OSIPP Discussion Paper : DP-2021-E-004

Elections accelerate inefficiencies in local public good provision
with decentralized leadership

February 25, 2021

Nobuo Akai*
Professor, Osaka School of International Public Policy (OSIPP), Osaka University

Takahiro Watanabe†
PhD. Student, Graduate School of Economics, Osaka University【Keywords】Election. Decentralized leadership. Interregional transfer【JEL Classification】H71. H72. H77【Abstract】This paper introduces the election process to the traditional decentralized
leadership model, where the central government does not have a pre-commitment
ability, and interregional transfer is optimally designed ex post. In the traditional
decentralized leadership model, it has been shown that local public good provision is
distorted by ex post transfer. The purpose of this paper is to examine how the
introduction of the election process affects inefficiencies in the decentralized leadershipsituation. Our results show that the direction of this distortion depends on thecommitment environment, and the degree of this distortion depends on the degree of
spillover.

*†Corresponding author. E-mail: akai@osipp.osaka-u.ac.jp
E-mail: sge028wt@student.econ.osaka-u.ac.jp

1

Introduction

In January 2015, the radical left-wing party, led by Alexis Tsipras, won the election in Greece with apromise of anti-austerity. Why was anti-austerity supported by the people even when the European
Union (EU) called for austerity in Greece as a condition of additional fiscal support?
The reason why the Greek people took this extreme position may be related to the rescue ex postby the EU. Even if Greece did not impose severe austerity, the EU may have been expected to support
Greece ex post by increasing transfers. A very radical ex ante position might have been important toGreece in order to induce transfers from the EU. Given this expectation, the policy leader in Greece
is likely to be strategically selected in an election.
The eﬀect of the ex post interregional transfer by the central government has been analyzed
theoretically in the context of the lack of commitment. When the central government cannot commit
to the policy, it faces a chance to redesign its policy ex post after observing the result in the economy
or society. This situation can be modeled for local governments as Stackelberg leaders and for thecentral government as a Stackelberg follower. Such a model structure is often called “decentralized
leadership.” Under decentralized leadership, it is shown that local public goods may be either underor overprovided, depending on local governments’ ex ante policy. However, some studies show that
resource allocation is socially eﬃcient when local governments commit to the provision of pure public
goods ex ante (e.g., Caplan et al. 2000; Koethenbuerger 2004, 2008; Akai and Sato 2008; Caplan
and Silva 2011; Silva 2014, 2015; Akai and Watanabe 2020). In particular, in previous literature, theimportance of the type of local governments’ commitment in terms of social welfare has been focusedon the decentralized leadership model (e.g., Akai and Watanabe 2020).
In previous models, the election stage where the representative who promises the policy is elected
is not considered. It is interesting to incorporate the election stage into the decentralized leadershipmodel from the perspective of reality and analyze how the introduction of the election process aﬀects
ineﬃciencies previously presented in the decentralized leadership model.
In the absence of ex post interregional transfers, there exists some previous literature that considers
the election process in the model with interregional competitive interactions among local governments.
The policy maker is strategically elected by voters, taking their eﬀect on the election in other regions1

into account, the behavior of which is often called “strategic delegation.” Several studies derive
the eﬀects on the local tax or expenditure policies, the degree of strategic delegation, and resource
allocation in Nash equilibrium. However, in these previous studies, no ex post interregional transfer
is considered. 1
This paper analyzes how the consideration of the election process improves or exacerbates theresource allocation in decentralized leadership where the central government cannot commit to its
policy ex ante and can design interregional transfer ex post.
The main results are as follows. In the neutral situation where the median voter is elected in theabsence of ex post transfer, ex post transfer aﬀects the political outcome, and the policy maker who
prefers diﬀerent policies from the median voter is elected. As a result, the resource allocation of local
public good provision under the presence of the election process is further distorted, in addition tothe original distortion by the ex post transfer in the model without the election process.
The direction of its distortion depends on whether the policy maker’s ex ante policy is committed
to local public good provision or the local tax rate. When the policy maker in each region commits
to local public good provision ex ante, the policy maker with the stronger preference for local public
goods would be elected, the degree of which depends on the degree of the spillover eﬀect of local public
goods. Resource allocation is more distorted by the higher level of local public good provision, except
for the case of perfect spillover. The increase of the degree of the spillover mitigates the ineﬃciencyof the resource allocation, and this distortion can be fully canceled out in the case of perfect spillover.
By contrast, when the policy maker in each region commits to its local tax rate, the policy makerwith the weaker preference for local public goods is elected, and resource allocation is more distortedwith the lower level of the local public good provision. In this case, this distortion cannot be canceledout even in the case of perfect spillover, while the eﬃciency of resource allocation is improved as thedegree of the spillover increases.
This paper is structured as follows. The basic model is explained in Section 2. Then, we analyze
two scenarios. In Section 3, we analyze the scenario where the policy maker commits to local public1
One exception is Susa (2019), who analyzes electoral outcomes with equalization transfer in a tax competition
framework. The equalization is based on the diﬀerence at the capital level, the total of which is constant. The incentive
is not biased in Nash equilibrium. By contrast, we analyze the transfer on the levels of private consumption or local
public goods, the total of which is not constant in the model.

2good provision. In Section 4, we analyze another scenario where the policy maker commits to the local
tax rate. In Section 5, we compare the eﬀect of ex post interregional transfer on the elected policy
maker between scenarios. Section 6 concludes the paper.

2

The model

Consider an economy with two regions, i = A, B. 2 There are two local governments and one central
government. The population size of each region is normalized to one. Each region provides a local
public good gi , which is measured in per capita terms and may generate interregional spillovers. All
individuals j in region i enjoy private consumption cij .
Individuals have diﬀerent local public goods preference. We denote the local public goods preference of individual j in each region by θj . This preference in each region is identically and symmetrically
distributed over the interval [θ, θ], so the median is equivalent to the mean. The larger an individual’sθj is, the stronger his/her preference for local public goods is.
Each individual j in both regions is characterized by the local public goods preference parameterθj . The preference of a type θj citizen in each region is:u(cij ) + θj v(gi , g−,i ; λ)= log ci + θj [log gi + λ log g−i ], i = A, B, ∀j, i ̸= −i(1)

We assume the additively separable utility function, which is a functional form adopted in Besley and
Coate (2003), to clearly define the eﬀect of ex post interregional transfer on the election of the policy
maker.

3

λ represents the degree of spillover of local public goods. If λ = 0, spillover eﬀects areabsent: individuals in region i do not care about local public good provision in region −i. The larger
the value of λ, the larger the degree of spillover. If λ = 1, individuals care about the local public
good provided in the other region as well as the local public good produced in their own region. We

2

For simplicity, we analyze two regions. Our results would not change even if N regions were considered.
Under the additively separable utility function, the distortion does not occur in the model without ex post transfers.
Therefore, it is possible to derive the eﬀect of the introduction of ex post transfers clearly. By contrast, Kemp and RotaGraziosi (2019) assume a utility function that satisfies ∂ 2 v(gi , g−,i ; λ)/∂gi ∂g−i ̸= 0. In their paper, strategic delegation
takes place even without ex post transfers. See Rota-Graziosi (2019) for detailed explanations.
33

assume:Assumption 1

0<λ≤1

(2)

We assume that 0 < λ is the necessary condition for cij > 0 and gi > 0, i = A, B, ∀j in thesubgame-perfect equilibrium. We also assume:
Assumption 2
1
1> θM >
1−λ
1+λ

(3)

Assumption 2 also ensures an interior solution in the subgame-perfect equilibrium.
Local government i levies a lump sum tax ti on all residents who live in the region i, and the tax
revenue is used for the local public good provision gi , which is measured in per capita terms. Supposethat yi is the exogenous per capita income of individuals in region i, then private consumption ofindividuals in region i is given as follows.

cij = yi − ti = ci , i = A, B, ∀j(4)Note that the decision ti directly links to the level of private consumption, given the exogenous income.
Now the budget constraint of local government i can be written as:

gi = ti + si ,i = A, B(5)where si denotes the per capita transfer from the central government to the region. Turning to thebudget constraint of the central government, the expression becomes:sA + sB = 0

4(6)si can be either positive or negative.4 The central government can control the transfer to pursue its
own objectives, but cannot commit to the transfer policy; therefore, the transfer is optimized ex post.
Given the central and local budget constraints, we can describe the overall resource constraint asfollows.

cA + cB + gA + gB = yA + yB

2.1

(7)

BenchmarkWe first derive the socially optimal amount of local public goods. The social optimum serves as abenchmark in order to evaluate the outcomes of political decision making under ex post interregionaltransfers. We define the social optimum as the outcome that maximizes the sum of utilities of all
individuals in both regions. Because individuals in each region are symmetrically distributed over theinterval [θ, θ], and with population size normalized to one, social welfare is equal to the sum of utilitiesof median voters in both regions. We denote the position of the median in both regions by θM . Hence,max{ci ,gi }i=A,B

S = log cA + θM [log gA + λ log gB ]+ log cB + θM [log gB + λ log gA ]s.t. cA + cB + gA + gB = yA + yB

First-order conditions become:
1
−α=0
cA
1
−α=0
cB
1
λ
θM
+ θM
−α=0
gA
gA
1
λ
θM
+ θM
−α=0
gB
gB

4

In our model, negative transfer implies ex post taxation of the local government by the central government.

5

(8)
(9)
(10)
(11)

where α is a Lagrangian multiplier associated with the constraint of the abovementioned optimization
problem. We can rewrite first-order conditions as follows.
∗∗
∗∗
c∗∗
A = cB = c1
λ1+ θM ∗∗ = ∗∗
∗∗
gA
gA
c
1
λ
1
θM ∗∗ + θM ∗∗ = ∗∗
gB
gB
c
θM

(12)
(13)
(14)

By substituting condition (12) into equation (7), we obtain:c∗∗ =∗∗ − g ∗∗yA + yB − gA
B
2

(15)

∗∗
∗∗
gA
= gB
= g ∗∗(16)

From conditions (13) and (14), we obtain:

Combining equations (15) and ((16) with (13) (or (14)) yields:g ∗∗ =

2.2(1 + λ)θM (yA + yB )2[(1 + λ)θM + 1]

(17)

Timeline

The timeline of our model is defined as follows.
1. In each region, the policy maker is simultaneously elected from among the individuals throughmajority voting. The authority to determine the local policy within a region is delegated to theindividual selected in this election.
2. Given the environment related to the committed policy variables, the local policy is determinedby the policy maker selected through the election in Stage 1.
3. Having observed local policies within both regions committed in Stage 2, the central government
designs the transfer si . Finally, given all policies of governments, each individual consumes and6gains utility.
Regarding ex ante commitment of the policy maker in each region, we consider following two scenarios.
In Scenario I, the policy maker commits to the level of the local public provision gi ex ante with thelocal tax rate ti remaining as residual ex post. By contrast, the local tax rate is pre-committed in
Scenario II, and gi is determined ex post, after the central transfer is designed. In either scenario, thecentral government is the Stackelberg follower. Because the concept of a subgame-perfect equilibrium
is applied, we solve each scenario backwardly.

3

Scenario I: gi is committed ex ante

3.1

Stage 3: Ex post policy making of the central government

Given that gi is already committed ex ante, ti is adjusted ex post so as to balance the local budget
ti = gi − si , with si transferred from the central government. 5 Then the central government chooses
si to maximize the sum of utilities of median voters in both regions. 6 The optimization problem
solved by the central government in the third stage is given as follows.

max UAM + UBM

sA ,sB= log(yA − gA + sA ) + θM [log gA + λ log gB ]+ log(yB − gB + sB ) + θM [log gB + λ log gA ]s.t. sA + sB = 0

The first-order condition is:
1
1
−
=0
cA cB

5

(18)

Then private consumption is adjusted by the transfer through the change of ti .
Here, we simply consider the case of a benevolent central government in order to focus on the distortion of theregional election under a benevolent central government.
6

7

Condition (18) states that the ex post interregional transfer si is chosen to equalize the marginalutilities of private consumption across regions. This condition implies:cA = cB = c(19)

yA + yB − gA − gB
2

(20)

Therefore, we obtain:c=

Substituting equation (20) into ci = yi − gi + si , we obtain the following.
∂si
1= > 0, i = A, B
∂gi
2
∂s−i
1
= − < 0, i = A, B, i ̸= −i
∂gi
2

(21)
(22)

The denominator is 2 in equations (21) and (22) because we assume two regions.

3.2

Stage 2: The policy maker’s ex ante policy

Let the utility level of the policy maker in region i be denoted by UiP , and the policy maker’s local
public goods preference denoted by θiP . Taking the local public good provision in the other region
g−i as given, the policy maker determines gi in his/her region to maximize his/her utility. Therefore,
the optimization problem solved by the policy maker in each region is given as follows. 7

max UiP = log c + θiP [log gi + λ log g−i ]gis.t. c =yA + yB − gA − gB
2

The first-order condition is:
( )
1
1
1
+ θiP = 0, i = A, B
× −
c
2
gi
7

(23)

In this stage, the policy maker is able to commit to the policy he/she decides, and individuals know it in the firststage election.

8

From condition (23) and equation (20), we obtain the reaction function of region i as follows.

gi (g−i ) = −θiPθiP (yA + yB )g−i +, i = A, B, i ̸= −i
1 + θiP
1 + θiP(24)

Solving equation (24) for i = A, B, we obtain:gi (θAP , θBP ) =θiP (yA + yB ), i = A, B
1 + θAP + θBP(25)

yA + yB2(1 + θAP + θBP )(26)

Combining equation (20) with (25) yields:c(θAP , θBP ) =3.3

Stage 1: Election of the policy makerIn the first stage, the policy maker is elected by majority voting in each region. Individuals in eachregion vote for a candidate based on their local public goods preference. Because of the median voter
theorem, the individual located at the median of the distribution of the preference is the decisive voter
in his/her region. Taking the result of the second stage into account and the choice of the other region
as given, the median voter in each region decides to whom the authority to decide the level of thelocal public good provision is delegated. Hence, the optimization problem considered by the medianvoter in region i is given as follows.

max UiM = log c(θAP , θBP ) + θM [log gi (θAP , θBP ) + λ log g−i (θAP , θBP )]θiP

yA + yB2(1 + θAP + θBP )θiP (yA + yB ), i = A, B, i ̸= −igi (θAP , θBP ) =1 + θAP + θBP

s.t. c(θAP , θBP ) =The first-order condition is:
[
]
1 ∂gi
1 ∂g−i1 ∂c+ θM+λ= 0, i = A, B, i ̸= −ic ∂θiPgi ∂θiPg−i ∂θiP

9(27)

This condition can be rewritten as follows.

−1
1 + θAP + θBP[+ θM

1 + θ−iPλ−θiP (1 + θAP + θBP ) 1 + θAP + θBP]= 0, i = A, B, i ̸= −i(28)

Therefore, we obtain the reaction function of region i as follows.

θiP (θ−iP ) =θMθMθ−iP +, i = A, B, i ̸= −i
1 + λθM
1 + λθM(29)

Solving equation (29) for i = A, B, we obtain:

I∗
I∗
θAP
= θBP
= θPI∗ =θM
1 − (1 − λ)θM

(30)

Substituting equation (30) into (25) and (26), the equilibrium levels of the local public good andprivate consumption in each region are derived as follows.
θM (yA + yB )(1 + λ)θM + 1
[1
−
(1
−
λ)θ
M ](yA + yB )cI∗ =2[(1 + λ)θM + 1]

I∗
I∗
gA
= gB
= g I∗ =

(31)
(32)

First, we examine the direction of strategic delegation. Comparing the policy maker in the equilibrium with the median voter, we have:θPI∗ > θM

if 0 < λ < 1(33)

θPI∗ = θM

if λ = 1(34)

Thus, when the degree of spillover of local public goods is less than one, the median voter in eachregion delegates authority to the individual with stronger local public goods preference to decide thelocal public good provision. By contrast, when the degree of spillover is equal to one, the medianvoter in each region is elected as the policy maker.
Next, we examine local public good provision in equilibrium. Remembering that the socially

10optimal level of local public good provision is g ∗∗ = (1 + λ)θM (yA + yB )/{2[1 + (1 + λ)θM ]}, we have:g I∗ > g ∗∗if 0 < λ < 1(35)

g I∗ = g ∗∗if λ = 1(36)

Thus, when the degree of spillover of local public goods is less than one, local public good provision in
equilibrium is overprovided relative to the social optimum. By contrast, when the degree of spilloveris equal to one, local public good provision in equilibrium coincides with the social optimum.
We can also derive local public good provision in the absence of election of the policy maker. In
this case, the local public good provision is determined directly by the median voter. We refer to thiscase as the “no election case.” This level of provision is derived by substituting θAP = θBP = θM into
equation (25). Let g I∗ |θP∗ =θM represent the local public good provision in the no election case, thenwe obtain the following.

g I∗ |θP∗ =θM =θM (yA + yB )1 + 2θM(37)

Comparing the case with and without election of the policy maker, we have: 8 :g I∗ > g I∗ |θP∗ =θM > g ∗∗if 0 < λ < 1(38)

g I∗ = g I∗ |θP∗ =θM = g ∗∗if λ = 1(39)

When the degree of spillover of local public goods is less than one, the local public good provision in
the presence of election is not coincident with the social optimum and is excessively provided relative
to that in the absence of election. By contrast, when the degree of spillover is equal to one, local
public good provision even in the presence of election coincides with the socially optimal level.
The results of Scenario I are summarized as follows.
Proposition 1
8Comparing the no election outcome with the social optimum, we obtain the following inequality.
g I∗ |θP∗ =θM ≥ g ∗∗ ⇔ 1 ≥ λTherefore, equations (38) and (39) hold.

11

(a) Assume λ = 1. Then, local public good provision in the subgame-perfect equilibrium coincides
with the social optimum, i.e., g I∗ = g ∗∗ . The median voter is elected as the policy maker, i.e.,θPI∗ = θM .
(b) Assume λ ∈ (0, 1). Then:(b-1) The median voter delegates the authority to the individual with stronger local public goods
preference to decide the policy, i.e., θPI∗ > θM .
(b-2) Local public goods are overprovided relative to the social optimum, i.e., g I∗ > g ∗∗ .
(b-3) Compared with the no election case, local public good provision in the subgame-perfect equilibrium is greater, i.e., g I∗ > g I∗ |θI∗ =θM > g ∗∗ .
P

The intuition of Proposition 1 is given as follows. First, as shown in (a), the degree of spillover
has the crucial role of achieving the socially optimal allocation. This result can be interpreted as the
combination of the results from both the decentralized leadership model and the strategic delegation
model. In the decentralized leadership model, it has been shown that the incentive eﬀect of ex postinterregional transfer is fully canceled out by the incentive eﬀect of the perfect spillover. In articles
on strategic delegation, it has been shown that the strategically elected policy maker coincides withthe median voter under the separable utility function. The special situation with both the separable
utility function and perfect spillover makes resource allocation optimal.
By contrast, for (b) with imperfect spillover, the result dramatically changes. In addition to thefact that resource allocation is biased under imperfect spillover, because of the incentive eﬀect of theinterregional transfer, the strategically elected policy maker does not coincide with the median voter
even under the separable utility function. In particular, the individual with stronger preference for
local public goods is elected as the policy maker, because the higher level of local public good provision
is desirable in order to induce the higher level of transfer ex post (see equation (21)). As a result,the level of the local public good provision is accelerated by the presence of the policy maker election
stage. 99The results of Proposition 1 seem to be similar to Besley and Coate (2003) and Dur and Roelfsema (2005). in both
papers, the reason for obtaining these results is due to the integration of regional budgets by centralized (cooperative)
decision making, which is diﬀerent from our results arising from cost sharing by ex post transfers under decentralized
decision making.

12

𝜃𝐵𝑃

𝜃′𝐴𝑃 𝜃𝐵𝑃

𝜃𝐴𝑃 𝜃𝐵𝑃𝜃𝐴𝑃 = 𝜃𝐵𝑃𝜃𝐵𝑃 𝜃𝐴𝑃

𝜃𝑀

𝜃𝐴𝑃

𝜃𝑀

Figure 1: Best responses at the electoral stage in Scenario I.

Figure 1 illustrates changes in electoral outcomes depending on the degree of spillover in Scenario
I. For the slope and intercept of the best response function in Stage 1 represented by equation (29),
we obtain:
2
θM
∂
θM
=−
<0
∂λ 1 + λθM(1 + λθM )2(40)

Therefore, the degree of spillover shifts the best response function of region A downward. This is′ (θrepresented by the shift from θAP (θBP ) to θAPBP ) in Figure 1. Of course, the best response functionof region B also shifts downward, so that the intersection of best response functions of both regions
shifts to the southwest on the 45-degree line. As a result, the local public goods’ preference of thepolicy maker elected in each region approaches the median voter’s preference. This means that the
local public good provision in the equilibrium decreases. That is, we have:θ2 (yA + yB )
∂g I∗
=− M
<0
∂λ
[(1 + λ)θM + 1]2(41)

The reason for the relationship between the degree of spillover and the electoral outcome is thatthe higher spillover eﬀect decreases the incentive to induce the transfer to its own region (in otherwords, the incentive for strategic delegation) due to the increased benefit from the local public good13

provision in the other region. Under perfect spillover (i.e., λ = 1), the incentive for strategic delegation
disappears, so the elected policy maker is consistent with the median voter. As it approaches themedian voter, the local public good provision in equilibrium also decreases, while the socially optimum
level increases with the increase of the degree of the spillover. Finally, the local public good provision
coincides with the social optimum.

4

Scenario II: ti is committed ex ante

4.1

Stage 3: Ex post policy making of the central government

In this section, we consider another scenario in which the policy maker in each region commits to the
local tax rate ex ante. Because ti is already committed ex ante, in contrast to Scenario I, gi is adjusted
ex post such as to balance the local budget gi = ti + si . Therefore, the optimization problem solvedby the central government in the third stage is given as follows.

max UAM + UBM

sA ,sB= log cA + θM [log(tA + sA ) + λ log(tB + sB )]+ log cB + θM [log(tB + sB ) + λ log(tA + sA )]s.t. sA + sB = 0

The first-order condition is:(1 + λ)θM

1
1− (1 + λ)θM
=0
gA
gB

(42)

Condition (42) states that the central transfer si is chosen to equalize the marginal utilities of local
public goods across regions. This condition implies:gA = gB = g

14

(43)

Therefore, we obtain:g=tA + tB
2(44)

Substituting equation (44) into gi = ti + si , we obtain the following conditions.
∂si
1= − < 0, i = A, B
∂ti
2
∂s−i
1
= > 0, i = A, B, i ̸= −i
∂ti
2

4.2

(45)
(46)

Stage 2: The policy maker’s ex ante policy making

In the second stage, the policy maker determines ti in his/her region to maximize his/her utility,
taking the local tax rate in the other region t−i as given. Therefore, the optimization problem solvedby the policy maker in each region is given as follows.

max UiP = log ci + θiP [log g + λ log g]tis.t. ci = yi − ti , i = A, B
g=tA + tB2

The first-order condition is:
[
]
1
1 1
1 1
+ θiP
× +λ ×= 0, i = A, B−
yi − ti
g 2
g 2

(47)

From condition (47) and equation (44), we obtain the reaction function of region i as follows.

ti (t−i ) = −(1 + λ)θiP yi
1t−i +, i = A, B, i ̸= −i(1 + λ)θiP + 1(1 + λ)θiP + 1(48)

Solving equation (48) for i = A, B, we obtain:ti (θAP , θBP ) =θiP yi [(1 + λ)θ−iP + 1] − θ−iP y−i, i = A, B, i ̸= −i(1 + λ)θAP θBP + θAP + θBP

15

(49)

Substituting equation (49) into ci = yi − ti and equation (44) yields:
θ−iP (yA + yB ), i = A, B, i ̸= −i(1 + λ)θAP θBP + θAP + θBP1(1 + λ)θAP θBP (yA + yB )g(θAP , θBP ) = ×
2 (1 + λ)θAP θBP + θAP + θBP

ci (θAP , θBP ) =

4.3

(50)
(51)

Stage 1: Election of the policy makerAs presented in Section 3.3, the optimization problem considered by the median voter in region i isgiven as follows.

max UiM = log ci (θAP , θBP ) + θM [log g(θAP , θBP ) + λ log g(θAP , θBP )]θiP

θ−iP (yA + yB ), i = A, B, i ̸= −i(1 + λ)θAP θBP + θAP + θBP1(1 + λ)θAP θBP (yA + yB )g(θAP , θBP ) = ×
2 (1 + λ)θAP θBP + θAP + θBP

s.t. ci (θAP , θBP ) =The first-order condition is:
[
]
1 ∂g
1 ∂g
1 ∂ci
+ θM
+λ
= 0, i = A, B
ci ∂θiPg ∂θiPg ∂θiP(52)

This condition can be rewritten as follows.

−[(1 + λ)θ−iP + 1]
(1 + λ)θAP θBP + θAP + θBP[](1 + λ)θ−iP+ θM= 0, i = A, B, i ̸= −i
θiP [(1 + λ)θAP θBP + θAP + θBP ](53)

Therefore, we obtain the reaction function of region i as follows.

θiP (θ−iP ) =(1 + λ)θM
θ−iP , i = A, B, i ̸= −i(1 + λ)θ−iP + 1(54)

Solving equation (54) for i = A, B, we obtain:

II∗
II∗
θAP
= θBP
= θPII∗ =16(1 + λ)θM − 1
1+λ

(55)

Substituting equation (55) into (50) and (51), the equilibrium levels of private consumption and local
public goods in each region are derived as follows.
yA + yB(1 + λ)θM + 1[(1 + λ)θM − 1](yA + yB )g II∗ =
2[(1 + λ)θM + 1]

II∗
II∗
cII∗
=
A = cB = c

(56)
(57)

As in Scenario I, we examine the direction of strategic delegation. Comparing the policy maker in
equilibrium with the median voter, we obtain the following.

θPII∗ − θM = −

1
1+λ

(58)

Because λ ∈ (0, 1], we have:θPII∗ < θM

(59)

Thus, regardless of the degree of spillover, the median voter in each region delegates authority to theindividual with weaker local public goods preference to determine the local tax rate.
Next, we compare local public good provision in equilibrium with the social optimum. Then, we
obtain the following inequality.
g II∗ − g ∗∗ = −yA + yB2[(1 + λ)θM + 1]

(60)

Because λ ∈ (0, 1], we have:g II∗ < g ∗∗(61)

Thus, regardless of the degree of spillover, local public goods in equilibrium are underprovided relative
to the social optimum. Unlike Scenario I, the socially optimal provision of the local public good isnever achieved in equilibrium. Now, we also derive local public good provision in the no election case.

17

This is derived by substituting θAP = θBP = θM into equation (51). Then, we obtain:g II∗ |θP∗ =θM =(1 + λ)θM (yA + yB )2[(1 + λ)θM + 2]

(62)

Clearly, we obtain:g II∗ |θP∗ =θM < g ∗∗(63)

Comparing the case with and without the election of the policy maker, we obtain the following inequality.

g II∗ − g II∗ |θP∗ =θM = −yA + yB[(1 + λ)θM + 1][(1 + λ)θM + 2]

(64)

Therefore, we obtain:g II∗ < g II∗ |θP∗ =θM < g ∗∗(65)

Thus, regardless of the degree of spillover, there are more local public goods provided in the absenceof election than in the presence of election, but neither coincide with the social optimum.
The results of Scenario II are summarized as follows.
Proposition 2(a) Local public good provision in the subgame-perfect equilibrium never coincides with the social
optimum, irrespective of the degree of spillover eﬀect λ.
(b) For any λ:(b-1) The median voter delegates authority to the individual with weaker local public goods preference to decide the policy, i.e., θPII∗ < θM .
(b-2) Local public goods are underprovided relative to the social optimum, i.e., g II∗ < g ∗∗ .
(b-3) Compared with the no election case, local public goods in the subgame-perfect equilibrium
are less provided, i.e., g II∗ < g II∗ |θP∗ =θM < g ∗∗ .
18

The intuition of Proposition 2 is given as follows. In this scenario, interregional transfer tends todepress local public good provision, and the election accelerates this downward incentive because thepolicy maker with weaker preference for local public goods who prefers a lower level of the local tax
rate will induce a higher level of transfer ex post.

𝜃𝐵𝑃𝜃𝐴𝑃 = 𝜃𝐵𝑃𝜃𝑀𝜃𝐵𝑃 𝜃𝐴𝑃𝜃𝐴𝑃 𝜃𝐵𝑃𝜃′𝐴𝑃 𝜃𝐵𝑃𝜃𝑀

𝜃𝐴𝑃

Figure 2: Best responses at the electoral stage in Scenario II.

Figure 2 illustrates changes in electoral outcomes depending on the degree of spillover in Scenario
II. For the best response function in Stage 2, represented by equation (54), we obtain:∂θiP (θ−iP )θM θ−iP=> 0, i = A, B, i ̸= −i∂λ[(1 + λ)θ−iP + 1]2(66)

Therefore, with the increase of the degree of spillover, the best response function of region A shifts′ (θupward. This is depicted by the shift from θAP (θBP ) to θAPBP ) in Figure 2. Of course, the best

response function of region B also shifts upward, so that the intersection of best response functions ofboth regions shifts to the northeast on the 45-degree line. In the equilibrium, the local public goods
preference of the policy maker elected in each region approaches the median voter’s preference. Thisshows that local public good provision also increases in equilibrium. That is, we have:∂g II∗θM (yA + yB )=>0∂λ[(1 + λ)θM + 1]2

19

(67)

Therefore, increasing the degree of spillover decreases the incentive for strategic delegation, namely
the increase of θPII∗ , and increases local public good provision with the reduction of private consumption
in equilibrium. This change might be desirable in the sense that the local public good gap between
equilibrium and the social optimum becomes small as the degree of spillover increases. (We can derive
this by diﬀerentiating the right-hand side of equation (60) with respect to λ.)Compared with Scenario I, even in the case of perfect spillover, local public good provision in
equilibrium does not coincide with the social optimum as shown in (a) in Scenario II. In Scenario I,
the enhanced marginal incentive for providing local public good by ex post interregional transfer isperfectly compatible with the socially desirable incentive level under perfect spillover. By contrast, in
Scenario II, the reduced marginal incentive for providing the local public good by ex post interregionaltransfer cannot be compatible with the socially desirable incentive level, which requires enhancing theprovision of public goods. Therefore, each region in Scenario II has an incentive to keep private
consumption at some level while the incentive for strategic delegation toward the higher level ofconsumption is not completely eliminated, even if the degree of spillover is perfect. As a result, theelected policy maker still has a smaller incentive for raising the local tax rate (or providing the local
public good) compared with the median voter, and local public good provision in equilibrium is stillless than the socially optimal level, even if the degree of spillover is perfect.

5

Opposite eﬀects of interregional transfer on electoral outcomes

Table 1 summarizes the eﬀect of interregional transfer on the elected policy maker, θP∗ , compared withthe case without election, θM . Under the setting adopted in this paper, the election is not distorted in
the case without transfer, θP∗ = θM . 10 Starting from this point, introducing the transfer aﬀects theelected policy maker, except for the case with commitment to local public good provision with perfectspillover. This exception is caused by the fact that the distortion from the interregional transfer is fully
canceled out by the perfect spillover. Generally, eﬀects from the two types of commitments consideredin this paper are in the opposite direction to the electoral outcome. In the case with commitment tolocal public good provision, the policy maker with stronger preference for local public goods is elected.
10

The case without transfer corresponds to the decentralized outcome in Besley and Coate (2003) and Dur andRoelfsema (2005).

20

Transfer〇

Scenario I
𝒈-commitment

✕

𝟎<𝝀<𝟏

𝝀=𝟏

𝜽𝐈∗
𝑷 > 𝜽𝑴𝜽𝐈∗
𝑷 = 𝜽𝑴𝟎<𝝀≤𝟏

𝜽𝑷∗ = 𝜽𝑴

Scenario II
𝒕-commitment

𝜽𝐈𝐈∗
𝑷 < 𝜽𝑴

Table 1: Eﬀect of interregional transfer on electoral outcomes in each scenario.

By contrast, in the case of commitment to the tax rate, namely the level of private consumption,
the policy maker with weaker preference for local public goods is elected. These perfectly opposite
directions of eﬀect are caused by the opposite direction of incentives due to diﬀerent commitments.

6

Conclusion

We show that, in the neutral situation where the median voter is elected without transfer, the representative who diﬀers from the median voter is elected, and resource allocation is distorted more after
the election process. The direction of this diﬀerence in the preference of the elected policy makerdepends on whether ex ante policy can be committed to the local public good provision or to the local
tax rate by the policy maker.
When the policy maker in each region commits to local public good provision ex ante, then thepolicy maker with stronger preference for local public goods is elected, and resource allocation ismore distorted with the higher level of the local public good provision, except for the case of perfectspillover. In addition, the spillover mitigates the ineﬃciency of resource allocation, and this distortion
can be fully canceled out in the case of perfect spillover.
By contrast, when the policy maker in each region commits to the local tax rate ex ante, thenthe policy maker with weaker preference for local public goods is elected, and resource allocation is21

more distorted with a lower level of local public good provision. In this case, this distortion cannot
be canceled out even in the case of perfect spillover.
This result may lead to the following policy implications. In the situation where there exists ex
post transfer due to the lack of central government’s commitment ability, the election accelerates theineﬃciency of local public good provision. The direction of this distortion depends on the commitment
environment. Moreover, the degree of this distortion depends on the degree of spillover. Therefore,
it might be desirable for the central government to regulate the policy of the policy maker elected,
depending on the commitment environment and the degree of spillover.
Finally, this paper has some limitations. We assume a logarithmic form of utility function forsimplicity of analysis. We assume interregional symmetric distribution of the preference for local
public goods and intraregional symmetric income distribution. Extensions to the model with a general
type of utility function and these asymmetries may give new insights to our research in the future.

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