ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E14-3

Strategic Delegation in Asymmetric Tax
CompetitionbyHikaru Ogawa
Taiki Susa

February 2014

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Strategic Delegation in Asymmetric Tax
Competition
Hikaru Ogawa∗Taiki Susa†

Abstract
This study examines asymmetric tax competition under representative
democracy systems. The findings show that the degree of asymmetry
between countries affects the result of elections in each country, where
the citizens select a policymaker to set a tax rate for the country. In
particular, under certain conditions, a decisive voter in the election canselect a citizen whose share of the country’s capital is higher than thedecisive voter’s own share.

Keywords: Tax competition; Strategic delegation; Terms of trade
JEL classification D72, H30, H87∗ School of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japanemail: ogawa@soec.nagoya-u.ac.jp† School of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japanemail: TaikiSusa@gmail.com

1

1

Introduction

Under representative democracy that is found in several Western countries, citizens seriously consider which candidates to vote for, because they know it willinﬂuence the policies implemented after the election. Representative democracy, as a collective decision-making system, is thought to work well to govern
our societies and to be irreplaceable by any other political regimes. Social
structures worldwide, however, are undergoing signiﬁcant changes such as the
sharp increase in the mobility of capital, goods, and workers. These changes
are often a result of globalization, which also inﬂuences the features and validity of decision-making in a representative democracy (Rodrik, 2012). Oneof the features of the growth of globalization throughout the world is market
integration; tax competition theory is an important strand in analyzing market
integration. This theory has a long history dating back at least to Zodrow andMieszkowski (1986) and Wilson (1986). Curiously, however, in the literature on
tax competition, the issues of representative democracy and political competition have largely been left out. Therefore, the impact of increasing globalizationon the consequences of elections and formulation of public policies is less wellunderstood.1
Recently, however, Ihori and Yang (2009) incorporated the stylized form ofrepresentative democracy with citizen candidates into the canonical model oftax competition.2 As a part of their ﬁndings, they show that in symmetric tax
and political competition, a decisive voter in the election tends to delegate theauthority to set the tax rate to a poor citizen, or a citizen whose capital shareis lower than that of the decisive voter.
In this study, we focus on examining who is selected as a policymaker inan asymmetric tax competition setting.3 Rapid globalization has led to ﬁscal
competition among non-homogeneous countries, and tax competition theories
recognize the analytical importance of considering regional heterogeneity, atleast since Bucovetsky (1991).
1 Although the issue of strategic delegation under representative democracy, which is themain subject of our study, has not been explored much in the literature, the effects of policy
setting in a direct democracy, that is, a simple median voter model, have been studied intensively. See, for instance, Fuest and Huber (2001), Borck (2003), Grazzini and Van Ypersele(2003), and Lockwood and Makris (2006) among others.
2 Though few studies deal with tax competition under strategic delegation, there are two
exceptions. In the early stage, Brückner (2001) introduces the strategic delegation approach
into the tax competition model to examine the effects of tax coordination. Pal and Sharma(2011) study strategic delegation under Stackelberg tax competition and show that politicaldelegation takes place only in the follower country, not in the leader country.
3 It is fair to mention that Ihori and Yang (2009) use the symmetric model of tax and political competition to explore the implications for efficient provision of public goods. Therefore,
the selection of a policymaker is not their major concern.

2

The introduction of regional heterogeneity brings about a change in equilibrium characteristics. For example, in asymmetric tax competition with strategicdelegation, there are three types of equilibrium. In one of the two countries, forthe decisive voter, the following may hold: (i) the authority to make policies isdelegated to the rich in the election; (ii) the authority is delegated to the poor;or, (iii) the decisive voter picks him/herself as the policymaker. Conversely, inthe other country, the decisive voter always chooses the poor in equilibria. The
distinction among the three equilibria is because of the degree of asymmetry between the two countries. Particularly, if the regional asymmetry is higher thana certain level, it leads to type (i) equilibrium, a ﬁnding that diﬀers noticeably
from those of Ihori and Yang (2009) for the symmetric world.
The terms of trade between a capital-exporting and capital-importing country in tax competition plays a key role in creating the critical diﬀerence from
Ihori and Yang’s (2009) results. When capital crosses national borders, theasymmetric countries have incentives to manipulate their terms of trade (Bondand Samuelson, 1989; Gordon, 1992). This is because capital importers, in general, prefer a lower capital price so that their payment for borrowings is reduced,
whereas capital exporters prefer a higher capital price, so as to receive higher
returns from their investment. Thus, asymmetric countries face conﬂicts withregard to the price of capital and they try to manipulate the capital price byusing capital tax/subsidy instruments. Whereas standard tax/subsidy competition is motivated by the attraction of mobile tax bases, for example, capital for
public goods provision, the incentives to manipulate the terms of trade also leadgovernments to alternative forms of capital tax/subsidy competition (DePaterand Myers, 1994; Eggert, 2000; Itaya et al., 2008; Ogawa, 2013).
Whereas our study is motivated by Ihori and Yang (2009), another closely
related study is Persson and Tabellini (1992) that develops a somewhat diﬀerent
tax competition model from ours.4 In their model, there exist two countries
with diﬀerent tax rates. Depending on the position of the median voter in eachcountry, one country chooses a low capital tax rate and the other chooses ahigh tax rate. The tax rate diﬀerential in the integrated capital market causes
capital ﬂows. Furthermore, the median voter in the capital-importing country
has an incentive to delegate the right to choose the tax rate to the poor, because
the poor prefer a higher tax rate to meet redistribution objectives. The hightax chosen by the poor can help to reap the rents of foreign investors. The
median voter in the capital-exporting country has the opposite incentive; thatis, he/she might delegate the right to set the tax rate to the rich, who have
4 Persson and Tabellini (1994) compare the outcomes between representative democracy
and direct democracy by using the same framework.

3

incentives to choose a lower tax rate, because this tax rate would help to guard
against capital outﬂow.
The critical diﬀerence in our study from Persson and Tabellini (1992, 1994)
is the incentive for delegation. They describe an incentive for delegation that isbased on the manipulation of tax-exporting eﬀects. That is, the delegation of
the right to set a tax rate to the rich or poor depends on how the countries canreap the rent of absentee taxpayers. In contrast, we focus on how the terms oftrade aﬀect the incentive for delegation. This variation in the mechanism fordelegation produces a diﬀerent result; in Persson and Tabellini (1992, 1994),
delegation to the rich may occur in the high-tax country, but in our study, it
appears in the low-tax country.
This paper is organized as follows. In the next section, we develop a modelin which the two countries are asymmetric in production technology; a citizencandidate election to determine a policymaker takes place in each country before
tax competition begins. The equilibria of our model are presented in Section
3, and the main results are presented in Section 4. In Section 5, we provide
a discussion of the shift from direct to representative democracy from the perspective of tax competition. In Section 6, we present the conclusions of ourstudy and discuss the limitations and areas of further research .

2

The model

The model constructed here follows that of Ihori and Yang (2009) that considersa two-stage game, similar to Besley and Coate (2003). These models originate
from the citizen-candidate models by Osborne and Slivinski (1996) and Besley
and Coate (1997). In the ﬁrst stage, a simple-majority election takes place ineach country to pick a citizen as a policymaker. This policymaker governs thecountry and determines a tax rate in the next stage. In the second stage, tax
policies are selected simultaneously by the individuals elected as policymakers
in both countries. We solve this game backward to determine the equilibrium.
The economy consists of two countries, i = S, L; their population sizes aredenoted by Ni . Individuals in each country have the same claim to labor, but
unequal claims to capital. The initial amount of capital owned by individuals
in country i is given by K̄i . An individual j in country i has θij k¯i units ofcapital as an initial endowment, where k¯i is the amount of average capital incountry i, k¯i ≡ K̄i /Ni , and θij (≥ 0) represents the deviation from the average.
If individual j is not endowed with initial capital, θij = 0. Correspondingly,
if individual j’s initial capital endowment is just equal to the average (k¯i ),θij = 1, implying that θij > 1 if individual j has more capital, as compared4

to the average. Because positively skewed distributions of income are often
observed in practice, we assume that the median claim to capital in a country
is smaller than the mean (average) claim in this model, that is, θiM < 1, whereθiM denotes the position of the median in country i. At this stage, however, we
do not exclude θiM ≥ 1.
In each country, perfectly competitive ﬁrms produce numeraire private goods
with CRS technology, using labor and capital, Fi (Ki , Ni ) = (Ai − (Ki /Ni ))Ki .
This can be rewritten based on the per labor term as f i (ki ) = (Ai −ki )ki , where
ki represents the capital per labor employed in country i and Ai , the countryspeciﬁc parameter, stands for the productive eﬃciency of ﬁrms.5 We assume
that Λ = AL − AS > 0, without loss of generality.6 To concentrate on a single
source of regional asymmetry, we assume K̄i = K̄ and Ni = N ; therefore, k¯i = k̄in the following analysis. In this case, the total amount of capital employed for
production in this economy is 2K̄.
Each government levies a unit tax at rate Ti on mobile capital employedwithin the country. Perfect mobility of capital between countries and the capitalmarket clearing conditions implyr = fki (ki ) − Ti ,(1)2k̄ = kL + kS ,(2)

where r is the price of capital. Using (1) and (2), we have the amount of capitalin country i and the price of capital as follows:
Ai − A−i − Ti + T−i,4Ω 4k̄ + TL + TS
−
,
2
4

ki

= k̄ +

(3)

r

=

(4)

where Ω ≡ AL + AS . Let the preference of an individual j in country i beu(cij ) = cij , where cij represents the individual’s consumption of the private
good. The individual’s income is composed of labor income, f i (ki ) − fki (ki )ki ;rent from capital, rθij k̄; and a lump-sum transfer from the government of thecountry, gi . Hence, the consumer’s budget constraint is given by
5 The quadratic function has a nice feature that enables us to obtain outcomes in an explicit
form, and thus has been used in Bucovetsky (1991), Wildasin (1991), Peralta and Van Ypersele(2005), Itaya et al. (2008), and Kempf and Rota-Graziosi (2010), among others.
6 The method used to express the regional differential in technology does not affect themain result of this study, but the coexistence of capital importing and exporting countries is
crucial. Therefore, we express the regional asymmetry in terms of Ai , because this produces
a simpler and more efficient expression.

5

cij = f i (ki ) − fki (ki )ki + rθij k̄ + gi .

(5)

As each government ﬁnances the lump-sum transfer with a tax on capital, thegovernment’s budget constraint is given by
gi = ti ki .

(6)

Using (1), (5), and (6), the utility function can be written as u(cij ) = f i (ki ) +r(θij k̄ − ki ). This implies that the utility is composed of the gross national
product per capita and the net income from capital investment. With thisassumption, we can create the situation in which manipulation of the terms oftrade is the sole incentive to use the capital tax (Peralta and Van Ypersele,
2005; Itaya et al., 2008; and Ogawa, 2013).

3

Equilibrium

The timing of the game is deﬁned as follows.
1. In each country, a policymaker is elected from among the citizens througha majority voting. The authority to choose the capital tax rate in the
country is delegated to this policymaker.
2. Tax rates Ti are determined simultaneously and independently by thepolicymaker for each country.
Because the concept of a sub-game perfect Nash equilibrium is applied, we solve
the model backward.

3.1

Second Stage: Tax competition

Let the policy-maker in country i have θiP k̄ units of capital. Given a tax ratein the other country, T−i , the policymaker determines the tax rate in his/hercountry by solving the following maximization problem:

maxTi

uiP = (Ai − ki )ki + r(θiP k̄ − ki ),s.t.

(3) and (4).

The ﬁrst-order condition gives us the following reaction function for country i:
Ti (T−i ) =1
4k̄ − 4k̄θiP + Ai − A−i
T−i +
.
3
3
6

(7)

Solving (7) for i = S, L, we obtain the tax rate of country i in the equilibriumof the following sub-game:8k̄ − 6k̄θiP − 2k̄θ−iP + Ai − A−i.
(8)4
Substituting (8) into (3)-(4), the equilibrium values are yielded as follows:
Ti =2k̄θiP − 2k̄θ−iP + Ai − A−i,8Ω + 2k̄θLP + 2k̄θSP − 8k̄r=.
2ki = k̄ +

3.2

(9)
(10)

First Stage: Voting in the election

A simpliﬁed process of representative democracy is applied in this model, where
each citizen in a country is a candidate who can be selected as a policymakerand has a right to vote on this decision as well. Thus, we have two questions
to be answered: (i) who is the decisive voter of the selection? and (ii) who isselected as the policymaker to determine the capital tax rate of the country?
These questions are addressed in order in the next subsections.
3.2.1

Who becomes the decisive voter?

The citizens of each country do not vote on a tax policy directly; they vote for
an individual based on the amount of capital owned by him/her. Therefore,
we need to show that citizens’ preferences exhibit single-peakedness over θij .
From the second-order condition, ∂ 2 uij /∂Ti2 < 0, the single-peakedness of anindividual’s preference over the tax rate is conﬁrmed. Once a citizen in country
i is selected as a policymaker, he/she chooses a tax rate in accordance with (7).
Thus we can assure that Ti determined by the policymaker of each country is
negatively monotonic in θij . This implies that the more capital a policymakerhas, the lower the tax rate he/she chooses. This fact induces single-peakednessof citizens’ preferences over θij .
From the induced single-peaked preference over θij , it follows that if a citizen
with θij k̄ units of capital prefers a candidate who has the initial amount of
′′
′
′
′′
capital θij k̄ over a candidate who has θij k̄, where θij < θij , then all citizens who
have a smaller amount of capital than θij k̄ must agree with the citizen having
θij k̄, and vice versa. This means that a citizen who is located at the medianof the distribution of capital share is the decisive voter in his/her country, andthus, he is a Condorcet winner of this political decision process.

7

3.2.2

Who becomes the policy maker?

To whom does the median voter in the country delegate the tax-rate setting
authority? Let the median voter of country i have θiM k̄ units of capital. Taking
the equilibrium values of the sub-game at the next stage into consideration, themedian voter confronts a maximization problem to determine a policymaker asfollows:maxθiPs.t.

uiM = (Ai − ki )ki + r(θiM k̄ − ki ),(9) and (10).

The ﬁrst-order condition of each country’s decisive voter yields the following
reaction function,1
16k̄θiM − 8k̄ − Ai + A−i
θ−iP +
.
(11)
5
10k̄
From (11), in the sub-game perfect Nash equilibrium of this game, the policymaker of each country, selected by the median voter, is characterized by theamount of capital as follows:θiP (θ−iP ) =20k̄θiM + 4k̄θ−iM − 12k̄ − Ai + A−i
.
(12)
12k̄
The tax rate, the amount of capital, and the capital price in the equilibrium arerespectively given as follows:
∗
=
θiP

Ti∗
ki∗
r∗

4(3 − θ−iM − 2θiM )k̄ + (Ai − A−i ),3(Ai − A−i ) + 4k̄(θiM − θ−iM )= k̄ +,12Ω=− 2k̄(3 − θLM − θSM ).
2
=

(13)
(14)
(15)

Before explaining the equilibrium outcome in detail, we make an assumption.
In the strategic delegation game presented above, from (14), it is straightforward
to verify that the following assumption guarantees nonnegative levels of capital.
Assumption 1. −4(3 + θLM − θSM ) < Λ/k̄ < 4(3 − θLM + θSM )If Assumption 1 is violated, all capital ﬂows to either of the two countries, andthe other country becomes inactive.

8

4

Selected Policymaker

4.1

Is the policy maker rich or poor?

By examining who is elected as the policymaker of each country through thestrategic delegation process, we answer the question of whether this person owns
a higher or lower capital share than the median citizen of the society. From (12),the capital shares of the median voter and the policy-maker in each country canbe compared as follows:2θLM + θSM − 3
Λ
,
−
3
12k̄
2θSM + θLM − 3
Λ
∗
θSP
.
− θSM =
+
3
12k̄

∗
θLP
− θLM =

(16)
(17)

In the following analysis, because the evidence shows that the income distribution is skewed to the right, we begin by analyzing the equilibrium characteristics
in the case of θiM ∈ [0, 1), deferring discussion of other cases until later.
In (16) and (17), the ﬁrst term on the right-hand side is strictly less thanzero when θiM ∈ [0, 1). The second term captures the eﬀect of asymmetry
between the countries. Leaving this asymmetric eﬀect out of consideration,
the median voter always chooses a citizen whose capital share is lower than∗his/her own share, that is, θiP< θiM for i = S, L when Λ = 0. This is also
what Ihori and Yang (2009) point out in their setting of symmetric countries.
Meanwhile, the asymmetry of the countries denoted by Λ(= AL −AS > 0) in thismodel inﬂuences the choice of policymaker by the median voter in each country,
particularly in country S. The eﬀects of regional asymmetry are summarized in
the following propositions.
Proposition 1. Assume that the income distribution is right-skewed, that is,θiM ∈ [0, 1). The decisive voter in country L delegates the power to set the
tax rate to the poor. The larger the magnitude of asymmetry (Λ) is, thelower is the policymaker’s capital share, as compared to that of the citizen
at the median of the capital distribution in the country.
∗< θLM for all θiM ∈ [0, 1).
Proof. From (16), θLP

Proposition 2. Assume that the income distribution is right-skewed, that is,θiM ∈ [0, 1). The delegation in country S is characterzed as follows.
Delegation to the poor: When Λ < 4k̄(3 − 2θSM − θLM ), the capital shareof the policy-maker is lower than that of the citizen at the median of
the capital distribution in the country.
9Delegation to the median voter himself/herself: When Λ = 4k̄(3−2θSM −θLM ), the citizen at the median votes for himself/herself.
Delegation to the rich: When Λ > 4k̄(3 − 2θSM − θLM ), the capital shareof the policymaker is higher than that of the citizen at the median of
the capital distribution in the country.
Proof. See (17).
In country L, the gap between the capital share of the median citizen and thepolicymaker is obviously widened with an increase in Λ. On the other hand, incountry S, this gap becomes narrower; it can be narrowed to zero, in which casethe median citizen votes for himself/herself to set the tax rate. Furthermore,
the arithmetic magnitude of the values can be reversed. When the asymmetry
illustrated by Λ is signiﬁcantly large to satisfy Λ > 4k̄(3 − 2θSM − θLM ), themedian citizen as the decisive voter chooses a candidate whose capital share ishigher than his/her own share.
Figure 1 is a graphical representation of our main results under Assumption
1, in which θM ≡ θSM = θLM is assumed in order to facilitate visualization. In
the range of θiM ∈ [0, 1), the decisive voter in country L always delegates theright to set the tax rate to the poor; in country S, however, it may be delegatedto the rich if Λ/k̄ is large.
0

Skewdenss ofDistribution

Negative

Positive
Λ/k̄
12

Λ/k̄ = 12(θM − 1)

θM < θSPθM > θLPΛ/k̄ = 12(1 − θM )
θM > θSPθM > θLP

θM < θSPθM < θLP
2

1

θM

Figure 1. Equilibrium classiﬁcation
Note. θLM = θSM = θM is assumed for simple visualization. Λ/k̄ < 12 under
Assumption 1.

10

4.2

What lies behind the decisive voter’s choice of policymaker?

In this section, we provide an intuitive interpretation of the results. A key
concept for this interpretation is the terms of trade between the capital importerand exporter. Interestingly, although country S exports capital at the national
level, a resident who imports capital at the individual level exists; he/she canbe a decisive voter in the election under certain conditions.
To explain the intuition behind the variation from the case of two symmetriccountries presented by Ihori and Yang (2009), we start our explanation with
Λ = 0. Figure 2 illustrates the reaction and indiﬀerence curves when Λ = 0.
depicts the reaction curve of the median voter in country i, if the citizen
Rmediat the median picks himself/herself as the policymaker. When this policymakersets the tax rate in the second stage, the equilibrium tax rates are represented
med
by point EM , the intersection of RL
and RSmed . The utility of the medianvoter in country i at point EM is given by the indiﬀerence curve displayed asūmed. Recognizing that the median voter obtains the utility level representedimed
by ūiwhen he/she chooses the tax rate, he/she is aware that his/her utility
would increase if the authority to choose the tax rate was delegated to others.
To further explain the median voter’s incentive to delegate authority in Figure
2, we take the median voter’s choice in country L as an example. Note thatthe median voter of country L(S) gains higher utility as the indiﬀerence curve
moves upward (to the right). The median voter in country L understands thatgiven the median voter’s choice in country S, RSmed , he/she can get higher(and maximum) utility if he/she delegates the right to set the tax rate to theindividual who chooses point EL , where RSmed is tangential to ūmed
L . In Figure 2,pol
RL represents the reaction curve of the individual who is chosen as the policymaker in the ﬁrst-stage election. Considering the negative monotonicity of Ti inpolmedθij , the location of RL
and RLmeans that the median voter chooses a citizen,
whose capital share is lower than that of the median voter himself/herself, as apolicymaker.
By doing so, the median voter can avoid an excessively low tax rate that
could have been realized in the Prisoner’s-dilemma-like equilibrium from thetax competition at the second stage. As the median voter in country S acts inthe same manner as the median voter in country L, the sub-game perfect Nashequilibrium is represented by point EP , where the median voters can obtainhigher utility than at point EM . In other words, median voters take advantageof the structure of representative democracy-policymakers have to set a policy
ex post, or after election, taking the policy of the other country as given, whereas
voters can evaluate a policy ex ante, or before election. Hence, the median voter
11strategically delegates to others, in particular, to the poor, and does not selecthimself/herself as the policymaker.
pol
RL

TS

med
RL

RSpol

EP

ūmed
S
ES

EL

EM

45o

RSmed
ūmed
L

TL

0

Figure 2. Reaction curves and indiﬀerence curves when Λ = 0.

0

TL

Rmed
L

pol
RL

ūmed
SM
EL

RSmed
ūmed
LM

ES′

′
EM

RSpol

EP′

TS

Figure 3. Reaction curves and indiﬀerence curves when Λ > 12k̄(1 − θM ) andθSM = θLM ≡ θiM ∈ [0, 1).
From the above-mentioned ideas, the reason for the median voter in country
L to delegate to a citizen whose capital share is lower than in a symmetric
12setting is quite straightforward. For simplicity, and without loss of generality,
assume θiM = θjM = θM . In this case, country L(S) imports (exports) capital;∗k̄ − kL= −Λ/12 < 0 < k̄ − kS∗ = Λ/12. Under Assumption 1, the median voter
in capital-importing country L is a net capital importer as well; θM k̄ − kL =−12(1 − θM ) − Λ/k̄ < 0. The position of the median voter in country L asa net capital importer leads him/her to delegate the right to set the tax rate
to the individual who has less capital than he/she has. This is because, given
the decisions made in country S, a tax increase in country L will reduce theprice of capital (see (4)). This will reduce the cost of capital borrowing andbeneﬁt the median voter. From (13), the median voter recognizes that the poor
prefers a higher tax rate; thus, if the median voter delegates the right to set the
tax rate to the individual who has less capital than the median voter, he/she
beneﬁts from the higher tax rate, and thereby, the lower capital price. That is,
the median voter in country L delegates the right to set the tax rate to the poorso as to reduce the capital price, and thereby, the interest payment for capitalmedborrowing. This delegation is captured by two reaction curves, RL
and RpolLin Figure 3, where RSmed is the tangential to ūmed
at
E
.
L
LM
In contrast, the median voter in country S turns out to be either a net
capital importer or exporter. Notice that the following relation holds in theequilibrium.
Λ<<
12k̄(1 − θM ) ⇔ θSM k̄ kS∗ .
>
>

(18)

(18) reveals that, when Λ < 12k̄(1−θM ), the median voter in country S behaves
as if he/she were a net capital importer and has an incentive to reduce thecapital price; whereas country S, as a whole, exports capital in the asymmetricsetting. Thus, in the election, the median voter chooses a poor citizen, or acitizen who owns a lower share of capital than he/she does, as shown in Figure
2. Meanwhile, when Λ is larger so as to satisfy Λ > 12k̄(1 − θM ), the medianvoter picks a richer citizen than himself/herself. A key of this result is thatthe median voter himself/herself is a net capital exporter at a personal level.
Figure 3 shows the equilibrium when the regional asymmetries are signiﬁcant:Λ > 12k̄(1 − θM ), in which the U-shaped indiﬀerence curve of the medianvoter in Figure 2 is inverted; the utility level becomes higher as the indiﬀerencemed
curve moves left. Taking RL
as given, the median voter picks that citizen
as a policymaker, whose capital share is higher than the median voter’s own
share, so that the selected policymaker chooses a lower tax rate, leading to ES′ .
Strategic delegation made in the ﬁrst stage in the two countries results in theinferior outcome that is represented by point EP′ in Figure 3.
Overall, the distribution of capital plays a key role in determining whether
13the median voter delegates the right to set the tax rate to the rich or poor.
Whether a rich or poor candidate is elected as the policymaker depends on themagnitude of asymmetry between the countries.
So far, we have considered the case of θiM ∈ [0, 1) that ﬁts with the positively
skewed income distribution. In closing this section, we mention the other cases.
Although there is a low possibility of its appearance, the negatively skewed
distribution with θiM > 1 may result in the outcome that the rich are elected
as policymakers in both countries (see Figure 1). This can be interpreted in asimilar manner. When θiM is suﬃciently large in both countries, the medianvoter in country L, as well as in country S, is positioned as the net capital
exporter. This position gives him/her the incentive to delegate the right to set
the tax rate to the rich, because he/she beneﬁts from the higher capital income
when the rich choose a lower tax rate, because that results in a higher price ofcapital. Using (16) and (17), we can summarize the above argument as follows.
Proposition 3. Assume that the income distribution is left-skewed, 1 ≤ θiM .
The decisive voter in country S delegates the power to set the tax rate to
the rich. The larger the magnitude of asymmetry (Λ) is, the higher is thecapital share of the policymaker, as compared to that of the citizen at themedian of the capital distribution in the country.
Proposition 4. Assume that the income distribution is left-skewed, 1 ≤ θiM .
The delegation in country L is characterized as follows.
Delegation to the rich: When Λ < 4k̄(2θLM + θSM − 3), the capital shareof the policymaker is higher than that of the citizen at the median of
the capital distribution in the country.
Delegation to the median voter himself/herself: When Λ = 4k̄(2θLM +θSM − 3), the citizen at the median votes for himself/herself.
Delegation to the poor: When Λ > 4k̄(2θLM + θSM − 3), the capital shareof the policymaker is lower than that of the citizen at the median of
the capital distribution in the country.

5

Discussion: A shift from direct to representative democracy

Since the era of the ancient Greek city-state of Athens, democracy has been oneof the main collective decision-making systems and political regimes over thehistory of most of our societies. Particularly in the highly developed countries of14

the modern world, few countries apply any political regime other than democracy. At some point in its long history, the original regime of direct democracy
metamorphosed into representative democracy. Presently, in most cases, voting
is recognized as being applicable to the choice of policymakers, not to the direct
choice of policy.
Political scientists claim that representative democracy is superior to direct
democracy for many reasons— in direct democracy, it is diﬃcult to consolidate
opinions and resolutions, exchange views and arguments, clearly identify whois responsible if the country is misgoverned, and so on. In other words, direct
democracy costs too much to implement as a collective decision-making system.
That is why the shift was made.
In addition to this reasonable explanation, our results also suggest anotherreason for the regime shift from direct to representative democracy. Let us
explain it by adding an additional stage, namely, commitment to the form of
democracy, to our model. Thus, the stage of political regime choice is added tothe two-stage game we have been dealing with. The game is then composed ofthree stages. First, the citizens of each country vote for either keeping direct
democracy or replacing it with representative democracy. Second, if representative democracy is applied as the political regime of the country in the ﬁrst
stage, an election is held to decide the policymaker for the country. Finally, thetax rates of each country are determined. Again, to ﬁnd a sub-game perfectNash equilibrium, we solve this game backward.
For simplicity, we assume that the distribution of capital endowment ineach country is symmetric, θLM = θSM = θM . In the ﬁrst stage, a citizen
at the median of the distribution is a decisive voter as we saw in the previous
two-stage game. We denote the utility of the median voter of country i as
uiM [L : regime, S : regime]. For instance, uLM [L : dir, S : rep] expresses theutility of the median voter of country L when direct democracy in country L
and representative democracy is applied in country S.
The median voters of both countries choose either direct or representative
democracy, foreseeing the results of the second and third stages. Let us ﬁrst
consider the decision-making of the median voter in country L. As actions are
selected simultaneously in this stage, the median voter of country L chooses theregime, taking a regime of country S as given. In the case where the regime ofcountry S is direct democracy, the median voter in country L compares his/her
utilities and picks the larger one as7

7 See Appendix.

15

uLM [L : rep, S : dir] − uLM [L : dir, S : dir] =[8(1 − θM )k̄ + Λ]2
> 0.
320

On the other hand, in a case where the regime of country S is representative
democracy, he/she compares similarly asuLM [L : rep, S : rep] − uLM [L : dir, S : rep] =17[12(1 − θM )k̄ + Λ]2
> 0.
3600

Hence, shifting to representative democracy is the dominant strategy for the
median voter of country L.
In the same way as for country L, we can conﬁrm that shifting to representative democracy is also the dominant strategy for the median voter in countryS:uSM [L : dir, S : rep] − uSM [L : dir, S : dir]=uSM [L : rep, S : rep] − uSM [L : rep, S : dir]=[8(1 − θM )k̄ − Λ]2> 0,
320
17[12(1 − θM )k̄ − Λ]2
> 0.
3600

Remarkably, the asymmetry between the countries is not crucial for this result.
Even when we assume the symmetric case, or Λ = 0, we can readily ascertainthat these hold. This shows that there is a reason for representative democracy
to be institutionalized in the tax-competition framework.

6

Concluding remarks

This study explored asymmetric two-country tax competition under representative democracy with citizen candidates. Under the symmetric setting, Ihori
and Yang (2009) found that the citizen who has less capital than the mediancitizen of the capital distribution is elected as a policymaker. By incorporating
regional asymmetries in production technology, we show that the equilibrium
pattern derived by Ihori and Yang (2009) prevails if the regional asymmetries
are not signiﬁcant. Our extension further shows that if the regional asymmetries
are signiﬁcant, a citizen who is richer than the median of the capital distribution, or the decisive voter himself/herself can be elected as the policymaker to
set a tax policy for the country.
A problem with our result is that it hinges on the assumption that all citizens
are candidates and we can cast our votes for anyone in the society. However,
the reality is quite diﬀerent: whereas almost anyone who has a right to vote in16

a democratic regime is also eligible to be elected a policymaker, persons who
can actually be candidates in an election are limited for various reasons. In
order to further strengthen our model in this study, we need to endogenize theconditions that decide who can be a candidate in an election. A few technicalproblems also remain. Speciﬁcally, the results of this study obviously depend on
the assumption that all tax revenues are returned to the residents in a lump-sum
manner. This assumption is made to determine the incentives to manipulate
the terms of trade. More general formulations of preferences with public goods
direct that Ihori and Yang’s (2009) result holds. Nevertheless, in a rather general
analysis, the type of selected policymaker would depend on the magnitude ofregional asymmetries and the equilibrium in which the rich resident is elected
as a policymaker could emerge.

Appendix
In this appendix, we derive the utilities of median-voter citizens for each case below that are used in the comparison of utilities under diﬀerent election schemes.
As mentioned in Section 5, we assume that the distributions of capital in eachcountry are symmetric or θLM = θSM = θM .
Direct-democratized L vs. Direct-democratized S. When both countries areunder direct democracy, we obtain utilities of the median voters in equilibrium
as follows. Under direct democracy, a policy proposed by the median voter isapplied and implemented. In other words, the median voters of each country are
selected as policymakers through election and can set tax rates as they want.
This means that the ﬁrst stage, the voting-for-the-election stage, is practicallyomitted and that θLP = θLM and θSP = θSM . Hence, using (9) and (10), thecapital allocation in each country and rate of return to capital are respectively
given by kL = k̄ + (Λ/8), kS = k̄ − (Λ/8), and r = (Ω + 4k̄θM − 8k̄)/2.
Substituting these values into the utility functions of the median voters uiM =(Ai − ki )ki + r(θiM k̄ − ki ), we obtain uLM [L : dir, S : dir] and uSM [L : dir, S :dir].
Direct-democratized L vs. Rep.-democratized S. The next case is when country
L is under direct democracy and country S is under representative democracy.
As deﬁned above, direct democracy in country L means θLP = θLM . On theother hand, in country S under representative democracy, the election for policymaker is held; with (11), θSP = θLM /5 + (16k̄θSM − 8k̄ + Λ)/10k̄. Hence,from (9) and (10), the equilibrium values of allocation of capital in each coun-17

try and rate of return to capital are, respectively kL = (Λ − 2k̄θM + 12k̄)/10,
kS = (−Λ + 2k̄θM + 8k̄)/10, and r = (3AL + 2AS + 14k̄θM − 24k̄)/5. Substituting these values into the utility functions of the median voters, we obtainuLM [L : dir, S : rep] and uSM [L : dir, S : rep].
Rep.-democratized L vs. Direct-democratized S. In this case, country L is under
representative democracy and country S is under direct democracy. Likewise,
we have θLP = θSM /5 + (16k̄θLM − 8k̄ + Λ)/10k̄ and θSP = θSM . Again, with
(9) and (10), the equilibrium values of allocation of capital in each country andrate of return to capital are, respectively, kL = (Λ +2k̄θM + 8k̄)/10, kS = (−Λ−2k̄θM +12k̄)/10, and r = (2AL +3AS +14k̄θM −24k̄)/5. Substituting these values
into the utility functions of the median voters, we obtain uLM [L : rep, S : dir]and uSM [L : rep, S : dir].
Rep.-democratized L vs. Rep.-democratized S. Finally, we consider the case we
focused on in the main text, that is, both countries are under representative
democracy. With (16) and (17), the equilibrium values of allocation of capitalin each country and rate of return to capital are, respectively, kL = k̄ + (Λ/12),
kS = k̄ − (Λ/12), and r = (Ω + 8k̄θM − 12k̄)/2. Substituting these values into
the utility functions of the median voters, we obtain uLM [L : rep, S : rep] anduSM [L : rep, S : rep].

References[1] Besley, T., Coate, S., (1997), An economic model of representative democracy, Quarterly Journal of Economics, vol.112, pp. 85-114.
[2] Besley, T., Coate, S., (2003), Centralized versus decentralized provision of
local public goods: A political economy approach, Journal of Public Economics, vol.87. pp. 2611-2637.
[3] Bond, E.W., Samuelson, L., (1989), Strategic behaviour and the rules forinternational taxation of capital, Economic Journal, vol.99, pp. 1099-1111.
[4] Borck, R., (2003), Tax competition and the choice of tax structure in a
majority voting model, Journal of Urban Economics, vol.54, pp. 173-180.
[5] Brückner, M., (2001), Strategic delegation and international capital taxation, ZEI Working Papers no. B22-2001, University of Bonn.
[6] Bucovetsky, S., (1991), Asymmetric tax competition, Journal of Urban Economics, vol.30, pp. 167-181.
18

[7] DePater, J., Myers, G.M., (1994), Strategic capital tax competition: A pecuniary externality and a corrective device, Journal of Urban Economics,
vol.36, pp. 66-78.
[8] Eggert, W., (2000), International repercussions of direct taxes,
zArchiv, vol.57, pp. 106-126.

Finan-[9] Fuest, C., Huber, B., (2001), Tax competition and tax coordination in amedian voter model, Public Choice, vol.107, pp. 97-113.
[10] Gordon, R., (1992), Can capital income taxes survive in open economies?,
Journal of Finance, vol.47, pp. 1159-1980.
[11] Grazzini, L., van Ypersele, T., (2003), Fiscal coordination and politicalcompetition, Journal of Public Economic Theory, vol.5, pp. 305-325.
[12] Ihori, T., Yang, C.C., (2009), Interregional tax competition and intraregional political competition: The optimal provision of public goods under
representative democracy, Journal of Urban Economics, vol.66, pp. 210-217.
[13] Itaya, J., Okamura, M., Yamaguchi, C., (2008), Are regional asymmetries
detrimental to tax coordination in a repeated game setting?, Journal of
Public Economics, vol.92, pp. 2403-2411.
[14] Kempf, H. and Rota-Graziosi, G. (2010). Endogenizing leadership in tax
competition, Journal of Public Economics, vol.94, pp. 768-776.
[15] Lockwood, B., Makris, M., (2006), Tax incidence, majority voting andcapital market integration, Journal of Public Economics, vol.90, pp. 10071025.
[16] Ogawa, H., (2013), Further analysis on leadership in tax competition: The
role of capital ownership, International Tax and Public Finance, vol.20, pp.
474-484.
[17] Osborne, M.J., Slivinski, A., (1996), A model of political competition withcitizen candidates, Quarterly Journal of Economics, vol.111, pp. 65-96.
[18] Pal, R., Sharma, A., (2011), Political competition and leadership in tax
competition, Mumbai Working Papers 2011-024, Indira Gandhi Institute ofDevelopment Research.
[19] Peralta, S., van Ypersele, T., (2005), Factor endowments and welfare levels in an asymmetric tax competition game, Journal of Urban Economics,
vol.57, pp. 258-274.
19

[20] Persson, T., Tabellini, G., (1992), The politics of 1992: Fiscal policy andEuropean integration, Review of Economic Studies, vol. 59, pp. 689-701.
[21] Persson, T., Tabellini, G., (1994), Representative democracy and capitaltaxation, Journal of Public Economics, vol. 55, pp. 53-70.
[22] Rodrik, D. (2012), The globalization paradox: democracy and the future of
the world economy, W.W.Norton & Company.
[23] Wilson, J.D., (1986), A theory of interregional tax competition, Journal of
Urban Economics, vol.19, pp. 296-315.
[24] Zodrow, G.R., Mieszkowski, P.M., (1986), Pigou, Tiebout, property taxation, and the under-provision of public goods, Journal of Urban Economics,
vol.19, pp. 356-370.

20