Discussion Papers In Economics
And Business
Why Minimum Corporate Income Taxation Can
Make the High-Tax Countries Worse off: theCompliance Dilemma
Jean HINDRIKS
Yukihiro NISHIMURA

Discussion Paper 21-10

July 2021

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANWhy Minimum Corporate Income Taxation
Can Make the High-Tax Countries Worse oﬀ:
the Compliance Dilemma∗
Jean HINDRIKS† and Yukihiro NISHIMURA‡§

July 28, 2021
Abstract
Minimum taxation means that if a multinational enterprise (MNE)
declares its operations in a jurisdiction taxing less than the minimum
tax, the countries where the real economic activity takes place would
have the right to tax the diﬀerence. There is a revival of the minimum tax standard for two reasons. First, there is concern about thecomplexity of assigning taxing rights and the eﬀectiveness of proﬁtsplitting rules in eliminating proﬁt shifting. Second, the minimum
tax standard has the merit of tackling multinational tax avoidanceat its root. However, this argument ignores the strategic interaction
between minimum taxation and tax compliance. Building upon Hindriks and Nishimura (2021), we develop a framework in which eﬀective international tax compliance requires enforcement coordination
between countries (e.g. exchange of information). We show that under suﬃcient market asymmetry (translating into the tax diﬀerential),
minimum taxation may induce the low-tax countries to withdraw frominternational tax compliance agreements. We then show that such a
breakdown of cooperation can make the high-tax country worse oﬀ
compared to the absence of minimum taxation.
Keywords: Proﬁt shifting; Tax competition; Tax enforcement;
JEL Classiﬁcation: C72, F23, F68, H25, H87.
∗

Declarations of interest: none.
CORE (LIDAM) and Economics School of Louvain, Université catholique de Louvain,
Louvain-la-Neuve, Belgium.
‡
Correspondence Yukihiro Nishimura, Graduate School of Economics, Osaka University, 1-7 Machikaneyama-cho, Toyonaka-shi, Osaka, 560-0043, Japan.
E-mail:ynishimu@econ.osaka-u.ac.jp§
CESifo, Munchen, Germany.
†

1

1

Introduction

New technologies and the globalization of the economy have facilitated tax
avoidance through the shifting of proﬁts by multinational enterprises (MNEs)
to low-tax jurisdictions. This is the essence of base erosion and proﬁt shifting(BEPS, hereafter referred to as “proﬁt shifting”). In 2020, the OECD/G20
Inclusive Framework on the BEPS project released blueprints which include“global minimum tax measures”. Minimum taxation means that if an MNE
declares its operations in a jurisdiction taxing less than the minimum tax, thecountries where the real economic activity takes place would have the rightto tax the diﬀerence. As stated by the most recent OECD appraisal, muchof the gains in tax collection would come from minimal taxation. There isa revival of the minimum tax standard for two reasons. First, there is concern about the complexity of assigning taxing rights and the eﬀectiveness of
proﬁt-splitting rules in eliminating proﬁt shifting.1 Second, the minimum tax
standard has the merit of tackling multinational tax avoidance at its root.
However, this argument ignores the strategic interaction between minimum
taxation and tax compliance. Building upon Hindriks and Nishimura (2021),
we develop a framework in which eﬀective international tax compliance requires enforcement coordination between countries (e.g., strict monitoringand inspection, more eﬃcient information sharing, reinforcement of tax oﬃcials’ skills and competence).
We consider a simple two-country model with diﬀerent market sizes. The
MNE shifts proﬁts from the division in the high-tax country to that in the
low-tax country, subject to a concealment cost. Countries choose their enforcement eﬀort levels. The tax enforcement shares the properties of joint
production with individual eﬀorts, where the sharing of the production gains
leads to a non-trivial incentive problem. We then compare the equilibria
for the noncooperative and cooperative enforcement choices. In the latter
scenario, countries choose enforcement levels to maximize their joint wel1

The Pillar One of OECD (2021) proposes to start taxing multinationals as global ﬁrms
and distribute part of the global proﬁts where the value is created. Essentially, it involves
the shift from separate accounting (SA) to formula apportionment (FA). However, a shift
from SA to FA does not solve ﬁscal spillover problems and it may even aggravate them(Nielsen et al. (2010)). More fundamentally, each country has preferred sharing rules(for example, sales, capital, and labor) so that a group of countries would never agree
on allocation rules. In our paper, we consider the scope for beneﬁcial cooperation on tax
enforcement in the context of SA. As stated by the French Council of Economic Analysis(CEA), the introduction of a worldwide minimum eﬀective corporate tax rate (so-called
pillar 2 of the OECD (2021)) should be the main priority of international negotiations,whereas the redesigning proﬁt splitting rules has a negligible impact on tax revenues. See
Fuest et al. (2019).

2

fare, but they still determine tax rates noncooperatively. This case reﬂects
the current OECD framework to reinforce enforcement cooperation in which
each country still can freely choose its tax system and tax rates.
A key feature of our model is that both the low-tax and high-tax jurisdictions care about international tax compliance and are willing to contribute(albeit to a diﬀerent extent) to reinforce international tax compliance. Morespeciﬁcally, the model assumes pre-commitment on tax enforcement suchthat both countries can levy higher taxes. Indeed, if enforcements and taxes
were simultaneously chosen, then given the market asymmetry, the low-tax
jurisdiction would not agree to contribute to international compliance that
limits proﬁt shifting. Also, our argument that the minimum tax may unravelinternational agreement on tax compliance does not involve tax haven sincesuch jurisdictions are not willing to participate in such agreement in the ﬁrst
place.
We show that under suﬃcient market asymmetry (translating into the tax
diﬀerential), minimum taxation may induce the low-tax countries to withdraw from international tax compliance agreements. We then show that sucha breakdown of cooperation can make the high tax country worse oﬀ compared to the absence of minimum taxation. The minimum tax can harm
the high-tax country but not the low-tax country for which the tax ﬂoor isbinding.

2

Framework

2.1

The model

There are two countries, denoted by 1 and 2. A multinational enterprise(MNE) havs branches in each country. From the production decisions incountry i = 1, 2, the ﬁrm generates πi in country i. Then, at some cost, it
may shift proﬁts between branches to minimize the ﬁrm’s total tax liability.
In other words, it decides how much proﬁt to report, π̃i in country i, where
total reported proﬁt must equal total realized proﬁt (π̃1 + π̃2 = π1 + π2 ). In
order to focus on the proﬁt shifting activities of the ﬁrms, we assume thatproﬁt taxes do not change the equilibrium demand, supply and aggregate
proﬁt (similar to a widely used model by Kanbur and Keen (1993)):
π1 =

1−²
1+²
, π2 =, ² ∈ [0, 1)
2
2

(1)

² > 0 is a parameter for the market asymmetry, where Country 1 has thelarger domestic market. For convenience, we normalize the total actual prof3

its to be 1. For instance, if ² = 0.4 then country 1 has a proﬁt share of
1 + 0.4
π1 == 0.7 (before proﬁt shifting).
2
Given country i’s source-based tax rate ti on the reported proﬁt, the ﬁrm’s
proﬁt becomes (1 − t1 )π̃1 + (1 − t2 )π̃2 − C (πi , π̃i ). We introduce the following
convex and nonﬁscally-deductible concealment cost C (πi , π̃i ), which is widelyused in the literature:2
C (πi , π̃i ) = δ(e) (πi − π̃i )2 , i = 1, 2 and k = a, b.

(2)

Several explanations are in order. First, δ(e) is a scaling factor for resource
costs associated with proﬁt shifting. It reﬂects the cost of hiring accounting
experts to produce the required documents, expected penalties to be paid to
the government, or the expected market sanction when caught cheating on
tax liabilities. In the context of tax evasion, a standard assumption in theliterature is that such costs are increasing and convex in the extent of proﬁt
shifting (tax evasion), |πi − π̃i |, regardless of the direction of proﬁt shifting(i.e., it is cost equivalent to shift proﬁts outward or inward).
Second, δ(e) = δ(ei , ej ) depends on the governments’ enforcement eﬀorts
ei , ej , such as tougher monitoring, more eﬃcient information sharing, andthe eﬀorts to negotiate and reach agreements with the other country’s tax
authority. δ(e) is an increasing function of ei and ej , such that stricter enforcement implies a higher δ(e). Moreover, in reality, dispersed (unilateral)
enforcement eﬀorts between involved countries are less eﬀective in aggregate.3 For instance, a lack of tax-relevant information provided by the hostcountry makes the taxable income unclear to the home country, and the tax
authorities cannot address tax fraud eﬀectively. To formalize the imperfect
substitutability of enforcement eﬀorts, we adopt the following CES formula:()− 1δ(e1 , e2 ) = 0.5 e1 −ρ + 0.5 e2 −ρ ρ , ρ ≥ −1.

(3)

The enforcement technology (3) is exogenous. The polar cases are: (i) ρ = −1
(perfect substitutes: total enforcement is based on the average enforcement);
0.5(ii) ρ → 0 (the Cobb–Douglas case δ(e1 , e2 ) = e0.5
1 e2 ); and (iii) ρ → ∞ (theweakest–link case δ(e1 , e2 ) = min[e1 , e2 ], where total enforcement is based onthat of the lowest enforcer). For example, if during the mutual agreement
2

For example, see Hauﬂer and Schjelderup (2000), Swenson (2001), Kind et al. (2005),
Peralta et al. (2006), Devereux et al. (2008), Nielsen et al. (2008), and Keen and Konrad(2013). See also Huizinga and Laeven (2008) and Amerighi and Peralta (2010) for aslightly diﬀerent speciﬁcation.
3
Klassen and Laplante (2012) showed that proﬁt shifting in a given country depends
not only on the enforcement of the regulations in the home country but also on theimplementation of the regulations in the host country.

4procedure, the low-tax country can exercise a veto power on the transfer
price and taxable incomes of the MNEs, then the enforcement technology
becomes closer to the weakest–link formula.
The tax revenue in country i is:)(
Ri = ti π̃ia + π̃ib
We assume that governments seek to maximize their ﬁscal revenue net of theenforcement cost (the tax administration costs). This feature is similar toa widely used model by Kanbur and Keen (1993). We assume that ti ≤ 1,
2
for i = 1, 2. Assuming a quadratic cost of enforcement (c(ei ) = η (e2i ) ) for
simplicity, welfare in country i is:
Wi = Ri − η(ei )2,2where η > 0 is a parameter for the enforcement cost. For simplicity, we set
η = 1 for the rest of the paper.4

2.2

Proﬁt shifting by the ﬁrm

We consider a three-stage game with the following sequence of events. In
the ﬁrst stage, both countries set their enforcement eﬀorts. In the second
stage, both countries choose their tax rates. In the third stage, multinational
enterprises compete à la Cournot in each local market and choose a level ofproduction in each country and the amount of proﬁt to be shifted.
Regarding enforcement and tax timing, we assume that the enforcement
eﬀorts are chosen ﬁrst and taxes are chosen later. Any alternative timing
leads to e2 = 0: the small country would always choose zero enforcement. In
turn, when ρ ≥ 0, it leads to zero taxes for both countries.5 Our enforcementthen-tax timing rationalizes the BEPS project which is to promote voluntary
tax enforcement to increase the tax capacity of member states.
The model is solved by backward induction. In this subsection, we analyze
the decisions of the ﬁrms in each country, given the tax t = (t1 , t2 ) andenforcement e = (e1 , e2 ) choices made earlier. The ﬁrm chooses the quantities
4

In most of the paper, we can restrict η = 1 without loss of generality. The exceptions
are when either the asymmetry parameter ² or the minimum tax parameter τ below is sufﬁciently large in the cooperative regime. A suﬃcient condition for interior tax equilibriumis η ≥ 33/32 in these speciﬁc cases.
5
In Hindriks and Nishimura (2018), we considered the scenario that the tax rate andenforcement eﬀort are chosen simultaneously and noncooperatively. We showed that there
is no equilibrium with positive taxes in pure strategy. The case when the sequence ofdecisions is reversed is available upon request to the authors.

5to produce in each market and the proﬁt to report, (π̃1 , π̃2 ), to maximize theafter-tax proﬁt net of the proﬁt-shifting cost, as follows:(1 − t1 )π̃1 + (1 − t2 )π̃2 − δ(e)(π1 − π̃1 )2 ,subject to π̃1 + π̃2 = π1 + π2 . The ﬁrst-order condition for π̃1 yields:−t1 + t2 − 2δ(e)(π̃1 − π1 ) = 0.

(4)

Proﬁt taxes do not change supply and aggregate proﬁt. However, proﬁttaxes change the distribution of proﬁt shares (reported proﬁt) between countries via proﬁt shifting. (1) and (4) derive the following Stage-3 outcome:π̃1 =1 + ² t1 − t2
1 − ² t1 − t2−
≡ π̃1 (t, e), π̃2 =+≡ π̃2 (t, e).
2
2δ(e)
2
2δ(e)

(5)

The reported proﬁt in country i consists of (a) actual proﬁts πi that
depend on the market size ² and (b) the amount of proﬁt shifting πi − π̃i . The
latter is proportional to the tax diﬀerence ti − tj and inversely proportional
to the total enforcement δ(e).
From (5), given the equilibrium proﬁt shifting, country i’s tax revenue
net of the enforcement cost is, with η = 1:)((ei )2
1 + ²i ti − tj(ei )2
Wi = ti π̃i (ti , tj , e) −
= ti
−
−
,
(6)
2
2
2δ(e)
2
where ²1 = ² = −²2 .

2.3

Tax choices under the minimum tax

In the second stage of the game, each country noncooperatively chooses its
own tax rate ti (i = 1, 2) to maximize (6). This stage is divided into two
substages. Given e in Stage 1, the governments ﬁrst set the mimimum tax
in Stage 2.0, prior to the tax competition in Stage 2.1.
To see how we set the minimal-tax policies, we ﬁrst derive the Nashequilibrium in the absense of the minimal taxation. The ﬁrst-order conditionsare:
1 + ²i ti − tj
−1
∂Wi
=
−
+ ti
= 0.
∂ti
2
2δ(e)
2δ(e)
N
They yield the following equilibrium taxes, denoted by (tN
1 (e), t2 (e)):
(
(
)
)
3+²
3−²
N
N
t1 (e) = δ(e)and t2 (e) = δ(e)
.
3
3

6

(7)

(8)

6
From (8), the binding minimum tax has to be t > tN
2 . For the minimum tax
Nstandard t > t2 , the tax choice becomes:
(
)
1+²
t
M
M
t2 = t, t1 = δ(e)
+ ,
(9)
2
2

where the latter comes from the high-tax country’s tax reaction function
M◦from (7). (tM
1 , t2 ) intersects with the 45 -line at t = δ(e)(1 + ²) (tax harmonization). This tax equalization policy is assumed to be the upper bound of
the minimum tax rate. Therefore, we consider that the governments choose
the minimum tax from the following range:()
3−²t = τ δ(e), τ ∈(10), 1 + ² ≡ (τ , τ )3Here we set t to be conditional on the choice of δ(e) in the previous stage.
This is a natural tax policy given the enforcement pre-commitment. As theunconstrained equilibrium tax rates (8) are conditional on the international
enforcement level, we consider that the minimum tax standard is also condiM
tional on δ(e). From (5), for π̃iM ≡ π̃i (tM
1 (e), t2 (e), e), we have:π̃1M =1+² τ
3−² τ(e) − tM
1 + ² tM
2 (e)
− 1
=
+
and π̃2M =
− .
2
2δ(e)
4
4
4
4

(11)

For the range of (10), we have π̃1M ≥ 1/2 for all τ ∈ (τ , τ ) and ² ∈ (0, 1).
In equilibrium, the proﬁt shares (reported proﬁts) as well as the proﬁt shifting π1 − π̃1M are independent of enforcement levels (e1 , e2 ) and enforcement
technology δ(e). The higher enforcement simply scales up the tax gap by
the same proportion (tax rates are proportional to international tax compliance). In equilibrium, the higher tax compliance is oﬀset by a higher tax gap
so that the extent of proﬁt shifting is unchanged. Moreover, minimum taxation increases in equilibrium the proﬁt share of the high-tax country at theexpense of the low-tax country (tax convergence eﬀect). The tax revenues
M
RiM (e) = tMi (e)π̃i (i = 1, 2) are as follows for all ² ∈ (0, 1) and τ ∈ (τ , τ ):R1M (e) =

δ(e)
δ(e)
(1 + ² + τ )2 ≥ R2M (e) =τ (3 − ² − τ ) .
8
4

(12)

The minimum tax τ increases the revenue gap. This is because the minimum
tax increases the proﬁt share of the high-tax country. This change in proﬁt
6Note that this formulation includes the current proposals of country-by-country (CbC)
minimum taxation, in which the income declared in the low-tax country may in part besubject to taxation in a high-tax country. This induces the low-tax country to matchthe minimum tax standard t2 = t, for otherwise the high-tax country would collect theresidual tax.

7

shares will in turn change enforcement incentives of both the high tax andlow tax countries.

3

Enforcement choices

In the ﬁrst stage, the governments in each country choose their enforcement eﬀort levels, taking into account the behavior in the subsequent stages.
We ﬁrst examine noncooperative enforcement choices, where each countryMchooses ei (i = 1, 2) simultaneously and independently. Let (eM
1 , e2 ) be thenon-cooperative enforcement equilibrium under minimum tax τ .

3.1

Enforcements are substitutes

As an illustration, we ﬁrst consider that enforcements are perfect substitutes(ρ = −1) so that the international compliance is based on the the arithmetic
mean of enforcement levels δ−1 ≡ 0.5e1 +0.5e2 . Given ej , country i maximizes(ei )2
WiM (ei , ej ) = RiM (ei , ej ) −where RiM (e)’s are given in (12). The ﬁrst2
order conditions with respect to country i’s enforcement choice yield for allτ ∈ (τ , τ ) :
(
)2
1+²+τ
τ (3 − ² − τ )
M
e1 =
, eM
(13)
2 =
4
8
Plugging the equilibrium enforcement into the welfare function, we have(eM )2Wi (eM ) = RiM (eM ) − i(i = 1, 2).
2
We now turn to the international compliance agreement. Here, bothcountries choose their enforcement levels to maximize their joint welfare.
This reﬂects an agreement regarding the level of information exchange in the
tax treaty. However, in keeping with the current OECD framework to reinforce enforcement cooperation in which each country still can freely choose
tax rates, we assume that countries set taxes (ti ) noncooperatively. Therefore, countries choose e = (e1 , e2 ) anticipating the noncooperative tax game
M
M
M
(tM
1 (e), t2 (e)) and tax revenues (R1 (e), R2 (e)) in (12). That is,)∑(e2i
e2 e2jM
max
Ri (ei , ej ) −(14)= max R1M (e) + R2M (e) − i − .
ei ,ejei ,ej222i
The ﬁrst-order conditions give the cooperative enforcement levels êM =M(êM
1 , ê2 ) given by:
(
)2
1+²+τ
τ (3 − ² − τ )MMê1 = ê2 =+488

Enforcement eﬃciency requires both countries to exert the same enforcement eﬀorts because of the convex cost function and the symmetry of theenforcement technology. When ρ = −1, enforcement cooperation doubles international tax compliance level (relative to no tax compliance agreement).
The positive ﬁscal externality of enforcement ∂RjM /∂ei > 0 for i 6= j is now
internalized by the tax compliance agreement. Such cooperation induces the(êM )2(i = 1, 2). The large country unwelfare levels Wi (êM ) = RiM (êM ) −2ambiguously gains from the tax compliance agreement (W1 (êM ) > W1 (eM )for all τ and ² > 0). However, for the low-tax country, there are oﬀsetting
eﬀects. The international tax compliance agreement involves extra enforceM
ment êM
2 − e2 from the low-tax country that is increasing in ². As a result,even though the tax compliance agreement involves higher revenues also forthe low-tax country (R2M (êM ) − R2M (eM ) > 0), this country may prefer thenoncooperative regime. The following proposition states the conditions on
the market asymmetry and the minimum tax such that the low-tax country
prefers the tax compliance agreement.
Proposition 1 Suppose that ρ = −1, and τ ∈ (τ , τ ).
(i) For the high-tax country, W1 (êM ) > W1 (eM ) for all ² and τ .
(ii) For the low-tax country, given τ , there exists a cutoﬀ level of asymmetry ²M (−1, τ ) such that W2 (êM ) > W2 (eM ) iﬀ ² < ²M (−1, τ ).
(iii) The cutoﬀ level of asymmetry ²M (−1, τ ) is decreasing in τ .

3.2

Enforcements are complements

For a1 ≡(1 + ² + τ )2
(3 − ² − τ )and a2 ≡ τ
we have (see the Appendix):84() −1−ρ
ρ
ρ
1
ρ
− 2+ρ
− 2+ρ
M
ei = 0.5 0.5 a1+ 0.5 a2
ai 2+ρ (i = 1, 2)(15)

When enforcement eﬀorts are complements, the international compliance isincreasing with enforcement alignment: δ(e∗ + ∆, e∗ − ∆) < δ(e∗ , e∗ ) for ∆ >0. As shown in Hindriks and Nishimura (2021), increasing complementarity(larger ρ) induces partial enforcement alignement but it is not suﬃcient tooﬀset the ﬁrst-order eﬃciency loss from enforcement dispersion. As a result,at the non-cooperative enforcement equilibrium, international compliance isdecreasing with the degree of complementarity (δ(eM ) is decreasing in ρ).
Turning to enforcement cooperation, the ﬁrst-order conditions of the joint
welfare maximization are
(
) 1+ρ
−ρ
−ρ −ρ
0.5e−ρ−1(a1 + a2 ) − ei = 0 (i = 1, 2)
0.5e
+
0.5e
1
2
i
9

M
Hence the cooperative enforcement levels are êM
1 = ê2 = 0.5(a1 + a2 ). We
now analyze the implication of the introduction of the minimum taxation
when enforcements are complements.

Proposition 2 Suppose that ρ = 0 or ρ = ∞, and τ ∈ (τ , τ ).
(i) For the high-tax country, W1 (êM ) > W1 (eM ) for all ρ, ² and τ .
(ii) For the low-tax country, given τ and ρ, there exists a cutoﬀ level ofasymmetry ²M (ρ, τ ) such that W2 (êM ) > W2 (eM ) iﬀ ² < ²M (ρ, τ ).
(iii) The cutoﬀ level of asymmetry ²M (ρ, τ ) is decreasing in τ and increasing in ρ.
We now list those threshold values. For ρ = −1 (perfect substitutes) and
3−², and ²M (−1, τ ) ≡without minimum taxation, we have τ = τ =3²(−1) ≈ 0.259 is the threshold value below which the low-tax country beneﬁts from cooperation. Increasing τ reduces the cutoﬀ level, and eventually
we have ²M (−1, τ ) ≡ ²(−1) ≈ 0.172. For the Cobb-Douglas case (ρ = 0),²(0) ≈ 0.320 and ²(0) ≈ .211. For the perfect complement case (ρ = ∞), we
have ²(∞) ≈ 0.409, ²(∞) ≈ .268. Recall that ² = 0.4 is equivalent to a proﬁtshare of 0.7 for the large country in the absence of proﬁt shifting. In short,
enforcement cooperation does not take place when ² is in its intermediate
values, where both the upper-bound and the lower-bound are increasing in
the degree of enforcement complementarity.
The ﬁnal step (and most striking feature) of our argument about minimal
taxation is to show that the high-tax country can be worse oﬀ as a result of theminimum tax if it breaks down the international tax compliance arrangement.
So if enforcements are perfect substitutes, minimum taxation τ would break
the agreement if ²M (−1, τ ) < ² < 0.259: the international agreement issustainable without minimum taxation ² < 0.259 but it is not sustainable
under minimum tax.
3−²
Figure 1 illustrates the case of ρ = −1 and ² = 0.2. Between τ =≈30.933 (the Nash equilibrium) and τ ≈ 1.100, enforcement cooperation Pareto
dominates the noncooperative equilibrium, and the minimum tax is Pareto
improving. However, when the minimum tax is pushed beyond the pointτ ≈ 1.100 < 1 + ², the low-tax country prefers non-cooperative enforcement
to recover part of its tax base loss from minimum taxation. The breakdown of
enforcement cooperation makes the high-tax country worse-oﬀ. Interestingly,
the minimum tax can harm the high-tax country but it cannot harm the lowtax country. This is because the low-tax country has the option to opt-out
freely from the international compliance arrangement. This is what we callthe compliance dilemma of minimum taxation.
10

Figure 1: The minimum tax breaks the tax compliance agreement when τ is
suﬃciently high: ρ = −1, ² = 0.2, Ŵi = Wi (êM ) and Wi = Wi (eM )Note that ² > ²(ρ) is beyond the scope of mutually beneﬁcial cooperationeven without minimum taxation. Such cases include ² = 1 (no production
in country 2), which can be interpreted as country 2 being a tax haven.
For those cases, our compliance dilemma does not apply since enforcement
cooperation is not possible.

Appendix
Derivation of (15)(3 − ² − τ )(1 + ² + τ )2
and a2 ≡ τ, we have:
For a1 ≡
8
4
(
) 1+ρ
∂δ(e)
−ρ
−ρ −ρ
ai − ei = 0 ⇒ 0.5e−ρ−1
0.5e
+
0.5e
ai = ei (i = 1, 2).
1
2
i
∂ei

11

The above system of equations produces (15) in the text. When ρ = −1,(15) is equivalent to (13).

Proof of Proposition 1 and Proposition 2
Let τ (a) = min{a(3−²), 1+²}. Then τ (a) ∈ (τ , τ ) for a ∈ (a, a) with a = 1/3
1+²
and a =. For a < a, we evaluate W2 (êM ) and W2 (eM ) by setting
3−²τ = a(3 − ²). Numerically, we ﬁnd the threshold value ²̃(−1, a) such that
W2 (êM ) − W2 (eM ) is positive (negative) when ² < ²̃(−1, a) (² > ²̃(−1, a)).
Also, ²̃(−1, a) is decreasing in a. When a = a, we evaluate W2 (êM ) andW2 (eM ) by setting τ = 1 √+ ². In this case, W2 (êM ) − W2 (eM ) is positive(negative) when ² < 3 − 2 2 ≡ ²∗ ≈ 0.172 (² > ²∗ ). Let a∗ = (1 + ²∗ )/(3 −²∗ ) ≈ 0.414. By deﬁnition, at (a, ²) = (a∗ , ²∗ ), τ (a∗ ) = a∗ (3 − ²∗ ) = 1 + ²∗
and W2 (êM ) − W2 (eM ) = 0, and ²̃(−1, a∗ ) = ²∗ .
1 + ²̃(−1, a)
Taking these together, if a < a∗ , we have a < a∗ <and
3 − ²̃(−1, a)²̃(−1, a) > ²∗ . Deﬁne a(−1, ²) implicitly by a(−1, ²̃(−1, a)) = a. Thenτ (−1, ²) ≡ a(−1, ²)(3−²) is decreasing in ². Deﬁning ²(−1, τ ) by τ (−1, ²(−1, τ )) =
τ , ²(−1, τ ) is decreasing in τ for τ ∈ (τ , τ ).
The similar calculations yield W1 (êM ) − W1 (eM ) > 0 for all ² and τ . The
proof of Proposition 2 is similar to that of Proposition 1. Q.E.D.

References[1] Amerighi, O., Peralta, S. 2010. The proximity-concentration trade-oﬀ
with proﬁt shifting, Journal of Urban Economics 68, 90–101.
tax competition among governments, Journal of International Economics 39, 103–121.
[2] Devereux, M., Lockwood, B., Redoano, M., 2008. Do countries compete
over corporate tax rates? Journal of Public Economics 92, 1210–1235.
[3] Fuest, C., Parenti, M., Toubal, F. 2019. International corporate taxation: What reforms? What impact?, Les notes du conseil d’analyseÉconomique, 54, 1-12.
[4] Hauﬂer, A., Schjelderup, G., 2000. Corporate tax systems and crosscountry proﬁt shifting, Oxford Economic Papers 52, 306–325.
[5] Hindriks, J., Nishimura, Y., 2018. Taxing multinationals: The scope for
enforcement cooperation, CORE Discussion Paper, 2018/29.
12

[6] Hindriks, J., Nishimura, Y., 2021. Taxing multinationals: The scopefor enforcement cooperation, Journal of Public Economic Theory 23,487-509.
[7] Huizinga, H., Laeven, L., 2008. International proﬁt shifting within multinationals: A multi-country perspective, Journal of Public Economics 92,
1164–1182.
[8] Kanbur, R., Keen, M., 1993. Jeux sans frontieres: Tax competition
and tax coordination when countries diﬀer in size, American Economic
Review 83, 877–892.
[9] Keen, M., Konrad, K., 2013. The theory of international tax competition and coordination, in Auerbach, A., Chetty, R., Feldstein, M., Saez,E., (Eds.), Handbook of Public Economics, volume 5, North Holland,
Amsterdam, pp. 257–328.
[10] Kind, H.J., Midelfart, K. H., Schjelderup, G., 2005. Corporate tax systems, multinational enterprises and economic integration, Journal ofInternational Economics 65, 507–521.
[11] Klassen, K., Laplante, S., 2012. Are U.S. multinational corporations
becoming more aggressive income shifters?, Journal of Accounting Research 50, 1245–1285.
[12] Nielsen, S. B., Raimondos-Møller, P., Schjelderup, G., 2010. Company
taxation and tax spillovers: Separate accounting versus formula apportionment, European Economic Review 54, 121–132.
[13] OECD, 2021. International collaboration to end tax avoidance, Organisation for Economic Co-operation and Development, Paris,
https://www.oecd.org/ctp/beps/htm (accessed 16 July 2021).
[14] Peralta, S., Wauthy, X., van Ypersele, T., 2006. Should countries control
international proﬁt shifting?, Journal of International Economics 68,
24–37.
[15] Swenson, D., 2001. Tax reforms and evidence of transfer pricing, National Tax Journal 54, 7–25.

13