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Partial tax harmonization through
infrastructure coordination
Patrícia Sanz Córdoba
Bernd Theilen

Document de treball n.7- 2016

DEPARTAMENT D’ECONOMIA – CREIP
Facultat d’Economia i Empresa

UNIVERSITAT
ROVIRA I VIRGILI
DEPARTAMENT D’ECONOMIA 

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DEPARTAMENT D’ECONOMIA – CREIP
Facultat d’Economia i Empresa

Partial tax harmonization through
infrastructure coordination
Patricia sanz-córdoba, Bernd Theileny
April 2016

Abstract
In this article we analyze the role that infrastructure coordination plays to in
achieving partial tax harmonization in a coalition of asymmetric jurisdictions. We
…nd that infrastructure coordination with di¤erent investment levels can facilitate
partial tax harmonization between asymmetric jurisdictions when asymmetries are
not too large. Furthermore, agreeing on a common investment level can be even
more e¤ective in facilitating partial tax harmonization between asymmetric jurisdictions. Our results explain the harmonization of corporate tax rates observed in
the EU between 1995 and 2006 where there was simultaneous convergence of public
infrastructure investments facilitated via EU structural funds.
Keywords: Partial Tax Harmonization; Infrastructure Coordination
JEL Classi…cation Numbers: F15, F38, H20, H87

1

Introduction

Since the 1980s processes of economic integration have increased the international mobility of capital to an extent never observed before. This has led governments to engage
in …scal competition in order to attract more capital and to maintain investment levels.
As a result, we have observed an ongoing reduction of tax rates on corporate income to
ine¢ ciently low levels (Zodrow and Mieszkowski, 1986; Wilson, 1986; Bucovetsky and
Wilson, 1991). A major concern that this process has raised in developed countries is
that tax competition has caused a transfer of the tax burden from capital towards labor.
For example, the European Commission stated in 1996 that the implicit average tax on
capital had decreased from 44% to 35% at the expense of an increase in the implicit tax on
labor from 34% to 40.5% in European Union (EU) member countries from 1980 to 1994
Corresponding author. Departament d’
Economia and CREIP, Universitat Rovira i Virgili, Avinguda de la Universitat 1, 43204 Reus, Spain. Tel.: +34977759884; fax: +34977759810; email: patricia.sanz@urv.cat.
y
Departament d’
Economia and CREIP, Universitat Rovira i Virgili, Avinguda de la Universitat 1,
43204 Reus, Spain. Tel.: +34977759813; fax: +34977759810; email: bernd.theilen@urv.cat.

1

(European Commission, 1996). As a response to ine¢ ciently low capital tax competition
several authors have advocated the coordination of tax rates (Bucovetsky, 1991; Kanbur
and Keen, 1993; Fuest and Huber, 2001; Devereux and Fuest, 2010; Keen and Konrad,
2012). Although it is generally recognized that the global harmonization of capital taxes
is almost impossible to achieve, recent research has nevertheless paid increasing attention to the conditions that would allow for partial tax harmonization between a coalition
of countries (Burbidge et al, 1997; Konrad and Schjelderup, 1999; Beaudry et al, 2000;
Brøchner et al, 2007; Conconi et al, 2008; Bucovetsky, 2009; Bettendorf et al, 2010; Vrijburg and de Mooij, 2010; Eichner and Pething, 2013).1 This is especially the case in the
EU where di¤erent proposals for the coordination of capital taxation have been made.2
Indeed, in Figure 1 we observe that corporate taxation in the EU, while following the
global tendency of declining tax rates, experienced a convergence of tax rates during the
period 1995 to 2006 between high and middle income countries to around 30%. After the
2003 enlargement of the EU, we have yet to observe a further convergence of corporate
taxation between low income countries on the one hand and high and middle income countries on the other hand. The results in the literature hardly explain this harmonization
of capital taxation during the 1995-2006 period because the di¤erent productivity levels
between EU countries render (partial) tax harmonization more di¢ cult (Keen and Konrad, 2012). Interestingly, if we take a look at the per capita investment in infrastructure
in EU member countries in the same period, as displayed in Figure 2, we observe that the
period of convergence of tax rates between high and middle income countries is accompanied by a more intensive increase in the middle income countries which surpassed per
capita infrastructure investment in high income countries in 2001. It should be noticed
that this convergence of infrastructure investments is not accidental but is directed by
the EU as a major part of public infrastructure investments …nanced via EU structural
funds that amounted to a total of 100.5 billion euro during the period 2000-2006. Thus,
in Figure 3 we observe that in middle and low income countries a substantial number of
total infrastructure investments were …nanced by the EU. For example, in Greece more
than 70% of infrastructure investments were …nanced by the EU.
In this article we analyze the role that infrastructure coordination has played in achieving …scal harmonization between a coalition of asymmetric countries. For this purpose, we
use the tax competition model developed by Zodrow and Mieszkowski (1986) and Wilson
(1986) in which, as in Konrad and Schjelderup (1999), we allow a subset of jurisdictions
to form a tax coalition. We modify the framework of Konrad and Schjelderup (1999)
by allowing for asymmetries in productivity levels between jurisdictions and by assuming that governments make infrastructure investments that enhance the productivity of
private …rms. In our three jurisdiction model, jurisdictions di¤er in their productivity
levels. Jurisdictions 1 and 2 decide whether to form a coalition in which commitments
1

Keuschnigg et al. (2014) de…ne tax coordination and harmonization in the EU as follows: “tax coordination refers to a cooperative tax setting, where countries or a group of them build on domestic tax
systems to render them compatible with the aims of the Union as formulated the Treaty on the European
Union. Consequently, countries deliberately give up parts of their autonomy in tax matters” More.
over, “harmonization is viewed as tighter coordination, leading to almost identical or at least similar tax
systems, tax bases and tax rates within a Union”
.
2
See Dankó (2012) for further information about the proposals for corporate tax harmonization.

2

are credible. We analyze a three stage game. In stage 1, jurisdictions 1 and 2 decide
whether to coordinate tax rates and infrastructure investments. Once a decision is taken,
the levels of infrastructure investments are decided in stage 2. Finally, in stage 3, for a
given level of infrastructure the tax rates are chosen. All decisions at each stage are taken
simultaneously by all jurisdictions (and the tax coalition). Once the stage 2 subgames are
solved, our analysis leads to the comparison of the following cases: 1) No coordination,
2) partial tax harmonization without infrastructure coordination; 3) partial tax harmonization with infrastructure coordination where we distinguish between: a) infrastructure
coordination with di¤erent investment levels, and b) infrastructure coordination with a
common investment level. The main …ndings of our analysis are that, …rst, partial tax harmonization is welfare enhancing if jurisdictions are not too di¤erent in their productivity
levels. Second, infrastructure coordination with di¤erent investment levels can facilitate
partial tax harmonization between asymmetric jurisdictions. Third, while infrastructure
coordination with a common investment level uses fewer instruments than in the former
case, it can be even more e¤ective in facilitating partial tax harmonization between asymmetric jurisdictions. We believe that especially this last result can give an explanation
for the convergence of corporate tax rates observed in the EU in the decade before the
economic crisis in 2008.
Our analysis is related to several studies. The general model of tax competition was
developed by Zodrow and Mieszkowski (1986) and Wilson (1986) and has shown that the
Nash equilibrium capital tax rates chosen by each jurisdiction are not socially optimal.3
Asymmetries between jurisdictions that allowed them to di¤er in population size were
…rst introduced by Bucovetsky (1991). He …nds that these kinds of asymmetries exacerbate ine¢ ciencies in capital taxation. As simultaneous tax coordination by all countries
is unlikely to be established, the literature has focused on tax coordination of a subset of
countries that might be able to create mechanisms or institutions that allow a credible
commitment to maintaining jointly agreed tax rates. Konrad and Schjelderup (1999) have
shown that such partial tax coordination can increase the welfare of the participating jurisdictions. This depends on the response of jurisdictions from outside the tax coalition and
the relative size of the tax union. Thus, a necessary condition for a welfare enhancing effect is that tax rates are strategic complements and that jurisdictions are not too di¤erent.
Brøchner et al. (2007) study partial tax coordination in the EU, using a general equilibrium model. Their conclusions suggest that corporate tax coordination would generate
moderate welfare growth and that all schemes for coordination leave some EU member
states as winners and others as losers, thus meaning that the elaboration of compensation
mechanisms is required in order to maintain the coordination agreement. Conconi et al.
(2008) analyze the three alternative scenarios of tax coordination (non-coordination, partial coordination, and harmonization) in a speci…c context of two distortions on capital
taxation: tax competition (downward pressures) and time-consistent con…scatory taxation (upward pressures when governments have incentives to levy corporate taxes that
are too high once capital is installed). They …nd that partial tax coordination bene…ts all
jurisdictions if capital is su¢ ciently mobile, so it is more desirable and sustainable in such
a situation when compared to harmonization or non-cooperative equilibrium. Vrijburg
3

See Keen and Konrad (2012) for an overview on the literature regarding this matter.

3

and de Mooij (2010) generalize the analysis of Konrad and Schjelderup (1999), comparing
welfare levels and equilibrium tax rates in the three alternative scenarios of tax coordination and asymmetric jurisdictions. They analyze the case in which the coalition acts
as a leader so it foresees the strategic tax reaction by the last jurisdiction when deciding
its own tax policy. Their analysis determines that the improvement of welfare in the
coalition formation depends on the strategic complementarity of tax rates which is not
fully guaranteed. Under partial tax coordination, if the union acts as leader, the coalition tends to increase tax rates more if tax rates are strategic complements. Coalitions
between large countries are more likely than coalitions between small countries due to a
larger common gain from internalized tax spillovers. Additionally, small jurisdictions are
better o¤ under no-coordination than under harmonization, so they would never agree to
coordinate their taxes (although they prefer the partial tax coordination agreement over
harmonization). A model in which governments do not choose only capital tax rates but
also infrastructure investment levels has been developed by Keen and Marchand (1997).
They show that simultaneous capital and infrastructure competition not only yields ine¢ ciently low tax rates but also ine¢ ciently high infrastructure investments. Becker and
Fuest (2010) analyze the e¤ects of infrastructure coordination using a model in which
countries compete for the location of pro…table …rms. They …nd that the coordination of
infrastructure investments between two countries can mitigate tax competition between
these countries. While our model is based on the capital tax competition literature as
opposed to the literature on interjurisdictional competition for pro…table …rms, the main
di¤erences between their and our model is that we focus on tax harmonization and allow for asymmetries between countries and, most importantly, policy responses of third
countries. This last aspect is especially relevant if the results are to be used to analyze
tax harmonization policies in the EU which, due to market globalization and increased
international capital mobility, depend more and more on tax policies of countries outside
the EU. Finally, Han (2013) analyzes how infrastructure investments a¤ect partial tax
harmonization between symmetric jurisdictions and …nds it can harm both tax coalition
members and nonmembers, which is in contrast to the classical result that partial tax
harmonization is Pareto improving in such a case. The main di¤erence from our paper
is that infrastructure investments in his analysis are not subject to coordination between
jurisdictions as he focuses exclusively on the coordination of tax rates.
The rest of the paper is organized as follows. Section 2 sets up the model. Section
3 focuses on the benchmarks without infrastructure coordination. Section 4 and Section
5 include the main results in which infrastructure coordination with di¤erent investment
levels and with a common investment level is analyzed, respectively. Finally, Section 6
contains the conclusion. The proofs are in the Appendix.

2

The model

Consider the tax competition model developed by Zodrow and Mieszkowski (1986) and
Wilson (1986) in which, as in Konrad and Schjelderup (1999), we allow a subset of jurisdictions to form a tax coalition. In this article their framework is modi…ed by allowing
for asymmetries in productivity between jurisdictions and by assuming that governments
4

provide local public goods that enhance the productivity of private …rms. To be precise,
consider N = 3 jurisdictions, indexed by i = 1; 2; 3, each inhabited by an identical number of immobile residents with mass one who each supply one unit of labor. The total
amount of capital is …xed and normalized to 1. The initial capital stock per worker in
each jurisdiction is assumed to be symmetric, i.e., k i = 1 . Output is produced using
3
capital and labor and the production function is written in intensive form, fi (ki ), with
the standard assumptions of fi0 > 0, fi00 < 0, where ki denotes the capital per worker
employed in jurisdiction i. Following the literature (Hindriks et al., 2008; Hauptmeier,
2012; Han, 2013; Eichner and Pething, 2013; among others), we assume a linear quadratic
production function
fi (ki ) = ( +

i

2
ki , i = 1; 2; 3;

+ gi ) ki

(1)

where gi is the level of infrastructure investment provided by the government in jurisdic2
tion i at cost ci (gi ) = gi =2 and > 0. Eq. (1) implies that jurisdictions even with equal
infrastructure investments di¤er in the level of their productivity levels. Without loss of
generality we assume 1 = 0. Furthermore, to guarantee nonnegative equilibrium values
19
we restrict the analysis to ( 2 ; 3 ) R = 2 0; 1 2 18 < 3 < 19 28 2 .
2
9
5
Countries compete in choosing a unit per capital tax rate ti to attract mobile capital
from the rest of the world. Capital is mobile between jurisdictions such that the net
return to capital, , is determined by the following arbitrage condition:
= fi0 (ki )

for i = 1; 2; 3.

ti

P
The arbitrage condition together with the market clearing condition ( ki = 1 ) implies
that the amount of capital invested in jurisdiction i is given by:
ki =

1 (2
+
3

i

j

h)

+ (2gi

gj
6

gh )

(2ti

tj

th )

,

(2)

where i; j; h = 1; 2; 3; j 6= i; h 6= i; j.4
The tax rates in jurisdiction i are chosen by governments to maximize the welfare Wi
of its residents:5
Wi = fi (ki )

fi0 (ki ) ki + ti ki

2
2
gi =2 = ki + ti ki

2
gi =2,

(3)

where fi (ki ) fi0 (ki ) ki is labor income, and ti ki are tax revenues used to …nance public
goods.
We assume that jurisdictions 1 and 2 will be able to credibly commit to a common tax
rate and, therefore, are able to form a tax coalition. If it is bene…cial for both jurisdictions
to form a tax union, our assumptions imply that jurisdiction 2 is the more productive
jurisdiction in the tax coalition, while the jurisdiction outside the tax coalition, jurisdiction
3, can be either more productive than both members of the tax coalition ( 3
2 ), less
productive than both jurisdictions ( 3 < 0), or more productive than jurisdiction 1 but less
4

When not stated otherwise, we assume these conditions for all of our further expressions.
For example, this corresponds to the assumption that tax rates are determined by the median voter
and that the median voter has no capital endowment (see Borck, 2003).
5

5

productive than jurisdiction 2 (0
3 < 2 ). The timing of the game is as follows. First,
in stage 1, jurisdictions 1 and 2 decide whether to coordinate tax rates and infrastructure
investments. Once a decision is taken, infrastructure investments are decided in stage 2.
Finally, in stage 3, for a given level of infrastructure, tax rates are chosen. All decisions
at each stage are taken simultaneously by all jurisdictions (and the tax coalition).

3

No infrastructure coordination

3.1

No tax harmonization

First, consider the noncooperative game in which each jurisdiction chooses its infrastructure investment and capital tax rate separately. In stage 3, the rate ti that maximizes
welfare in Eq. (3) is:6
ti =

1 (2
+
4

i

j

h)

+ (2gi
8

gj

gh ) + tj + th

.

(4)

From Eq. (4) we see that tax rates are strategic complements. Furthermore, the optimal
tax rate is increasing in the jurisdiction’ infrastructure investment and decreasing in the
s
infrastructure investments of other jurisdictions. The stage 3 Nash-equilibrium tax rates
are given by:
gj gh
1 2i
j
h + 2gi
(5)
ti = +
3
9
where the condition @ti =@tj < 1 in Eq. (4) guarantees the stability of the equilibrium.
In stage 2, jurisdiction i chooses the optimal level of infrastructure gi that maximizes
welfare, which after substitution of the expressions in Eqs. (5) and (2) into (3) writes as:
Wi = 2

1 2
+
3

i

h

j

+ 2gi
9

gj

gh

gj

2

2
gi
.
2

gh )

(6)

The best-response function of jurisdiction i is:7
gi =

8
(3 + 2
65

i

j

h

(7)

which means that infrastructure investments are strategic substitutes. The stage 2 Nashequilibrium infrastructure investments are given by:
N
gi =

8
8
+
(2
27 57

i

j

h) .

(8)

Substituting Eq. (8) into Eq. (5) yields the equilibrium tax rates:
tN =
i
6
7

3
1
+
(2
3 19

i

j

h) .

Notice that from substitution of Eq.(2) in Eq.(3) we have that Wi is concave in ti .
2
W
Concavity of Wi is given as @@g2 i = 65 < 0.
81
i

6

(9)

N
Using this expression we obtain for infrastructure investments gi = 8 tN such that the
9 i
welfare in jurisdiction i is:
130 N 2
t
.
(10)
WiN =
81 i
Regarding the tax rates and infrastructure investments in the di¤erent jurisdictions
we obtain from Eqs. (8) and (9) that infrastructure investments and tax rates are higher
N
N
in the more productive jurisdiction (i.e., gi > gj , tN > tN i¤ i > j ). From the
j
i
literature we know that the Nash equilibrium outcome yields ine¢ ciently low tax rates
and an underprovision of public goods. Furthermore, when jurisdictions can choose their
infrastructure investments freely, in the Nash equilibrium, infrastructure investments are
too high (Keen and Marchand, 1997). We state this as a …rst result:

Lemma 1 Under no coordination, in all jurisdictions, the Nash equilibrium tax rates
and the provision of public goods are ine¢ ciently low and infrastructure investments are
ine¢ ciently high.

3.2

Partial tax harmonization

Now, following Konrad and Schjelderup (1999), consider that jurisdictions 1 and 2 form
a coalition subgroup which jointly maximizes the welfare of this group (i.e., W1 + W2 )
to choose a common tax rate, tc , on which both jurisdictions agree publicly and can
credibly commit. Jurisdiction 3, simultaneously, determines its tax rate t3 . The level of
infrastructure in stage 2 is decided separately by all jurisdictions. The stage 3 equilibrium
tax rates are:
2 3 + g1 + g2 2g3
1+ 2
tc = 1 +
,
(11)
6
1
2 3 + g1 + g2 2g3
1+ 2
t3 =
.
(12)
2
12
In stage 2, as in the previous case, the three jurisdictions choose their infrastructure
noncooperatively. The equilibrium infrastructure investments are given by:
43
4
23
23
T
+
(13)
gi =
i
j
3 , i; j = 1; 2; i 6= j,
45 105
21
105
14
8
8
16
T
(14)
g3 =
1
2+
3.
45 105
105
105
Substituting Eqs. (13) and (14) into Eqs. (11) and (12) yields the equilibrium tax rates:
16
8
tT =
+
( 1 + 2 2 3) ,
(15)
c
15 35
7
4
( 1 + 2 2 3) .
(16)
tT =
3
15 35
Using these expressions and noting that 1 = 0, equilibrium values of infrastructure can
3
3
T
T
T
be written as g1 = 23 tT 10 2 , g2 = 23 tT + 10 2 , and g3 = 2 tT . Social welfare levels are:
48 c
48 c
3 3
!
!
!2
i
i
i
5 T ( 1) 2
1 T ( 1) 2
1 23 T ( 1) 3
WiT =
tc +
tc +
t +
(
2
2
2 , i = 1; 2, 17)
4
5
4
5
2 48 c
10
T
W3 =

16 T
t
9 3

2

(18)

:
7

Jurisdictions 1 and 2 will choose a common tax rate when both jurisdictions obtain a
higher welfare, i.e., when WiT > WiN for i = 1; 2. The following result shows when this is
the case.
Lemma 2 For given 3 , 9( 2 ; 3 ) 2 R partial tax harmonization takes place when the
jurisdictions in the tax coalition are not too di¤erent, i.e., when 2 is small. The welfare
gains from partial tax harmonization for jurisdiction 2 are larger than for jurisdiction 1.
The result obtained in Lemma 2 allows R to be separated into two areas which are
displayed in Figure 4A. Partial tax harmonization is bene…cial for jurisdictions 1 and 2
if they are not too di¤erent in their e¢ ciency levels (i.e., in Area T ). If jurisdiction 2
is much more e¢ cient than jurisdiction 1, partial tax harmonization is not bene…cial for
jurisdiction 1. This is even more the case when the jurisdiction outside the tax coalition
is more productive (see Area N ). Regarding the e¤ect of partial tax harmonization, as
expected, we …nd that the jurisdictions that form part of the tax coalition increase their
tax rates (tT > tN for i = 1; 2), while jurisdiction 3 increases (decreases) its tax rate
i
c
when its productivity is low (high).8 Accordingly, in Area T , while jurisdictions 1 and
2 gain from tax harmonization, the jurisdiction outside the tax coalition obtains higher
(lower) welfare when its productivity is low (high).9 Finally, while jurisdictions 1 and 2
increase their infrastructure investments after tax harmonization, jurisdiction 3 increases
(decreases) its infrastructure investments when its productivity is low (high).10 In light
of the result in Lemma 1, this implies that while partial tax harmonization allows the
ine¢ ciencies in tax rates to be reduced it increases the ine¢ ciencies in infrastructure
investments which are now even higher than under no coordination.

4

Infrastructure coordination

4.1

No tax harmonization

As shown in Lemma 1, all jurisdictions would bene…t from a joint reduction of infrastructure investments. To see if this will also be the case when a subgroup of them coordinate
their infrastructure investments, consider that jurisdictions 1 and 2 coordinate their infrastructure investments in stage two by choosing g1 and g2 to maximize joint welfare.
Jurisdiction 3, simultaneously, determines its own level of infrastructure. In stage 3, …rst,
we consider that all jurisdictions choose their capital tax rate separately. Thus, the stage
3 Nash equilibrium tax rates are given by Eqs. (5). In stage 2, joint welfare maximization
of jurisdictions 1 and 2 yields the following Nash equilibrium values:
76
4
+
(33 i
549 305
184
8
=
( 1+
549 61

I
gi =
I
g3

28
2

j

5 3 ) , i; j = 1; 2; i 6= j,

(19)

2 3) .

To be precise, we have that tT > tN for 3 < 1 2 + 133 , and tT < tN for 3 > 1
3
3
3
3
2
87
2
T
N
However, notice that the region in < where W3 < W3 is very small ( 3 >
T
N
example, W3 < W3 when 1 = 2 = 0, and 3 = 2:1.
1
10
T
N
T
N
We have g3 > g3 for 3 < 2 2 + 0:1155, and g3 < g3 for 3 > 1 2 + 0:1155.
2
8

9

8

(20)
133
2 + 87 .
1
2 2 + 2:0980).

For

Substituting Eqs. (19) and (20) into Eqs. (5) yields the equilibrium tax rates:
19
1
+
(114
61 305
9
23
( 1+
=
61 61

tI =
i

i

69

tI
3

2

2 3) .

45 3 ) , i; j = 1; 2; i 6= j,

j

(21)
(22)

Again, using these expressions and noting that 1 = 0, equilibrium values of infrastructure
4
4
I
I
I
can be written as g1 = 4 tI 15 2 , g2 = 4 tI + 15 2 , and g3 = 8 tI . Social welfare levels are:
9 1
9 2
9 3
WiI

= 2

I
W3 =

1
2

2
tI
1

130 I
t
81 3

2

4
( 1)
15

4 I
t
9 1

2

i

2

, i = 1; 2

(23)

.

(24)

Jurisdictions 1 and 2 will coordinate their infrastructure investments when both jurisdictions obtain a higher welfare, i.e., when WiI > WiN for i = 1; 2.
Lemma 3 For given 3 , 9( 2 ; 3 ) 2 R where partial infrastructure coordination takes
place. This is the case when the jurisdictions in the tax coalition are not too di¤erent,
i.e., when 2 is small. The welfare gains from partial infrastructure coordination for
jurisdiction 2 are larger than for jurisdiction 1.
From Lemma 3 we see that partial infrastructure coordination will take place when
jurisdictions 1 and 2 are su¢ ciently symmetric (Area I in Figure 4B), while in case of large
asymmetries there will be no infrastructure coordination (Area N ). The consequences
of a partial coordination of infrastructure investments are a reduction in infrastructure
investments in jurisdictions 1 and 2 while investments in jurisdiction 3 increase.11 Capital
tax rates in jurisdictions 1 and 2 decrease after infrastructure coordination in order to
compensate the loss of attractiveness of their jurisdictions because of lower infrastructure
investments. Jurisdiction 3 increases its capital tax rate.12

4.2

Partial tax harmonization

Now, consider that jurisdictions 1 and 2 form a coalition subgroup which chooses both,
a common capital tax rate tc and the level of infrastructure investments g1 and g2 that
maximize the joint welfare of this group. Jurisdiction 3, determines its own level of
infrastructure and capital tax rate. The stage 3 equilibrium tax rates are the same as in
the partial tax coordination case and, thus, are given by Eqs. (11) and (12). In stage
2, joint welfare maximization of jurisdictions 1 and 2 yields the following equilibrium
infrastructure investments:13
I
I
N
Notice that gi gi = 0:1579 + 0:1521 i 0:2269 j + 0:0748 3 < 0 for W1 N ( 2 ; 3 ) > 0, i = 1; 2,
32
I
N
and g3 g3 = 31 293 (9 2 18 3 + 38) > 0.
4
12
We have: tI
tN = 17385 (45 3 + 252 i 297 j 95) < 0, i = 1; 2, and: tI
tN =
3
3
i
i
4
18 3 + 38) > 0.
3477 (9 2
2
@ 2 (W1 +W2 ) @ 2 (W1 +W2 )
103
13
Notice that su¢ ciency is guaranteed as @ (W1 +W2 ) =
144 < 0 and
@g 2
@g 2
@g 2
11

@ 2 (W1 +W2 )
@g1 @g2

1

2

=

67
144

> 0.

9

1

2

35
32 i 27 j 5 3
+
, i; j = 1; 2; i 6= j,
(25)
177
59
4 ( 1 + 2 2 3)
62
T
.
(26)
g3 I =
177
59
Substituting Eqs. (25) and (26) into Eqs. (11) and (12) yields the equilibrium tax rates:
T
gi I =

56 12
+
( 1 + 2 2 3) ,
(27)
59 59
31
6
tT I =
( 1 + 2 2 3) .
(28)
3
59 59
Under the assumption that 1 = 0 equilibrium values of infrastructure can be written as
5
1
2
5
T
T
T
g1 I = 24 tT I 1 2 , g2 I = 24 tT I + 2 2 , and g3 I = 3 tT I such that social welfare levels in the
c
c
3
2
di¤erent jurisdictions are:
tT I =
c

WiT I

=

5 T I ( 1)i
t +
4 c
2

2

!

1 T I ( 1)i
t +
4 c
2

2

!

1
2

5 T I ( 1)i
t +
24 c
2

2

!2

, i = 1; 2, 29)
(

16 T I 2
t
.
(30)
9 3
The results in Lemmas 2 and 3 have shown that jurisdictions 1 and 2 gain from both tax
harmonization and infrastructure coordination when asymmetries are not too large. This
leads us to expect that partial tax harmonization is easier to achieve when jurisdictions in
the tax coalition coordinate their infrastructure investments. The following result states
this formally.
T
W3 I =

Proposition 1 Infrastructure coordination between asymmetric jurisdictions that form a
tax coalition can facilitate (hinder) partial tax harmonization when the productivity level
of the jurisdiction outside the coalition is low (large).
From Lemma 3 we know that both jurisdictions gain from infrastructure coordination
when their productivity levels are not too di¤erent. Comparing cases A and C in Figure 4,
we observe that these additional gains enlarge the area in which partial tax harmonization
is welfare enhancing for both jurisdictions (area T I compared to area T ). Therefore, we
have that infrastructure coordination allows partial tax harmonization agreements to be
reached between asymmetric jurisdictions when this would not be possible without the
coordination of infrastructure investments. A comparison of tax rates and infrastructure
investments under no coordination and partial tax harmonization with infrastructure
coordination shows that the jurisdictions that form the tax coalition increase tax rates
and decrease infrastructure investments when jurisdiction 3’ productivity is not too high.
s
This means that both kinds of ine¢ ciency (too low tax rates and too high infrastructure
investments) are reduced inside the tax coalition in this case. When jurisdiction 3’
s
productivity is large, the only di¤erence is that jurisdiction 2 increases its infrastructure
investments instead of decreasing them.14 Regarding the jurisdiction outside the tax
1
From Eqs. (9) and (27): tT I
tN = 3363 (2071 + 1215 2 837 3 ) > 0 for all ( 2 ; 3 ) 2 R and
c
1
1
N
T
N
t2 = 3363 (2071 378 2 837 3 ) > 0 for all ( 2 ; 3 ) 2 R. From Eqs (8) and (25) we have: g1 I g1 =
1
1
TI
N
1683 3 ) < 0 for all ( 2 ; 3 ) 2 R and g2
g2 = 30 267 (2983 7920 2 1683 3 ).
30 267 (2983 + 9603 2
14

tT I
c

10

coalition we …nd that its behavior crucially depends on its productivity level. When
jurisdiction 3’ productivity is low (high), it increases (decreases) capital tax rates and
s
infrastructure investments.15

5
5.1

Infrastructure coordination through common investment levels
No tax harmonization

The former analysis has shown that asymmetries between jurisdictions are an obstacle
to achieving capital tax harmonization or the coordination of infrastructure investments.
Therefore, as an alternative to the type of coordination analyzed before, consider that
jurisdictions 1 and 2 decide to reduce asymmetries between jurisdictions by agreeing
on a common level of investments, gc . This will allow the di¤erence in investments to
be reduced and, consequently, should facilitate tax coordination. Formally, in stage 2,
jurisdictions 1 and 2 choose the common level of investments gc to maximize joint welfare.
Simultaneously, jurisdiction 3 determines its own level of infrastructure. In stage 3, all
jurisdictions choose their capital tax rate separately. Thus, the stage 3 Nash equilibrium
tax rates are given by Eq. (5) and welfare levels by Eq. (6). In stage 2, joint welfare
maximization of jurisdictions 1 and 2, and welfare maximization of jurisdiction 3 yields
the following Nash equilibrium values:
2
61
16
=
61

IC
gc
=

1

IC
g3

3

+

2
61
8
61

4
61
8
61

2

2

76
,
549
184
.
1+
549

3

(31)

+

(32)

Substituting Eqs. (31) and (32) into Eq. (5) yields the equilibrium tax rates:
19
1
+
(44 i
61 183
23
9
=
( 1+
61 61

tIC =
i
tIC
3
Noting that
2
= 4 tIC
27 2
9 2

1

17
2

j

27 3 ) , i = 1; 2

(33)

2 3) .

(34)

IC
= 0, equilibrium values of infrastructure can be written as gc = 4 tIC +
9 1
8 IC
IC
and g3 = 9 t3 . Social welfare levels are:

2
,
27 2

WiIC = 2
IC
W3
=

1
2

2
tIC
2

130 IC
t
81 3

2

4 IC
t
9 2

( 1)i 2
27

2

!2

, i = 1; 2

(35)

.

(36)

Lemma 4 For given 3 , 9( 2 ; 3 ) 2 R where partial infrastructure coordination with common investment levels takes place. This is the case when the jurisdictions in the tax
15

This can be observed immediately from Eqs. (9) and (28) as tT I tN =
3
3
T
N
and from Eqs. (8) and (26) as g3 I g3 = 30 2 (1098 2 2196 3 + 817).
267

11

1
3363

(189

2

378

3

+ 646)

coalition are not too di¤erent, i.e., when 2 is small. The welfare gains from partial infrastructure coordination with common investment levels for jurisdiction 1 are larger than
for jurisdiction 2.
Comparing Lemmas 3 and 4, we observe that both kinds of infrastructure coordination
(i.e., with di¤erent investment levels and with a common investment level) are welfare
enhancing when the jurisdictions inside the coalition have similar productivity levels (i.e.,
in areas I and IC in cases B and D, respectively, in Figure 4). However, whereas under infrastructure coordination with di¤erent investment levels larger welfare gains are obtained
by the more productive jurisdiction (in this case jurisdiction 2), under infrastructure coordination with a common investment level it is the less productive jurisdiction (jurisdiction
1) that obtains larger welfare gains. This stems from the fact that agreeing upon a common investment level eliminates the di¤erence between the infrastructure investments of
jurisdictions 1 and 2 and, therefore, makes jurisdiction 1 more and jurisdiction 2 less
attractive for capital investments. Infrastructure coordination allows jurisdictions 1 and
2 to reduce infrastructure investments and, thus, to reduce ine¢ ciencies in these investments; however, at the same time tax rates decrease, which increases ine¢ ciencies.16 In
contrast, the jurisdiction outside the tax coalition increases infrastructure investments
and tax rates.17

5.2

Partial tax harmonization

Finally, consider that jurisdictions 1 and 2 form a coalition subgroup which chooses both
a common capital tax rate tc and a common level of infrastructure investments gc that
maximize the joint welfare of this group. Again, jurisdiction 3 determines its infrastructure
investment and capital tax rate independently. The stage 3 equilibrium tax rates are the
same as under partial tax coordination and, thus, are given by Eqs. (11) and (12). The
equilibrium infrastructure investments are given by:
5 ( 1 + 2 2 3)
35
+
,
177
118
62
4 ( 1 + 2 2 3)
.
=
177
59

T
gc IC =

(37)

T
g3 IC

(38)

Substituting Eqs. (37) and (38) into Eqs. (11) and (12) yields the equilibrium tax rates:
56 12
+
( 1+
59 59
31
6
=
( 1+
59 59

tT IC =
c

2 3) ,

(39)

tT IC
3
16

2

2

2 3) .

(40)

2
From Eqs. (9) (8), (33) and (31) we have: tIC tN = 3477 ( 38 + 113 2 + 18 3 ) < 0, tIC
1
1
2
2
N
IC
g1 = 31 293 ( 2470 + 2709 2 + 1170 3 ) < 0, and gc

2
IC
131 2 + 18 3 ) < 0 gc
3477 ( 38
2
( 2470 3879 2 + 1170 3 ) < 0
31 293
8( 2 ; 3 ) 2 IC in Figure 4D.
17

From Eqs (9), (8), (32) and (34) we have: tIC tN =
3
3
(9 2 18 3 + 38) > 0, 8( 2 ; 3 ) 2 IC in Figure 4D.

32
31 293

12

4
3477

(9

2

18

3

IC
+ 38) > 0, and g3

tN =
2
N
g2 =
N
g3 =

Under the assumption that 1 = 0 equilibrium values of infrastructure can be written
5
T
T
as gc IC = 24 tT IC , and g3 IC = 2 tT IC such that social welfare levels in the di¤erent
c
3 3
jurisdictions are:
WiT IC
T
W3 IC

5 T IC ( 1)i
=
+
t
4 c
4
16 T IC 2
=
.
t
9 3

2

1 T IC ( 1)i
+
t
4 c
4

2

1
2

5 T IC
t
24 c

2

, i = 1; 2, (41)
(42)

Proposition 2 Infrastructure coordination through the choice of a common investment
level allows partial tax harmonization between asymmetric jurisdictions that cannot be
achieved by infrastructure coordination with di¤erent investment levels. This is the case
when jurisdiction 2’ productivity is large and the productivity of the jurisdiction outside
s
the tax coalition is low.
A comparison of cases C and E in Figure 4 shows that partial infrastructure coordination in which jurisdictions agree upon a common investment level allows an agreement
to be reached on partial tax harmonization that cannot be achieved under infrastructure
coordination with di¤erent investment levels. This is the case when jurisdictions 1 and 2
are fairly asymmetric and jurisdiction 3’ productivity is high (i.e., in area T IC). This res
sult is obtained because under partial tax harmonization with infrastructure coordination
through a common investment level, even when jurisdictions are asymmetric, jurisdiction
1 gains from infrastructure coordination (see Lemma 4) while jurisdiction 2 gains from
tax coordination (see Lemma 2). Under partial tax harmonization with infrastructure
coordination through di¤erent investment levels only the more productive jurisdiction
(i.e., jurisdiction 2) gains from the formation of a tax coalition when asymmetries in the
tax coalition are high. Comparing both kinds of infrastructure coordination we also observe from Eqs. (27) and (39) that tax rates are the same in both cases (tT IC = tT I )
c
c
while jurisdiction 1 (jurisdiction 2) inverts more (less) in infrastructures in the case of infrastructure coordination through a common investment level.18 The jurisdiction outside
the tax coalition chooses the same capital tax rate and infrastructure investment in both
cases.19

6

Conclusions

Tax harmonization has become an important concern in most developed economies because tax competition has constantly decreased capital tax rates over recent decades and
has led to a shift of the tax burden from capital towards labor. As the global harmonization of capital taxation is unlikely to be achieved, the literature has focused on the
conditions that allow tax harmonization in a coalition of countries. In this article we analyze how such a partial tax harmonization is in‡
uenced by a simultaneous coordination
of infrastructure investments. Two kinds of infrastructure coordination are considered:
18
As tT IC
c
5
TI
g2 = 24 tT I
c
19

T
= tT I , from Eqs. (25) and (39) it follows that g1 I =
c
1
5 T IC
T IC
+ 2 2 > 24 tc
= gc .
See Eqs. (28), (26), (40) and (38).

13

5 TI
24 tc

1
2 2

<

5 T IC
24 tc

T
= gc IC , and

infrastructure coordination with di¤erent investment levels, and infrastructure coordination with a common investment level. We obtain that infrastructure coordination can
facilitate partial tax harmonization. This is the case when the coalition partners are not
too di¤erent in their productivity levels. Furthermore, we …nd that infrastructure coordination with a common investment level enables partial tax harmonization even when
asymmetries between coalition members are substantial. This result explains the harmonization of corporate tax rates observed in the EU between 1995 and 2006 where there
was a simultaneous convergence of public infrastructure investments facilitated via EU
structural funds.
Our result has an important policy implication. As asymmetries between jurisdictions
are an important handicap to accomplishing tax harmonization, a primary objective of
policy makers should be to reduce these asymmetries. The coordination of infrastructure
investments can be an instrument to achieve this objective. Our analysis has shown that
even a reduction of public infrastructure investments in some jurisdictions can be welfare
enhancing for all coalition members when this …nally leads to a harmonization of tax rates
in the tax coalition.
Our analysis also opens up interesting lines for further research. As our analysis has
been limited to three jurisdictions it would be interesting to study how our results generalize with more jurisdictions. Furthermore, our analysis could be complemented by
considering other forms of public tax decision making. For example, as in Borck (2003)
the choice of the tax structure could be considered in a majority voting model in which
jurisdictions compete in tax rates. Finally, our analysis is based on a horizontal coordination of tax rates and infrastructure levels. As tax decisions are taken both at the state
level and at regional and local levels, it would be interesting to analyze how the interplay
of horizontal and vertical coordination of tax rates and infrastructure levels would change
our results.

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Appendix
Proof of Lemma 1. Suppose all jurisdictions increase tax rates by an amount ,
Then welfare becomes:
N
N
N
Wi (tN + ; tN + ; tN + ; gi ; gj ; gh ) =
i
j
h

130 N
t
81 i

2

> 0.

+ tN > 0
i

which proves that a joint tax increase by all jurisdictions increases welfare compared to
the no cooperation case (N ). As the provision of public goods equals tax revenues ti ki
and ki does not change when all jurisdictions increase tax rates by the same amount, it
follows immediately that public goods provision is too low. Finally, consider a reduction
N
of infrastructure investments of the amount in all jurisdictions (0 < < gi , 8i). Then
welfare becomes:
N
Wi (tN ; tN ; tN ; gi
i
j
h

N
; gj

N
; gh

) = tN
i

which proves the last statement.

16

2

N
+ gi

1
2

>0

Proof of Lemma 2. From Eqs. (10) and (17) we have:
T
W2

N

( 2; 3)

1699
61 527 2 13 207
+
+
36 450 884 450 2 53 865
6427
23 837
3457 2
2 3+
3
3
265 335
2653 350
269 325
> 0 for 8( 2 ; 3 ) 2 R.
T
W2

N
W2 =

2

Jurisdiction 2 is always better o¤ under partial tax harmonization. Regarding jurisdiction
1, from Eqs. (10) and (17) we have:
T
W1

N

T
W1

( 2; 3)

+

25 166 2
59 608
1 699
2
36 450 1 326 675
269 325
3 457 2
6 427
3+
3
2 653 350 3 269 325

N
W1 =

38 576
442 225

2

2

T
T
T
95
with W1 N (0; 0) = 0:0466 > 0, W1 N ( 252 ; 0) = 0:0395 < 0 and @ W1 N =@ 2 =
0:0872 3 0:0379 q 0:2213 < 0 for ( 2 ; 3 ) R. Thus, there is a unique function fT N ( 2 ) =
2
T
13 566 967 708 2
143 033 254 000
418 981 654 000
854 791 115 728
W1 N ( 2 ; 3 ) =
2 + 8712 168 921 de…ned by
2
93 339
3457 2
11 950 849
322 672 923
0
which
separates
R
in
two
areas
with
T N
T N
W1
( 2 ; 3 ) > 0 for 2 < fT N ( 2 ) and W1
( 2 ; 3 ) < 0 for 2 > fT N ( 2 ). Finally,
notice that
T
W2

N

( 2; 3)

T
W1

N

33 559
33 559
2
379 050
189 525
> 0 for 8( 2 ; 3 ) 2 R.

( 2; 3) =

3

+

5983
12 825

2

Thus, the welfare gains from partial tax harmonization are larger for jurisdiction 2.
Proof of Lemma 3. From Eqs. (10) and (23) we obtain
I
W2

N
W2

I
W1

N
W1

10 168
(9 2 18 3 + 38)
2972 835
> 0 for 8( 2 ; 3 ) 2 R.
=

2

Thus, jurisdiction 2 always gains from infrastructure coordination when jurisdiction 1
gains. Therefore, it is su¢ cient to analyze when this is the case. We have that:
I
W1

N

( 2; 3)

I
N
W1 ( 2 ; 3 ) W1 ( 2 ; 3 )
16 616
1 777 664
61 360 2
=
2
2
2 712 609 12 089 529
28 633 095
16 616 2
33 232
1 777 664
+
3+
3
12 089 529
5 726 619
60 447 645

2 3

I
I
I
95
with W1 N (0; 0) = 0:0061 > 0, W1 N ( 252 ; 0) = 0:0180 < 0 and @ W1 N =@ 2 =
0:0294 3 0:0102 2 0:0621 < 0 for ( 2 ; 3 ) R. Thus, there is a unique function fI N ( 2 ) =
p p
I
19
3477
31 34 + 3584 2 de…ned by W1 N ( 2 ; 3 ) = 0 which separates R in two
9
10 385
335
I
I
areas with W1 N ( 2 ; 3 ) > 0 for 2 < fI N ( 2 ) and W1 N ( 2 ; 3 ) < 0 for 2 >
fI N ( 2 ).

17

Proof of Proposition 1. First, consider jurisdiction 2. We have:
T
W2 I

T

( 2; 3)

467 779
5951 819 2
2
2
153 512 100
7675 605
261 092 2
522 184
261 092
+
3+
3
38 378 025
16 447 725
7049 025
> 0 for 8( 2 ; 3 ) 2 R.
T
W2 I

T
W2 =

3

+

467 779
3289 545

2

Jurisdiction 2 is always better o¤ under partial tax harmonization with infrastructure
coordination (T I) than under partial tax harmonization (T ) (and under no coordination
(N ), as shown in the proof of Lemma 2).
Second, for jurisdiction 1 we have:
T
W1 I

T

( 2; 3)

T
T
W1 I ( 2 ; 3 ) W1 ( 2 ; 3 )
2359 393 2
1816 711
1816 711
=
2 3
2+
153 512 100
38 378 025
16 447 725
522 184
261 092
261 092 2
+
3+
38 378 025 3 16 447 725
7049 025

2

T
T
T
95
with W1 I T (0; 0) = 0:0370 > 0, W1 I T ( 252 ; 0) = 0:0068 < 0 and @ W1 N =@ 2 =
0:0473 3 p
0:0307 2 0:1105 < 0 for ( 2 ; 3 ) R. Thus, there is a unique function fT I T ( 2 ) =
T
548 877
747
7
13 2 139168 2 de…ned by W1 I T ( 2 ; 3 ) = 0 which separates R in two areas
3
522 184
40
with
T
T
W1 I T ( 2 ; 3 ) > 0 for 2 < fT I T ( 2 ) and W1 I T ( 2 ; 3 ) < 0 for 2 > fT I T ( 2 ).
Furthermore, we have:
T
W1 I

N

( 2; 3)

T
W1 I ( 2 ; 3 )
1553 449
=
45 239 076
183 355
+
22 619 538

N
W1 ( 2 ; 3 )
1777 417
1521 943
2
2 3
2+
11 309 769
5357 259
424 555
297 925
2
3+
3
5357 259
5075 298

2

T
T
T
95
with W1 I N (0; 0) = 0:0837 > 0, W1 I N ( 252 ; 0) = 0:0463 < 0 and @ W1 N =@ 2 =
0:1346 3 0:0687 2 0:3318 p 0 for ( 2 ; 3 ) R. Thus, there is a unique function fT I N ( 2 ) =
p <
T
113115 1521943
1121
2 35218557 2 7712640 2 + 696800 de…ned by W1 I N ( 2 ; 3 ) =
2
330039
183355 2 1100130
TI N
0 which separates R in two areas with W1
( 2 ; 3 ) > 0 for 2 < fT I N ( 2 ) and
T
W1 I N ( 2 ; 3 ) < 0 for 2 > fT I N ( 2 ).
Finally, notice that functions fT N ( 2 ), fT I N ( 2 ) and fT I T ( 2 ) have a single intersection point in R at ( 2 ; 3 ) = (0:1711; 1:0892) which separates R in three areas (displayed
in Figure 4C):

1. Area T I: ( 2 < fT I T ( 2 ) and 2 < fT I N ( 2 )) where WiT I ( 2 ; 3 ) > WiN ( 2 ; 3 )
and WiT I ( 2 ; 3 ) > WiT ( 2 ; 3 ), i = 1; 2, such that the equilibrium outcome is T I
which is preferred by all jurisdictions.
T
T
T
2. Area T : (fT I T ( 2 ) < 2 < fT N ( 2 )) where W1 ( 2 ; 3 ) > W1 I ( 2 ; 3 ), W2 I ( 2 ; 3 ) >
T
W2 ( 2 ; 3 ) and WiT ( 2 ; 3 ) > WiN ( 2 ; 3 ), i = 1; 2. The equilibrium outcome is T
as jurisdiction 1 does not agree to coordinate infrastructure investments which is
the preferred outcome for jurisdiction 2.

18

N
T
3. Area N : ( 2 > fT N ( 2 ) and 2 > fT I N ( 2 )) where W1 ( 2 ; 3 ) > W1 I ( 2 ; 3 ),
T
N
W1 ( 2 ; 3 ) > W1 ( 2 ; 3 ). The equilibrium outcome is N as jurisdiction 1 loses from
both partial tax harmonization and partial tax harmonization with infrastructure
coordination.

Proof of Lemma 4. From Eqs. (10) and (35) we obtain
IC
W1

N
W1

IC
W2

N
W2

6 2
7268
24 452
2
2+
93 879
61
198 189
260
130 2
3+
1539
3249 3
> 0 for 8( 2 ; 3 ) 2 R,
=

2 3

which proves the second statement. Jurisdiction 2’ welfare gains are:
s
IC
W2

N

( 2; 3)

IC
N
W2 ( 2 ; 3 ) W2 ( 2 ; 3 )
16 616
543 626 2
245 440
=
2
2
2712 609 12 089 529
5726 619
33 232
245 440
16 616 2
+
3+
3
12 089 529
5726 619
12 089 529

2 3

IC
IC
IC
95
with W2 N (0; 0) = 0:0061 > 0, W2 N ( 252 ; 0) = 0:0164 < 0 and @ W2 N =@ 2 =
0:0203 3p 0:0899 2 0:0429 < 0 for ( 2 ; 3 ) R. Thus, there is a unique function fIC N ( 2 ) =
p
IC
19 1159
19 59 2 15 340 2 de…ned by W2 N ( 2 ; 3 ) = 0 which separates R in two areas
9
4154
2077
IC N
IC
with W2
( 2 ; 3 ) > 0 for 2 < fIC N ( 2 ) and W2 N ( 2 ; 3 ) < 0 for 2 > fIC N ( 2 ).

Proof of Proposition 2. First, consider jurisdiction 1. From Eqs (10), (17), (29),
and (41) we have that jurisdiction 1 is always better o¤ under tax harmonization with infrastructure coordination with common investment levels (T IC) than under no coordination (N ), tax harmonization (T ), and tax harmonization with infrastructure coordination
with di¤erent investment levels (T I):
7555 633 2
800 537
424 555
2
2
5075 298 180 956 304
10 714 518
551 903
183 355 2
297 925
+
2 3+
3
3
22 619 538
22 619 538
5357 259
> 0 for 8( 2 ; 3 ) 2 R,
261 092
13 990 897 2
4822 753
T
T
T
W1 IC T ( 2 ; 3 )
W1 IC W1 =
2
2+
7049 025 614 048 400
32 895 450
4822 753
261 092 2
522 184
2 3+
3
3
76 756 050
38 378 025
16 447 725
> 0 for 8( 2 ; 3 ) 2 R,
91
13
7
T
T
T
W1 IC T I ( 2 ; 3 )
W1 IC W1 I =
for 8( 2 ; 3 ) 2 R.
3
2
2 > 0
354 118
944
T
W1 IC

N

( 2; 3)

T
W1 IC

N
W1 =

19

Second, consider jurisdiction 2. From Eqs. (10) and (41) we have that jurisdiction 2 is
always better o¤ under tax harmonization with infrastructure coordination with common
investment levels (T IC) than under no coordination (N ):
T
W2 IC

N

( 2; 3)

1673 569 2
1396 387
424 555
2+
5075 298 180 956 304
10 714 518
918 613
183 355 2
297 925
2 3+
3
22 619 538
22 619 538 3 5357 259
> 0 for 8( 2 ; 3 ) 2 R.
T
W2 IC

N
W2 =

2

Thus, as both jurisdictions are better o¤ under T IC than under N , No harmonization
(N ) is not an equilibrium. Furthermore, from Eqs. (17) and (41) we have:
T
W2 IC

T

( 2; 3)

T
W2 IC

+

261 092
755 677
48 395 449 2
2
7049 025 614 048 400
6579 090
261 092 2
522 184
3+
3
38 378 025 3 16 447 725

T
W2 =

755 677
15 351 210

2

2

T
T
T
95
with W2 IC T (0; 0) = 0:0371 > 0, W2 IC T ( 252 ; 0) = 0:0175 < 0 and @ W2 IC T =@ 2 =
0:0492 3 0:15763 2 0:11486 < 0 for ( 2 ; 3 ) R. Thus, there is a unique function
p p
T
7
1239
290 645
13 1348 521 2
de…ned by W2 IC T ( 2 ; 3 ) = 0
fT IC T ( 2 ) = 3
1044 368
80 336 2
T
which separates R in two areas with W2 IC T ( 2 ; 3 ) > 0 for 2 < fT IC T ( 2 ) and
T
W2 IC T ( 2 ; 3 ) < 0 for 2 > fT IC T ( 2 ).
From Eqs. (29) and (41) we have:
T
W2 IC

TI

( 2; 3)

1
2832
for 8( 2 ; 3 ) 2 R.

T
W2 IC

< 0

T
W2 I =

2

(333

2

312

3

+ 728)

This result implies that of the two forms of tax harmonization with infrastructure coordination, jurisdiction 2 prefers infrastructure coordination with di¤erent investment levels
while jurisdiction 1 prefers infrastructure coordination with a common investment level.
Finally, notice that the intersection point of functions fT N ( 2 ), fT I N ( 2 ) and fT I T ( 2 )
lies on the right of function fT IC T ( 2 ). Thus, again we have three areas in R (displayed
in Figure 4E):
1. Area T I; T IC: ( 2 < fT I T ( 2 ) and 2 < fT I N ( 2 )) where WiT I ( 2 ; 3 ) > WiN ( 2 ; 3 ),
T
T
T
and WiT I ( 2 ; 3 ) > WiT ( 2 ; 3 ), i = 1; 2, W1 IC ( 2 ; 3 ) > W1 I ( 2 ; 3 ) and W2 I ( 2 ; 3 ) >
T IC
W2 ( 2 ; 3 ) such that the equilibrium outcome is either T I or T IC which are preferred by all jurisdictions to T and N .
T
2. Area T : (fT I T ( 2 ) < 2 < fT N ( 2 ) and fT IC T ( 2 ) < 2 ) where W1 IC ( 2 ; 3 ) >
T
T
T
T
T
W1 ( 2 ; 3 ) > W1 I ( 2 ; 3 ), W2 I ( 2 ; 3 ) > W2 ( 2 ; 3 ) > W2 IC ( 2 ; 3 ) and WiT ( 2 ; 3 ) >
N
Wi ( 2 ; 3 ), i = 1; 2. The equilibrium outcome is T as jurisdiction 1 does not agree
to coordinate infrastructure investments with di¤erent investment levels which is the
preferred outcome for jurisdiction 2, and jurisdiction 2 does not agree to coordinate
infrastructure investments with a common investment level which is the preferred
outcome for jurisdiction 1.

20

3. Area T IC: ( 2 > fT N ( 2 ) and 2 > fT I N ( 2 )) where WiT IC ( 2 ; 3 ) > WiN ( 2 ; 3 ),
T
N
i = 1; 2, W1 ( 2 ; 3 ) > W1 ( 2 ; 3 ). The equilibrium outcome is T IC as both jurisdictions prefer partial tax harmonization and infrastructure coordination with a
common investment level to no coordination, and jurisdiction 1 prefers partial tax
harmonization without infrastructure coordination to no coordination.

21

Figure 1: Combined corporate income tax rate of EU countries (period 1995-2011). Countries are classi…ed into high, middle and low income countries. High income countries comprise Austria, Belgium, Denmark, Finland, France, Germany, Netherlands, Sweden, and
United Kingdom. Middle income countries include Greece, Italy, Spain, and Portugal.
Low income countries encompass Czech Republic, Estonia, Hungary, Slovak Republic,
Slovenia, and Poland. Source: Own calculation based on OECD (2015).

Figure 2: Transport infrastructure investment per capita of EU countries (period 19952011). For country classi…cation see Figure 1. Source: Own calculation based on OECD
(2015).

22

Figure 3: Share of EU …nanced infrastructure investment in total infrastructure investment (period 2000-2006, period 2003-2006 for low income countries). For country classi…cation see Figure 1. Source: Own calculation based on OECD (2015) and Sweco (2008).

23

Figure 4: Equilibria are: No tax harmonization (N), Infrastructure coordination (I), Infrastructure coordination with Common investment levels (IC), partial Tax harmonization
(T), partial Tax harmonization with Infrastructure coordination (TI), partial Tax harmonization with Infrastructure coordination through Common investment levels (TIC).

24