ρe = 0,
the equilibrium output gap and the inﬂation in this case are


κ
γe Φ0
(1 − γe )Φ0
et − γu ε̃t +xt = − cη̃t + (1 − γu )μt +νt ,λ + κ2
σ
σ


λc
γe Φ0
(1 − γe )Φ0η̃t + (1 − γu )μt +νt .
et − κ γu ε̃t +πt =λc + κ2σσ
The ﬁrst terms of the equilibrium output gap and the 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
rate setting. Note that the second term of the inﬂation rate is as κ times as that of theoutput gap and κ is the slope of the New Keynesian Phillips curve. Thus, I ﬁnd that thecontrol error of interest rate due to imperfect information aﬀects the output gap directlyin the AD relation, (1), and then impacts the inﬂation through the AS relation, (2).
13The eﬀect mentioned above leads to the non-fundamental macroeconomic volatility:
the second and third terms of (12). So that, to reduce the volatility, it is beneﬁcial toappoint central bankers who place higher weights on output gap. This appears the second
and third terms in (13). The ﬁrst term of (13) reﬂects the famous result in the literaturethat sharing the relative weight with society is optimal under perfect information. 16
Therefore, the optimal weight given by (13) balances the beneﬁt of raising the weight toreduce the economic volatility due to common and idiosyncratic noise of the members’
information and its cost, excessive variance of inﬂation which the accompanying weak
response to the cost shocks brings.
Note that by the analysis above, information imperfectness requires ﬂexible inﬂation
targeters for the committee members through the channel of control error of the demandside.
I investigate the relationships between the optimal weight and the parameters, which
help me 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 the coordination motive among the committee members rises, their dependency
on the common information, 1 − γe , also rises and ineﬃciency due to the common noise∗> 0. When the society’s weight on output gap is high, the optimalincreases. So that, ∂λ∂r∗> 0. When an impact of output gap toweight correspodingly becomes higher: ∂λ∂λinﬂation rises, the control error of the demand side due to common and idiosyncratic noise∗> 0. When the innovationof information induces more excessive inﬂation. Thus, ∂λ∂κin the cost shock becomes larger, the marginal cost of raising the weight on output gap(and thus weakening the response to cost shock) increases, which leads to a lower optimal∂λ∗weight: ∂σ
2 < 0.
ψ
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
16

(14)
pν
2
≥ (1 − r) 1 − (1 − r) .
pηN

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

14

(15)

According to (13), I ﬁnd that both of changes in the parameters pη and pν have threeeﬀects on the optimal weight λ∗ :∂λ∗∂γe p−1γe ∂γe p−1γe2 p−2ηην2·= (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∂γe> 0. The ﬁrst term of the bracketed part
Consider the meaning of (16). Note that ∂pη
is the indirect negative eﬀect which is from the decrease of dependency of interest ratesetting on the common signal. The second term is the positive eﬀect which is from theincrease of dependency of interest rate setting on the private signal. The third term isthe direct negative eﬀect which is generated by the decrease of the economic volatility
due to noisiness of the private signal. It is easily shown that the third term dominates
the second term as long as r < 1. 17 Thus, the optimal weight is always decreasing in
the precision of the private signal on the cost shock.
∂γe< 0. The ﬁrst
The second assertion of Corollary 5, (15), is also intuitive. Note that ∂pνterm of the bracketed part of (17) is a positive eﬀect owing to an increase of the members’
dependency on common signals. As in (16), the second and third terms are the direct
and indirect negative eﬀects respectively. However, contrary to (16), the positive eﬀect
can dominate the two negative eﬀects when, for example, N is large and hence 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 increases the social loss. This is because the optimal weight increases in
the precision of the common signal on cost shock when it is suﬃciently noisy.

Corollary 6 The optimal weight on the 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.

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

3.1.2The 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. However, we review it brieﬂy for comparison with the resultof 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 lower 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, the social loss is reduced to22  σ 2

κ
λc
ψ
L =
+λ c
.
c
2
2
λ (1 − βρe ) + κ
λ (1 − βρe ) + κ
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 thisresult 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, the 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 =λc
ρj et ,λc (1 − βρe ) + κ2 e

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.
18
19

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

16

3.2

Optimality of Conservatism: The General Case

The general case where information is imperfect and the cost shock is serially correlated
is quite complex but I can analyze it with help of the limiting cases presented above.
For simplicity, I 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 Suppose that the social loss function L is convex with respect to λc . Then,the optimal weight on output gap is[σκ(1 − ρe ) + ρe λ]Λ − βρe κλ,κ − ρe Λ 2ση2(λ + κ2 )σν2γe2where Λ =·+ (1 − γe ) 2.
[σ(1 − βρe )(1 − ρe ) − ρe κ]σ2
N σψ2 /(1 − ρ2e )σψ /(1 − ρ2e )λ∗ = λ +Proof.
See Appendix B.
I ﬁnd by Proposition 3 that the parameter λ∗ can be both lower and higher than λ. In
2
2
2
ση2
∗
e
·
fact, λ∗ = λ + (1 − γe )2 (κ2 + λ) σσ2ν + (κ +λ)γ
2 > λ for ρe = 0 and λ < λ for suﬃcientlyNσψψ
large ρe because of limρe →1 λ∗ = 0. Recall the two limiting cases. On one hand, serial
correlation of the cost shock brings expectations eﬀect and lowers the optimal weight on
the output gap. On the other hand, imperfectness of the members’ information generates
extra economic volatility and requires ﬂexible monetary policy. Since the optimal weightin 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). Besides, since Λis small (large) when ση2 and/or σν2 are small (large), I obtain the following remark.
Remark 2 In the general case, inﬂation-minded committee members improve social welfare if their information on economic shocks is accurate. Otherwise, appointing outputminded committee members is optimal.
Summing up, the results of this section suggest that both of the inﬂation-minded andoutput-minded committee members have an advantage in improving the performanceof monetary policy. This fact hints the optimality of the compound monetary policy
committees, which is explored in the next section.

20

This condition holds for usual calibrations of the New Keynesian literature.

17

4

Optimal Structure of the Committee

This section studies the optimal structure of the committee. 21 In practice of monetary
policy, it is often pointed out that there is preference heterogeneity among members ofthe monetary policy committees. This may be because each member has characteristic
background, career and thus principle for the goal of monetary policy, especially on
trade-oﬀ between inﬂation and real objectives.

4.1

Preference Heterogeneity of the Members

I assume that L members of the monetary policy committee place a higher weight oninﬂation than the other members. Without loss of generality, I 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 actual monetary policy
committees are usually amalgams of both the groups, this assumption will be relaxedlater by considering the non-strategic situation where the coordination motive among
the members does not exist.
The modiﬁcation of the members’ preference generates heterogeneity of the problem
they face since the targets of the members are not homogeneous. By ρu = ρe = 0, thelevels of interest rate in period t in optimal policy under perfect information for the
hawkish and dovish members are respectively= σut + Φh et ,
ih∗
t

(18)

id∗
= σut + Φd et ,t(19)

and Φd = λdσκ. 23 Equations (18) and (19) display the role of heterowhere Φh = λhσκ
+κ2
+κ2
21

I abstract from serial correlation of demand shock and cost shock since it is not essential to understand the role of imperfect information. This does not matter qualitatively although serial correlationof cost shock generates the expectations eﬀect mentioned above and hence increases the importance of
inﬂation stabilization quantitatively. Besides, the approach I will take is applicable to the case where
demand shock and cost shock are serially correlated. The qualitatively similar results will be obtainedin the case where the shock is serially correlated by a few modiﬁcations.
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.
h
λd ρe +(1−ρe )σκe +(1−ρe )σκ23
Of course, I need to reset Φh and Φd to λλhρ(1−βρ
2 and λd (1−βρ )+κ2 respectively when I treat)+κee
the case where the shocks are serially correlated.

18

geneity of underlying preferences among the committee members. It makes a diﬀerence
between their responses to the cost shock. The members of Hawk group react to the costshock harder than the members of Dove group: Φh > Φd .
Since the target rates are distinct, 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
it
lt = Et−1 (1 − r)(it − it ) + r it −L−1m∈H\{j}and that of each member k ∈ D to


2
k
k
lt = Et−1 (1 − r)(ikt − id∗
)
+
r
ikt −
t



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 that each members of both groups cares the
position in the same group and the relationship with her fellows.
All committee members in both the groups are assumed to minimize their own loss
function above. The ﬁrst order conditions for both the problems are
ijt

=

j
j
(1 − r)Et−1
ih∗
t + rEt−1kkid∗
ikt = (1 − r)Et−1
t + rEt−1mm∈H\{j} it

L−1mm∈D\{k} it

N −L−1,for j ∈ H,

(20)

,

for k ∈ D.

(21)

Note that the problems of both the groups are mutually independent since every
member does not pursue coordination with the members of the opponent group. Thus, I
consider the following linear strategies as in the benchmark model:
ijt = σ γuh ϕjt + (1 − γuh )ϕct + Φh γeh ψtj + (1 − γeh )ψtc ,for j ∈ H,

(22)

ikt = σ γud ϕkt + (1 − γud )ϕct + Φd γed ψtk + (1 − γed )ψtc ,for k ∈ D,

(23)

where γuh , γeh , γud and γed are undetermined coeﬃcients.
Substituting (22) and (23) into (20) and (21), by the method of undetermined coeﬃcients, I can ﬁnd γuh , γeh , γud and γed . I 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 ,
pμ + (1 − r)pε(1 − r)pη= γed =
= γe .
pν + (1 − r)pηγuh = γud =γeh

19Nominal interest rate in period t set by the committee is determined by (22), (23)and (4) as follows.
1   j  k
i +
i
it =
N j∈H t k∈D t= σ ut + γu ε̃t + (1 − γu )μt + qΦh + (1 − q)Φd et

where η̃th =

+γe qΦh η̃th + (1 − q)Φd η̃td + (1 − γe ) qΦh + (1 − q)Φd νt ,jj∈H ηt(24)ηkt, 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 themethod of undetermined coeﬃcients, I obtain the equilibrium output gap and inﬂation
rate as follows. 24
1γeqΦh η̃th + (1 − q)Φd η̃td
xt = − qΦh + (1 − q)Φd et − γu ε̃t −σ
σ1 − γeqΦh + (1 − q)Φd νt ,(25)−(1 − γu )μt −
σ


κ
κγe
qΦh + (1 − q)Φd et − κγu ε̃t −qΦh η̃th + (1 − q)Φd η̃td
πt = 1 −σσκ(1 − γe )qΦh + (1 − q)Φd νt .
(26)
−κ(1 − γu )μt −σ

The equilibrium 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 .
I 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

 Φ d 2 Φ h 2qΦ + (1 − q)Φd
1 2 2
2
2
2
V [x] =σψ ++ (1 − q)σηγ σ + γe q
σ
N u ε
σ
σ
24
25

I omit the derivation because it is long but straightforward.
σ2ψI have to replace σψ2 by 1−ρ
2 when I analyze the case of serial correlation.
e

20



h
d 2
2 2
2 qΦ + (1 − q)Φ
2+ (1 − γu ) σμ + (1 − γe )
σν ,
(27)
σ



 Φ d 2 Φ h 2 qΦh + (1 − q)Φd 2
κ2 2 2222σψ ++ (1 − q)σηγ σ + γe q
V [π] = 1 − κ
σ
N u ε
σ
σ


h
d 2
2 2
2
2 qΦ + (1 − q)Φ
2+κ (1 − γu ) σμ + (1 − γe )
σν .
(28)
σ
By (3), (27) and (28), I obtain the following result immediately.
Corollary 7 Given q, the asymptotic variances of the output gap and the inﬂation rate
are decreasing in N and thus so is social loss. That is, the larger the monetary policy
committee is, the social welfare is improved unless the proportion of the sizes of Hawk
and Dove group changes.
This is a variant of Corollary 1. Note that the substantial diﬀerence of the model inthis section from the benchmark model is the existence of preference heterogeneity among
the committee members. 26 Since the role of the ratio q is only to determine the responseof the monetary policy committee to the cost shock, it does not make a diﬀerence on
the role of the committee size N . Thus, in this model, enlarging the committee always
improves social welfare by mitigating the volatility due to noisy private signals of thecommittee members.

4.2

The Optimal Personnel Organization

In actual, the members of the monetary policy committees are usually chosen from theinside and outside of the central banks subject to the legal mandates which mention the
proportions explicitly. The empirical researches report preference heterogeneity between
both the groups and the results of the previous section tell us that this is meaningful
in view of social welfare. So, how should the seats of the committees be allocated toboth? The rest of this section addresses this question, that is, the optimal personnel
organization problem of the monetary policy committee. The approach is to ﬁnd theratio q 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 canbe obtained in the analytical way. First, I provide a characterization of the optimal ratio.
26

The abstraction of serial correlation of cost shock does not aﬀect this point.

21

Proposition 5 Let the optimal ratio of the size of Hawk group to the whole of the committee be q ∗ . Thenq ∗ = argmin |q  − q̃|,q  ∈Q

where Q = { N2 , ..., NN−2 } 27 and
2

q̃ =

γe 2
ση − Φd (κ2 + λ)(1 − γe )2 σν2σκ − Φd (κ2 + λ) σψ2 − (Φh + Φd )(κ2 + λ) 2N(Φh − Φd )(κ2 + λ) σψ2 + (1 − γe )2 σν2

.

(29)

Proof.
See Appendix C.
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 the diﬃculty of discreteness of q but qualitative analyses of q ∗ is easily
conducted by making use of continuity of q̃.
h
I next provide a simple but important limiting result. Let Θ = ΦΦd . Since heterogeneity of underlying preferences aﬀects only the responses of the members’ target to thecost shock as (18) and (19) show, I interpret Θ as a measure of 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 acompound of hawkish and dovish persons. 29
Later, in the discussion on Proposition 6, Q is reset to {0, N1 , ..., NN−1 , 1}. See footnote 29 andAppendix E.
28
There is 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, I neglectsuch a case.
29
Since I adopt the beauty contest games in the process of decision-making in the monetary policy
committee, I assume here that both the two groups have at least two members. So, in this setting,the monetary policy committee is always a compound. However, the discussion on Proposition 6 below
makes sense because it does not depend on the structure of the beauty contest framework substantially.
That is, similar results hold even under assumptions which allow the case where one group occupies thewhole committee. For a detail explanation for this point, see Appendix E.
27

22

Proposition 6
2

σ2

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

2

σ2

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

Proof.
See Appendix D.
To gain an intuition for Proposition 6, consider the case of perfect information: σν2 =ση2 = 0. I obtain the following corollary immediately from Proposition 6.
Corollary 8 Suppose that information of the committee members on the cost shock isperfect, 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 the optimal weight in this case. Hence, to approximate interest ratesetting to optimum with respect to the policy weight, it is suboptimal to appoint only
the members of Dove group. I similarly interpret 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 optimality of compound committees
is valid is stricter than that of 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(i.e.,large Θ) pushes up the lower bound of λd for optimality of the compound committees.
I interpret the second assertion of Proposition 6 in the same way.
The results of the previous section and Proposition 6 reﬂect 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’ preferences
is very small. It can be regarded as a theoretical justiﬁcation for that the actual monetary
policy committees consist of heterogeneous members with respect to preferences over the23

goals of monetary policy. It also answers for why the committees have replaced the single
policy makers in recent years by showing the merit of preference heterogeneity. 30
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 F.
These are intuitively plausible according to Corollary 4 and 6. Consider the ﬁrst assertion. Since enlarging the committee accommodates ineﬃciency of interest rate setting
due to imperfect information, it lowers the value of adding output-minded members. 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
information is considerably absorbed by aggregation. 31 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 of discretionary policy under
perfect information by a single policy makerκ
xt = − c π t
λ30
31Heterogeneity of members’ tastes is one of the substantial features of committee decision-making.
The actual sizes of the monetary policy committees are about 10. I provide a few examples later.

24

implies that excessive conservatism (i.e. very low λc relative to λ) leads to enormous
volatility of output gap. Thus, excessive liberalism generates small ineﬃciency relative
to excessive conservatism. This mechanism works also 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, I 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 = 0.65. These speciﬁcations do not makea diﬀerence in the qualitative results. I set σψ2 = 1 since what is important is not theabsolute value of σψ2 but the ratio of σν2 or 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 thequalitatively same results with other values. The size of the monetary policy committee
varies among countries. For example, the numbers of committee members of FOMC,
the MPC of 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 q̃.
[Figure 1 about here.]
Figure 1 illustrates it. This result is robust with respect to other parameters’ values.
The reason why q̃ is hump-shaped in κ is as follows. An increase in κ has three eﬀects
on q̃. First, even in the case of imperfect information, the channel of the third assertionof Proposition 7 is eﬀectual. Second, a decrease in the ratio of the response coeﬃcients25

on the cost shock in target rates of Hawk group and Dove group, Θ, reduces the relative
beneﬁt of appointing the output-minded persons rather than inﬂation-minded persons
for holding the ineﬃciency of imperfect information and coordination behavior. This
is interpreted as below. The larger the trade-oﬀ of monetary policy is, the closer theattitudes about inﬂationary pressure of inﬂation-minded and output-minded group are.
It reduces the merit of Dove group members for accommodating the volatility due toineﬃcient interest rate setting. Third, an increase of impact of output gap in inﬂation
enlarges the eﬀect of ineﬃcient interest rate setting on inﬂation as Corollary 4 shows.
The ﬁrst and second eﬀects dominate the third eﬀect for small κ and vice versa for large
κ. 32 The second and third do not exist under perfect information, which leads to themonotone result, i.e., the third assertion of Proposition 7.
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. By and large, 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 andhence 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 decreasein the intermediate values of σν2 in Figure 2.

5

Concluding Remark

Incorporating that monetary policy is conducted by committee 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. The results tell us that there is a merit of appointing liberal central bankers when32

In this example, the range of κ in which the third eﬀect dominates the ﬁrst and second eﬀects is not
so realistic in view of the empirical evidences. However, this paper focuses only on the mechanism thatprovides the result above.

26

the central bank can not perfectly control the demand side of the economy because ofimperfect information on economic shocks. This provides a theoretical justiﬁcation for
the fact that the actual monetary policy committees usually consist of members withheterogeneous preferences. It also explains why the committees have replaced the single
policy makers.
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
not easy to solve in formal models. Along the line of this paper, the key mechanism
for determination of the optimal size may be a harmful eﬀect of common information
which is augmented by adding committee members. Morimoto (2009) shows that theexistence of coordination behavior may break Condorcet’s (1785) jury theorem and theﬁnite optimal size of the committee is determined. Although Morimoto’s (2009) solution
is one plausible approach, there can be other distinguished one.
There is possibility of another extension. Riboni and Ruge-Murcia (2008) and GerlachKristen (2008) report 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, I obtainΦ − ρe Aπγe Φ, 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, I obtain
Aπ = βρe Aπ + κAx + 1, Bπ = κBx , Cπ = κCx , Dπ = κDx , Eπ = κEx .

(36)

Solving the ﬁrst equations of (35) and (36), I obtainκ
Ax = − c,λ (1 − βρe ) + κ2

Aπ =

λc
.
λc (1 − βρe ) + κ2

Thus, I obtain the equilibrium output gap and inﬂation rate in period t in the text.
Finally, I 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, I
ﬁnd asymptotic variance of output gap in the text. Similarly, I can calculate asymptotic
variance of inﬂation rate in the text.
28

Appendix B: Proof of Proposition 3
At ﬁrst, I ﬁnd the condition for L to be a convex function of λc . Diﬀerentiating L withrespect to λc formally, I obtain

σψ2
∂L
κ
c
=
)λ
+
λ
κ]
[
−
κ(1
−
βρ
e
∂λc
1 − ρ2e[λc (1 − βρe ) + κ2 ]3
κ2 + λ  γe 2 c+
[λ ρe + (1 − ρe )σκ][ρe κ − (1 − ρe )(1 − βρe )σ]ση2Nσ 1 − γ 2e2c2+(κ + λ)[λ ρe + (1 − ρe )σκ][ρe κ − (1 − ρe )(1 − βρe )σ]σν .
σ
Put

 2

ση2
γe
σν2
(λ + κ2 )2[σ(1 − βρe )(1 − ρe ) − ρe κ]Λ=·+ (1 − γe ) 2.
σ2
N σψ2 /(1 − ρ2e )σψ /(1 − ρ2e )Then, Λ > 0 since I assume that σ(1 − βρe )(1 − ρe ) > ρe κ here. I obtain

σψ2 
∂L
κ
c
=
·
Λ]λ
−
κ(1
−
βρ
)λ
−
σκ(1
−
ρ
)Λ
.
[κ
−
ρ
e
e
e
∂λc
[λc (1 − βρe ) + κ2 ]3 1 − ρ2e2∂ L
It implies that the condition for ∂λc 2 is κ > ρe Λ.
∂L
Therefore, I assume that κ > ρe Λ. Under this condition, the solution λ∗ of ∂λc = 0 isλ∗ =κ(1 − βρe )λ + σκ(1 − ρe )Λ
> 0.
κ − ρe ΛAfter some calculations, it can be reduced toλ∗ = λ +[σκ(1 − ρe ) + ρe λ]Λ − βρe κλ.
κ − ρe ΛThis completes the proof.

Q.E.D.

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



V [π] + λV [x] .
argmin−22q  ∈{ 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 of29∂ (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 κ2 σ−κ− (Φh − Φd ) σψ2
σ
σ



 h

2  h 2d 2d  hΦΦ − Φd  2
Φ
2 γe
2
2
2 q̃Φ + (1 − q̃)Φσν+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  2γe2  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, I obtain (29). 33 Since discrete convexity of V [π] + λV [x]with respect to q, the optimal ratio q ∗ must belong to the following set

 



L̃
L̃
+
1
2
N
−
2
= q− ≤ q̃ ≤ q+ =∪,.
q− , q+ ∃L̃ ∈ N, 2 ≤ L̃ ≤ N − 3,N
N
N
N
Moreover, since V [π] + λV [x] is quadratic in q and quadratic functions are symmetricwith respect to their axises, I ﬁnd that q ∗ is the nearest element of { N2 , ..., NN−2 } to q̃.
Q.E.D.

Appendix D: Proof of Proposition 6
Using (15), the numerator of (29) becomes
2

γe2 2
2
h
d
2
ση − Φd (κ2 + λ)(1 − γe )2 σν2σψ − (Φ + Φ )(κ + λ)σκ − Φ (κ + λ)
2N


2
2
2
σψ2 d
σ
γ
η
e
2
2
2 σν
·
=
− (κ + λ)(1 − γe ) 2
λ − λ − (Θ + 1)(κ + λ)
Φd2N σψ2σψσψ2 d  ∗γe2 ση2 
2
·
−
λ
+
(Θ
−
1)(κ
+
λ)
=
λ
.
Φd
2N σψ2dThis shows the ﬁrst assertion. Next, q̃ ≥ 1 if and only ifσκ − Φd (κ2 + λ) σψ2 − (Φh + Φd )(κ2 + λ)γe2 2σ − Φd (κ2 + λ)(1 − γe )2 σν22N η≥ (Φh − Φd )(κ2 + λ) σψ2 + (1 − γe )2 σν2 .
33

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

30

Dividing the both sides by Φh σψ2 , I have1 2
γ 2 ση2σ2(κ + λ) e · 2 ≥ λ + κ2 + (1 − γe )2 (κ2 + λ) 2ν ,λh + κ2 − 1 +
Θ
2N σψ
σψ
which is reduced to

It completes the proof.

1 2
γ 2 σ2λ ≥λ − 1−(κ + λ) e · 2ν .
Θ
2N σψ
h

∗

Q.E.D.

Appendix E: Supplementary Note to Proposition 6
Proposition 6 provides a necessary condition for optimality of a compound committee
but in the model of the main text, as a matter of form, I adopt the assumption which
excludes the possibility that one group occupies the whole committee. However, thissetting does not spoil the signiﬁcance of the assertion of Proposition 6. I show it in this
supplementary note by providing the settings which allow the case where only one groupoccupies the whole committee.
First, consider the case of r = 0. Since there is no coordination motive among themembers, I may assume that 0 ≤ L ≤ N . Under this assumption, I can treat thecase where the monetary policy committee is occupied by only one group. The set
Q in Proposition 5 is hence modiﬁed to {0, N1 , ..., NN−1 , 1}. Note that the assertion of
Proposition 6 holds in this setting according to its proof in Appendix D.
There is another setting which brings the same result as Proposition 6 in this paper.
Morimoto (2009), which explores the relationship between coordination behavior among
the members and the optimal size of the monetary policy committee, adopts the following
loss function of each member as the payoﬀ structure in the committee:N1  k 2
j
j
j
∗ 2
i
.
Et−1 r(it − it ) + (1 − r) it −N k=1 tk
In this setting, each member j can partially control the secondary objective, N1 N
k=1 itsince it contains her own voting rate, ijt . Therefore, by extending the setting to the caseof preference heterogeneity as in this paper, I can treat the case where the monetary
policy committee is occupied by only one group. Along the line of Morimoto (2009), in
this case, there is a unique equilibrium strategy such that for j ∈ H and k ∈ D,

ijt = σ[ρu ut−1 + γu ϕjt + (1 − γu )ϕct ] + Φh [ρe et−1 + γe ψtj + (1 − γe )ψtc ],ikt = σ[ρu ut−1 + γu ϕjt + (1 − γu )ϕct ] + Φd [ρe et−1 + γe ψtj + (1 − γe )ψtc ],31

where γu =(1−δ)σε−2

−2
−2
−2
r
1 σμ +N σε
(1− N
)(σμ
+σε−2 )−r(1− N)Nand γe =(1−δ)ση−2−2
σ −2 +N ση
N

r
1
(1− N
)(σν−2 +ση−2 )−r(1− N) ν. It isobvious that although these γe and γu are diﬀerent from those of this paper’s model, thesame result as Proposition 6 in this paper holds by the same discussion.

Appendix F: Proof of Proposition 7
I show the ﬁrst assertion as follows. It is immediately obtained from (29) that q ∗ isnon-decreasing in N and non-increasing in λ. By (29), I obtain2

γe 2(Φd + Φh )(κ2 + λ) 2Nση + (σκ − Φd (λ + κ2 )) + Φd (κ2 + λ) (1 − γe )2 σν2
∂ q̃
=
.
∂σψ2
(Φh − Φd )(κ2 + λ)(σψ2 + (1 − γe )2 σν2 )2∂ q̃, Φh = λhσκand λd > λh , I obtain that ∂σ
Since Φh > Φd by Φd = λdσκ2 ≥ 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. Let
us deﬁne the following function f : [0, 1] → R.

ση2+ Φd (1 − γe )2 σν2 ,2NThen, after some calculations, I obtainf (r) = (Φh + Φd )γe2f  (r) = −for every r ∈ [0, 1].

(1 + Θ)(1 − r)
Φd
∂γe
2−
·
.
∂r pν + (1 − r)pηNe
Since ∂γis negative, this proves the second assertion.
∂r
I ﬁnally prove the third assertion. By (29), under perfect information, I obtainq̃ =σκ − Φd (κ2 + λ)λd − λ=,(Φh − Φd )(κ2 + λ)(Θ − 1)(κ2 + λ)2

. Note that q̃ can be regarded as a function of κ2 . Diﬀerentiating q̃ with
where Θ = λλh+κ+κ2respect to κ2 , I obtaind∂Θ2(λd − λ) ∂κ
2 (κ + λ) + (Θ − 1)
∂ q̃
=−
.
∂κ2
(Θ − 1)2 (κ2 + λ)2
∂Θ
λ −λ
By ∂κ
2 = (λh +κ2 )2 , I 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 completed.

32

Q.E.D.

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34

0.44

0.42

0.4

0.38

q

˜

0.36

0.34

0.32

0.3

0.28

0.26

0

0.1

0.2

0.3

0.4

0.5

κ

0.6

0.7

0.8

Figure 1: The relationship between κ and q̃

35

0.9

1

0.5

q

∗

0.4

0.3
0
0.2
0.4

0.2

0.6

0

0.8

0.2
0.4

1

0.6

1.2

0.8
1

2

ση

1.4

1.2

1.6

1.4
1.6

1.8

1.8
2

2

Figure 2: The relationship between (ση2 , σν2 ) and q ∗36

σ2ν