A Global Minimum Tax for Large Firms Only:
Implications for Tax Competition∗
Andreas Haufler†

Hayato Kato‡

University of Munich

Osaka University

Abstract
The Global Minimum Tax (GMT) is applied only to firms above a certain size
threshold. We set up a simple model of tax competition and profit shifting byheterogeneous multinational firms to evaluate the effects of this partial coverage ofthe GMT. A non-haven and a haven country are bound by the GMT rate for large
multinationals, but can set tax rates for firms below the threshold non-cooperatively.
We show that the introduction of the GMT with a moderate tax rate increases tax
revenues in both the non-haven and the haven countries. Gradual increases in the
GMT rate, however, trigger a sudden change in the tax competition equilibriumfrom a uniform to a split corporate tax rate, at which tax revenues in the non-havencountry decline. In contrast, gradual increases in the coverage of the GMT neverharm the non-haven country. We also discuss the quantitative effects of introducing
a 15% GMT rate in a calibrated version of our model.
Keywords: multinational firms; tax avoidance; profit shifting; tax competition
JEL classification: F23, H25, H87∗

Financial support from the German Research Foundation through CRC TRR 190 (Haufler)and the Japan Society for the Promotion of Science (JP20H01495, JP22K13388) (Kato) is
gratefully acknowledged. This study is conducted as a part of the Project “Economic Policy
Issues in the Global Economy” undertaken at the Research Institute of Economy, Trade andIndustry (RIETI). Kato thanks the University of Munich for their hospitality while part ofthis paper was written. We thank Real Arai, Ruby Doeleman, Antoine Ferey, EmanuelHansen, Makoto Hasegawa, Jota Ishikawa, Mick Keen, Yoshimasa Komoriya, Jonas Löbbing,
Mohammed Mardan, Jakob Miethe, Kenichi Nishikata, Hirofumi Okoshi, Pascalis Raimondos,
Dirk Schindler, Karl Schulz, and Georg Thunecke for helpful discussions. Thanks also to seminarand conference participants at the IIPF in Utah State, Goettingen, Osaka, Kyoto, Shimane, QUT
Brisbane, Ryukoku, Gakushuin, CESifo Munich, and RIETI for useful comments.
†

Seminar for Economic Policy, LMU Munich, Akademiestr. 1, 80799 Munich, Germany. e-mail:Andreas.Haufler[at]econ.lmu.de‡
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043,
Japan. e-mail: hayato.kato[at]econ.osaka-u.ac.jp

1

Introduction

Profit shifting by multinational enterprises (MNEs) has long been a major problem forcorporate taxation worldwide. According to estimates by Wier and Zucman (2022,
Table 1), more than one third of all corporate profits of multinationals are shifted to
tax havens.1 The important role of tax havens for profit shifting is confirmed in manyother studies (e.g., Davies et al., 2018; Bilicka, 2019). In response to the large revenue
losses caused by profit shifting, the OECD has launched an action plan to fight baseerosion in OECD countries, and in particular the profit shifting to tax havens (OECD,
2013a,b). A core development in this endeavor is the introduction of a global minimumtax (GMT), to be applied to large MNEs (OECD, 2020b,c). The GMT with a tax rate of
15% has been agreed upon by a group of more than 130 countries in 2021 (among themseveral tax havens), and most of these countries are expected to have the GMT enacted
by 2026.2 The global revenue gains from a 15% GMT are estimated to be in the rangeof 155-192 billion USD, or 6.5 to 8.1% of global corporate tax revenues (Hugger et al.,2024).3
An important limitation of the GMT is, however, that it applies only to “large”
multinationals, defined as multinational groups that have had no less than 750 million
EUR in total annual revenues in at least two out of the last four years.4 Figure 1
shows that, according to the Orbis database of Bureau van Dijk, about 30% of all
multinational enterprises (MNEs), which are responsible for about 90% of all MNE profits,
have consolidated accounts above this threshold and are therefore covered by the GMT.5
Nevertheless, a substantial amount of MNE profits exceeding 300 billion EUR remains
outside the scope of the GMT. Moreover, the MNE sample in Orbis is not comprehensive
and the database is known for oversampling large firms (Bajgar et al., 2020). Therefore,a coverage rate of the GMT of 90% of all MNE profits is probably an upper bound of the1

Using macroeconomic data, Tørsløv et al. (2023) estimate the magnitude of profit shifting by MNEs
in OECD countries, several developing non-OECD countries, and tax haven countries/territories in 2015.
Wier and Zucman (2022) report updated estimates of Tørsløv et al. (2023).
2
The United States has already enacted, in its 2017 Tax Cuts and Jobs Act, a tax on Global Intangible
Low-Tax Income (GILTI) that works in many respects like a GMT. See Clausing (2020).
3
Baraké et al. (2022, Table 1) break down the global revenue changes of the GMT by country andarrive at a revenue gain of around 50-60 billion EUR for the United States, and gains of similar magnitude
for the EU as a whole. Estimates of both Hugger et al. (2024) and Baraké et al. (2022) are based onmodels where governments and multinational firms mechanically respond to the GMT. Wang (2020) sets
up a quantitative corporate tax framework that endogenizes the behavior of both firms and governments.
Using similar frameworks, Ferrari et al. (2023) and Shen (2024) quantify the effects of the GMT.
4
Since 2016, multinational groups above this threshold size are also required to file individual reportson their activities, profits and taxes paid in each of the countries in which they have a presence (countryby-country reporting).
5This corresponds to the estimate of the OECD, which arrives at a coverage rate of 90% of profits,using the Orbis database and other data sources (OECD, 2020b, # 505, p. 233). In practice, non-EUR
countries express the 750 million EUR threshold value in their domestic currency using the average foreignexchange rate for the December month of the previous fiscal year (OECD, 2020a, p. 9).

1

Figure 1: GMT coverage

Source: Orbis database, own calculations.
Notes: The left bar in each year shows the share of MNEs covered by the GMT out of all MNEs. The
right bar in each year shows the share of pre-tax profits earned by MNEs covered by GMT out of
pre-tax profits by all MNEs. The MNEs covered by GMT are those whose annual revenues exceeds 750
million EUR in at least two of the last four years out of all MNEs. See Data Appendix for details.

true profit share covered by the global minimum tax.
One implication of this incomplete coverage is that low-tax countries might respondto the introduction of the GMT by using a split (or “bifurcated”) corporate tax system,
where a lower tax rate applies to firms below the GMT threshold (Deloitte, 2021). In
fact, such a split is inherent in the regulation that tax havens are allowed to implement
the GMT by raising their (low) general tax rate only for MNEs above the GMT threshold
through a specific top-up tax.6 Tax havens are fully aware of this option. Ireland, forexample, has already decided to keep its general tax rate at 12.5%, but top up the tax
rate to 15% for Irish affiliates of foreign-based MNEs (Department of Finance, 2023).
Against this background, this paper asks the following three questions. First, underwhich conditions will tax competition lead to discriminatory tax policies in either the nonhaven or the haven countries? Second, is the introduction of the GMT revenue-increasing
for non-haven and haven countries? And third, are small reforms of the GMT, given
by either an increase in the tax rate or an increase in the coverage rate of the GMT,
revenue-increasing for each of the countries involved, and for the world? To answer these,
we build a simple two-country model where a non-haven country and a haven countrycompete for the profits of a heterogeneous set of multinational firms, which have agreed
to implement the GMT with incomplete coverage. Both countries can decide to commit,in the first stage, to set the GMT rate for all its multinationals, or not. In the second
6This is known as the Qualified Domestic Marginal Top-Up Tax (QDMTT). See Devereux (2023) fora discussion.

2

stage, if a country does not commit, it can either set a uniform tax rate above the GMTlevel, or split its tax rate and choose a lower rate for firms below the GMT threshold. In
the third stage, multinationals take their profit-shifting choices.
Our analysis shows that the introduction of a partial GMT leads to a sequence oftax competition regimes between the haven and the non-haven. We show that if the
GMT rate is binding for the tax haven, but still low enough, the tax haven will choose
to commit to the GMT rate for all MNEs, in order to increase the (uniform) tax ratein the non-haven country. As the GMT rate is further increased, however, it is first thehaven country and then also the non-haven country that do indeed split their tax rates in
the non-cooperative tax equilibrium. At this regime-switching GMT rate, the non-havencountry discretely loses tax revenues. Except at this rate, the non-haven always gains
from gradual increases in the GMT rate, whereas the haven gains only for sufficiently
low levels of the GMT, and loses revenue otherwise. Gradual increases in the coverage ofthe GMT have similar effects, with the important difference that they never reduce tax
revenues in the non-haven country and in the world. These results suggest that even if
both countries benefit from the introduction of a moderate GMT rate, conflicts of interest
will arise once the GMT rate, or the GMT coverage, is increased.
In a final step, we calibrate our model using corporate tax rates and the estimatesof profit shifting in a worldwide sample of countries (Tørsløv et al., 2023). In ourcalibrated economy, upon the introduction of the GMT, both the haven and the nonhaven countries increase their single tax rate for all MNEs and gain more tax revenues.
Any further increase in the GMT rate causes the haven country to lose tax revenues,
however. Moreover, starting from a GMT rate of 18-19%, the haven country will start
splitting its tax rate and impose a discretely lower tax rate on small multinationals notcovered by the GMT. This in turn leads to a large loss for the non-haven country, equal
to around 4% of its tax revenues from multinationals.
Our model contributes to the recent theoretical literature on the effects of introducing
a GMT in tax competition. In a model with many non-haven and haven countries,
Johannesen (2022) shows that the effects of introducing a GMT on welfare, i.e., thesum of tax revenues and capital income of residents, are fundamentally ambiguous for
non-haven countries. This is because the increase in havens’ tax rates due to the GMT
raises tax revenues in the non-havens but lowers the profits of MNEs, and thus capitalincome, by limiting the scope of profit shifting. Hebous and Keen (2023) also analyze
the effects on welfare in a model where two countries differ in terms of both their size
and their valuation of public spending. Their quantitative results indicate that GMTlevels up to 17-20% can constitute strict Pareto improvements, increasing welfare in both
high-tax and low-tax countries. Hindriks and Nishimura (2022) consider governments
who choose not only tax rates but also tax enforcement. They show that the introduction3

of the GMT hinders tax enforcement cooperation between the high-tax and the low-tax
country, making the high-tax country worse off. Finally, Janeba and Schjelderup (2023)
study a three-country model where two non-haven countries compete for real FDI while
simultaneously competing for profit shifting with a third, tax-haven country. In thissetting the introduction of the GMT intensifies tax competition for real FDI. While tax
revenues in the non-haven countries will still increase if they compete via corporate tax
rates, net revenue gains are zero if competition is via lump-sum subsidies.
All these models have in common that the GMT must be levied uniformly on all
firms, thus ignoring the existence of a threshold below which the GMT does not apply.
In our model, in contrast, this threshold plays a critical role as it allows countries to use
different tax rates on firms with revenues above and below the threshold. This featurelinks our model to the literature on discriminatory tax competition. This literature has
analyzed whether tax revenues are higher in the non-cooperative tax equilibrium whencountries may, or may not, set different tax rates on tax bases with different degrees ofinternational mobility (Janeba and Peters, 1999; Keen, 2001; Janeba and Smart, 2003).7
In our setting, tax discrimination will not be profitable for either country in the absenceof the GMT, but it will arise in equilibrium if a sufficiently high level of the GMT is
imposed. A distinct, but closely related literature has addressed the issue of whether the
existence of tax havens – by allowing non-haven countries to tax-discriminate in favor ofmobile, multinational firms – increases or reduces tax revenues and welfare in the nonhaven countries (Slemrod and Wilson, 2009; Hong and Smart, 2010; Johannesen, 2010;
Elsayyad and Konrad, 2012).
Our analysis proceeds as follows. In Section 2 we set up our model of tax competitionand characterize the Nash equilibria that result in different tax regimes. Section 3 thenturns to the revenue effects of introducing a GMT, and of increasing its tax rate andcoverage. Section 4 calibrates our model to real-world data and quantifies its effects.
Section 5 concludes.

2

The model

2.1

Setup

We consider a tax competition model between a non-haven country, indexed by n, and a
tax-haven country, indexed by h. There are a large number of heterogeneous, multinational
enterprises (MNEs), each having an affiliate both in the non-haven and in the haven. The
7This literature has been extended to cover differences in country size (Bucovetsky and Haufler,2007), and imperfect competition in product markets (Gaigné and Wooton, 2011). A related type of
discrimination arises when profit shifting is monitored by governments in a deliberately loose way (Peralta
et al., 2006).

4affiliate in the non-haven makes exogenous profits in this country, π, which are distributedin the range [π, ∞), with a cumulative distribution function F (π). Hence, all real activity
occurs in the non-haven country, and this is where the “true” profits accrue in its entirety.
MNEs can shift a share θ ∈ [0, 1] of their non-haven affiliate’s profits to their haven
affiliate, in order to maximize their post-tax profits.8
We assume that both countries’ objective is to maximize tax revenues. This is astandard assumption in models of corporate tax competition, and it is motivated by
the specific focus on tax revenue increases in non-haven countries that underlies the
GMT proposal (see footnote 3). We assume that both countries have signed the GMT
agreement, and are therefore bound to set a tax rate no smaller than the GMT rate,tM .9 However, the GMT applies only to MNEs that make exogenous profits no smaller
than πM , called “large MNEs” in our analysis. Therefore, countries remain free to set alower tax rate than the GMT for all MNEs that make profits less than πM , called “small
MNEs.”
Since the GMT is prescribed as a minimum tax for large firms, it becomes a reference
point for countries’ tax-setting. Specifically, it allows both countries to commit to the tax
rate set by the GMT, and doing so for all MNEs, not only for the large ones.10 Thus, thetax competition game in our model has three stages. In the first stage, the non-haven andhaven countries simultaneously choose whether to commit to the GMT rate for all MNEs,
or not. In the second stage, the country that commits to the GMT in the prior stage sets
the GMT rate, whereas the country that does not commit either sets a single non-GMT
rate for all MNEs (which has to be no smaller than the GMT rate to be permitted), or
it sets different tax rates for large and small MNEs. In the final stage, MNEs engage in
profit shifting, given the tax rates in the two countries. We solve this three-stage gameby backward induction. The equilibrium concept we rely on is the sub-game perfect Nashequilibrium, which we call the tax-competition equilibrium.
8This is the simplest possible setting for profit shifting, and sufficient for our purposes. See e.g.,
Krautheim and Schmidt-Eisenlohr (2011) for a similar assumption. In particular, this setting avoids thepossible non-existence of Nash equilibria that arise in models where the location of individual firms is
endogenous (Baldwin and Okubo, 2009; Davies and Eckel, 2010; Haufler and Stähler, 2013).
9
Devereux (2023) discusses how the specific institutional setting of the GMT, in particular the UnderTaxed Payments Rule (UTPR), gives incentives to both non-haven countries and haven countries to join
the GMT agreement, once this has been initiated by a critical number of large non-havens. Note alsothat we assume the tax base of the GMT to be the same as that of national corporate taxes, thus ignoring
extra tax deductions (labelled “substance-based income exclusion”) under the GMT. See Schjelderup andStähler (2024) for a study focusing on the latter issue.
10This is related to the literature on endogenous timing, or leadership, in tax competition, wherecountries commit in a pre-play stage to set taxes early or late. See Kempf and Rota-Graziosi (2010).

5

2.2

Profit shifting by multinationals

MNEs shift a share θ of their profits π from their non-haven affiliate to the haven affiliate,while bearing transaction costs. The latter can either be thought of as concealment costs,
which have to be incurred to hide the profit shifting from the non-haven country’s tax
authorities, or as the expected fine that is to be paid when profit-shifting is detected
and sanctioned. We assume that profit-shifting costs C are convex and, for analytical
simplicity, quadratic in the level of profit-shifting, θπ. Higher total profits make it easier,however, to hide a given amount of profit-shifting.11 Therefore, the total shifting costs
for a firm with profits π are C(π) = (θπ)2 /π = θ2 π. A MNE that maximizes its global
after-tax profits given the tax rates tn and th in the non-haven and the haven country
respectively, then faces the following problem:max (1 − tn )(1 − θ)π + (1 − th )θπ −
θ

δθ2 π
,
2

(1)

where δ > 0 is an exogenous cost parameter that captures the ease with which profits canbe shifted across countries. This parameter incorporates, in particular, any efforts thatcountries take to prevent profit-shifting, such as the newly enacted country-by-country
documentation requirements.12 The MNEs’ optimal choice of θ is then:θ=tn − th,δ(2)which is independent of π and therefore holds for all MNEs simultaneously.13
The optimal θ defined by (2) allows us to incorporate the MNEs’ adjustment to tax
differentials in a very simple and compact form. It implies that MNEs of different size will
respond to international tax differentials with the same tax base elasticity. Substituting(2) in (1), the tax base of a MNE with profits π in the non-haven country is T B =[1 − (tn − th )/δ]π. This yields a tax base elasticity of an individual MNE in the non-haven
Bn /T Bn
= δ−(ttnn−th ) , which is independent of π.
country such that εn = − dTdt
n /tn
It seems safe to say that the relationship between the size of firms and their responsivenessto tax is inconclusive. Media coverage of tax avoidance by gigantic multinationals gives animpression that bigger firms have a higher tax-base elasticity. However, there are several
studies which find the opposite result that the tax-base elasticity is indeed higher for small
firms (not necessarily MNEs, e.g., Devereux et al., 2014; Coles et al., 2022; Auliffe et al.,2023). Therefore, assuming that the tax base elasticity is independent of firm size may
11This specification is widely used in the literature on profit shifting (e.g., Hines and Rice, 1994;
Huizinga and Laeven, 2008).
12
In Hindriks and Nishimura (2022), this cost parameter is endogenously chosen by governments, either
cooperatively or non-cooperatively.
13
In principle, our analysis can incorporate θ < 0, which occurs if tn < th . However, this case will
never arise in a tax-competition equilibrium.

6

be considered a useful and not unrealistic benchmark. The assumption that the tax baseelasticity is independent of the size of MNEs implies that there is no reason per-se forcountries to differentiate tax rates between MNEs of different size. However, as we will see
below, a split tax regime can nevertheless occur in equilibrium as a result of introducing
a GMT for large firms only.

2.3

Governments’ tax setting choices

Before examining the effects of GMT, we first solve the unconstrained maximization
problem of the two countries in the absence of a GMT. In this case, the non-havencountry n maximizesZ ∞tn (1 − θ)πdF = tn (1 − θ)Π,max Gn =tn

πR∞
where Π ≡ π πdF are the total profits (before shifting) earned by all MNEs in country n.
Analogously, the tax-haven country h maximizesZ ∞max Gh =thth θπdF = th θΠ,πwhere the assumption of equal tax base elasticities for all MNEs implies that tax revenues
depend only on the aggregate before-shifting profits of MNEs, but not on the profit
distribution across firms.
Using the profit-shifting choices of MNEs in (2), we obtain the first-order conditionsof the two countries as follows:




∂Gn
tn − thtn∂Ghtn − thth= 1−
Π − Π = 0,=
Π − Π = 0,
∂tn
δ
δ
∂th
δ
δ
where the first term in each FOC is the mechanical effect of increasing the tax rate on agiven tax base, whereas the second term is the behavioral effect due to changes in the tax
base that arise from the MNEs profit-shifting choices.
Solving the first-order conditions of the two countries yields best response functions:14
tn =th + δ
for π ∈ [π, ∞),2tn
for π ∈ [π, ∞).
2

(3)

δ
for π ∈ [π, ∞),
3

(4)

th =

Equilibrium taxes are then
t0n =
14

2δ
for π ∈ [π, ∞),
3

t0h =

The second-order condition of both countries’ optimal tax problems are trivially satisfied.

7

and equilibrium tax revenues are
G0n =

4δ
Π,
9

G0h =

δ
Π.
9

(5)

The superscript 0 represents the unconstrained equilibrium, which we call Regime 0.
Regime 0 also emerges as an equilibrium in a world with a GMT, if the GMT rate is lower
than both tax rates given in (4), and hence non-binding.
This benchmark equilibrium has the usual properties. A tax haven without an independenttax base will choose one-half of the tax rate of the large country, and both tax rates
are rising in the cost parameter of profit shifting, δ. To ensure that the non-haven’s
unconstrained tax rate is below unity, we need to restrict the cost parameter for profit
shifting. Hence we assume δ < 3/4 in the following.15 Finally, substituting the equilibriumtax rates in (4) back into the multinationals’ first-order condition (2) gives
θ0 =1
t0n − t0h
= .
δ3

The property of our model that, in the unconstrained tax equilibrium, all multinationals
shift one-third of their profits to the tax haven makes our model particularly simple towork with. At the same time, this share of shifted profits is quite close to empiricalestimates of profit shifting, as we will see in Section 4.
Our results for the benchmark equilibrium are summarized as follows.
Proposition 1 (Regime 0: Unconstrained tax equilibrium without GMT)
Consider a tax-competition game between the non-haven and haven country in the absenceof a GMT and assume δ < 3/4. In the tax-competition equilibrium, each country sets asingle unconstrained maximizing tax rate for all MNEs with π ∈ [π, ∞) given by (4).

2.4

Tax regimes

With a GMT in place, there is a first stage of the game in which each country chooses tocommit or not to a single GMT rate, labelled tM , for all MNEs. This gives rise to four
possible combinations of commitment choices, which are shown in Table 1. For example,
Gi (C, N ) stands for the total tax revenues of country i ∈ {n, h} when the non-havencountry n chooses to commit and the haven country h does not. One can immediately
see that the combination (C, C) (both countries commit) can never occur in equilibrium.
15

From (4) the condition for t0n < 1 is δ < 3/2. In the course of our analysis, we need the stricter
condition δ < 3/4, however, to ensure that all possible equilibrium regimes can emerge. See the discussionof Proposition 2 below.

8This is because these first-stage choices would lead to a zero tax difference between thetwo countries and zero tax revenues for the haven. Therefore, the haven always has anincentive to deviate from (C, C). Finally, we assume that countries choose to commit, if
the commitment choice does not make any difference to their revenues.
Table 1: Payoff matrix of the commitment gameNon-haven

Haven
Not commit

Not commit
Commit to GMT

Gn (N, N ),Gn (C, N ),Commit to GMT

Gh (N, N )Gh (C, N )Gn (N, C),

Gh (N, C)—

The two countries choose their tax rates in the second stage. If they do not commit
to a single GMT in the first stage, they may either set a single non-GMT rate for all
MNEs, or set different rates for MNEs of different size. MNEs with profits equal to or
greater than the threshold πM , i.e., π ∈ [πM , ∞), are subject to the GMT requirement(large MNEs), whereas those with π ∈ [π, πM ) are not (small MNEs). We denote by φthe share of total profits earned by large MNEs, or the coverage rate of the GMT:
R∞

πdF
πM
φ ≡ R∞
=
πdF
π

R∞
πM

πdF

Π

,

(6)

which is exogenously given. Once the tax rates in both countries i ∈ {n, h} are determined,
the MNEs choose their levels of profit shifting from (2).
Let us first state the full characterization of the sub-game perfect Nash equilibrium of
the three-stage tax competition game, before commenting on each regime. It is immediate
to see that if tM is lower than the haven’s unconstrained rate t0h = δ/3, the GMT has
no effect on either country’s decision and Regime 0 emerges. Thus Proposition 2 below
starts from tM ≥ t0M ≡ t0h = δ/3. As tM is continuously increased from t0h to unity, thetax competition equilibrium passes through four different regimes.

Proposition 2 (Equilibrium regimes with binding GMT)
Consider a GMT rate such that tM ≥ t0M ≡ δ/3 with δ < 3/4. As tM is continuously
increased, the tax-competition equilibrium is characterized by the following four regimes:(i) Regime 1: tM ∈ [t0M , t1M ≡ 2δ/3).
The non-haven sets a single unconstrained
revenue-maximizing tax rate and the haven commits to a single GMT rate:
t1n =tM + δ
for π ∈ [π, ∞),29t1h = tM for π ∈ [π, ∞).

t1M , t2M ≡ δh1 − 31q2(1−φ)2−φi(ii) Regime 2: tM ∈. Both the non-haven and the havensplit their tax rates and the non-haven chooses a tax rate in excess of tM for large
MNEs:


δ/3 for π ∈ [π, π )
2δ/3
for
π
∈
[π,
π
)
M
M
2
2
,
th =
.
tn =
t
(t + δ)/2 for π ∈ [π , ∞)for π ∈ [π , ∞)MM(iii) Regime 3: tM ∈ [t2M , t3M ≡ 4δ/3].
the haven splits its tax rate:

M

M

The non-haven commits to a single GMT andt /2 for π ∈ [π, π )
M
M
t3h =
.
t
for
π
∈
[π
,
∞)
M
M

t3n = tM for π ∈ [πM , ∞),Both the non-haven and the haven split their tax rates(iv) Regime 4: tM ∈ (t3M , 1].
and both countries choose a tax rate below the GMT for small MNEs:
2δ/3 for π ∈ [π, π )
M
t4n =
,
t
for π ∈ [π , ∞)MM
δ/3 for π ∈ [π, π )
M
t4h =
.
t
for π ∈ [π , ∞)M

M

Proof: See Appendix A.1.
In the following we go through the different regimes, which are divided by the three
threshold GMT rates {tiM }i=1,2,3 . We call these the regime-switching rates.
In Regime 1, where tM is rising above t0M , the haven’s unconstrained maximizing
rate t0h = t0M falls short of tM and the haven is forced to set tM for large MNEs. By
contrast, the non-haven’s unconstrained rate is still above the GMT, so that the nonhaven is not bound by the GMT. Therefore, the non-haven will choose not to commit
to the GMT in this regime, and the first-stage equilibrium is determined only by thehaven’s commitment choice. The latter affects only tax revenues from small MNEs, since
the haven must set tM for large MNEs, regardless of whether it commits. Given the nonhaven’s non-commitment, the haven’s total revenues when it commits and those when it
does not are respectively,(tM + δ)/2 − tM
Gh (N, C) = tM
(1 − φ)Πδδ 2δ/3 − δ/3Gh (N, N ) =(1 − φ)Π
3δ
(tM + δ)/2 − tM
+ tM
φΠ,
δ


(tM + δ)/2 − tM
+ tM
φΠ,
δ

(7)

where we have substituted the non-haven’s tax rate on small MNEs in the second stage
10

from its best response function (3).
The second term in each function Gh (N, ·) are tax revenues from large MNEs, which are
independent of the haven’s commitment choice. What matters for the haven is therefore
the first term, i.e., tax revenues from small MNEs. In Regime 1, we see from (7) that
Gh (N, C) − Gh (N, N ) ≥ 0 and the haven will obtain more revenues, if it commits. The
reason is that this induces the non-haven to set a higher tax rate for small MNEs, (tM +δ)/2 > 2δ/3. In response to the haven’s commitment, the non-haven will in turn alsochoose a uniform tax rate that exceeds its unconstrained level.
In Regime 2, where tM > t1M ≡ 2δ/3, the GMT becomes binding for the non-havencountry as well. In contrast to Regime 1, the level of the GMT in this regime is highenough that commitment by the haven would reduce the tax differential between thetwo countries and thus shifted profits to the haven significantly. Thus, non-commitment
becomes the dominant strategy for the haven country, i.e., Gh (N, C) − Gh (N, N ) < 0, andthe haven undercuts the GMT for small MNEs. For the non-haven, the trade-off is thento either commit and set tM for all MNEs, or not to commit and set a tax rate in excessof the GMT, tn = (tM + δ)/2 > tM , for large MNEs, but a tax rate below the GMT,
tn = 2δ/3 < tM , for small MNEs. At the moderate level of the GMT in this regime,
the non-haven can gain more revenues by exceeding the GMT for large MNEs, and thuschooses not to commit, Gn (N, N ) > Gn (C, N ). The upper boundary of Regime 2, t2M , isrising in the GMT coverage rate, φ, and thus Regime 2 holds for a wider range of tM , asa higher coverage rate makes revenue gains
fromq largei MNEs more important.
h12, the haven continues to undercut
In Regime 3, where tM > tM ≡ δ 1 − 3 2(1−φ)
2−φthe GMT for small MNEs. For the non-haven, however, the GMT is now so close to its
tax rate for large MNEs under non-commitment, tn = (tM + δ)/2, that committing to
the GMT causes few revenue losses for large MNEs. The non-haven will therefore benefit
from committing, and Gn (C, N ) ≥ Gn (N, N ), as this induces the haven to set a higher
tax rate for small MNEs. Hence commitment serves the same purpose for the non-havenin this regime, as it does for the haven in Regime 1.
Finally, in Regime 4, where tM > t3M ≡ 4δ/3, the international tax differential forsmall MNEs becomes very large, if the non-haven keeps its commitment to the GMT.16
To avoid large tax base losses from small MNEs, the non-haven therefore abandons its
commitment and undercuts the GMT for small MNEs, Gn (N, N ) > Gn (C, N ). Again, thisargument is analogous to the argument for the haven to end its commitment in Regime 2.
In equilibrium, both countries split their tax rates and set their unconstrained tax rates
for small MNEs, while adhering to the GMT for large MNEs.
The sequence of regime-specific equilibria for different values of tM is shown graphically16

Excluding tax rates above unity, Regime 4 can only occur when δ < 3/4. This is the reason forimposing this constraint from the start of our analysis (see footnote 15).

11

Figure 2: Equilibrium tax rates for different GMT rates

Notes: The figure shows the equilibrium tax rates in the non-haven (a) and the haven (b). Parametervalues are (φ, δ) = (0.9, 0.279) given in Table 2, but they do not affect the qualitative behavior. The
horizontal axis is the exogenous GMT rate starting from tM = 0.1 above t0M = δ/3 = 0.093. The solid
curve in each panel is the equilibrium rate in the corresponding equilibrium regimes; the dottedhorizontal line is the unconstrained equilibrium rate in Regime 0.

in Figure 2, where the solid curves give the tax rate(s) in the tax-competition equilibrium,
and the dotted curve gives the unconstrained equilibrium tax rate t0i . Tax rates in bothcountries generally tend to rise as the GMT increases, but there are distinct patterns in
the different regimes. At the switch from Regime 1 to Regime 2, the non-haven country
splits its tax rate and its tax rate for small MNEs drops discontinuously. At the switchfrom Regime 2 to Regime 3, the non-haven returns to a single tax rate, but this implies
that its tax rate for large MNEs falls discontinuously. Finally, in Regime 4, the non-havenonce again splits its tax rate, leading to a discontinuous fall in the tax rate for small MNEs.
In contrast, the haven country adheres to the GMT in taxing large MNEs in all regimes.
From Regime 2 onward, however, the haven splits its tax rate and charges a lower tax forsmall MNEs. In Regimes 2 and 4, this tax rate corresponds to the unconstrained tax rate
t0h = δ/3, whereas in Regime 3 it is above t0h , in response to the non-haven’s commitment.

12

3

Revenue effects of the GMT

3.1

Introduction of the GMT

Having fully described the tax-competition equilibrium in each regime, we can now turnto the effects that introducing the GMT has on tax revenues in the two countries. We
first compare revenues in the tax-competition equilibrium to those in the unconstrained
equilibrium, Regime 0. This is summarized in:
Proposition 3 (GMT introduction)
Consider the tax-competition equilibrium with GMT, as summarized in Proposition 2,
and assume the GMT coverage rate is not too low so that φ ∈ (3/4, 1). Compared to theunconstrained equilibrium (Regime 0), the introduction of a binding GMT rate leads to:(i) a rise in tax revenues in the non-haven country for all Regimes 1 to 4.
(ii) a rise in tax revenues in the haven country for Regime 1, but a fall in tax revenues
for Regimes 2 to 4.
(iii) a rise in world tax revenues for all Regimes 1 to 4.
Proof: See Appendix A.2.
The intuition for Proposition 3 is straightforward for the non-haven country. Since the
GMT is first binding for the haven and pushes this country’s tax rate upward in Regime 1,
the non-haven will necessarily gain from a GMT that affects only the other country. In
Regimes 2 to 4, the haven splits its tax rate, but it is still bound by the GMT for large
MNEs. Therefore the non-haven always has an option to set tM for large MNEs, and theunconstrained tax rate, t0n = 2δ/3, for small MNEs. This clearly benefits the non-havenbecause it cannot lose tax base through the profit shifting of its large MNEs, whereas
the competition for small MNEs is the same as in Regime 0. This is indeed the outcome
in Regime 4. In Regimes 2 and 3 the non-haven deviates from this policy by choosing
a tax rate above the GMT for large MNEs in Regime 2, or by committing to set the
GMT also for small MNEs in Regime 3. However, the non-haven will only do so if these
deviations offer additional tax revenue, relative to the “default policy” chosen in Regime 4.
Therefore, the non-haven must gain from introducing a GMT in all of Regimes 1 to 4,
relative to Regime 0, and for all levels of φ ∈ (0, 1).
Matters are different for the haven country. In Regime 1, the haven is forced toincrease the tax rate for large MNEs and, by the haven’s own commitment, also for small
MNEs. This commitment by the haven raises in turn the uniform tax rate levied by
13

the non-haven. Effectively, the GMT works as a coordination device in Regime 1 and it
increases tax rates in both countries from their inefficiently low levels in the benchmark
of Regime 0. Therefore, the haven will also gain from the introduction of the GMT in
Regime 1.
For higher levels of the GMT, however, the haven will lose revenues. This is mostobvious in Regime 4, where both countries set the GMT for large MNEs, and choose theirunconstrained tax rate for small MNEs. In this regime, the haven still secures positive tax
revenues from underbidding the non-haven for small MNEs, but these revenues must be
strictly less than those in Regime 0 because only a fraction (1 − φ) of the total aggregate
profits is subject to this tax competition. In Regimes 2 and 3, the haven loses revenues
for a different reason. In both regimes, the international tax differential for large MNEs
is smaller than in Regime 0, implying that less profits are shifted to the haven. When the
GMT coverage rate is sufficiently large, so that φ ∈ (3/4, 1), this revenue loss from large
MNEs is the dominant effect for the tax haven.
Finally, the gains to the non-haven exceed the losses to the haven country in all regimes
where the effects are counteracting. Therefore, the GMT introduction results in higher
aggregate (worldwide) tax revenues in all regimes, and for all coverage rates φ.
Overall, our results in Proposition 3 show that the interests of haven and non-havencountries are aligned only in Regime 1, where tM is only slightly above t0h . In the remaining
Regimes 2 to 4, there is a conflict of interests between the two countries, in the sense thatthe non-haven benefits from the introduction of a higher GMT, whereas the haven country
loses.17 To evaluate the revenue effects of the GMT, and the incentives that havens haveto agree to its introduction, it is therefore critical to determine which regime is inducedby the current GMT rate of 15%. We will analyze this issue for a calibrated economy in
Section 4. Before doing so, however, it is also relevant to analyze the effects of two more
gradual reforms, increases in the GMT rate tM , and in the GMT coverage rate φ. Bothare likely reform options after the GMT has been introduced.

3.2

Gradual reform I: increasing the GMT rate

The effects of a marginal increase in the GMT rate can be summarized as follows:
Proposition 4 (Gradual reform: increasing GMT rate tM )Consider the tax-competition equilibrium with GMT, as summarized in Proposition 2, andassume the GMT coverage rate is not too low such that φ ∈ (1/4, 1). A marginal increase
17

This conflict of interest does not exist in (Johannesen, 2022, Proposition 6), where havens gain fromthe introduction of a GMT at any level, as long as profit shifting is not completely eliminated. The reason
is that Johannesen (2022) models many identical tax havens that are in Bertrand competition with eachother. Therefore, revenues in the unconstrained tax competition equilibrium are zero for each haven, andany positive GMT rate generates a revenue increase for the representative haven.

14

in the GMT rate has the following effects:(i) tax revenues in the non-haven country strictly increase in all regimes, except at thefirst regime-switching point, t1M , where they discretely fall.
(ii) tax revenues in the haven country increase in Regime 1 as long as tM < δ/2, thendecrease in the remainder of Regime 1 and in Regime 2, then rise in Regime 3, andare zero in Regime 4. Marginal revenues in the haven discretely fall at the last two
regime-switching points, t2M and t3M .
(iii) tax revenues in the world strictly increase within all regimes, but fall at the three
regime-switching points, t1M , t2M and t3M .
Proof: See Appendix A.3.
As is true for the introduction of the GMT (Proposition 3), the non-haven generally
gains from a gradual increase in the GMT rate tM . In Regimes 1 and 2, this is because
the non-haven’s equilibrium tax rate is rising in tM while the international tax differential
for large MNEs simultaneously narrow, so that fewer profits are shifted to the tax haven.
In Regimes 3 and 4, where the tax differential for large MNEs is zero, raising tM without
inducing large MNEs to shift profits to the haven must benefit the non-haven.18
An interesting discrete drop in the non-haven’s revenue occurs, however, at the firstregime-switching point t1M . At this point, the haven country changes its behavior fromcommitting to the GMT for all MNEs to splitting its tax rate for large vs. small MNEs.
This intensifies competition for small MNEs and thus discontinuously reduces both thetax base and the tax rate for small MNEs in the non-haven country.
For the haven country, the marginal effects of tM display several non-monotonicities.
In Regimes 1 and 2, there are two fundamentally counteracting effects as a higher tM
raises the tax rate levied by the haven on large MNEs, but at the same time fewer profits
are shifted to the tax haven. In the first part of Regime 1, for tM ∈ [t1M , δ/2), thepositive first effect dominates and the haven benefits from an increased level of tM . Thispattern is reversed, however, in the remaining part of Regime 1, where tM ∈ [δ/2, t2M ],and also in Regime 2. In Regime 3, where the non-haven commits, a higher tM widens thetax differential for small MNEs, leading to increased tax revenues in the haven country.
Finally, in Regime 4, the haven’s revenues are independent of tM , as the haven’s tax baseis zero for large MNEs, whereas tax rates on small MNEs are unaffected by tM .
Moreover, the haven country discretely loses tax revenues at the regime-switching
points t2M and t3M , where its opponent changes its behavior. At t2M , the non-haven starts
18

In Regime 3, the international tax differential for small MNEs widens and the non-haven may earn
less revenues from them as tM rises. For revenue gains from large MNEs to dominate, the coverage shareof the GMT, φ, must exceed 1/4. This condition is clearly fulfilled for the existing GMT, as we see in
Figure 1.

15

committing to tM for all MNEs and therefore shuts down the profit shifting of large MNEs.
At t3M the non-haven stops committing to the GMT rate, fueling competition for small
MNEs.
Taking the results of the two countries together, the effect of marginal increases in tM
on worldwide tax revenues are dominated by the effects on the non-haven country, andare therefore positive. The negative, discontinuous effects at the regime-switching points
are caused by the non-haven at t1M , and by the haven country at t2M and t3M . We will
illustrate these results in our quantitative analysis in Section 4.

3.3

Gradual reform II: increasing GMT coverage

Finally, we analyze the marginal effect of the GMT coverage rate φ while keeping the
GMT rate tM fixed. As shown in (6), this is achieved by reducing the threshold profit
level πM above which the GMT rate must be charged. The results are summarized in:
Proposition 5 (Gradual reform: increasing GMT coverage rate φ)Consider the tax-competition equilibrium with GMT, as summarized in Proposition 2. A
marginal increase in the GMT coverage rate of φ ∈ (0, 1) has the following effects:(i) tax revenues in the non-haven country are unaffected in Regime 1 and strictlyincrease in Regimes 2 to 4;(ii) tax revenues in the haven country are unaffected in Regime 1 and strictly decrease
in Regimes 2 to 4, except at the regime-switching point t2M , where they discretelyrise.
(iii) world tax revenues are unaffected in Regime 1 and strictly increase in Regimes 2
to 4.
Proof: See Appendix A.4.
In Regime 1, an increase in φ has no effect on revenues in either country, because
both countries levy uniform tax rates. Changing φ does have effects, however, in theother regimes, where one or both countries split their tax rates. Since the equilibrium tax
differential is always greater for small MNEs than for large MNEs, a higher φ, meaning lesspresence of small MNEs, reduces aggregate profit shifting. This unambiguously hurts thehaven and benefits the non-haven. From the global perspective, more GMT coverage isalways desirable, as it reduces pressure on tax competition for the profits of small MNEs.
There is one situation, however,q thei haven can gain from a higher φ. Suppose
h in which
12
and the equilibrium is in Regime 3. The
that tM is slightly above tM = δ 1 − 3 2(1−φ)
2−φ16non-haven reacts to an increase in φ by stopping to commit to a single GMT, leading
to an equilibrium switch to Regime 2 (as dt2M /dφ > 0). In Regime 2, the non-haven’s
optimal tax rate for large MNEs rises above the GMT and this in turn increases profit
shifting to the haven.
In summary, Proposition 5 shows that changes in the GMT coverage rate φ have
opposing revenue effects in non-haven and haven countries in Regimes 2 to 4, but not in
Regime 1. This underscores our findings from Propositions 3 and 4 that mutual gains
both from the introduction of the GMT and from gradual increases in the GMT rate canonly arise in Regime 1. However, one notable difference between the two gradual reforms
is that a higher φ never harms the non-haven country and the world. We now turn to theissue of which regime we can expect for the currently imposed GMT rate.

4

Quantitative implications

In this section we analyze a calibrated version of our model, and explore its quantitative
revenue effects. We calibrate our benchmark model without GMT to match basic dataon international profit shifting. We set the total pre-tax profits of MNEs (Π) to 2, 590
billion USD, as reported in Tørsløv et al. (2023). The coverage rate of the GMT is set
at φ = 0.9, in accordance with OECD (2020b) and our own calculations from the ORBIS
database (see Table B.1 in the appendix). We then calculate the cost parameter of profit
shifting, δ, to exactly match the GDP-weighted average of effective tax rates in non-havencountries of 18.6%, as reported in Tørsløv et al. (2023). Table 2 reports calibration results.
Among the non-targeted moments, our calibration arrives at a share of shifted profits of
33.3%, which closely matches the share of shifted profits in the data (37.4%), as reported
in Tørsløv et al. (2023). Our model somewhat underestimates the haven tax rate and theaggregate revenue loss in the non-haven countries, as compared to their corresponding
values in the data.
Figure 3 shows the effects of introducing a GMT at various tax rates tM for thiscalibrated version of our model. The figure shows both the resulting tax regimes and theequilibrium tax revenues for both non-haven and haven countries, as compared to thelevel of tax revenues in the unconstrained tax-competition equilibrium (G0i ). The mostimportant result is that the introduction of the GMT with a tax rate of 15% leads to a
tax equilibrium in Regime 1. In this regime, the tax haven finds it profitable to commit to
the GMT rate for all MNEs; see Proposition 2(i). Also, both countries will gain from theintroduction of the GMT, as stated in Proposition 3. In fact, panel (b) in Figure 3 showsthat a 15% GMT rate is very close to the haven country’s global (i.e., regime-independent)
revenue maximum in our calibrated model.
The calibrated revenue gain of a 15% GMT rate is around 106 billion USD for the non17

Table 2: Calibration of the modelParameter

SourceΠ = 2, 590bUSD

Total pre-tax profits of MNEs

Tørsløv et al. (2023)

φ = 0.9

Profit share of MNEs covered by GMT

OECD (2020b) / Orbis

δ = 0.279

Cost of profit shifting

Calibrated

Targeted moment

Model

Data

SourceCorp. tax rate of non-haven: tn = 2δ/3

18.6%

18.6%

Tørsløv et al. (2023)

Non-targeted moment

Model

Data

SourceCorp. tax rate of haven: th = δ/3

9.3%

13.7%

Tørsløv et al. (2023)

Share of MNE’s shifted profits: θ

33.3%

37.4%

Tørsløv et al. (2023)

Non-haven’s revenue loss: tn θΠ161bUSD

247bUSD

Tørsløv et al. (2023)

Notes: Data are from 2019. Definition of non-haven and haven countries follow Tørsløv et al. (2023).
The non-haven countries are 30 OECD and 7 major developing countries. There are 40 haven countries
across the world. The corporate tax rate of the non-haven and haven countries is a GDP-weighted
average of effective tax rates.

haven and 10 billion USD for the haven country. These values do not depend on specificvalues of the coverage rate φ, since both countries optimally set a uniform tax rate acrossall MNEs in Regime 1. This implies that worldwide tax revenues, GW ≡ Gn +Gh , increaseby 116 billion USD.19 The quantitative revenue estimates of introducing a 15% GMT aresummarized in Table 3.
Table 3: Quantitative effects of introducing a 15% GMT
Non-haven

Haven

World

Tax rate before GMT introduction

18.6%

9.3%

—–

Tax rate after GMT introduction

21.4%

15%

—–

Revenue change in bUSD (% change)

106 (33.0%)

10 (11.8%)

116 (28.7%)

Note: Results are based on the calibrated parameter values described in Table 2.

Further marginal increase in the GMT rate beyond 15% will, however, not benefit thehaven country. As is shown in panel (b) of Figure 3, this fall in tax revenues for the havencountry continues until tM = t1M = 0.186. When tM exceeds this level, the tax equilibrium
19

This compares with estimated revenue gains for the EU countries of 55 billion EUR by Baraké et al.
(2022), and OECD estimates of global revenue gains in the range of 155-192 billion USD (Hugger et al.,2024). The percentage increases in corporate tax revenue in our model are not comparable to those in
Baraké et al. (2022) and Hugger et al. (2024), as there are no domestic firms in our model.

18

Figure 3: Quantitative effects of introducing the GMT

Notes: The figure shows tax revenues in the non-haven (a), the haven (b), and the world (c). Worldwide
revenues are the sum of those in the two countries, GW ≡ Gn + Gh . Parameter values are from Table 2.
The horizontal axis is the exogenous GMT rate and the vertical axis is tax revenues in billion USD. The
solid curve in each panel is tax revenues in the corresponding equilibrium regimes; the dotted horizontal
line is tax revenues in Regime 0.

switches from Regime 1 to Regime 2. As stated in Proposition 3, this regime switch is
associated with a discrete loss in tax revenues in the non-haven country and in the world.
The reason is that at this regime-switching rate t1M , the haven country starts splitting
its tax rate and discretely reduces the tax rate for small MNEs. Specifically, the havencountry’s tax rate for small MNEs falls from t1M = 18.6% to t0h = 9.3% (the unconstrained
tax rate). As a result of the increased competition from the haven, the non-haven also
reduces its tax rate on small MNEs from 23.2% to 18.6%.
The revenue implications of this discontinuous change from Regime 1 to Regime 2 aresummarized in Table 4 for different levels of the GMT coverage rate φ. While φ does not19

affect the regime-switching rate t1M , it affects the quantitative implications of the switch.
In general, a lower φ puts more emphasis on competition for small MNEs in Regime 2,
and thus leads to a greater revenue loss for the non-haven country and for the world.
Table 4: Quantitative effects of switch from Regime 1 to Regime 2
GMT coverage rate: φ

80%

85%

90%

GMT rate at regime switch: t1M = 2δ/3

18.6%

18.6%

18.6%

Revenue change in non-haven (bUSD, %)−36 (−7.7%)−27 (−5.7%)−18 (−3.7%)

Revenue change in haven (bUSD)

0

0

0

Total revenue change (bUSD, %)−36 (−6.2%)−27 (−4.6%)−18 (−3.1%)

Note: Results are based on the calibrated parameter values in Table 2 other than φ.

To summarize, the revenue effects of the current GMT at a rate of 15% turn out tobe rather favorable in our calibrated model. This is because the GMT rate is low enoughto lead to a Regime 1 equilibrium where the haven country chooses to commit to the
GMT rate for all MNEs including small ones not covered by the GMT agreement. In
response, the uniform tax rate levied by the non-haven country is also increased beyond
its unconstrained tax rate. The introduction of the GMT therefore acts as a coordination
device between the non-haven and the haven county and both gain substantial amountsof tax revenues in the resulting Regime 1 equilibrium. However, all further increases in
the GMT rate will harm the haven country. Moreover, a moderate 3.6 percentage point
increase in the GMT rate to a level of 18.6% would trigger a splitting tax schedule in
the haven, resulting in non-negligible revenue losses in the non-haven country and in theworld. These results are similar to the quantitative evaluation of the GMT by Hebous
and Keen (2023), where GMT rates up to 17-20% generate Pareto improvements for both
non-haven and haven countries. However, the abrupt switch to Regime 2, which causes
revenue losses for the non-haven and the world, can arise only in a setting where countries
have an incentive to choose split tax rates once the GMT rate exceeds a critical level.

5

Conclusion

In this paper we have analyzed the effects of a global minimum tax (GMT) that is confinedto large MNEs, thus leaving at least 10% of the global multinational tax base outside its
scope. Using a simple model with profit shifting by heterogeneous MNEs, we have shownthat this partial coverage of the GMT gives rise to a sequence of tax competition equilibria
between a non-haven and a haven country. In particular, introducing a moderate GMT
rate does not cause tax splitting by any of the two countries and leads to greater tax
revenues in both countries. Following the introduction of the moderate GMT rate, gradual20

increases in either the GMT rate or the GMT coverage create a conflict of interest between
the two countries. One important difference between the two gradual reforms is that ahigher GMT coverage rate never harms the non-haven and the world.
The calibrated version of our model suggests that, upon the introduction of the current
GMT rate of 15%, the most likely regime is one where the non-haven sets a uniform tax
rate above the GMT for all MNEs, whereas the haven country sets the GMT rate for
all MNEs. Both countries are likely to gain tax revenues. Therefore, worries that the
introduction of a 15% GMT rate might lead to split tax regimes in haven countries are
not confirmed by our model. While this finding seems to contradict the Irish example
stated in the introduction, the majority of non-haven countries have yet to decide their
new tax structures following the introduction of the GMT, and Ireland may still commit
to a 15% tax rate on all MNEs in response. As the GMT rate is further increased from
15%, however, there will be incentives to split the tax rate and set a lower tax rate forsmall multinationals that are not covered by the GMT. This incentive will first arise forthe haven country, but eventually also for the non-haven. At the switch of regimes where
the haven country splits its tax rate, the non-haven country and the world experience a
discrete, substantial revenue loss.
Our model can be extended in several directions. A first important assumption of
our analysis has been that the pre-tax profits of MNEs are fixed. An extended versionof our model would incorporate a real response to tax rates, lowering the pre-tax profits
of all MNEs, in addition to inducing profit shifting. A second important assumption has
been that the tax base elasticity is the same for all MNEs in our model. The empiricalevidence on this issue is inconclusive, but it would be interesting to consider the casewhere the tax base elasticity is higher for large firms. In such a setting it is no longer
clear that tax discrimination always leads to lower tax rates on small multinationals,
but tax discrimination could also go in the opposite direction. Finally, a third extension
would be to incorporate a splitting response of multinationals, in order to benefit frompotentially lower tax rates on small MNEs. We leave these extensions to further research.

21

Appendix A: Proof of Propositions
A1. Proof of Proposition 2
Regime 1: tM ∈ [t0M , t1M ], where t1M ≡ 2δ/3
If tM is equal to or slightly higher than t0M = δ/3, the haven always has to set a GMT
for large MNEs with π ∈ [πM , ∞), whether it chooses to commit or not in the first stage.
In response to this, the non-haven chooses not to commit and sets the unconstrained
maximizing rate for large MNEs as tn = (tM + δ)/2. Non-commitment is the non-haven’s
dominant strategy since the unconstrained rate is higher than the GMT: tn = (tM +δ)/2 >tM . The tax-competition equilibrium is thus determined by whether the haven commits
or not.
If the haven commits in the first stage, the tax rates and tax revenues in the secondstage equilibrium are
tn = (tM + δ)/2 for π ∈ [π, ∞),th = tM for π ∈ [π, ∞),(A.1)

tM (δ − tM )(tM + δ)2Π,
Gh (N, C) =Π,(A.2)
Gn (N, C) =4δ2δ
where Gn (N, C) and Gh (N, C) are equilibrium revenues in country i ∈ {n, h} when the
non-haven does not commit (N ) and the haven commits (C). If neither of the twocountries commits, the equilibrium tax rates and tax revenues in the first stage are instead

tn =


2δ/3

for π ∈ [π, πM )(tfor π ∈ [πM , ∞)(tM + δ)24δ
φ + (1 − φ) Π,
4δ
9M + δ)/2Gn (N, N ) =

,

th =


δ/3

for π ∈ [π, πM )tfor π ∈ [πM , ∞)MGh (N, N ) =

,

(A.3)


tM (δ − tM )
δφ + (1 − φ) Π,
2δ
9
(A.4)

where both countries split their tax rate for small and large MNEs. Comparing thehaven’s revenues yields
Gh (N, C) − Gh (N, N ) = −(1 − φ)(tM − δ/3)(tM − 2δ/3)
.
2δ

(A.5)

If tM ∈ [t0M = δ/3, t1M ], where t1M ≡ 2δ/3, this is non-negative; hence the haven chooses tocommit in the first stage. The tax rates and the revenues in tax-competition equilibrium
are respectively given by (A.1) and (A.2).
qhiRegime 2: tM ∈ (t1M , t2M ), where t2M ≡ δ 1 − 13 2(1−φ)
2−φ1
If tM exceeds tM = 2δ/3, (A.5) becomes negative. Hence, given the non-haven’s non-22

commitment, the haven no longer chooses to commit. Also, if the non-haven commits to
tM for all MNEs, the haven’s best response is non-commitment, Gh (C, N )−Gh (C, C) > 0,
since otherwise it would obtain zero revenues, Gh (C, C) = 0. Therefore, the haven’s
dominant strategy is non-commitment and the tax-competition equilibrium is determinedby whether the non-haven commits or not.
If neither of the two countries commits in the first stage, the tax rates and the revenues
in equilibrium of the first stage are respectively given by (A.3) and (A.4). By contrast, if
the non-haven chooses to commit and the haven chooses not to commit in the first stage,
the equilibrium tax rates and revenues are respectively given byt /2 for π ∈ [π, π )
M
M
th =
t
for π ∈ [πM , ∞)M

tn = tM for π ∈ [π, ∞),tM (2δ − tM )Gn (C, N ) = tM φ +(1 − φ) Π,2δGh (C, N ) =(A.6)

t2M (1 − φ)
Π,
4δ

(A.7)

Comparing the non-haven’s revenues yields
9(2 − φ)tM (tM − 2δ) + δ 2 (16 − 7φ)Π.
Gn (C, N ) − Gn (N, N ) = −
36δ

(A.8)

This is negative if"

1tM < t2M ≡ δ 1 −3

s#2(1 − φ)
,
2−φ

(A.9)

noting that t2M > t1M = 2δ/3. Hence, for tM ∈ (t1M , t2M ), the non-haven chooses not tocommit in the first stage. Tax rates and revenues in the tax-competition equilibrium arethen given by (A.3) and (A.4).
Regime 3: tM ∈ [t2M , t3M ], where t3M ≡ 4δ/3
If tM exceeds t2M , as defined in (A.9), the revenue difference in (A.8) becomes nonnegative. This implies that, given the haven’s non-commitment, the non-haven chooses
to commit. When tM increases further and reaches tM = δ > t2M , the non-haven isconstrained by the GMT, tn = (tM + δ)/2 ≤ tM = δ. If neither of the two countries
commits, their tax rates and revenues in the second-stage equilibrium are

tn =


2δ/3

for π ∈ [π, πM )tfor π ∈ [πM , ∞)M

Gn (N, N ) =

,

th =


δ/3

for π ∈ [π, πM )tfor π ∈ [πM , ∞)M

9φtM + 4δ(1 − φ)
Π,
9

23

Gh (N, N ) =,(A.10)

δ(1 − φ)Π.
9

(A.11)Given the haven’s non-commitment, the non-haven compares GN (C, N ) in (A.7) withGn (N, N ) in (A.11). This gives2δ − t2M4δ−(1 − φ)Π,Gn (C, N ) − Gn (N, N ) =2δ
9


(A.12)

which is non negative as long as tM ∈ [t2M , t3M ] holds, where t3M ≡ 4δ/3. Intuitively,by committing to a single GMT for all MNEs, the non-haven induces a higher tax rateon small MNEs in the haven country, and therefore gains greater revenues from small
MNEs. Combining this result with the fact that the haven’s dominant strategy throughout
Regime 3 is non-commitment, we get a tax-competition equilibrium in Regime 3 where
the non-haven commits and the haven does not. The equilibrium tax rates and revenues
in the two countries are respectively given by (A.6) and (A.7).
Regime 4: tM ∈ (t3M , 1]
For tM ∈ (t3M , 1], (A.12) becomes negative, implying that the non-haven chooses not
to commit, given the haven’s non-commitment. Since the haven’s dominant strategy
remains non-commitment, the tax-competition equilibrium is such that neither of thetwo countries commits and the tax rates and revenues are respectively given by (A.10)
and (A.11).
This completes the proof of Proposition 2. 

A2. Proof of Proposition 3
We denote regime-specific revenues for country i ∈ {n, h} in regime J ∈ {1, 2, 3, 4} by GJi
and aggregate (world) revenue by GJW = GJn + GJh . The revenue changes from introducing
GMT for the non-haven, the haven, and the world are then calculated as follows.
Regime 1: tM ∈ [t0M , t1M ], where t0M ≡ δ/3 and t1M ≡ 2δ/3.
We get from (A.2) and (5):4δ(tM − δ/3)(tM + 7δ/3)(tM + δ)2Π− Π=
Π > 0,
4δ
94δ
tM (δ − tM )
δ
(tM − δ/3)(tM − 2δ/3)G1h − G0h =Π− Π=−
Π > 0,2δ92δ
(tM − δ/3)(tM − 11δ/3)
G1W − G0W = −Π > 0.
4δqhi
Regime 2: tM ∈ (t1M , t2M ], where t2M ≡ δ 1 − 31 2(1−φ).
2−φG1n − G0n =24

We get from (A.4) and (5):9φtM (tM + 2δ) + δ 2 (16 − 7φ)
4δ
(tM − δ/3)(tM + 7δ/3)
Π− Π=
φΠ > 0,36δ
94δ
(tM − δ/3)(tM − 2δ/3)
φ(9tM δ − 9(tM )2 − 2δ 2
20
Π=−φΠ < 0,Gh − Gh =18δ2δ(tM − δ/3)(tM − 11δ/3)
G2W − G0W = −φΠ > 0.
4δ
G2n − G0n =Regime 3: tM ∈ [t2M , t3M ], where t3M ≡ 4δ/3.
We get from (A.7) and (5):18δtM − 9(tM )2 − 8δ 2 φ(tM )2+
Π > 0,
18δ2δ(tM )2 (1 − φ)δ9(tM )2 (1 − φ) − 4δ 2
G3h − G0h =Π− Π=Π < 0 for φ > 3/4,4δ
936δ
9tM [4δ − tM (1 − φ)] − 20δ 2
G3W − G0W =Π > 0.
36δ
G3n − G0n =where the first term in the squared bracket of G3n − G0n is non-negative for tM ∈ [t2M , t3M ].
The expression G3h − G0h reaches a regime-specific maximum at tM = 4δ/3 and is nonpositive at this level of tM for φ ∈ (3/4, 1).
Regime 4: tM ∈ (t3M , 1].
We get from (A.11) and (5):4δ
9tM − 4δ9φtM + 4δ(1 − φ)
Π− Π=φΠ > 0,999
δ(1 − φ)δ
δG4h − G0h =Π − Π = − φΠ < 0,
9
9
9
9t
−
5δ
M
φΠ > 0.
G4W − G0W =9

G4n − G0n =This completes the proof of Proposition 3. 

A3. Proof of Proposition 4
The effects of an increase in tM on tax revenues in the non-haven, the haven and theworld in each regime are as follows.

25

Regime 1: tM ∈ [t0M , t1M ], where t0M ≡ δ/3 and t1M ≡ 2δ/3.
∂G1n
∂tM

=

From (A.2), we get(tM − δ/2) ≥ 0 if tM ∈ [t0M , δ/2]=−Π,
< 0 if t ∈ (δ/2, 1]
∂tM
δ

∂G1h

tM + δ
Π > 0,
2δ

M∂G1W(tM − 2δ)=−Π > 0,∂tM2δ
where ∂G1h /∂tM = 0 holds at tM = δ/2.
Regime 2: tM ∈ (t1M , t2M ), where t2M ≡ δ∂G2ntM + δ
=φΠ > 0,∂tM2δ

h

1 − 13q2(1−φ)
2−φ

i
.

∂G2h
(tM − δ/2)=−
φΠ < 0,∂tM
δRegime 3: tM ∈ [t2M , t3M ], where t3M ≡ 4δ/3.

From (A.4), we get∂G2W(tM − 2δ)=−φΠ > 0.
∂tM
2δFrom (A.7), we get(δ − tM )∂G3n= φ+(1 − φ) Π
∂tM
δ
∂G3h
(1 − φ)Π
∂G3W
2δ − tM (1 − φ)=> 0,=
Π > 0.
∂tM
2δ
∂tM
2δ
where G3n has a regime-specific minimum at t3M = 4δ/3. For this level of tM , φ > 1/4
guarantees ∂G3n /∂tM > 0.
Regime 4: tM ∈ (t3M , 1].

From (A.11), we get∂G4n= φΠ > 0,
∂tM

∂G4h
= 0,
∂tM

∂G4W
= φΠ > 0.
∂tM

At the three regime switching GMT rates, t1M , t2M and t3M , tax revenues in the nonhaven, the haven, and the world change as follows.
Change from Regime 1 to 2 at t1Mδ
G2n − G1n t =t1 = − (1 − φ)Π < 0,MM
4
δ
G2W − G1W t =t1 = − (1 − φ)Π < 0.
MM
4

G2h − G1h t =t1 = 0,M

M

Change from Regime 2 to 3 at t2M
G3n − G2n t =t2 = 0,MM

G3h − G2h t =t2 = G3W − G2W t =t2 =
M

M

M

M

9t2M [t2M (1 + φ) − 2δφ] − 4δ 2 (1 − φ)
Π < 0.
36δ

26

Change from Regime 3 to 4 at t3M
G4n − G3n t =t3 = 0,MG4h − G3h t =t3 = G4W − G3W t =t3 = −
M

M

M

M

M

δ(1 − φ)Π < 0.
3This completes the proof of Proposition 4. 

A4. Proof of Proposition 5
The effects of an increase in φ on tax revenues in the non-haven, the haven and the worldin each regime are as follows.
Regime 1: tM ∈ [t0M , t1M ], where t0M ≡ δ/3 and t1M ≡ 2δ/3.
∂G1n
= 0,
∂φ

∂G1h
= 0,
∂φ

Regime 2: tM ∈ (t1M , t2M ], where t2M ≡ δRegime 4: tM ∈ (t3M , 1].
∂G4n
=
∂φ



4δ
tM −
9

From (A.4) we get∂G2h(tM − δ/3)(tM − 2δ/3)=−φΠ < 0,∂φ2δ

Regime 3: tM ∈ [t2M , t3M ], where t3M ≡ 4δ/3.
∂G3n(tM )2=
Π > 0,
∂φ
2δ

∂W 1
= 0.
∂φ

q
i
h
2(1−φ)
1
.
1− 3
2−φ

∂G2n
(tM − δ/3)(tM + 7δ/3)=
Π > 0,∂φ4δ
∂W 2(tM − δ/3)(tM + 11δ/3)=
Π > 0.
∂φ4δ

From (A.2) we get

From (A.7) we get∂G3h(tM )2=−
Π < 0,∂φ4δ

∂W 3(tM )2=
Π > 0.
∂φ4δ

From (A.11) we get∂G4hδ= − Π < 0,∂φ
9
Π > 0,

∂W 4
=
∂φ



5δ
tM −
Π > 0.
9

Among the three regime-switching GMT rates, only t2M depends on φ and it increases
with φ. If tM = t2M , and the equilibrium is in Regime 3 initially, an increase in φ triggers
a regime switch to Regime 2. This switch has no effects on revenues in the non-havencountry, G2n − G3n t =t2 = 0, but it increases revenues in the haven and the world byM

M

G2h − G3h t =t2 = G2W − G3W t =t2 = −
M

M

M

M

9t2M [t2M (1 + φ) − 2δφ] − 4δ 2 (1 − φ)
Π > 0.
36δ

This completes the proof of Proposition 5. 

27

Appendix B: Data for Figure 1
We select MNEs from the Orbis based on the following criteria.
• Global Ultimate Owner with foreign subsidiaries. The threshold ownership is 50.01%.
• C1: MNEs report only consolidated accounts, not unconsolidated accounts.
The numbers on which Figure 1 is based are given in Table B1. In column A, tocalculate the pre-tax profits of all MNEs in a given year, we exclude those with missing
revenues (“Operating revenue (Turnover)”) and pre-tax profits (“P/L before tax”). In
column B, MNEs subject to the GMT are those with annual revenues of no less than 750
million EUR in at least two years of the last four years. Using column A and B, column C
reports the share of MNEs subject to the GMT in terms of pre-tax profits and numbers.

Table B1: MNEs in the Orbis database
A: All MNEs

B: MNEs ≥ 750mEUR

C: Share = B/A

Year

Pre-tax profits

NumberPre-tax profits

NumberPre-tax profits

Number

2018

2320

8656

2066

2333

0.89

0.27

2019

2430

8416

2216

2437

0.91

0.29

2020

1985

7920

1793

2228

0.90

0.28

2021

3564

8803

3239

2627

0.91

0.30

Source: Orbis database, own calculations.
Note: Pre-tax profits are in billion EUR.

28

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