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Cutting down on inefficient public expenditure and central bank independence
土居, 丈朗(Doi, Takero)
Keio Economic Society, Keio University
2006
Keio economic studies Vol.43, No.1 (2006. ) ,p.1- 19
This paper shows that inefficient public expenditure can be institutionally curtailed
by an independent central bank in the international economy. We conclude that an
independent central bank promotes budgetary efficiency. An advantage of ouranalysis from the angle of public economics is to treat the relation between central
bank independence and fiscal policy (public goods provision). When the central
bank is not independent of the fiscal authority, that is, when fiscal policy isdetermined before monetary policy, the public good is oversupplied. When thecentral bank is independent (monetary policy is predetermined), however, theexpenditure level is efficient. We also
show that it is important to cooperate to make each central bank independentinternationally.
Journal Article
https://koara.lib.keio.ac.jp/xoonips/modules/xoonips/detail.php?koara_id=AA00260
492-20060001-0001

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KEIO ECONOMIC STUDIES 43(1), 1-19 (2006)

CUTTINGDOWN

ON INEFFICIENT

TakeroPUBLICEXPENDITURE
AND CENTRAL BANK INDEPENDENCE

Doi

Faculty of Economics, Keio University, Tokyo, JapanFirst version received January 2006; final version accepted September 2006

Abstract: This paper shows that inefficient public expenditure can be institutionallycurtailed by an independent central bank in the international economy. We conclude
that an independent central bank promotes budgetary efficiency. An advantage of ouranalysis from the angle of public economics is to treat the relation between central bankindependence and fiscal policy (public goods provision). When the central bank is notindependent of the fiscal authority, that is, when fiscal policy is determined before monetary policy, the public good is oversupplied. When the central bank is independent(monetary policy is predetermined), however, the expenditure level is efficient. We also
show that it is important to cooperate to make each central bank independent internationally.
Keywords:

Central Bank Independence,

JEL Classification

Number:Public Goods, Cash-in-advance

Model.

H41, E61, E62, E58.

I.

INTRODUCTION

Recently, two topics relating to fiscal and monetary policies have been discussed indeveloped countries; budget deficits and central bank independence (CBI). The former
has been caused by increasing inefficient public expenditure, and the latter prevents
it from being monetized, which gives rise to inflation. Especially in Japan, reducing
budget deficits and revising the Bank of Japan law become subjects of discussion in thesame period.
We try to analyze the relation between CBI and fiscal policy as well as monetary
policy in this paper. We will show that CBI is significant not only to prevent inflation
Acknowledgements. I wish to thank Hiroshi Fujiki, Shinichi Fukuda, Toshihiro Ihori, Hidehiko Ishihara, Masahiro Kawai, Akihiko Matsui, Masayuki Otaki, Shumpei Takemori, and Masatoshi Yoshida for
helpful comments. I am also grateful for comments of an anonymous referee. This study was supported by
a Grant-in-Aid Scientific Research (No. 17730208) from the Ministry of Education, Culture, Sports, Scienceand Technology of Japan. Any remaining errors are mine.
E-mail:Copyright©2006, by the Keio Economic Society
1

2

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ECONOMICSTUDIESbut also to cut inefficient public expenditure. In previous theoretical research on CBI,e.g. Rogoff (1985), Persson and Tabellini (1990), Cukierman (1992), Alesina and Gatti(1995), Walsh (1995), wallet and Walsh (1996), and Beetsma and Bovenberg (1997a,b), the relation between CBI and monetary policy were investigated. They showedmechanisms to induce inflationary policy, and concluded that CBI is important to prevent inflation. However, they did not mainly treat the relation between CBI and public
expenditures theoretically.
Absence of CBI is one of causations that the government increases public expenditures and fiscal deficits, since the central bank can easily monetizes fiscal deficits at
the request of the government implicitly and explicitly. In the other words, in order toequilibrate the government budget constraint, not budget cut or tax hike but seigniorageis used. It implies that the government is the leader and the central bank, which is notindependent, is the follower as a setting of a Stackelberg game.
In order to prevent the central bank from monetizing, the monetary authority becomes
independent from the government. In case of an independent central bank, the government cannot depend on monetization of fiscal deficits by the central bank. We express
this situation as a Stackelberg game in which the central bank behaves as a leader andthe government behaves as a follower.'
In case of Japan, it is important to analyze how reinforcing independence of the Bankof Japan affect fiscal policy. Koizumi administration has implemented fiscal reconstruction, which implies reduction of public investments and then fiscal deficits, since 2001.
On the other hand, the Bank of Japan has strengthened independence since 1998 .
Now we use a two-large-country model with cash-in-advance constraints in order toinvestigate the idea that inefficient public expenditure can be institutionally curtailed byan independent central bank from the angle of public economics. Households in bothcountries face the cash-in-advance constraints: they have to purchase goods with the
producer's currency. And consumption of not only a private good but a public goodincrease the household's utility. Policymaker in each country decides the levels of apublic good provision and a lump-sum tax, and the money supply, to maximize his own
households' utility. Hence, we can analyze fiscal and monetary policies simultaneously,
and have the microeconomic foundation of the objective functions in our model.2
We have other advantages in our model. First, we can examine welfare analysis ofresource allocation. We will focus on the efficient provision of public goods supported
by an independent central bank in this paper.
Second, we deal with policy in a large open economy. Previous theoretical studies on
CBI mainly analyze monetary policy in a closed or small open economy. Economies in
1 In Section III, we will define CBI in our model.
2 We adopt a two -country model with cash-in-advanceconstraints; nevertheless we do not imply that wedeny the loss function approach used in previous studies on CBI, and its conclusion.

Their approach include a

priori that the policymaker's welfare is worse off by raising the inflation rate, were often used as the objectiveof the central bank. The reason for this is that the central bank stabilizes the price level, and prevents ahousehold sustaining disutility due to inflation. This means that the central bank considers the household's
utility. In this sense, our model is relevant to these works.

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3

EXPENDITURE

developed countries are in fact large, and interactive effects of policies among industrial
countries are negligible.
Using a large open economy model, we can explicitly investigate effects of policies on price level and interest rate and interaction among policies inthese countries.
We will explain the following results using our model.
When the central bank is
not independentof the fiscal authority, that is, when fiscal policy is determined before
monetary policy, the public good is oversupplied,because government can choose public good provision with respect to the issue of money. But when the central bank is
independent,
that is, when monetary policy is predetermined,
efficient.
Because the government
cannot control the public
seigniorage.

Thus, an independent

penditure.
This paper proceeds

as follows.

the expenditurelevel isgood in anticipationofcentralbank promotes

cuts of inefficient

SectionII demonstrates

the model

public ex-

and analyzes

thefirst best solution. Section III examines the results of policies when the fiscal and monetary authorities operate separately.
Also we show that inefficient public expenditure
can be cut down by an independent central bank. Section IV compares both regimes:
one with central bank independence
Finally, section V is the conclusion.

and the other withoutII.

centralbank independence.

THE MODEL//. /. A two-country model with cash-in-advance constraints
First, we show the model. This is a two-country model with cash-in-advance constraints, used by Lucas (1982), Helpman and Razin (1984), Canzoneri (1989), Martin(1994), and so on. The setting follows Canzoneri (1989) and Martin (1994). The household in this model consumes a private good and a public good which the government
provides. So this is appropriate for the analysis of fiscal and monetary policy in aninternational economy.
Suppose there are two countries, home country (country h) and foreign country(country f). They are symmetric and large: each one affects the other. We assume
households are homogenous, live infinitely, and cannot migrate. The population in eachcountry is assumed to be unity (constant). Both countries produce a single private good,whose (real) amounts of period t are yt (>0) and yt* (>0) units.3 To avoid unnecessary complications, we presumed yt and y7 are exogenously given in each period.4
Hereafter,
distributed

asterisks denote foreign country in all variables.
These outputs
in cash among households
in both countries at the beginningare equallyof the next

period.

3 At period 0 , the economy has the initial endowment y_ i or y* 1.
4 This assumption is the same as Canzoneri (1989) and Martin (1994) . The assumption is also supportedby the findings of Alesina and Summers (1993): There is no correlation between the degree of CBI and real
growth rate. Incidentally they also find there is negative correlation between the degree of CBI and inflation
rate.

r-o

4

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The utility functions
lows:

ECONOMIC

of representative

STUDIEShouseholds

in both countries

are given as fol-00

u = Est (logct+ loggt), 0<,B<1

(1)

r=0
00

u*= E fit(logct+ loggr)

0<8<1

(1')

where ct and gt are respectively (real) consumption of a private and a public good per
capita. 8 is a discount factor (the same in both countries). We assume that the twocountries' goods are perfect substitutes and have no trade costs . Hence the exchange
rate between both currencies at period t, et, is satisfied as follows
Pc = er pr,*(2)where pr and pt* are home and foreign currency prices of the private good .
Households face cash-in-advance constraints. They need a home currency when theypurchase the home good, and a foreign currency when they purchase the foreign good;they cannot purchase the foreign good with a home currency, or the home good with aforeign currency.5 So they satisfy the following conditions at period t:

mht ? Ptcht ,mfr ? Pt eft ,(3)mhr> ptchr,

mft > pi cft ,(3')

wheremht and mft are respectivelythe home households' home and foreigncurrency(nominal)demandfor privateconsumptionat the beginningof period t per capita,chi
and cft are respectivelythe home households'home and foreigngood (real)consumptionper capita. Householdscan purchasethe bondsissuedby bothgovernmentsin cash.
We presumethat the home bond is traded by only the home currencyand the foreign
bond is traded by the foreigncurrency.The bonds issued by both governmentsare assumedto be perfect substitutes.Since the bond marketsare assumedto be perfect,thegrossrates of interestare equalin both bonds by arbitrage(say il).
The cash flowof the home householdsfor period t is expressedash
mht + Prbhr + Pitt = Pr-lYt-l/2 + prrr—lbht-l
Mft + Prbit = Pr-tYr 1/2 + Prrr-tb .fr-t •So the budget

constraintof the home households

for period

t is expressedin moneyterms

mht + etm ft + Prbhr+ etPr bit + Prrr
= Pt—tyt-l/2 + etpt* 1Yr 1/2 + Prrt-tbht-l + erPrrt-lbft-l ,(4)

5 This is the seller's system as defined by Helpman and Razin (1984).
6 Since the bonds issued by both governments are perfect substitutes a nd the home households satisfy (3),they adjust money demand for both currencies by the cash-in-advance constraints of private consumption.
The same thing can be said of the foreign households.

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where bht and bp are per capita (real) demand for home and foreign debt at the beginning of period t, rt is per capita (real) lump-sum tax. The households pay the tax incash. We can also write the cash flow of the foreign households for period t is expressedasmh,+ Ptbht= pt-lYt-l/2 + Ptrt_ibhr-l ,mfr + Prbit + pit = Pt*__ly1/2 + pt rt-lbfr-l
Hence the budget constraintof the foreign households

in a like manner;

flintier+mfr+Ptbht/et+ptbft+Ptrr= Pt-iYt-l/2et+ Pt-lYr 1/2+ prrr-lbhr-leer+ pt rt-lbft
Using(2)and(3),(4)and(4') arerewrittenas
Ct+ bf + ti = Pt-IYr-l/2Pt + Pt-lYt 1/2Pt + rt-ibt-i ,ct + bf + rt = pt-lYt-ll2Pt + Pr-iYt 1/2Pt + rt_ Ibt 1
wherect = Chi+ cft, bf = bht+ bft Ct*- chi+ cf r, bf = bht+ bft

(4')

(5)
(5')

Second, both policymakers)ficymakers (fiscal and monetary authorities) collect lump- sum andseigniorage taxes andind issue debt, and provide a public good. The public geol d in eachcountry, however, is only supplied to the household in that country. We as sume that themarginal rate of transformation
ansformation between the public good and a private good is unity inboth countries for eachinch period. Since we suppose policymakers purchase a
rate goodin their own countryty to provide the public good, they face cash-in-advance constraints,
too.

mht?Ptgt,mft?Ptgr •Hencethe budgetconstraintof the homeand foreignpolicymakerat periodt are (analogous stepsleadingto the foreignconstraint)-hi' Pt + rt-idt-l = (Mt - Mt-l)/Pt + rt + di
mgtIPt+rt-idt=(Mt- Mt*1)llst*+ rt*+ d~whereMt is the total amountof (nominal)moneysupplyper capita in the beginningof
period t. In our paper, we assume rt > 0 in each country.7di denotes total amountof (real)debt per capita at the beginningof period t. Then the bond market clearing
conditionbecomesbht+
For simplicity,

we unify

both

=di,

bit+!ft=dr .

conditions;bf + bf = di + dr .(6)
7 Becausethe government, as shown later, if we allow lump-sum
subsidy, the larger a seigniorageand lump-sum
subsidy
sets, the higher the utility of household
becomes
at the equilibrium.
We set the assumption
toavoid the situation
infinitethat the government

in this model.

increases

the levelsof seigniorageand lump-sum

subsidy

to become

1

6KEIO

ECONOMIC STUDIESIn the bond market, both households and governments behave as price takers.
Similarly, the good market clearing condition in both countries becomes

chi+chi+gt=Yt,

eft+cfi+gr=yr

It is convenient to combine both conditions;ct + gt + cl + gr = Yt + yr ,(7)

In the good market, both households and governments also behave as price takers .
The equilibrium conditions of the money market are

Mt=mht+mht+mht,
Using the good market clearing

conditions,Mt = prYr,
For giveny, and y,,

pricelevelsMt*
the above conditions

are rewrittenas

Mt = pi yr .

are determinedin both money

markets

when both

policymakers
choose the quantity of money.
Now, we define the growth rate of money:

ht = (Mt —Mt-l)/Mt < 1 ,ht = (Mr —Mt 1)/Mt < 1 .

Then(Mr —Mt-l)/Pt = hrYt, (Mt —M7_1)/p' = hr yt .
So the governmentbudgetconstraintsare rewrittenas
gt+rt—idt-l =htYt+rt+dr,(8)g, +rt_idr 1 =hiyi +rt +di,(8')
and the household

budget constraints

are rewrittenasct + bf + rt = (1 —ht)Yt/2 + (1 —hr )Yt/2 + rt—lbf-l ,cl +br +rt =(1 —ht)Ytf2+(1 —hi)ytl2+rt-lbr-l

(9)
•(9')

11.2. First best solution
We consider Pareto optimal allocation in the two-country economy as the benchmark
case. In the same way as Canzoneri (1989), a world social planner maximizes theweighted sum of utilities of both households.
cc

max—

tat,cr ,bf,br ,gt,gr ,Et,ti*'hi ,hi ,di,dr)
100

+ —2

E et(logct+ loggt)

2 t =0+ log gr)t=0s.t. (6), (7), (8), (8), (9), (9'), rt > 0 ,rt > 0 .

As we consider two symmetric countries, the weight of utility of each household is

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7EXPENDITURE

equated(theweightis 1/2).This optimalsolution(firstbest solution)is8
ct=gt=ct=gr=(Yr+yr)/4.
The derivation of the above condition is given in Appendix A. This resource allocation
is efficient, because Samuelson (1954)'s rule is held in each country.9 In this model, themarginal rate of substitution between the public good and the private good for the household is ct/gt (home country) or c'/g' (foreign country) at period t, and the marginal
rate of transformation between the public good and the private good is unity from theassumption. The above solution shows that the Samuelson rule is held in each country.
Moreover the solution implies the equilibrium when both policymakers take cooperative
policies.
III.

EQUILIBRIAWHEN

THE CENTRALBANKIS INDEPENDENTAND NOTINDEPENDENT

111.1. A definition of an independent central bank
Actually, fiscal and monetary authorities are separated in deciding policies whether
they are interdependent or not. We consider policies when the fiscal authority (government) and the monetary authority (central bank) determine them separately, The fiscal
authority determines fiscal policy: It can control the amount of a public good provision
and a lump-sum tax. The monetary authority decides monetary policy: It can set thequantity of money supply and (non-monetized) debt. In this section, we consider what
is central bank independence in our model.
When the central bank can decide a monetary policy without the interface of the government and the Congress, we call it an `independent central bank'. Hence, we define
an independent central bank as a central bank that can choose the levels of hr and drbefore the government decides fiscal policy in our model. In other words, an independent central bank can determine a monetary policy before the government chooses thelevels of fiscal deficits (equal to lump-sum tax revenue minus expenditure). If a central
bank determines a monetary policy after the government has already determined a fiscal
policy, it can only choose a level of monetization to finance fiscal deficits decided by
the government. Therefore, in this situation, a central bank is not independent of thegovernment.
This definition is justified by previous research. Grillin, Masciandaro, and Tabellini(1991), Cukierman, Webb, and Neyapti (1992), and so on, which design the indexes of
CBI, define the policymaking of the central bank without monetizing the fiscal deficit as
one of factors regarding CBI. Also, Tabellini (1987) investigates a central bank which
8 In this solution,any levelsof tr, r7 , hr, and h' satisfythefollowingconditions;
yt+yr*

hr yr + rt =,hryr+r=
4

9 In this modelof utilities, The Samuelson

are not crucial.

rule is held,

unless**Y'r±vi*,4weightsof eachcountry

is 1/2. Therefore

the weights

8

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ECONOMICSTUDIES

is freed from the obligation to monetize the fiscal deficit and as a result establishes areputation of independence. So, we define an independent central bank as a central bankthat decides a monetary policy before the government determines a fiscal policy.
We discuss two situations: 1) the central bank is not independent in deciding monetary policy, and 2) the central bank is independent. The former is the case where thegovernment decides fiscal policy before the central bank: the government is the leader,
and the central bank is the follower in deciding policy. Since the central bank must act
under a given fiscal policy, the central bank is not independent. The latter is the case inwhich the central bank decides fiscal policy before the government: the central bank is
the leader, and the government is the follower, so the central bank is independent.
Now, in order to keep our analysis simple, we assume that both a government and acentral bank maximize the utility of the representative household in their own country.
In other words, their objective functions are the same as the utility function of the representative household in each country. This assumption implies that there exist no conflict
between a fiscal authority and a monetary authority with respect to preference. We willshow that the outcome under an independent central bank is different from that under adependent central bank even if a fiscal authority and a monetary authority have the same
objective function. If the objective function of a central bank is different from that ofa government, it is obvious that both outcomes may be different.10 We emphasize thedifference of institutions rather than preference in our discussion.
Moreover, we consider two equally large countries in consideration of industrial
countries. Hence we only examine simultaneous-move games between two countries
in our model: Agents in each country maximize their objective functions given choicesin the other country. Our analysis focuses on a Nash equilibrium. We are not interested
in the leader-follower relationship between two countries.
111.2. An equilibrium without an independent central bankIn this section, we analyze the case where a central bank is not independent in bothcountries. The process of decision making is as follows. In the first step, the government
determines the amount of a public good provision and a lump-sum tax to maximize thehousehold utility. Fiscal deficit, the difference between a public good provision and a
lump-sum tax, is filled by issuing money or debt. In the second step, the central bankdecides the quantity of money supply to maximize the household utility given his own
fiscal policy and foreign policies. Finally, households choose their consumption anddemand of debt to maximize their utility under the given policies. Both countries makedecisions simultaneously.
To investigate an equilibrium under this situation, we use the method of backward
induction. So, in the first place, we solve the household's optimization problem. The
home household's problem is as follows.

max (1) s.t. (9) given gt, rt, di, ht, gr , r7 , 7, ht .
lc,,b)

10 Beetsma and Bovenberg (lggia , b), Dol, Ihori, and Mitsui (2006) and among others investigate policy
effects by using a model that the objective function of a central bank is different from that of a government.

Dol: CUTTINGDOWNON INEFFICIENTPUBLICEXPENDITUREg
The first-order conditions reduce to
Ct = pit—let—i •(10)
The derivation of the above condition is given in Appendix B. Similarly the foreign
household chooses

Ci = /jrt—ICI-l•(10')
to maximizeits utility. We can interpret(10) or (10') as the response functionof thehousehold.
The centralbankchoosesthe amountof moneyor debt supplyas given (10) or (10'),its owngovernment'spolicy, and policiesin the other country.Then the home central
bank's problemis givenby
max (1) s.t. (8), (9), (10) given gt, rt, gr , r7 , d7, ht •[hi,ell)
The first-order conditions reduce to
9t = 2ct ,(11)9t = /srt-lgt-l•(12)(12) is equivalent of (10). Then (12) will be omitted hereafter. Using (8), (9), and (11),the response function of the home central bank is written as

htyt = —gt—2tt + yt + (1 —ht )Yt —2(bf —rt—Ibt-l)(13)
where bf in (13) implicitly satisfies (10).
In the same way, the foreign central bank's problem is given bymax (1) s.t. (8), (9), (10) given gt, rt, di, ht, gt , rt .
(hi4l
The

first-orderconditions

reducetog7 =2ct ,

(11')

(12')
.9 = art-lgi 1 •Using 03), (9), and(12') is equivalentof (10'). Then (12') will be omittedhenceforth.Using(11), the responsefunctionof the foreigncentralbank is writtenas
hi yt = —gr—2rt + y7 + (1 —ht)Yr—2(bf —rt-lbf 1)

di = 2gt + rt —yt —(1 —ht)Yt+ 2(b(13')

wherebl in (13') implicitlysatisfies(10').
The homehome government's
government's oobjective is
Finally,each governmentdecidesfiscalpolicy.Themax (1) s.t. (8), (9), (10), (13), rt > 0
t9t it)given g$, tr , dr , ht .

1

10This implies

KEIO

ECONOMICSTUDIESthe lower rt is, the better it becomes.

Hence,

it sets rt = 0, and1

gt = 2 (Yt+ (1 - hi )yt - tr_idr-l - 2(bf - rt-ibr-I)}(14)wherebf in (14) implicitlysatisfies(10),and di in (14) implicitlysatisfies(13).
Similarly,the foreigngovernmentchoosesrt = 0, and
gt= -2{yt+ (1 - hr)Yr- tr_idr 1 - 2(bl - rt-lbr-l)}(14')
to maximizethe utility of the foreignhousehold,wherebf in (14') implicitlysatisfies(10'), and dr in (14') implicitlysatisfies(13').
Now,we discussa Nash equilibriumunderthe above systemin both countries.(11)and (11') are always held with any policy. These imply that this equilibriumis notefficient:these do not satisfy the Samuelsonrule. Why does the equilibriumbecome
inefficient?In the abovesystem,eachgovernmentpredeterminesthe provisionof public
good.Wenow considerthe case that the homegovernmentraises gt. In orderto financeit, the home governmentcan levy a lump-sumtax or delegatefinancingfiscaldeficits
to the home centralbank. If rt increasesby one unit for an increaseof gt, ct has todecreaseby one unit in (9). While if ht yt increasesby one unit, gt increasesby one
unit in (8) and ct decreasesa half unit in (9). Thereforethe home governmentprefersa seignioragetax to a lump-sumtax, and collectsthis seignioragetax from the foreign
householdexcessively.Because,in thiscase, gt increasesby one unit and ct decreases
halfunit,that is, this relationshipdoesnot satisfythe Samuelsonrule. Thesephenomena
are causednot by interactionbetweenboth governments,that is, factorsin a largeopen
economy model, but by absenceof independentcentral banks. Main feature of the
two-large-countrymodelappearsin SectionIV.
Incidentally,from(11) and (11'), the governmentdebtshaveno effecton both private
andpublic goods consumption:Obviouslythe Ricardianequivalenceis held. Then we
assume di = di = 0 without loss of generality. So bf = br = 0. Since they are
symmetric,from (7), (11), and (11'), the quantityof consumptionis
ct = c = (yr + y7)/6 ,gt=gt*=(Yt+yr)/3.

The policies of the central banks are, in this equilibrium,

ht = (Yt+ Yr)/3Yr,

hr = (Yr+ y)/3y7.

111.3. An equilibrium with an independent central bank
Next, we analyze the case where the central bank is independent
The process
the quantity

in both countries.

of decision making is as follows. In the first step, the central bank decidesof money supply to maximize household
utility. In the second step, thegovernment
determines the amount of a public good provision and a lump-sum
maximize household utility given its own monetary policies and foreign policies.

tax toSince

the money supply is predetermined,
the amount of a public good provision must be equal
to a lump-sum tax and money or debt. Finally, households
choose their consumption

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11

and demand of debt to maximize their utility are given policies. Both countries makedecisions simultaneously.
We discuss an equilibrium under this situation. The household's optimization problems that we solve first are the same as in section III.2. So we already gain the condition(10) and (10').
In the second stage, the government chooses the amount of public good provisionand lump-sum tax given (10) or (10'), its own central bank's policy, and policies in theother country. Then the home government's problem is presented bymax (1) s.t. (8), (9), (10), r > 0

Ig,,r,)

given di, hr, gt*,rt , di , hr .

From the first-order conditions, we obtain (12), andgt = ct.(15)The derivation of the above condition is given in Appendix C. We can interpret (15) as
the response function of the home government.
Similarly, the foreign government's problem given bymax (1') s.t. (8'), (9'), (10'), rt > 0 given gt, rt, di, ht, d7, h; .
(gr,tr)and, we obtain(12), andgt = Ct* C.(15')
We can interpret(15') as the responsefunctionof the foreigngovernment.
Finally,each centralbank decidesmonetarypolicy. The home centralbank's objectiveis
max (1) s.t. (8), (9), (10), (15), r t > 0 given gt , rt, d, hi .
th,,dr)This impliesthat the larger ht or di is, the better its utilitybecomes.So it setshtyt + 2dt = 4gt —Yt—(1 —ht )Yt + 2(bf —rt—Ibt-l) + 2rt_idt-l ,

(16)

or

shtyt + 2dt = —4tt+ yt + (1 —ht )yt —2(bf —rt—Ibt-l) + 2rt—I
di-l •The home centralbank follows(16) and decidesthe amountof homemoneysupply.
In a like manner,the foreigncentralbank's problemreducesto
max (1')(hr,dr)s.t. (8'), (9'), (10'), (15'), rt > 0 given 9t, r7, di, ht •This impliesthat the larger ht or d7 is, the better the utility of the foreignhousehold
becomes.So the foreigncentralbank sets
htyt+ 2dt= 4 .9—4— (1 —ht)Yr+ 2(bl —rt—^bl-l)+ 2rt—Idt(16')
or

34 yt +24 = —4rt + yt + (1 —ht)Yt —2(bf —rt-l bf-l) + 2rt-l di 1

12

KEIO

ECONOMICSTUDIES

Theforeigncentralbankfollows(16') anddecidesthe amountof foreignmoneysupply.
Now, we analyzea Nash equilibriumunder the abovesystem in both countries.According to (15) and (15'), these are consistentwith the Pareto optimal allocation. In
other words,the Samuelsonrules are held in both countries.
Moreover,to comparewith the levels in section111.2,we supposethe governments
set it = it* = 0. From (10), (10'), (15),and (15'),the governmentdebts haveno effecton both privateand public goodsconsumption:Obviouslythe Ricardianequivalenceis
held again. Then we assumedi = d7 = 0 withoutloss of generality.So bf = b7 = 0.
Since theyare symmetric,from (7), (15),and (15'), the amountof consumptionis
cr=gr=ct* =gr =(Yt+y7)/4.
In this equilibrium,

the central banks choose

hr = (Yr+ Y7)/4Yr, hi = (Yr+ y7)/4y7 •These imply the growth rates of money supply are lower than the rate in section 111.2;
this is inefficient. Why does this equilibrium become efficient? In the above system,
each government determines the provision of public good after deciding on monetary
policies. We now consider the case that the home government raises gt. In order tofinance, it can only levy a lump-sum tax. If gt increases by one unit, rt has to increaseby one unit in (8). Then ct decreases by one unit in (9). Since the relationship between
increase of gt and decrease of ct becomes one-to-one, The Samuelson rule is satisfied.
Thus, inefficient budgets are curtailed by an independent central bank.
These results also suggest that even if policymakers in both countries are not cooperative in their policies, the achieved equilibrium is Pareto optimal when the central bankis independent of the government in both countries.
IV.

THE SIGNIFICANCEOF CENTRALBANKINDEPENDENCE

Whatis the equilibriumif the centralbankis not independentin eithercountry?Now,
considerin the situationwherethe homecentralbank is not independentand the foreign
central bank is independent.Using the above results, the home policiesare presentedby (11), (14), and rt = 0, and the foreignare (15') and (16'). Then assumingtr = 0,
di = d7 = 0, andbf = bf*= 0, we obtain
ct=ct* =97=(Yt+yt)/5,
9t =2(yt+yt)/5.
The derivation of the above conditions is given in Appendix D. These suggest that, in
this equilibrium,
home households
become better off and foreign households
becomeworse off than when both central

banks are independent.

This phenomenon
is driven by a feature of the two-large-country
model. Resource
which can be used by households in both countries in each period is limited. Resource
allocationin one county affects one in another country in the large open economy

Dol:model.

ThoughCUTTING

DOWN

allocation

ON INEFFICIENT

betweena private

PUBLIC

13

EXPENDITURE

good and a public

good is optimal

in for-eign country, which has an independent
central bank, a public good in home country
whose central bank is not independentis over provided.
Households
in foreign country consume fewer amounts of a private good and a pubic good. Hence the utility ofhouseholds
in foreign country is worse than that in home country.
We gain the symmetric result when the foreign central bank is not independent and thehome is independent.
Table I shows the above results. It implies the game in this paper
is the prisoners'
dilemma.
If either central bank is not independent,
the equilibrium
does not achieve Pareto optimal allocation.
Moreover, the equilibrium
is stable where
both countries adopt the system in which the central bank is not independent.
If both countries adopt the system in which the central bank is independent, the equilibrium

can achieve

Paretopelling the fiscal authority

optimalallocation.

to provide

Table I.

Therefore

CBI is significant

in com-public good efficiently.

PayoffMatrixin Both Countries

Foreign
Not independent

Independent
Yr +Yr4

Independent(yr+y7))
4
)

(Yr+v

vt+

5

5

YI
4
Home

—),

2(Yr + y7))

5
Y/ + Yr

C-------slY (-------6+ y7
fyr + y75--------)
s-----------l

Not independent

3

Yr+

5

6

3

Theupperrowdenotes(ct, gt), and thelowerrow denotes(c;', g7) in eachcell.

V.

This paper discusses

CONCLUDING

the relationship

REMARKSbetween

CBI and fiscal policy,

using a two-country cash-in-advancemodel in the international
economy.
When the central bankis not independent of the government,that is, when fiscal policy is predetermined,thepublic good is oversupplied.
Because the government can decide public good provisionin anticipationof money supply.
It forces the central bank to finance fiscal deficit.
Furthermore,
the central bank substantiallymonetizes the fiscal deficit, if it is forced.
The fiscal deficit can be filled with a seigniorage tax which is the source of inefficiency,
and a policymakerin one country has the incentive to levy with seignioragetax uponcitizens in the other country.
In other words, each government
decides fiscal policy
without considering the negative externality of seigniorage to the other country. Hencethe growth rate of money

supply is excessively

high and the public good is oversupplied.

14

KEIO ECONOMICSTUDIES

When the central bank is independent,monetary policy is predetermined, however,
the expenditure level is efficient. Because the government cannot decide fiscal policy inanticipation of seigniorage.
The central bank decides a monetary policy considering the
response of the government.
It sets the money supply rule. Moreover the government's
only control is to levy a lump-sum tax in order to provide a public good . Also a lumpsum tax is not a distortionary
tax. So the government
appropriately
collects the fiscal
revenue. Therefore the public good is efficiently supplied.
We show that inefficient public expenditure can be cut down by an independentcen-tral bank. Notice that the central bank in our model plays a role as not preventing frommonetizing,but making the government
recognize the Samuelson rule. The distortion
with seigniorage
finds not inflation affecting output , but tax distortion.
These settings
are different

from those of previous

works.

As mentioned by previous studies, the main role of the central bank is the stabilizationof the price level by controllingmoney supply or interest rates. To carry this out , itis necessary that the central bank be independentof the government
or any politicalpressure. An independent central bank can preventand fiscal deficits from monetizing.

high inflation increasing

seigniorage

We obtain a following policy implication from our result. When the central bank is
independent
in each country, this equilibrium
is Pareto efficient, even if each policymaker does not cooperate to decide its policies each other. We also say CBI is significant for efficiency when international
policy coordination
fails in world economy . In
the middle of the 1980s, industrial countries cooperated to decide monetary policies inorder to depreciate the value of dollar. This cooperation,
however, did not fully succeed.
After that, they moved onto CBI. Our result implies that it is important for budgetary
efficiency that all policymakers
establish independent central banks.
This paper shows CBI is important not only because the central bank averts high inflation and monetizing but also because inefficient public spending is curtailed. In otherwords, CBI becomes a commitment
device for budget cuts. The source of inefficiency
is not monetizing the fiscal deficit but excessive collection of seigniorage in our model .
If policymakers
create excessively
high inflation rates, and collect more seigniorage,
then policymakers excessively increase the quantity of a public good and the household
decreases its consumptionof a private good."
Moreover the cause of excessive collection is that each government decides fiscal policy without considering
the negative
externality of seigniorage on the other country. Therefore, CBI is important
independent central bank can play a role in preventing it in the international

because an
economy.

REFERENCES

Alesina, A., and Gatti, R. (1995). Independent

central banks: Low inflation at no cost? , American Economic

Review vol. 85, pp. 196-200.

In this model,

money

does

not affectoutputthat is exogenous,

and the money

policymakers
heighten
the growth rate of money, the inflation rate increases
constant.
Money is used for exchange
and the collectionof tax .

illusiondoes

not occur.

at the same rate when

output

If
is

Dol:

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PUBLICEXPENDITURE

15

Alesina, A., and Summers, L. H. (1993). Central bank independence and macroeconomic performance: somecomparative evidence, Journal of Money, Credit, and Banking vol. 25, pp. 151-162.
Beetsma, R. M. W. J. and Bovenberg, A. L. (lggia). Central bank independence and public debt policy,
Journal of Economic Dynamics and Control vol. 2 I , pp. 873-894.
Beetsma, R. M. W. J. and Bovenberg, A. L. (I ggib). Designing fiscal and monetary institutions in a secondbest world, European Journal of Political Economy vol. 13, pp. 53-79.
Canzoneri, M. B. (1989). Adverse incentives in the taxation of foreigners, Journal of International Economics
vol. 27, pp. 283-297.
Cukierman, A. (1992). Central Bank Strategy, Credibility and Independence: Theory and Evidence, MIT
Press, Cambridge, Mass..
Cukierman, A., Webb, S. B., and Neyapti, B. (1992). Measuring the independence of central banks and its
effect on policy outcomes, World Bank Economic Review vol. 6, pp. 353-398.
Dol, T., Ihori, T., and Mitsui, K. (2006). Sustainability, debt management, and public debt policy in Japan,
in Ita, T., and Rose, A., eds., Fiscal Policy and Management in East Asia, East Asia Seminar on
Economics Vol. 16, The University of Chicago Press, forthcoming.
Grilli, V., Masciandaro, D., and Tabellini, G. (1991). Political and monetary institutions and public financial
policies in the industrial countries, Economic Policy vol. 13, pp. 340-392.
Helpman, E., and Razin, A. (1984). The role of saving and investment in exchange rate determination underalternative monetary mechanisms, Journal of Monetary Economics vol. 31, pp. 271-298.
Lucas, R. E., Jr. (1982). Interest rates and currency prices in a two-country world, Journal of Monetary
Economics vol. 10, pp. 335-359.
Martin, P. (1994). Monetary policy and country size, Journal of International Money and Finance vol. 13,
pp. 573-586.
Persson, T., and Tabellini, G. (1990). Macroeconomic Policy, Credibility and Politics, Harwood Academic
Publishers, Chur.
Rog off,K. (1985). The optimal degree of commitment to an intermediate monetary target, Quarterly Journalof Economics vol. 100, pp. 1169-1189.
Samuelson, P. (1954). The pure theory of public expenditure, Review of Economics and Statistics vol. 36,
pp. 273-291.
Tabellini, G. (1987). Central bank reputation and the monetization of deficits: The 1981 Italian monetaryreform, Economic Inquiry vol. 25, pp. 185-200.
wallet, C. J., and Walsh, C. E. (1996). Central-bank independence, economic behavior, and optimal term
lengths, American Economic Review vol. 86, pp. 1139-1153.
Walsh, C. E. (1995). Optimal control for central bankers, American Economic Review vol. 85, pp. 150-167.
APPENDIX
The

correspondingA:

THE DERIVATION

Lagrangefunction

OF THE FIRST BEST SOLUTION

is expressedas

L=E/3,[1_(logct+loggt)+2(logcr+loggt)+t(Yt+yt-ct-gt-ct-gi)
11t-o+ µt(htYr + ti + di - 9t - rt-ldr-l) + At*(hrYr + ti + (17- gt - rt-ldr 1) ,+At{(1 -ht)Yt/2+(1 -ht)Yr/2+rt_ibt_i- ct -bf -ti}
+

where

{(1-ht)Yt/2+(1t , At, At*,µt, and µt-hr)yt/2+rt-lbrl-cl -br - tr }are the Lagrange multipliers. Its first order conditions arel6KEIO

ECONOMIC STUDIES

a _,B`2ct—r—At=
0,ac*=fst2c*——~i=0,
aLt+l~r+Irt—/st~t=0,aL

tabt= )6t+IAt+lit—13`),t*=0, abaL
1aL-_,~--4.r—l~r=0,*——r—/~r_tagr (2gtagr

1=0

2gr

~

a-='3`{µt—A,t}=0,a~—'3t{µ`Ar}=0,
rt
aL

tAt

yt

At*yiaL _t*Atyt_A~yi_aL—$t+1/-ti+Irt+$ti-~t= 0,aL=st+1µr+I

ant={pip—2—2=0,ah~—{tut*y`2
20,_
rt+~stAt= 0 .

adt-=adj

Hence µt = µt = At = Ar. So ct = gr = ct = g. From (7), ct = 9t = ct* = gr =(Yt+yt)/4.
APPENDIXB: THE DERIVATION
OF(10) ^ (14)The corresponding Lagrange function of the home household is given as00

L = E,et [flogct+ loggt}
t=o+Ar{(1—hr)Yr/2+(1 —hr)yr/2+rt_ibr_1 —ct —bf—zt}],
where At is the Lagrange multiplier. Its first order conditions are
aL
acth'

=Rt1—
),t=
ctabt

0aL=fit+1At+lit—sr~r=0.

Then these satisfy (10). From (10),ct=~tr—ICt_1=

IB`+lrrlrt-2... tor—lc-l •So ct can be expressed as the function of p, rt _ 1, rt -2, • • • , r_ 1, and c_ 1. Hereafter, ct
and bf in (9) are assumed to satisfy (10).
The corresponding Lagrange function of the home central bank is given as00

L = E,3t[{logct+ loggt}
t=0+ /it (hryr + Ti+ di —gt —rt—1
di-l)+ Xi{(1—ht)yr/2 + (1 —hr )yr /2 + rt_1br_1 —ct —bf —ti]]
where At, and µt are the Lagrange multipliers. Its first order conditions are
aL_pt—Yryr=0,aL_—pt+1
aht2ctgtadt

ti

rt/gr+1+pr/gr

= 0

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17

EXPENDITURE

Then these satisfy(11) and (12).
Substituting(8) into (9),Ct+ br + tr = yt/2 + (1 - hi )Y7/2 + rt-ibt-l - (gr+ tr_idt-I - tr + di)/2
And substituting(8) into the aboveequation,
Cr+ br + ti = yr/2 + (1 - hi )y7/2 + rr-ibr-I - (gr+ rr-idt-l - ti)/2- {2gr+ tr —Yr- (1 - hr )y7 + rr-idr-I + 2(br - rr-lbbt-I)}12 .
Moreoversubstituting(11) into the aboveequation
gt = {-tr + Yr+ (1 - hi )Y7- 2(br - tr-l br-l) - rr-Idr-l}/2
Therefore

the optimization

problemof the homegovernmentis rewrittenasmaxu = E/3t(2loggr- log2){gr,l-r) t=0s.t. gr = {-tr +Yt + (1 —ht )Y7- 2(br - tr_ibr-l) - rr-idt-l}/2,

tr > 0given g7, t7, d7, hi .
The corresponding

problemof the home governmentis rewritten

as00

u = E pt[2log(—tr+ yr+ (1- hi)yr- 2(bf- rr-lbt-l)- rr-idr-I}- 3log2].
r=0
Its first ordercondition

is
au2

=<
0.
artgr ,Btl
Then tr = 0. Thereforegr is givenas (14). Analogousstepslead to the foreign.
In this equilibrium,if dr = 0 and br = 0, gr = hryr from (8), and gt = (Yr+yr )/2 - h; yr /2 from (9). Similarly,if di*= 0 andbr = 0, g7 = ht y; from (8') , andg7 = (Yr+ Y)!2 - hryr/2 from (9'). Moreover,
9t = (Yr+Y7)l2-gi/2=(Yr+Y7)/2-(Yr+y7)/4+gt/4.
So gt = (Yr+ 4)13 and cr = (yr + yr )/6. From tr = 0, hr = (Yr+ yr)/3yr. Similarly,—

97 = (Yr+Y7)l2-gxl2=(Yr+Y7)/2-(Yr+y7)14+g7/4.
So g7 = (Yr+ yt )13 and c7 = (yr + Yr)/6. Fromtr = 0, 14 _ (yr + yr)/3yr . These
quantities,Cr,gr,C, and g7, satisfy(7).
APPENDIX
C: THEDERIVATION
OF(15) AND(16)The first order conditionof the home householdis given as (10). Hereafterwe presumeCrandbr in (9) satisfy(10).
The correspondingLagrangefunctionof the homegovernmentis given as

l8KEIO

ECONOMICSTUDIES00

L = E,Bt[log{(1—ht)Yt/2+ (1—ht)yr/2+ rt—tbt—t—bf—rt}t—o+ log(htyt + ti + di —rt_idt-l)]

Its first order condition is—8L_pt{—1+1
art—Ctgt=0Then these satisfy (15). Also it sets ti = 9t —htYt — di + rt—tot—t
Substituting (8) and (15) into (9),2ct+ bf+ rt—idr-l—htYr—di = (1 —ht)Yt/2+ (1 —ht )Yr/2 + rt—1
bf—t
MoreoverCt = htytl4 + (di —rt—tot-l)/2 + ytl4 + (1 —hi )yr /4 —(bf —rt_ibt—t)/2
Therefore

the optimization

problemof the home central bank is rewritten

as00

maxu = E ,Bt(2logct)(ht,di)t =0s.t. ct = htyt/4 + (dr —rt—tot-o/2 + Yt/4 + (I —hr )Yr/4—(bf —rt—for—I)/2,
given gt,ti,dht.
The correspondingproblemof the home centralbank is rewrittenas
00

u = E,Bt[2log{htYt/4+ (di—rt_idt-l)/2+ Yt/4
t=o

+ (1 —ht)Yr/4 —(bf —rt—tbt-l)/2}1.
Its firstorderconditionsare
au _1
1
au
11
aht2i8ict 4yt> 0 ,adj=2,8ict
2> 0 .
This impliesthat the larger ht or (It is, the better its utility becomes. So it sets (16).
Analogoussteps lead to the foreign.
In this equilibrium,if rt = 0, di = 0, and bf = 0, gt = ht yt from (8), and gt =(Yr+ y7)/3 —hi4is/3 from (9). Similarly,if t7 = 0, 617= 0, and b; = 0, = hr yrfrom (8'), and g~ = (Yt+ 4)13 —htyt/3 from (9'). Moreover,
9t=(Yt+yt)13-9713=(Yt+yr)/3—(Yt+yt)/9+97/9.
So gt = (Yt+ y;')/4 and ct = (Yt+ Y7)/4. From ti = 0, ht = (Yt+ yr)/4yt. Similarly,
gr=(Yt+yr)/3—glls=(Yr+yr)/3—(Yt+yr)/9+g7/9.

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19

So g7 = (Yr+ Y7)/4 and ct = (yr + y;')/ 4. From r7 = 0, ht = (yt + yt)/4yt . These
quantities, ct, gt, c;', and g7, satisfy (7).

APPENDIX
D: THEDERIVATIONOFANEQUILIBRIUM
WHENTHEHOMECENTRAL
BANKISNOTINDEPENDENTANDTHEFOREIGNCENTRAL
BANKIS INDEPENDENT
We now presumedi = di = 0 and bf = bf = 0. Using the above results, thehome policies are presentedby (11), (14), and zt = 0. Namely,gt = 2ct, ti = 0, andgt = ht yt. From(9), gt = (yt + y7)/2 —ht y7/2. The foreignpolicymakerare (15') and(16'). The foreignis assumedto set i7 = 0. Namely,g7 = c7, ti = 0, and g7 = ht y7.
From (9'), gt = (yt + y7)/3 —ht yt/3. Then we obtain
gr = (yr+yt)/2-8712=(yt +y7)12— (yt +y7)/6+gr/6.
So gt = 2(Yr+ y7)/5 and ct = (yt + y7)/5. Similarly,
97=(Yt+yt)/3—gr/3=(Yt+Yt)/3—(Yt+y7)/6+
gt*/6.
Then g7 = ct = (yt + y7)/5. These quantities,ct, gt, c;', and g7, satisfy(7).