ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E11-1

Partial Coordination in Local Debt Policies
byHikaru Ogawa
Junichi Nagami

January 2011

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Partial Coordination in Local Debt
Policies
Hikaru Ogawa
Nagoya University
Junichi Nagami
Japan Finance Corporation

Abstract
The eﬃciency of decentralized local debt policy under partial andfull coordination is examined. The earlier studies show that independent regional governments issue an excessive amount of local public
debt, and call on the central government to place restrictions on local
debt policies. This paper compares several rules of coordinated debt
policies to show that the central government intervention is not required to carry out an eﬃcient local debt policy. The main argument
is that a form of partial coordination results in the eﬃcient outcome
rather than a full coordination in local debt policies.

Keywords. local public debt, migration, partial coordination
JEL classiﬁcation. H41, H71, H74

1

1

Introduction

A paper by Bruce (1995) analyzes the eﬃciency of debt policies by regional
governments, where individuals have a short-run attachment to a particularregion but are free to migrate between regions in the long-run. The mainargument of Bruce’s paper is that regional governments issue an excessive
amount of local public debt compared with a debt policy carried out by
a central government. The purpose of our paper is to re-examine Bruce’s
argument under simple rules of coordinated local debt policies to show thatthe central government intervention is not required to carry out an eﬃcientdebt policy.
Economists are much concerned with the eﬃciency of local debt issuance.
Bruce’s view on the ineﬃcient local debt issuance was established by Musgrave (1959) in relation with Ricardian equivalence; Ricardian equivalence
fails in local public debt since individuals who migrate can avoid a future
tax burden by moving to other regions when local public debts are repaid.
The avoidance of debt burden by migration is the cause of bilking problem
in local debt ﬁnancing, i.e., if the transmigrants can shit the burden of debt
onto the future residents, they under-evaluate the cost of local debt ﬁnancing
thereby over-issue the local debt. The advocacy of local debt limitation by
central government is referred to this bilking problem. The bilking problem
with the issues on debt neutrality is directly linked with normative properties arousing the interest of the economist for a long time. For instance,
in 1970’s, heated debates have been generated on Wagner (1970)’s analysis, which demonstrates that individuals who recognize the probability of
relocating to a new jurisdiction demand an excessive amount of local public
debt [Hand and Mitchell (1971), Aronson (1971), and Wagner (1971)]1 .
1

On the back of these studies, Tsuneki (1985), Akai (1994), and Ogawa and Yano
(2007) provide the examination on Ricardian equivalence for local public debt, having
been centered on the role of land taxation. The main difference of our paper with those is2

With the background of market globalization, the studies from the 1990’s
have also been considered the interactions between local public debt, migration and taxation. Speciﬁcally, the political eﬀort to create broad economic
union is recognition of the importance of regional debt management. Integration such as the European Union must have promoted strong correlation
among national governments’ debt policies compared to the past less closed
market. Similar to Bruce’s view, the main argument in the literature isthat since shifts in the intertemporal pattern of local taxes occur in diverse
ways, the ineﬃciencies associated with the choice of local public debt are
still present2 .
One of the signiﬁcant features that make our model diﬀerent from previous local debt studies is that we consider a form of coordination in local
debt policies. Much of the studies mentioned above has assumed that theregional governments completely independent in issuing and repaying local
public debt. This is somewhat surprising since the regions often act harmoniously in local debt ﬁnancing3 . Speciﬁcally, since it is hard for small
that, to achieve the first-best outcome, we set a simple coordination rule for debt issuanceand do not rely on the taxation on land. The role of land in achieving the efficient outcomein the local debt financing has been indicated by Daly (1969) and Oates (1972) in the earlystage.
2
Under two-period and two regions economy with migration, Schultz and Sjostrom(2001) show that regional governments undersupply public goods while it over-accumulates
local public debt. Wellisch and Richter (1995) show that neutrality of local public debt is
not guaranteed since shifts in the intertemporal pattern of local taxes change the net wealthof local property owners if distortionary residence-based taxes are imposed to service thelocal debt. Weichenrieder (1999) propose the ‘pay as you finance’ scheme to overcome
the inefficiencies in local debt finance. Schultz and Sjostrom (2004) incorporate the voting
process into the model to show that local public debt would be over-accumulated. Furthermore, under an alternative analytical framework, Homburg and Richter (1993) provide anegative argument on the efficiency of local public debt issuance when individuals freely
migrate between regions.
3
Many countries apply some form of local debt coordination as well as the restrictions
to local government budgeting and borrowing, but in various forms and to varying degrees.
For instance, it has been widely recognized that the Public Pfandbriefea and the Credit
Locale de France in effect assume the role of coordinate local debt in Germany and France,
respectively, but the forms of system differ to some tune. See Dafflon (2002) for thecomprehensively review of European local debt management.

3

regional governments that have less credence in the bond market to raise
funds, these small regional governments frequently issue public bonds cooperatively by establishing the organizations for the joint issuance of public
debt and/or by concluding policy agreement. These organizations and agreements have diﬀerent schemes for raising and repaying public debt, that makeus to examine the eﬃciency of local debt policies under diﬀerent scheme ofcoordinated debt policies. In sum, Bruce (1995) discusses the eﬃciency of local debt policies in the non-cooperative framework, but we further consider
several regimes of coordinated local debt policies. Speciﬁcally, this paper
sheds light on the question of what type of coordination helps to internalize
the externalities and eliminates the bilking problem in local debt policies.
Two speciﬁc forms of policy coordination are analyzed in a model where
the economy is made up out of two symmetric jurisdictions. One form
covers coordination either in the issuance or in the repayment of local debt.
This type of policy accord is referred to partial coordination. The otherform is a full coordination that covers coordination both in the issuanceand repayment of local public debt. The results demonstrate that eﬃcient
outcome is obtained in the partial coordination where regional governments
coordinate the issuance, but independently repay the local debt. Full policy
coordination can solve the bilking problem, but it causes a new trouble, what
one calls common pool problem. Partial coordination in debt repayment
results in the worst outcome that involves both bilking and common poolproblem.
The paper is organized as follows. Section 2 presents the basic model,
following Bruce (1995). In Section 3, we ﬁrst classify four regimes of decentralized debt policies. Then, the analysis is devoted to derive the equilibriumof each regime. The equilibrium properties are compared in section 4. Section 5 concludes the paper.

4

2

Model

2.1

Assumptions

To highlight the diﬀerences of the results derived in coordinate and noncoordinate debt polices, the model follows Bruce (1995), which develops the
non-cooperative model of local debt policy. Throughout this paper we use
the two regions (i = w, e) and two-period (t = 1, 2) model. The superscript i
denotes the region and the subscript t indicates the time period, respectively.
In each region, there exists a single regional/local government. The
population of this economy is constant over time and is assumed to equaln̄. We will henceforth follow the convention that a bar on top of a variable
denotes a ﬁxed value of variable. Denoting nit as the population in region ieat period t, we have n̄ = nw
t + nt . Following Bruce (1995)’s assumption that

individuals have a short-run attachment to a particular region but are free
to migrate between regions in the long run, we assume individuals choose
there region of residence only in the second period of their life. Hence, thepopulation in each region in the ﬁrst period is constant and is given by n¯i .
1

All individuals, working for two-period, are alike in their initial endowments
for labor. Each individual has one unit of homogeneous labor in each period
and supply it in the individual’s region of residence. All individuals haveidentical preferences described by the utility function, given by U (cit ), where
cit is the consumption of private goods (Uc (cit ) > 0, Ucc (cit ) < 0).
The production of private goods in region i requires the use of labor andland. The production function in region i is F i (nit ), where nit is the amountof labor and land is omitted from the expression to simplify the notationi(Fni > 0, Fnn< 0). The individual budget constraint of individual residing

in region i at period t is formally given by
cit + τti = wti ,5(1)

where τti is the lump-sum tax/transfer, wti is the residents’ income. By
assuming that the return to the land is portioned equally amoung the current
residents of the region, we assume wti = F i (nit )/nit .
Government collects a certain amount of revenue by issuing debt in theworld market. The revenue made by debt issuance is distributed to theindividuals in a lump-sum manner. In this paper, we disregard real public
expenditure, so that tax revenues are used only for servicing the public debt.
The new debt issued in period t reaches maturity in period t + 1, so that
τ1i < 0 and τ2i > 0 in general.

2.2

Centrally Planed Economy

In this part, we ﬁrst examine the coordinated debt policy carried out by acentral planner.
Second Period. Individuals move freely between the two regions only inthe second period to respond to diﬀerentials in utility level so that utility
levels are equalized. Formally, the substitution of (1) into the utility function
gives the migration equilibrium in the second period as follows.
U

F w (nw
2)
− τ2w
w
n2



=U



F e (n̄ − nw
2)
− τ2e
w
n̄ − n2(2)

From (2), the regional population in the second period, ni2 , can be obtained
as a function of the tax rates; ni2 (τ2i , τ2j ). The diﬀerentiation of (2) withrespect to the tax rates yields
dnit /dτti = Uc (ci2 )/∆,
dnit /dτtj= −Uc (cj2 )/∆,

e ˆe
i i
i
i i
i −2
ˆi
ˆw
where ∆ ≡ Uc (cw
2 )Fn + Uc (c2 )Fn , and Fn ≡ [n2 Fn (n2 ) − F (n2 )](n2 ) . To

ensure stable migration equilibrium, we assume the case of ‘excess popu6

lation’, Fˆni < 0 (i = w, e), implying ∆ < 0 [Atkinson and Stiglitz (1980,
p.528-535)].
Substitution of ni2 (τ2i , τ2j ) into the utility function in the second-period
yields the common indirect utility value as V (τ2i , τ2j ).
First Period. Since individuals are ﬁxed in the region of residence, the¯eregional population is exogenously ﬁxed in the ﬁrst-period: n¯w
1 and n1 =n̄ − n¯w . Then the life-time utility obtained in region i is given by U (w¯i −
1
1
¯
i
i j
i
τ1 ) + δV (τ2 , τ2 ), where δ is the discount factor and w1 is the (ﬁxed) labor

income obtained in the ﬁrst period: w̄1i = F i (n¯i1 )/n¯i1 .
The optimization problem for the central planner is now deﬁned as follows:maxτ1e ,τ1w ,τ2e ,τ2ws.t.

U (w¯1w − τ1w ) + δV (τ2w , τ2e ),U (w¯1e − τ1e ) + δV (τ2w , τ2e ) ≥ Ū ,(3)w
w w w e¯w e
R[n¯w
1 τ1 + (n̄ − n1 )τ1 ] + τ2 n2 (τ2 , τ2 )w ee+(n̄ − nw
2 (τ2 , τ2 ))τ2 = 0. (4)To determine the eﬃcient tax rate under centrally planned economy, we
maximize the utility of a representative household living in region w subject
to the constraints (3) and (4). (3) reﬂects that the utility of residents inregion e is ﬁxed at a certain level. (4) is the intertemporal budget constraint,
where R denotes the gross rate of interest determined in the world debt
market4 . Denoting λ as the Lagrangian multiplier associated with (3), andsolving the problem, the ﬁrst-order conditions become asUc (cw
1)
Uc (ce1 )λn¯w
1,n̄ − n¯w
1

=

4

(5)

The interest rate is, thus, R − 1. We can replace zero with a constant parameter in(4) since a tax revenue of zero is not crucial.

7we
Fnw (nw= Fne (n̄ − nw
(6)2 ) − c22 ) − c2 ,



w
w
w
w
¯
¯
n̄ − n2n̄ − n1
n
n
1
1
1
1
+ 2
+ 1
= δR
(7)
.
e
w
e
n̄ Uc (c2 )n̄ Uc (c2 )n̄ Uc (c1 )n̄ Uc (cw1)

(5) is the condition for the eﬃcient allocation of private goods between thetwo regions in the ﬁrst-period. (6) is the eﬃcient condition of population
allocation and describes the optimal locational pattern for individuals in thesecond-period. The marginal social beneﬁts of mobile individual must be
equalized across regions. (7) is the condition for intertemporal allocation¯eof private goods. If the two regions are symmetric (n¯w
1 = n1 = n̄/2), (5)becomes ase
Uc (cw
1 ) = Uc (c1 ),(8)which can be also derived in the diﬀerent manner of the maximization of utilitarian social welfare function. Under (8), the migration constraint implieseUc (cw
2 ) = Uc (c2 ). Hence (7) reduces to

Uc (ci1 ) = RδUc (ci2 ).

(9)In the following section, (9) will be compared with decentralized equilibrium
derived under the debt policies by local governments.

3

Decentralized Debt Policies

3.1

Classification of the Debt System

Decentralized local debt polices are characterized by a taxation in the secondperiod, τ2i , and the amount of debt issuance in the ﬁrst-period, B i . We haveno public goods in this economy, so that the governments’ revenue raised by
the bond issuance will hand out to the individuals as the lump-sum transfer,which is denoted by τ1i .
In the decentralized debt market, local governments often establish theﬁnancial organizations (authorities) to provide debt services in co-operation
8

with other local governments. To establish joint authorities, individual governments enter into a mutual basic contract regarding on the debt issuance.
It is often the case that small local governments in particular have participated to raise funds through cooperative debt issuance and repayment.
Although these organizations have diﬀerent schemes for raising and repaying public debt, we shall distinguish the following four regimes of local debt
system.
Regime (a). The local governments choose the amount of local debt issuance and repay their debt independently.
τ1i = −B i /n¯i1andτ2i = RB i /ni2

Regime (b). The local governments non-cooperatively choose the amountof local debt issuance, but they repay their debt cooperatively.
τ1i = −B i /n¯i1

τ2w = τ2e = R(B w + B e )/n̄andRegime (c). The local governments choose the amount of local debt issuance cooperatively, but they repay their debt independently.
τ1w = τ1e = −(B w + B e )/n̄and

τ2i = RB i /ni2

Regime (d). The local governments choose the amount of local debt issuance cooperatively. In addition, they repay their debt cooperatively.
τ1w = τ1e = −(B w + B e )/n̄and

τ2w = τ2e = R(B w + B e )/n̄

Clearly, Regime (a) copies Bruce’s analysis, where the debt is chosen
non-cooperatively by each local government and each government is responsible for the debt its past residents took on. The partial coordination is9characterized by Regime (b) and (c). In Regime (b), the local governments
repay collectively and choose debt independently, while they choose debt
level cooperatively and repay independently in Regime (c). The Regime(d) describes the case of full coordination, in which the debt level is chosencollectively and repaid collectively.
In the following analysis, to focus on the eﬃciency of decentralized debt
policies, we assume that the local governments voluntarily make interregional transfers so that the allocation of population is eﬃcient in the secondperiod [Myers (1990) and Bruce (1995)]. This assumption allows us to isolate
the intertemporal eﬃciency problem of local debt policies from the eﬃciency
issues on horizontal allocation of population.

3.2

Regime (a)In Regime (a), the private goods consumption in the second-period is expressed byci2 =F (ni2 ) − Y i + Y j
RB i
−
,
ni2
ni2

(10)

where Y i ≥ 0 denotes the interregional transfers made by local governmenti.
The condition for migration equilibrium, thus, is given by
U



w
w
e
F (nw
2 ) − RB − Y + Y
nw
2



=U



F (ne2 ) − RB e − Y e + Y w
ne2



.

e
With n̄ = nw
2 + n2 , this equation gives us the second-period population inregion i as ni2 (Y i , Y j , B i , B j ). The comparative statics results yield
∂ni2
∂B i

=

RUc (ci2 )
< 0,
ni2 H

∂ni2
∂B j

= −

RUc (cj2 )
nj2 H
10

> 0,

(11)
(12)

∂ni2
∂Y i

=

nj2 Uc (ci2 ) + ni2 Uc (cj2 )ni2 nj2 H

< 0,

(13)

where
H≡



w
w
[Fn (nw2 ) − c2 ]Uc (c2 )
nw
2



+





[Fn (ne2 ) − ce2 ]Uc (ce2 ),ne2and H < 0 is assumed for the stability of the migration equilibrium. Substituting ni2 (Y i , Y j , B i , B j ) into the second-period utility function, we have
V (Y i , Y j , B i , B j ). The comparative statics show




∂V
∂Y i

∂V
Uc (ci2 ) [Fn (ni2 ) − ci2 ](∂ni2 /∂Y i ) − 1
= −
=
,
∂Y j
ni2

(14)

∂V
∂B i

= −

∂V
Uc (ci2 ) [Fn (ni2 ) − ci2 ](∂ni2 /∂B i ) − R
=
.
j
∂B
ni2

(15)





The local government i wishes to maximize the lifetime utility of theresident, taking the tax rates and the amount of debt issuance of otherregions as given. Noting that, in Regime (a), the lump-sum transfer received
by the individuals in the ﬁrst-period is given by B i /n¯i , the maximization1

problem will be deﬁned as
max U

B i ,Y i

F (n¯i1 ) B i
+ ¯
n¯i
ni
1

1



+ δV (Y i , Y j , B i , B j ).

Solving the problem, we have5

Uc (ci1 ) δUc (ci2 ) [Fn (ni2 ) − ci2 ](∂ni2 /∂B i ) − R
+
= 0,
ni
n¯i

(16)

2


Uc (ci2 ) [Fn (ni2 ) − ci2 ](∂ni2 /∂Y i ) − 1≤ 0, Y i ≥ 0,
ni2



i
i
i
i
i
i Uc (c2 ) [Fn (n2 ) − c2 ](∂n2 /∂Y ) − 1
= 0.
Y
ni2
1

(17)
5

i

We assume B > 0 and disregard why local governments issue public bonds. Jensen
and Toma (1991) is one of the studies examining the reason local governments issue bonds
in a framework of interregional competition.

11

Note that (14) indicates that non-negativity constraint on the inter-regionaltransfer cannot be binding in both regions. Hence, assuming that it binds
only in one of the two regions, we haveFn (ni2 ) − ci2 = Fn (nj2 ) − cj2 ,(18)which is identical to (6). This means that the eﬃcient allocation of population is achieved through interregional transfer made by local governments.
Inserting (11) and (18) into (16), we haveUc (ci1 ) =n¯i1RδUc (ci2 ).
n̄

(19)

Comparing (9) with (19), we have Uc (ci1 ) < RδUc (ci2 ) since n¯i1 /n̄ < 1. This
stands for the excessive consumption in the ﬁrst-period caused by the excessive debt ﬂotation. Summarizing above discussion, we conﬁrm the following
result.
Proposition 1 (Bruce (1995)). When the local governments choose theamount of local debt issuance and repay their debt independently, they overissue the local debt in the ﬁrst-period; Uc (ci1 ) < RδUc (ci2 ).
The reason behind this result is provided in Bruce (1995) as follows.
While the debt issuance made by local government i gives beneﬁts only on
residents in region i since there is no migration in the ﬁrst-period, the future cost of this debt issuance is diluted by migration in the second-period.
Hence, the local governments under-evaluate the cost of debt issuance, sothat they demand an excessive amount of public debt. In addition to Bruce’s
interpretation, we can provide an alternative expression to put the explanation in more detail. Since both regions are overpopulated, they have incentives to reduce the regional population by raising the second-period tax

12rate, implying an increase in the ﬁrst-period debt issuance. While the population outﬂow induced by an increase in the tax rate increases the utilityof its own residents, it externally reduces the utility of residents residing inother region. This negative externality is ignored in the local governments’decision-making so that the local governments issue public debt excessively.

3.3

Regime (b)In Regime (b), local governments repay their debt cooperatively, while theychoose the amount of local debt issuance independently. Then, the private
goods consumption in the second-period is given byci2 =F (ni2 ) − Y i + Y j
R(B i + B j )
−
.
n̄
ni2

(20)

The condition for migration equilibrium is now given by
U



w
e
R(B w + B e )F (nw2)−Y +Y
−
nw
n̄
2



=U





R(B w + B e )F (ne2 ) − Y e + Y w
−
.
ne2
n̄

e
With n̄ = nw
2 + n2 , this equation gives us the second-period population inregion i as ni2 (Y i , Y j , B i , B j ). The comparative statics results show
∂ni2
∂B i
∂ni2
∂B j
∂ni2
∂Y i

RUc (ci2 )< 0,n̄ΓRUc (cj2 )
= −
> 0,
n̄Γ
nj2 Uc (ci2 ) + ni2 Uc (cj2 )< 0,=
ni2 nj2 Γ

(21)

=

(22)
(23)

where
Γ≡



w

 

e

w

e

R(B +B )w[Fn (nw]Uc (cw[Fn (ne2 ) − ce2 − R(B n̄+B ) ]Uc (ce2 )2 ) − c2 −
2)
n̄
+
nw
ne2
2

and Γ < 0 is assumed. Substituting ni2 (Y i , Y j , B i , B j ) into the secondperiod utility function, we have V (Y i , Y j , B i , B j ). The comparative statics
results show
13



,

∂V
∂Y i
∂V
∂B i



i



j

Uc (ci2 ) [Fn (ni2 ) − ci2 − R(B n̄+B ) ](∂ni2 /∂Y i ) − 1
∂V
= −
=
,
∂Y j
ni2

=

(24)





R(B i +B j )ii](∂ni2 /∂B i ) R∂Vi  [Fn (n2 ) − c2 −
n̄
−
=
U
(c
)
− .
c
2
∂B j
n̄
ni2

(25)

Noting τ1i = −B i /n¯i1 in Regime (b), the maximization problem of thelocal governments can be deﬁned as follows.
max U

B i ,Y i

F (n¯i1 ) B i
+ ¯i
n¯i
n
1

1



+ δV (Y i , Y j , B i , B j ).

Solving the problem, we have


i



j

R(B +B )ii](∂ni2 /∂B i ) R
Uc (ci1 )i  [Fn (n2 ) − c2 −
n̄
+
δU
(c
)
−  = 0,
c
2
i
n̄
n2
n¯i1





(26)

Uc (ci2 )R(B i + B j )](∂ni2 /∂Y i ) − 1 ≤ 0, Y i ≥ 0,
[Fn (ni2 ) − ci2 −
i
n̄
n2
Y

i





Uc (ci2 )[Fn (ni2 ) − ci2 − τ2 ](∂ni2 /∂Y i ) − 1 = 0.
ni2
(27)

By assuming that the non-negativity constraint on the inter-regional transfer
binds only in one of the two regions, from (27), we have the identical equation
with (6), indicating the population allocation is eﬃcient.
With the same procedure in Regime (a), using (6) and (21), (26) reducestoUc (ci1 ) =n¯i1 ni2
RδUc (ci2 ).
(n̄)2

14

(28)

Since (n̄)2 > n¯i1 ni2 , Uc (ci1 ) < RδUc (ci2 ). Therefore, we have our second result
as follows.
Proposition 2. When the local governments repay their debt cooperatively, while they independently choose the amount of local debt issuance,
they over-issue the local debt in the ﬁrst-period; Uc (ci1 ) < RδUc (ci2 ).

3.4

Regime (c)In this regime, the second-period equilibrium is as same as Regime (a).
Hence, equations (10)-(15) are valid. In the ﬁrst-period, the local governments choose the level of debt issuance cooperatively, so that the maximization problem of local government is given by
max U

B i ,Y i

F (n¯i1 ) B i + B j
+
n̄
n¯i
1



+ δV (Y i , Y j , B i , B j ).

Solving the problem, we have

Uc (ci1 ) δUc (ci2 ) [Fn (ni2 ) − ci2 ](∂ni2 /∂B i ) − R
= 0,
+
n̄
ni2




Uc (ci2 ) [Fn (ni2 ) − ci2 ](∂ni2 /∂Y i ) − 1≤ 0, Y i ≥ 0,
ni2
Y

i





(29)



Uc (ci2 ) [Fn (ni2 ) − ci2 ](∂ni2 /∂Y i ) − 1
ni2

= 0.
(30)

As before, since the non-negativity constraint on the inter-regional transfer
binds only in one of the two regions, from (30), we have (6). With the sameprocedure in Regime (a) and (b), substituting (6) and (11)into (29), we haveUc (ci1 ) = RδUc (ci2 ).

15

(31)

(31) is identical to (9), showing that the decentralized debt policy is eﬃcient.
Thus, we have third result of this paper as follows.
Proposition 3. When the local governments choose the amount of local
debt issuance cooperatively, but they repay their debt independently, theychoose eﬃcient level of debt issuance; Uc (ci1 ) = RδUc (ci2 ).

3.5

Regime (d)The second-period equilibrium is as same as Regime (b). Hence, equations(20)-(25) could be applied in this regime. Since τ1i = −(B i + B j )/n̄, themaximization problem of local government is deﬁned as
F (n¯i1 ) B i + B j
max U++ δV (Y i , Y j , B i , B j ).
n̄
B i ,Y in¯i1Solving the problem, we haveij[Fn (ni2 ) − ci2 − B +B](∂ni2 /∂B i ) R
Uc (ci1 )n̄+ δUc (ci2 )
−
n̄
n̄
ni2


Uc (ci2 )Bi + Bj](∂ni2 /∂Y i ) − 1[Fn (ni2 ) − ci2 −
i
n̄
n2
Y

i







= 0, (32)≤ 0, Y i ≥ 0,

Uc (ci2 )Bi + Bjii](∂ni2 /∂Y i ) − 1
[F
(n
)
−
c
−
n
2
2
n̄
ni2



=0
(33)

As before, since the non-negativity constraint on the inter-regional transfer
binds only in one of the two regions, from (33), we have (6). Substituting(6) and (21)into (32), we haveUc (ci1 ) =ni2RδUc (ci2 ).
n̄

(34)

Since ni2 /n̄ < 1, we have Uc (ci1 ) < RδUc (ci2 ). Summarizing, we have theﬁnal result.

16

Proposition 4. When the local governments choose the amount of local
debt issuance and repay their debt cooperatively, they over-issue the local
debt in the ﬁrst-period; Uc (ci1 ) < RδUc (ci2 ).

4Comparison and Interpretations

We compare the equilibrium properties in each regime with oﬀering theintuitive interpretation of the results. If we compare (19) with (28), we ﬁndthat the debt level in Regime (b) is greater than the one in Regime (a)since (n̄)2 /(n¯i ni ) > n̄/n¯i . Since both Regime (a) and (b) results in over1 2

1issuance of public debt, the local debt policy in Regime (b) increases theexcessive debt accumulation further. This is simply because the cooperative
repayment of debt potentially involves an additional source of over-issuanceof debt, along with the source of excessive debt accumulation originatedfrom bilking problem; Under Regime (b), local governments are possible tocharge the burden of debt repayment not only on the residents in its own
region but also individuals residing in other regions. This causes the familiar
common pool problem: The resident fully internalizes the beneﬁt of its debt
issuance in the ﬁrst-period, but (as repayment is shared) it internalizes only
a fraction of ni2 /n̄ of the social marginal cost of local debt issuance in thesecond-period. This factor acts to reduce cost of debt issuance so that it
makes local governments issue bonds further.
By contrast, in Regime (c), the beneﬁt of debt ﬁnancing lump-sum subsidies in the ﬁrst-period does not fasten within the region. It spreads tothe individuals of other regions, and that local government does not underevaluate the beneﬁt of debt issuance. Furthermore, local governments haveno ways to charge the burden of debt repayment on the individuals living inother region, since the repayment of debt is conducted independently. These
lead local governments evaluate their cost and beneﬁt of debt issuance cor-17

rectly. In Regime (d), although the cooperative debt issuance contributes
to buﬀer against over-issuance of debt and succeeds in avoiding the bilking
problem, the common pool problem is generated by the cooperative repayment of debt, that leads local government issues excessive debt.
For further illustration, consider the familiar utility function: U (cit ) =ln cit . In the symmetric equilibrium, we have6
Ba = Bd =F (2 − Rδ)F (4 − Rδ)F (1 − Rδ), Bb =, Bc =,
R(2 + δ)R(4 + δ)R(1 + δ)(35)

where Bi is the amount of local debt in regime i and F ≡ F (n̄/2). (35)shows that Bc < Ba = Bd < Bb for all δ > 0. To provide some insight ofwelfare ranking, we obtain the indirect utility level as follows;
4F (R + 1)
2F δ(R + 1)
+ δ ln,Rn(δ + 2)n(δ + 2)8F (R + 1)
2F δ(R + 1)= ln
+ δ ln,Rn(δ + 4)n(δ + 4)2F δ(R + 1)
2F (R + 1)
+ δ ln,= ln
Rn(δ + 1))n(δ + 1)

Ua = Ud = ln
UbUcwhich show that Uc > Ua = Ud > Ub for all δ > 0.
In sum, when local governments in Regime (c) choose debt level cooperatively they internalize the externality associated with migration- which is
not internalized in Bruce’s original set up (Regime (a))— and the resulting
debt level is eﬃcient. Neither Regime (c) nor Regime (d) leads to a ﬁrst
best level. Speciﬁcally, the ineﬃciency is aggravated, and that the welfare
is the lowest when the repayment is collective— this reﬂects the well known
common pool problem explained above.

6

The proof is available upon request.

18

5

Final Remarks

In this paper we follow Bruce (1995) and have formulated a simple two region and two period model to examine the eﬃciency of local bond ﬁnancing
in a regional economy. With a simple coordination regarding on the amountof debt issuance between the two regions, the decentralized debt policies canachieve the ﬁrst best outcome. More speciﬁcally, if the local governments
partially coordinate to choose the amount of local debt issuance cooperatively, but they repay their debt independently, the decentralized local
debt polices results in the eﬃcient outcome. In one sense, this is hardly
a surprising result since the beneﬁt of debt issuance is weekend by the cooperative debt ﬂotation since the beneﬁts of debt issuance spread to otherregion. However, this result is still a striking result, and it should be apparent that only the cooperation on debt issuance is needed, meaning that
local governments must not cooperate repaying their debt. Rather, if they
cooperate both in debt issuance and repayment, they are caught up in thecommon pool problem and would over-issue the bond, as is the case with
non-cooperative decentralized debt policies studied in Bruce (1995).
The basic model does at least suggest that a harmonizing public debt
policy is needed, but the full coordination is not required. The results
show that partial coordination may well be an eﬀective mechanism by which
local governments are forced to internalize the externalities of their own
local public debt issuance. Our analysis contributes to clarify which kind ofpolicy coordination is eﬃciency enhancing and that too much coordination
may even harm eﬃciency. We believe that this result contributes to thediscussion on harmonizing debt policies among the local governments in acountry. In addition, political eﬀort to create broad economic union such as
the European Union is another recognition of the importance of our result.
The analysis provides a framework for rationalizing the debt policy of the19European Union as the EU tries hard to coordinate national debt issuanceand the Union leaves it to its members to repay accumulated debt7 .
We believe the result derived in this paper is contributory to develop an
eﬃcient system for decentralized debt policies. In parallel, however, it should
also be noted that some of the assumptions, such as the absence of householdsavings, the constant interest factor, and the ‘excess population’ could be
modiﬁed. Speciﬁcally, the assumption on the constant interest factor should
be relaxed because it is natural to consider some kind of coordination in debt
ﬁnancing aims lowering the borrowing cost. By relaxing these assumptions,
we can oﬀer more general examination in the future research.

Acknowledgment
Earlier version of this paper has been presented at 2008 JAEA Meeting,Doshisya University and Hokkaido University. The authors thank Yoshio
Itaba, Kazutoshi Miyazawa, Tadashi Yagi, Noritaka Kudoh and Jun-ichi
Itaya for helpful comments. The research has been supported by grants
from the Japan Society for the Promotion of Science (No.20330055) and the
Zengin Foundation for Studies on Economics and Finance.

References[1] Akai N. (1994), Ricardian equivalence for local government bonds, Economics Letters 44, 191-195.
[2] Aronson J.R. (1971), A comment on optimality in local debt limitation,
National Tax Journal 24, 107-108.

7

The agreement of the coordinate issue of local debts started in 2003 in Japan has also
intended to have the aspect that each jurisdiction repays its debt independently while itissues the debt cooperatively.

20

[3] Atkinson A.B. and J.E. Stiglitz (1980), Lectures on Public Economics,
McGraw-Hill.
[4] Bruce N. (1995), A ﬁscal federalism analysis of debt policies bysovereign regional governments, Canadian Journal of Economics, supplement 28, 195-206.
[5] Daﬄon D. (2002), Local public finance in Europe: Balancing the budget
and controlling debt, Edward Elgar Pub.
[6] Daly G.C. (1969), The burden of the debt and future generations inlocal ﬁnance, Southern Economic Journal, 36, 44-51.
[7] Hand J.H. and W.E. Mitchell (1971), Optimality in local debt limitation: Comment, National Tax Journal 24, 101-106.
[8] Homburg S. and W.F. Richter (1993), Harmonizing public debt andpublic pension schemes in the European Community, Journal of Economics supplement 7, 51-63.
[9] Jensen R. and E.F. Toma (1991). Debt in a model of tax competition,
Regional Science and Urban Economics 21, 371-392.
[10] Musgrave R. (1959), The Theory of Public Finance, New York,
McGraw-Hill.
[11] Myers G.M. (1990), Optimality, free mobility, and the regional authority in a federation, Journal of Public Economics 43, 107-121.
[12] Oates W. (1972), Fiscal Federalism, Harcourt Brace Jovanovich, NewYork.
[13] Ogawa H. and M. Yano (2007), Local public debt with overlapping
generations, Economics of Governance 8, 51-59.
21

[14] Schultz C. and T. Sjostrom (2001), Local public goods, debt and migration, Journal of Public Economics 80, 313-337.
[15] Schultz C. and T. Sjostrom (2004), Public debt, migration and shortsighted politicians, Journal of Public Economic Theory 6, 655-674.
[16] Tsuneki A. (1985), On the neutrality of local public bond in a spatial
economy, Economic Studies Quarterly 36, 46-52.
[17] Wagner R. (1970), Optimality in local debt limitation, National Tax
Journal 23, 297-305.
[18] Wagner R. (1971), Optimality in local debt limitation: Reply, National
Tax Journal 24, 109-111.
[19] Weichenrieder A.J.(1999), Local public investment and debt limitation
in a federation, CESifo, manuscript.
[20] Wellisch D. and W.F. Richter (1995), Internalizing intergenerational
externalities by regionalization, Regional Science and Urban Economics
25, 685-704.

22