Welfare Impact of Profit Shifting in an Open Economy
Rui PanAugust 30, 2024

Abstract
Does trade liberalization enhance the welfare of impact profit shifting in asymmetric non-havens? Investigating the interplay between trade liberalization andthe effectiveness of corporate profit shifting, we construct a three-country model
encompassing heterogeneous firms and a monopolistic competition goods market.
The model comprises two non-havens and one tax haven, allowing firms to relocate
profits to the tax haven. The two non-havens exhibit asymmetry in the concentration of multinational enterprise (MNE) headquarters within the manufacturingsector, with a developed country characterized by a large share of MNEs. Ourfindings reveal that developing countries may experience welfare deterioration while
highly developed countries may benefit from the existence of a tax haven. However,
we further demonstrate that the relationship between the welfare impact of profit
shifting and MNE share exhibits a non-monotonic pattern. Additionally, we uncover the non-monotonic relationship between trade liberalization and the welfare
impact of profit shifting.
Keywords: trade gains, profit shifting, welfare
JEL Codes:F21 F23 H26 H87

1Introduction

This paper delves into the intricate interplay between trade liberalization and the welfare
impact of profit shifting on non-haven developed and developing countries in the context
of profit shifting by firms to tax havens. As defined by the OECD (1998), tax havens arecharacterized by the imposition of either no or minimal nominal taxes, while simultaneously presenting themselves, or being perceived as such, as destinations for non-residents
seeking to escape the higher tax burdens of their home countries. These tax havens exert
a profound influence on the global economy. Tørsløv, Wier, and Zucman (2018) estimatethat multinational firms shifted approximately 600 billion dollars of profits to tax havens
in 2015. Furthermore, the Institute on Taxation and Economic Policy reported in 2017that at least 366 Fortune 500 companies maintain subsidiaries in tax haven countries(Phillips et al., 2017).
The impact of tax havens on the welfare of non-havens has been a topic of enduringscholarly inquiry. Research has primarily focused on the direct effects of tax havens
on non-havens, such as alterations in tax rates and the deadweight loss associated withprofit-shifting activities. A prevailing view posits that tax havens ultimately harm nonhaven welfare. This stems from their ability to erode the tax base of non-havens anddivert resources towards unproductive activities. Intriguingly, some studies have identified
countervailing effects, suggesting potential benefits associated with tax havens. However,a significant portion of the existing literature on tax havens adopts a small open economy
framework, analyzing the impact on a single non-haven country in isolation from a tax
haven. This approach inherently restricts the analysis of the effects of tax havens on tax
rates and profit-shifting activities within a single non-haven. Consequently, the crucial
questions of how resource allocation among non-havens and trade liberalization influence
the welfare effects of profit shifting to tax havens remain largely unexplored.
To bridge this theoretical gap, we construct a general-equilibrium model encompassing
multiple countries to elucidate the impact of tax havens on economic activity within asymmetric non-haven economies and the interplay with trade liberalization. More specifically,in our economic space, there are two non-havens and one tax haven. To show different
impacts on developed and developing countries, we let the non-havens be asymmetric in
the sense that they have different amounts of MNEs. More specifically, these MNEs aremonopolistically competitive and owned by the residents of each non-haven country in our
economy. One country is a representative of developed countries and has a larger share of
MNEs. An MNE has three affiliates: a domestic manufacturing parent firm (headquarters) that produces and sells domestically, a distribution affiliate in a non-haven foreigncountry for export only, and an affiliate in a tax haven for tax avoidance.
Our model elucidates three key mechanisms that influence the welfare effects: the1

profit-reallocation effect, the rate-reducing effect, and the shifting costs. The profitreallocation effect quantifies the impact of trade liberalization on the allocation of pre-tax
profits across domestic and export affiliates and hence on the structure of the tax bases
in non-havens. Generally, trade liberalization enlarges the profits of export affiliates andhence encourages the shifting activities and these affiliates. The rate-reducing effect captures how the presence of a tax haven incentivizes non-havens to adjust their tax rates
to remain competitive in attracting MNE taxable profits. This adjustment can potentially impact the net-tax profits earned by MNEs’ export affiliates. The effect of shifting
costs reflects the deadweight losses incurred by non-haven economies as a result of MNEs
engaging in profit-shifting activities. These deadweight losses arise from inefficiencies
associated with such practices.
Our analysis unveils several key findings regarding the welfare effects of profit shifting
and trade liberalization in non-havens. Firstly, our analysis reveals a non-monotonic
relationship between trade liberalization and the welfare effects of profit shifting in certain
scenarios. For developed countries, increased trade openness (reduced trade barriers)
initially enhances the gains from profit shifting when the level of trade openness is low.
However, these gains diminish as trade becomes increasingly unrestricted. Conversely,for developing countries, trade liberalization initially reduces the net benefits from profit
shifting when trade openness is low. However, as trade barriers fall and trade becomes
more open, the net benefits for developing countries actually improve.
In the absence of tax havens, trade liberalization traditionally leads to welfare gains
by lowering price indices in non-havens, as demonstrated in the New Trade Theory models by Arkolakis, Costinot, and Rodrı́guez-Clare (2012) (hereafter ACR). Our researchextends this understanding by showing that these gains from trade dominate when trade
openness is very low or very high, even when tax havens are present. Furthermore,through simulations, we demonstrate that the overall welfare effect of trade liberalization, which incorporates both the gains from trade and the impact of profit shifting,exhibits a non-monotonic relationship in a country with a very large share of MNEs andvery low concealment costs.
Furthermore, developing countries with a limited endowment of MNEs are demonstrably worse off in the presence of a tax haven. Conversely, highly developed countries witha substantial share of MNEs may experience welfare gains. However, this relationshipbetween the MNE share and the welfare impact exhibits a non-monotonic characteristic,
particularly when concealment costs are high.
When the MNE share is very low or very high, and concealment costs are significant,the impact of profit shifting becomes complex. Intense competition for a limited poolof MNEs (low share) or a saturated market (high share) disincentivizes non-havens fromaggressive tax rate reductions, weakening the rate-reducing effect. Simultaneously, the2profit-reallocation effect intensifies as a larger share of MNE profits are diverted to thetax haven. Additionally, substantial concealment costs exacerbate the deadweight losses
associated with profit-shifting activities. Consequently, under conditions of high concealment costs, the negative welfare effects stemming from the weakened rate-reducing effectand amplified shifting costs outweigh the potential benefits. Therefore, the overall impact of profit shifting on welfare diminishes as the MNE share increases, but only whenconcealment costs are high.
This paper contributes significantly to two ongoing debates within the field of international taxation. The first debate centers on whether the existence of tax havens negatively
impacts all non-havens. Previous research has explored various direct effects of tax havens
on non-havens with differing development levels. Slemrod and Wilson (2009) argue thattax havens can lead to wasteful spending by both firms and governments in non-havens.
Furthermore, tax competition intensifies as non-haven governments engage in a race tothe bottom, reducing tax rates below efficient levels in a cooperative scenario. This ultimately results in an undersupply of public goods, leading to a decline in welfare for
non-haven residents. However, Johannesen (2010) presents a contrasting viewpoint, suggesting that tax havens can, in some cases, actually increase tax revenue in non-havens
through a ”crowding-out effect.” This effect posits that tax havens incentivize low-tax
non-havens to raise tax rates to remain competitive. Hong and Smart (2010) introduce
an additional layer of complexity by highlighting the potential for tax havens to facilitate
investment. While tax planning by non-haven firms may reduce tax revenue, this loss canbe offset by attracting a greater volume of real foreign investment. The authors conclude
that under specific tax planning conditions, the existence of a tax haven can enhance
welfare. Choi, Furusawa, and Ishikawa (2020) present another counterpoint, arguing thata non-haven country’s welfare can improve under strict profit-shifting regulations (suchas transfer pricing caps) when a tax haven is present. This benefit arises because theability to shift profits via transfer pricing can lead to a lower perceived marginal costfor multinational enterprises (MNEs), ultimately stimulating production. In contrast tothese existing studies, our research unveils a novel mechanism: highly developed countries
can benefit from profit shifting due to a significant positive rate-reducing effect.
Our research also contributes to the ongoing discourse on the differential effects ofprofit shifting on developed and developing countries. Existing empirical studies havedocumented these disparities. Johannesen et al. (2020) highlight how multinational tax
avoidance practices lead to distinct tax policies in developed and developing countries.
Specifically, developing countries tend to adopt lower corporate tax rates in response totax havens. Furthermore, Tørsløv et al. (2022) estimate that while a significant portion of shifted profits originates from developed economies (like the United States), amuch smaller share ultimately benefits these countries. In contrast, developing countries3contribute a smaller portion of shifted profits but receive an even smaller share of theaccumulated benefits. Our theoretical model aligns with these empirical observations,suggesting that these differing impacts translate into unequal welfare effects across countries.
This paper further contributes to the theoretical understanding of how trade liberalization influences corporate profit-shifting behavior. Several studies have explored thisrelationship. Gao et al. (2019) analyze data from China and report that trade liberalization encourages increased profit shifting by firms in developing countries. Chen and Lin(2014) find similar evidence for developed countries using data from the United States.
Pan and Zeng (2023) also demonstrate that trade liberalization intensifies tax competition
among non-havens, further incentivizing profit shifting. However, a critical gap remains
in the literature: the welfare impact of trade liberalization on non-havens. Our research
addresses this gap by revealing a non-monotonic relationship between trade liberalizationand the welfare effects of profit shifting in certain non-haven economies.
This paper is structured as follows: Section 2 derives the equilibrium in the absenceof a tax haven. Section 3 explores the equilibrium under the presence of profit shifting
to a tax haven. Section 4 delves into the interplay between the MNEs’ share, tradeliberalization, and the welfare impact of profit shifting. Section 5 examines the aggregate
welfare effects of trade liberalization. Finally, Section 6 concludes the paper.

2

Model

We begin by establishing a benchmark scenario with two non-havens, denoted by i or j
(i, j = 1, 2), engaged in bilateral trade. In this initial framework, we assume the absenceof a tax haven within the economy. Then, we will introduce a tax haven in the later
sections. Each non-haven is populated by a unit mass of individuals. There are two
sectors: a differentiated goods sector (sector M) and a homogeneous good sector (sector
A). The homogeneous good is freely traded between the two non-havens, incurring no
trade costs. In contrast, the international trade of differentiated goods is subject toiceberg costs, denoted by τ .

2.1

Preferences

Following Pflüser (2004), in each of the two countries, individuals are assumed to haveidentical quasi-linear utility functions featuring a CES subutility function. This utility

4

function is characterized by:
Uj = α ln Qj + qjo , with Qj =

2 Z
X
i=1,2

σ
! σ−1

q̃ij (v)

σ−1
σ

dv

,

(1)

Ωij

where Ωij denotes the set of varieties consumed in country j and produced in countryi, qjo is the consumption of the numeraire good, and q̃ij (v) is the individual demand forvariety v ∈ Ωij . The elasticity of substitution between varieties is given by σ > 1. Qj
represents the aggregate consumption of the differentiated goods of a consumer in country
j. Parameter α ∈ (0, 1) is the intensity of preference for the differentiated good.
Utility maximization yields the following demand functions for a particular variety v
of country i consumed in country j:αpij (v)−σ,qij (v) = q̃ij (v) =
Pj1−σ

Pj =

" 2 Z
X
i=1,2

1
# 1−σ

pij (v)1−σ dv

(2)

Ωij

where pij (v) is the delivered price from i to j. Pj is the price index of the differentiatedgoods in country j.

2.2

The government

In both non-havens, governments levy proportional destination-based taxes on firm profits. This tax revenue is then redistributed equally among all individuals within the country.

2.3

Firms

In sector A, the homogeneous good is produced under constant returns to scale technology.
A single worker produces one unit of good A. Perfect competition prevails in this sector,
leading to zero profits for firms. Good A serves as the numeraire and is freely traded
between the two countries. Workers exhibit perfect mobility across sectors, resulting in a
uniform wage rate w = p0 = 1 across both countries.
In sector M , a continuum of MNEs operate under monopolistic competition. The
total mass of MNEs in the entire economy is denoted by N , which is assumed to be fixedand exogenous. Country 1 hosts n1 = s1 N of MNEs headquarters, while country 2 has
n2 = s2 N = (1 − s1 )N headquarters. We define a country as developing (developed) if
its share of MNE headquarters,si , is less than (greater than) 1/2. The two countries are
perfectly symmetric when s1 = s2 = 1/2.
An MNE operates in both non-havens with two affiliates: a domestic parent firm5

(headquarters) that produces and sells goods domestically, and an exporting affiliate
located in the foreign country responsible for exports. When exporting, the trade costs
between the two countries are the same and take an iceberg form, denoted by τ > 1.
A destination-based tax rule applies, requiring parent firms to pay taxes domesticallyand export affiliates to pay taxes to the foreign country where they operate. A domestic
manufacturing firm (i.e. headquarters) in country i produces qii (c) units of goods andsells them to the domestic market at a price pii (c). Furthermore, the distribution affiliate
in country j imports τ qij (c) units of goods from its domestic production plant in country
i. Meanwhile, only qij (c) units of goods are delivered to country j because of the iceberg
trade costs. In addition, we do not consider the profit shifting between the two nonhavens. Therefore, the import price of the distribution affiliate is the true marginal costc.
MNEs exhibit heterogeneity in their marginal costs of production, denoted by c. A
higher marginal cost typically reflects lower firm productivity. We characterize the distribution of marginal costs, G(c) in both countries using the Pareto distribution:G(c) =ccM

γ,

where cM is the upper bound of marginal cost in both countries and γ is the shapeparameter that captures the degree of firm heterogeneity. A large γ indicates a low
degree of firm heterogeneity. We assume γ > σ − 1 > 0 for aggregate profits to be finite.
Regardless of its productivity, each firm faces a demand curve with constant elasticity
σ and thus has the same profit-maximizing markup σ/(σ − 1). This implies that all firms
in both countries will set prices according to a specific pricing rule:pii (c) =

σc
,
σ−1

pij (c) =

στ c
.
σ−1

(3)

The price index in country j, denoted by Pj , is solved using equation (3) and is given by:
"
Pj =

X

Z cM
nj

i=1,2

0

σ
=
cM
σ−1



1
# 1−σ

pij (c)1−σ dG(c)

γ
γ−σ+1

1
 1−σ

1

1

[sj + (1 − sj )ϕ] 1−σ N 1−σ ,(4)where ϕ = τ 1−σ ∈ (0, 1] is the trade “freeness.” That is, a larger ϕ implies a smaller tradecost.
The pre-tax profit of an MNE headquartered in country i including both the domestic

6

firm and its export affiliate, is given by:
πi (c) = πii (c) + πij (c) = [pii (c) − c]qii (c) + [pij (c) − τ c]qij (c).

(5)

Combining (2), (3), and (4), the gross profit of an MNE is given byπi (c) = πii (c) + πij (c) =
where

α
A≡
σN

c1−σ ϕc1−σA+A,si + (1 − si )ϕ
si ϕ + 1 − si


γ−σ+1
γ



(6)

cσ−1
M

represents a composite term that incorporates several key model parameters. Specifically,
A captures the influence of the intensity of preference for differentiated goods (α), theelasticity of substitution (σ), the total number of MNEs (N ), the shape parameter of thePareto distribution (γ), and the upper bound of marginal cost (cM ).
The net-of-tax profit of an MNE in country i:
πin (c) = πiin (c) + πijn (c) = (1 − ti )πii + (1 − tj )πij ,(7)where ti and tj represent the tax rates in countries i and j, respectively.
In the case of non-profit shifting, the tax base in country i is given by aggregate
profits of all domestic firms (headquartered in country i ) and the export affiliates of
MNEs headquartered in country j:Πti = Πtii + Πtji =

α
,
σ

(8)

Where Πtii denotes the tax base from domestic firms in country i and Πtji denotes the tax
base from the export affiliates of MNEs headquartered in country j. These tax bases arecalculated as:
Z cM
si
α
t
Πii = niπii (c)dG(c) =,si + (1 − si )ϕ σ0
Z cM
(1 − si )ϕ αtΠji = nj
πji (c)dG(c) =,(9)si + (1 − si )ϕ σ0
Notably, the total tax base in country i is independent of the specific tax rates in bothcountries, and it differs from the total pre-tax profits of MNEs owned by individuals incountry i. πii (c) is the profits of a domestic manufacturing firm, and πji is the profits
of the distribution affiliate of a country 2’s MNE. Note that this Πti is different from thewhole pre-tax profits of MNEs owned by country i’s individuals.

7

Furthermore, the expenditure by individuals in country i on the domestic firms andforeign exporters is determined by the following equations:
Rii =

αsi
,
s + (1 − si )ϕRji =α(1 − si ),si + (1 − si )ϕ(10)respectively.
The total tax revenue in country i is then given by
Ti = ti Πti .

(11)This equation shows that the transfer payment in country i equals to the tax rate incountry i multiplied by the total tax base. In other words, the government in country icollects taxes from both domestic firms and foreign affiliates and then redistributes thisrevenue equally among all citizens.

2.4

Optimal tax rate in the non-shifting case

The aggregate private income of individuals in country i includes wages and net profits
of firms, which is given by
Ii = |{z}1 +wage(1 − ti )Πtii| {z }

net profits of domestic sales+(1 − tj )Πt| {z ij}.

(12)

net profits of exports

Under the quasi-linear preferences, the consumption of manufactured goods within acountry is the same for all individuals. Social welfare in country i is
Wi =α lnαPi− α + Ii + bi ,(13)

where Pi , bi and Ii are given by (4), (11) and (12), respectively. The government ofcountry i choose the optimal redistribution tax rate ti to maximize Wi , which is given by


dWi
α
si
=
1−
.
dti
σ
si + (1 − si )ϕ

(14)

o∗
o∗
Therefore, the optimal tax rates in both countries are to∗
1 = t2 = 1 if ϕ > 0, and t1 ∈ [0, 1]
and to∗2 ∈ [0, 1] if ϕ = 0. This result is stylized and consistent with Krautheim andSchmidt-Eisenlohr (2011). Without a tax haven, the large countries’ governments havethe motivation to charge taxes on firms and redistribute to domestic individuals withany additional trade-off. The main difference between this paper and Krautheim andSchmidt-Eisenlohr (2011) is that the tax revenue is redistributed to domestic individuals

8rather than producing a relatively more important public good. The incentive in thispaper is taxing foreign exporters.

2.5

Gains from trade

We firstly estimate the gains from trade in the case without a tax haven, namely no profit
shifting. From (14), the optimal tax rate in country i is

to∗
i =


1,

if ϕ > 0,(15)[0, 1], if ϕ = 0.

The two non-havens governments take all of the profits of MNEs and then transfer themto domestic individuals, which yields
T1o∗ = T2o∗ =

α
.
σ

(16)

Since all profits are taxed and then redistributed, private income in both non-havens
remains equal to the wage rate, which gives
I1o∗ = I2o∗ = 1.
Therefore, welfare in country i under the no-tax haven scenario is given by:
Wio∗ = α ln



α
Pi


−α+1+

α
.
σ

(17)

As emphasized by ACR, the gains from trade are largely determined by the change indomestic expenditure share and the elasticity of trade flows to trade cost in the trademodels.1 Let λi denote the share of expenditure on domestic manufacturing goods incountry i, which is given by
λi =

Rii
si
=
.
Rji + Rii
si + (1 − si )ϕ(18)

The second equality of (18) shows that λi is affected by both the headquarters share (si )and the trade freeness (ϕ). A large si indicates a large domestic expenditure share λi .
Furthermore, the change in domestic expenditure share with respect to trade costs is then1

In the later paper, ACDR (Arkolakis et al, 2019), the authors also emphasize the role of the procompetitive effect. However, in the Pflüger type utility assumed in this paper, the pro-competitive effectdoesn’t occur.

9

given by
λ̂i =1 − si
1 dλi
=−
< 0,
λi dϕ
si + (1 − si )ϕwhere the inequality is ensured by the fact that 0 < si < 1. The derivative of welfare
with respect to ϕ is now given by
dWio∗
λ̂i
=α×
.
dϕ
1−σ

(19)

where the positiveness of ∂(Wio∗ )/∂ϕ is ensured by the facts that λ̂i < 0 and σ > 1. α isthe total expenditure share on the sector M. According to (19), the “trade elasticity” is
1 − σ, which is consistent with ACR. The following lemma summarizes our findings:
Lemma 1 Without profit shifting, non-haven always benefit from trade liberalization.

3

Equilibrium under Profit shifting

Now, we introduce a tax haven into the economy. For simplicity, the tax haven is assumed
to have zero population (or no consumption).2 Furthermore, there are no production
activities in the tax haven.3

3.1

Shifting firms

To capture profit-shifting behavior, we follow previous studies on this topic (e.g., Zhao,
2000; Nielsen et al., 2003, 2008; Kind et al., 2005; Kato and Okoshi, 2022; Pan and Zeng,
2023) and assume that decision-making within MNEs is decentralized. In this framework,
each affiliate of an MNE located in a non-haven country makes an independent decision
about whether to shift profits to a tax haven country. This assumption reflects thefact that MNEs often have complex organizational structures and decisions about profit
allocation may not be made at a central headquarters but rather by individual affiliates
based on their specific circumstances.
An affiliate decides to shift profits to the tax haven if the potential tax savings outweighthe costs associated with concealment. Following Gumpert et al. (2016), we assume that2

The population of the Cayman Islands, the most famous tax haven, is 71100 in 2021. See https://www.caymancompass.com/2021/06/18/new-population-figures-move-reopening-goalposts/.
3
The assumption of no production and no population (or consumption) in the tax haven is common
in the literature. See Slemrod and Wilson (2009) and Hong and Smart (2010).

10

there is no corporate income tax in the tax haven country.4 Each affiliate incurs a fixed
cost, f , to conceal the transfer of profits to the tax haven. The decision of whether or
not to shift profits is essentially an all-or-nothing decision; an affiliate either shifts all of
its after-tax profits to the tax haven or keeps them in the non-haven. The shifting choiceof each affiliate depends on its marginal cost and the tax rate in its market country. A
high-productivity MNE’s affiliate is more likely to shift profits to the tax haven.
Let cii and cij denote the respective cutoff cost levels at which a domestic firm and an
export affiliate of country i’s MNEs become indifferent between utilizing the tax havenand paying taxes in the non-havens. These cutoff costs represent the marginal cost level
above which it becomes more profitable for a firm to shift profits to the tax haven after
accounting for the concealment cost f . Formally, the cutoff costs are determined byti πii (cii ) = f,(20)

tj πij (cij ) = f.

(21)

Solving (20) and (21), we obtain the following expressions for the cutoff costs:


A
cii =
f (si + (1 − si )ϕ)

1
 σ−1

1
σ−1

ti



Aϕ
cij =
f (1 − si + si ϕ)

,

1
 σ−1

1

tjσ−1 .

(22)

Due to the decentralization decision-making assumption, the cutoff costs for domestic
firms and export affiliates may differ. In other words, some MNEs only shift a portion of
their profits to the tax haven. Consequently, we focus more on the affiliate-level shifting
activities rather than the MNE level. The mass of shifting domestic firms and export
affiliates of country 1’s MNEs are then given by
nsii = ni G(cii ) = si N cγii c−γ
M ,

3.2

nsij = ni G(cij ) = si N cγij c−γ
M .

(23)

Remaining tax base

Given the tax rates of the two non-havens, only affiliates whose marginal costs are smaller
than their respective cutoff costs (as determined by equation (22)) will choose to shift
4Comparing with non-havens, most tax havens apply very low corporate tax rates which can beneglected. Furthermore, more than a third of tax havens offer a zero percent lowest available corporate tax
rate. See https://www.taxjustice.net/2019/05/28/new-ranking-reveals-corporate-tax-havens-behind-breakdown-of-global-corporate-tax-system-toll-of-uks-tax-war-exposed/11profits. The tax base remaining in a non-haven is given byZ cM
Πi = Πii + Πji = niZ cM
πii (c)dG(c) + nj

ciiπji (c)dG(c)
cji


ϵ
α
1
ϵ
α si + (1 − si )ϕϵ+1 α
tϵ ,
= −
σ
si + (1 − si )ϕ σ σN f si + (1 − si )ϕ ϵ + 1 i
where
ϵ=

(24)

γ−σ+1
>0
σ−1

according to the assumption of γ > σ − 1. The tax-base loss in country i is
α si + (1 − si )ϕϵ+1
Πsi = Πsii + Πsji =σ si + (1 − si )ϕ



α
1
ϵ
σN f si + (1 − si )ϕ ϵ + 1

ϵ

tϵi

(25)

where

ϵ
si
α
1
ϵ
tϵ ,
σ si + (1 − si )ϕ σN f si + (1 − si )ϕ ϵ + 1 i

ϵ
α
1
ϵ
α (1 − si )ϕϵ+1
s
tϵ ,
Πji =
σ si + (1 − si )ϕ σN f si + (1 − si )ϕ ϵ + 1 i
αΠsii =

represent the tax-base losses from domestic firms and foreign export affiliates, respectively.
Moreover, let Eijs and Eijs denote the shifted profits share of headquarters and export
affiliates of i’s MNEs and given by

ϵ
Πsii
α
1
ϵ
s
Eii = t =tϵΠii
σN f si + (1 − si )ϕ ϵ + 1 i

ϵ
Πsji
α
1
ϵ
ϵ
s
Eji = t = ϕ
tϵi .
Πij
σN f si + (1 − si )ϕ ϵ + 1

(26)
(27)

The transfer payment is then given by
Tih = ti Πi .

(28)

The aggregate private income of individuals in country i in the presence of a tax haven,denoted by Iih , is given by
Iih = 1 +X
(1 − tj )Πij + Πsij − nsij f .

(29)

j=1,2

The above equation captures several components of national private income: labor incomeP(= 1), after-tax profits of non-shifting affiliates (= j=1,2 [(1−tj )Πij ]), net profits of shift-12ing affiliates (denoted by
Welfare in country i iss
j=1,2 Πij and adjusted for concealment costs −(PPWi = α lnαPi− α + Iih + Tih ,sj=1,2 nij f ).

(30)

where Pi , Iih , and Tih are from (4), (29), and (28) respectively. In addition, it is noteworthy
that Pi is independent of the tax rates. The government of country i chooses the tax rate ti
to maximize the welfare Wi of (30). The trade-off of setting ti arises from several opposing
effects: the benefits from taxing foreign affiliates and profit-shifting reduced tax bases.
A higher tax rate increases the tax revenue collected from export affiliates of country j
operating in country i, contributing to the transfer payment(Ti = ti Πi ). However, a higher
tax rate also incentivizes more affiliates to shift profits to the tax haven, decreasing thedomestic tax base (Πi ).Furthermore, a higher ti leads to two negative effects for domestic
firms in country i. First, it reduces their after-tax profits ((1 − ti )Πii of Equation (29)).
Second, it incentivizes more domestic firms to shift profits to the tax haven, leading toa larger deadweight loss due to concealment costs(captured by −niis f in Equation (29)).
Both of these effects contribute to a decrease in the aggregate income of individuals incountry 1 (denoted by Iih in equation (29)). To maximize welfare, country i chooses the tax
rate ti that balances the benefits of higher transfer payments with the costs associatedwith a smaller tax base and lower aggregate income due to profit-shifting by domestic
firms.
We derive the optimal tax rate for country i in the lemma below.
Lemma 2 The optimal tax rate in country i ist∗i = min tin (si ), 1 , i = 1, 2
where

(31)


1/ϵ
(1 − x)ϕf σN (ϵ + 1)[x + (1 − x)ϕ]t (x) =.
αϵ
(ϵ + 1)(1 − x)ϕϵ+1 + xϵin

Proof: Using (30), the FOC to maximize the welfare in non-haven i is
dWi (1 − si )αϕ(tin (si ))−ϵ  in=× (t (si ))ϵ − tϵidti
σN (si + (1 − si )ϕ)=0.
Solving this equation for ti leads to the optimal tax rate formula presented in equation(31).
□
According to (31) in Lemma 1, the optimal tax rates in the non-havens can exhibit
13corner solutions. In particular, the optimal solution might be t∗i = 1 if the concealment
cost f is very large. This corner solution arises because a very high concealment costdiscourages profit-shifting so significantly that the non-haven country might choose to
maximize tax revenue by setting the maximum possible tax rate.
To focus on the interesting case where the tax rate plays a more nuanced role in
influencing profit-shifting decisions, we concentrate on interior solutions (where tin (si ) <1) in the subsequent analysis. This requires a small concealment cost, f . Specifically, asufficient condition for this is1−ϵαϵ(ϵ + 1) ϵ .
(32)
f<
Nσ
In the context of international tax competition, countries reduce their statutory tax
rates to attract mobile factors, like capital or MNE headquarters, which may result in a“race to the bottom”(i.e., Garretsen and Peeters, 2007; Keen and Konrad, 2013). In thispaper, profit shifting between non-havens is assumed away and therefore tax competition
for the mobile MNEs’ tax base only occurs between the non-havens and the tax haven.
This kind of competition reduces tax rates in the non-havens (i.e., from 1 to t∗i ), which isconsistent with the results in the previous literature on international tax competition andharmful tax havens (e.g., Slemrod and Wilson, 2009; Krautheim and Schmidt-Eisenlohr,2011).
Substituting t∗i = tin (si ) into the model, we obtain the following expressions for thecutoffs of domestic firms and export affiliates:1 ϵ(σ−1)(1 − si )ϕcM ,(ϵ + 1)(1 − si )ϕϵ+1 + si ϵ1 ϵ(σ−1)1siϕ∗cij = ϕ σ−1cM , i ̸= j.
(ϵ + 1)si ϕϵ+1 + (1 − si )ϵc∗ii =



(33)
(34)

The mass of shifting affiliates are
 ϵ+1
ϵ
(1
−
s
)ϕ
i
ns∗
=
s
N
,
i
ii
(ϵ + 1)(1 − si )ϕϵ+1 + si ϵ
 ϵ+1

ϵ
si ϕ
s∗
ϵ+1
.
nij = si N ϕ(ϵ + 1)si ϕϵ+1 + (1 − si )ϵ


(35)
(36)

The shifting profits of export affiliates in the two non-havens are givenΠs∗ij =ni

Z c∗ij0α si ϕϵ+1si ϕπij (c)dG(c) =, i ̸= j.
σ si ϕ + 1 − si (ϵ + 1)si ϕϵ+1 + (1 − si )ϵ

14

(37)

We then obtain
Eiis =

4

Πs∗
si ϕ
ii
,
=
t
Πii
(ϵ + 1)si ϕϵ+1 + (1 − si )ϵEijs =

Πs∗si ϕ1+ϵij.
=
Πtij(ϵ + 1)si ϕϵ+1 + (1 − si )ϵ(38)

Gains/losses from shifting

Profit-shifting to a tax haven affects the welfare of non-havens. To clarify the effects, We
decompose the welfare into two parts as
Wi∗ =

Wio∗
|{z}

+

welfare without a haven

Bi∗ ,
|{z}

(39)

net benefits

where Wio∗ is the welfare level in country i without a tax haven, and Bi∗ denotes the net
benefits (or losses when Bi∗ < 0) from the presence of a tax haven. The expression of Bi∗
isBi∗ = (1 − ∆ij )Πtij − (1 − ∆ji )Πtji − (n∗ii + n∗ij )f,

(40)

where
∆ij = (1 − Eijs )t∗j ,s ∗∆ji = (1 − Eji
)ti

(41)

denotes the effective tax rates (ETRs) of MNE exporting affiliates5 . Eq.(41) immediately
shows that the level of ETRs positively depends on the nominal tax rates and negatively
depends on the shifted profits share of export affiliates. A smaller share of shifted profits
and a higher level of nominal tax rate indicate a higher level of effective tax rate.
As shown in (40), the presence of a tax haven generates various effects of non-havens’
welfare through different channels. Without loss of generality, we mainly focus on thewelfare impacts of country 1 in the subsequent analysis for simplicity. Additionally, wedefine country 1 as a developed (developing) country if s > 1/2 (s < 1/2).
The presence of a tax haven can generate both gains and losses for country 1. The
gains are measured by (1−∆12 )Πt12 , which represents the total benefits received by country
1’s export affiliates operating in country 2 and reflects the increase in net-tax profits dueto the lower effective tax rate faced by the export affiliates. Without a tax haven, theeffective tax rate in country 2 would be 1 (as shown in equation 15). The presence of atax haven induces a lower effective tax rate in country 2 through two ways reducing thestatutory tax rate, t∗2 , and decreasing the tax base, Π12 . The former is a direct effect and5

Following Garcia-Bernardo et al. (2022), we define the effective tax rates as total tax payments ofan affiliate divided by its total profits.

15

the latter is an indirect effect as discussed in Tørsøv et al. (2023),.
The losses for country 1 stem from two sources: the reduction in effective tax rates
for foreign export affiliates from country 2 and the concealment costs associated with theprofit-shifting activities. The first source of is captured by (1 − ∆21 )Πt21 . Like country 1’s
export affiliates, those from country 2 can also find it profitable to shift profits to the tax
haven. This behavior reduces the effective tax rate in country 1 through two channels.
First, the lower statutory tax rate (t∗1 ) applied to country 2’s export affiliates leads to adecrease in tax revenue, represented by the term −(1 − t∗1 )Πt21 . Second, any profits shiftedto the tax haven by these affiliates (represented by Πs∗21 ) result in a complete loss of tax∗ s∗revenue for country 1, reflected by the term −t1 Π21 . The second source of loss is theconcealment cost (f ) paid by all firms engaging in profit-shifting. This cost represents a
deadweight loss that reduces the overall welfare in country 1. The total concealment costof country 1’s MNEs for shifting paid to the tax haven is −(n∗11 + n∗12 )f .

4.1

Effects of trade liberalization

In this section, we move to the analysis of the effects of trade liberalization. From (40), thenet benefits B1∗ depend on, the total taxable profits of exporting affiliates, Πt12 and Πt21 ,the effective tax rates faced by the exporting affiliates of two non-havens, ∆12 and ∆21 ,s∗
and the mass of shifting affiliates ns∗
11 and n12 . To clarify the impact of trade liberalizationon B1∗ , we analyze the effects of trade liberalization on the previous components one by
one in the following subsections.
4.1.1

Profit reallocation effectWe first focus on how an increase in trade freeness affects the pre-tax profits of exporting
affiliates. Taking the derivatives of Πt12 and Πt21 with respect to ϕ, we obtaindΠt12α(1 − s)s=> 0,dϕ
σ(1 − s + sϕ)2dΠt21α(1 − s)s=> 0.
dϕ
σ[s + (1 − s)ϕ]2(42)

When trade costs decrease, the exporting affiliates become more competitive in both nonhavens, leading to larger pre-tax profits. According to (40), we can calculate the aggregate
impact of the profit reallocation effect by
P R = (1 − ∆12 )

dΠt12
dΠt
− (1 − ∆21 ) 21 ,
dϕ
dϕ

16

(43)

whereP R|ϕ=0 =α(2s − 1),σs(1 − s)(44)


P R|ϕ=1 = f N (ϵ + 1)(1 − s)s 

1−s
1−s+ϵ



 1ϵ

1−s+ϵ

−


s 1/ϵ
s+ϵ

s+ϵ

.

(45)

It is easy to verify that1
P R|ϕ=0 ⋛ 0 if s ⋛ ,
2
and

4.1.2

1
P R|ϕ=1 ⋛ 0 if s ⋚ .
2Rate-reducing effectAs shown in 41, trade liberalization affects the effective tax rates faced by exporting
affiliates through two channels, changing the statutory tax rates and affecting the degreeof base erosion (or the share of shifted profits). We first investigate how the tax rates in
non-haven i are affected by trade freeness ϕ. Taking the derivative of t∗i with respect toϕ yields

 1+ϵ
ϵ
dt∗i
(1 − si )ϕf si N σ(ϵ + 1) [(1 − si )(ϵ + 1)ϕ (1 − ϕϵ ) + si ]=×dϕ
(1 − si )(ϵ + 1)ϕϵ+1 + si ϵα(1 − si )ϵϕ2
{z
}
{z
} |
|
+

+

(46)
> 0,
where s1 = s and s2 = 1 − s. The positiveness of (dt∗i )/(dϕ) indicates that trade liberalization leads to higher statutory tax rates in non-havens regardless of the share of MNE
headquarters. Intuitively, trade liberalization increases the profits of exporting firms,
which then increases the incentives for these firms to avoid taxes. And governments,
faced with a smaller tax base, can only raise tax rates to maintain tax revenues.
∗
Tking the derivative of E12with respect to ϕ yields∗
dE12(1 − s)sϵ(1 + ϵ)ϕϵ=>0
dϕ[(1 − s)ϵ + s(1 + ϵ)ϕ1+ϵ ]2(47)

Trade liberalization increases the share of shifted profits through two channels. Firstly, as
shown in (42), the exporting affiliates become more profitable and have large incentives
to shift profits to tax havens. Secondly, higher tax rates in non-havens and therefore

17larger tax gaps between the non-havens and the tax haven also encourage firms to avoid
taxation from non-havens. Wier and Zucman (2022) confirm the increase in the degree ofbase erasion for past decades and show that the share of global multinational profits (theprofits booked by corporations outside of their headquartered country) in global corporate
profits increased from 4% in the 1970s to about 16% in 2019.
Combining the effects of trade liberalization on statutory tax rates and tax bases, we
obtain the effective tax rate effect of economic integration, which is given by
∗
dE s
d∆12
s dt2
= (1 − E12)−t∗2 12 .
dϕ
dϕ
dϕ
|
{z
} | {z }

(48)

−

+

A reduction in trade costs leads to higher statutory tax rates and larger tax-base losses
in non-havens simultaneously. The rise in statutory tax rates, t∗i , has a positive impact
on the level of effective tax rates. Meanwhile, the larger tax-base losses negatively affectthe effective tax rates. Consequently, whether trade liberalization increases effective tax
rates depends on which effect is dominant.
Lemma 3 When a tax haven exists, trade liberalization increases the effective tax rate
for exporting affiliates of MNEs monotonically if they are headquartered in a non-havenwith a small share of MNEs (s < 1/(2 + ϵ)), otherwise, it increases the effective tax rate
when the trade freeness is small (ϕ < ϕ0 ) and decreases the effective tax rate when trade
freeness is large (ϕ > ϕ0 ), where ϕ0 ∈ (0, 1) is implicitly given byΓ(ϕ) ≡ (1 − s)2 + (1 − s)s(1 + ϵ)ϕ(1 − ϕϵ ) − sϕ1+ϵ [(1 − s)ϵ + s(1 + ϵ)ϕ1+ϵ ] = 0.
Proof: Using (48), we obtain the derivative of ∆12 with respect to ϕ as
(1 − s)ϵt∗2
d∆12
=
×Γ(ϕ)
dϕ
(1 − s + sϕ)ϕ[(1 − s)ϵ + s(1 + ϵ)ϕ1+ϵ ]2
|
{z
}
+

where
Γ(ϕ) ≡ (1 − s)2 + (1 − s)s(1 + ϵ)ϕ(1 − ϕϵ ) − sϕ1+ϵ [(1 − s)ϵ + s(1 + ϵ)ϕ1+ϵ ].
Therefore, we haved∆12
⋚ 0 if Γ(ϕ) ⋚ 0.
dϕ
In addition, the derivative of Γ(ϕ) with respect to ϕ isΓ′ (ϕ) = s(ϵ + 1) 1 − s − (1 − s)(2ϵ + 1)ϕϵ − 2s(ϵ + 1)ϕ2ϵ+118

whereΓ′′ (ϕ) < 0,

Γ′ (0) = (1 − s)s(ϵ + 1) > 0,

Γ′ (1) = −2(s + ϵ)s(ϵ + 1) < 0.

The inequalities above demonstrate that Γ′ (ϕ) is decreasing with ϕ, and is positive (negative) for sufficiently small (large) values of ϕ. Consequently, Γ(ϕ) is increasing (decreasing)in ϕ for small (large) values of ϕ. It follows that the global minimum of Γ(ϕ) must occur
at one of the endpoints ϕ = 0 or ϕ = 1. Moreover, the values of ϕ at ϕ = 0 and ϕ = 1,
are given as
Γ(0) = (1 − s)2 ,Γ(1) = 1 − s(2 + ϵ)respectively. For all s ∈ (0, 1), Γ(0) is strictly positive. Therefore, if Γ(1) < 0, whichholds for s > 1/(2 + ϵ), there exists a unique root ϕ0 ∈ (0, 1) of Γ(ϕ), and Γ(ϕ) is positive(negative) for ϕ ∈ (0, ϕ0 ) (ϕ ∈ (ϕ0 , 1)). Otherwise, Γ(ϕ) is strictly positive. Therefore,
the lemma is proved.
□
The aggregate rate-reducing effect on country 1 consists of the changes in the effective
tax rates faced by export affiliates of both non-havens:
RR = −Πt12

d∆21
d∆12
+ Πt21
,
dϕ
dϕ

(49)

where
RR|ϕ=0 = 0,(
RR|ϕ=1 = f N (1 − s)s(ϵ + 1)1−s[s(ϵ + 2) − 1 − ϵ] 1−s+ϵ(1 − s + ϵ)2

1/ϵ
+

)

s 1/ϵ
[s(ϵ
+
2)
−
1]
s+ϵ
.
(s + ϵ)2

It is easy to verify that1
RR|ϕ=1 ⋛ 0 if s ⋛ .
2
4.1.3

Shifting costs

In the two non-havens, trade liberalization has various effects on different types of affiliates. Taking the derivative of two types of affiliates of country 1’s MNEs of (6) withrespect to ϕ yields
dπ11 (c)(1 − s)c1−σ A=−
dϕ[(1 − s)ϕ + s]2
< 0,

(50)
19

dπ12 (c)(1 − s)c1−σ A=
dϕ[sϕ + (1 − s)]2
> 0.

(51)

Inequality (50) ((51)) indicates that the exporters’ (domestic firms’) become more (less)profitable with trade freeness. In other words, export affiliates are more likely to use
the tax haven to shift profit when trade costs become lower. The derivative of n∗11 withrespect to ϕ is
 2ϵ+1ϵs(ϵ + 1)2
(1 − s)ϕdn∗11=N× ϕϵ+1− ϕϵ+1 .
1
2
ϵ+1
dϕ
ϕ
(1 − s)ϵ + s(ϵ + 1)ϕ
|
{z
}

(52)

+

where


s
ϕ1 ≡
(1 − s)(ϵ + 1)

1
 ϵ+1

,

s1 ≡

ϵ+1
1
> .
ϵ+2
2

Furthermore, ϕ0 ≤ 1 holds only if s ≤ s1 . The derivative of n∗12 with respect to ϕ is
 2ϵ+1
ϵ
dn∗12
sϕ
2 ϵ−1
= N (1 − s)(ϵ + 1) ϕdϕ
(1 − s)ϵ + s(ϵ + 1)ϕϵ+1
{z
}
|

(53)

+

Therefore, we have the following lemma.
Lemma 4 (a) : The mass of shifting domestic firms increases with trade liberalization
first (ϕ < ϕ0 ), then decreases with it (ϕ > ϕ0 ), if the share of MNEs is small (s < s1 );otherwise, the mass of shifting domestic firms increases with trade liberalization monotonically. (b) : The mass of shifting export affiliates increases monotonically with tradeliberation.
Trade liberalization has two opposite effects on the mass of shifting domestic affiliates:
the positive effect of raising the statutory tax rates in non-havens and the negative effectof reduction in the pre-tax profits of these domestic affiliates. Consequently, which effectis dominant depends on the share of MNEs. When the share of MNEs in a country islarge, When a country has a larger proportion of multinational firms, this implies that the
number of foreign firms in the country is relatively small. Thus, while trade liberalization
increases the competitiveness of these foreign firms, their smaller numbers have a relatively
small impact on domestic firms. For export affiliates, trade liberalization simultaneously
increases their profit margins as well as the tax rates in non-havens, both of which havethe effect of facilitating their profit shifting. Consequently, the mass of shifting export
affiliates increases monotonically with trade liberation.
20

The derivative of C with respect to ϕ is given by
dn∗
dn∗
dC
= f 11 + f 12 ,
dϕ
dϕ
dϕ

(54)

whose first term is ambiguous and the second term is positive according to (52) and(53). Moreover, trade liberalization encourages the shifting costs when s is large enoughaccording to Lemma 4. Moreover, we havedC
= 0,
dϕ ϕ=0dC= f N (1 − s)s(ϵ + 1)
dϕ ϕ=1
4.1.4

(


 )
s 1/ϵ
1−s 1/ϵs(1 + ϵ) [1 + ϵ − s(ϵ + 2)] 1−s+ϵs+ϵ.
−(s + ϵ)2(1 − s + ϵ)2Aggregate impact of trade liberalization

Combining the profit reallocation effect, rate-reducing effect, and shifting profit effect oftrade liberalization, we now move to analyze the aggregate impact of trade liberalizationon the benefits of the presence of a tax haven. The derivative of the net benefits withrespect to ϕ is given by
dB1∗
dC=P R + RR −
dϕ
dϕ
d∆12
dΠt
d∆21
dΠt
dC
= − Πt12+ (1 − ∆12 ) 12 + Πt21
− (1 − ∆21 ) 21 −
dϕ
dϕ
dϕ
dϕ
dϕ


αs(1 − s)
1
1
=
−
2
σ
(1 − s + sϕ)(ϕ − sϕ + s)2
(

 1+ϵ
ϵ
1
s
(1 − s)+ f N (1 − s)(ϵ + 1)ϕ ϵ ×
1 − s sϵ + (1 − s)(ϵ + 1)ϕϵ+1
)

 ϵ+1
ϵ
(ϵ + 1) (sϕϵ+1 − s + 1)s−.
(1 − s)ϵ + s(ϵ + 1)ϕϵ+1 (1 − s)ϵ + s(ϵ + 1)ϕϵ+1(55)

Proposition 1 When the trade freeness is small, the developed (developing) country benefits (suffers) from the presence of a tax haven.

21

Proof: The derivative of (55) at ϕ = 0 is given by
dB1∗
dC= P R|ϕ=0 + RR|ϕ=0 −| {z } dϕ ϕ=0
dϕ ϕ=0| {z }=0=02s − 1 α=.
(1 − s)s σ
It is easy to verify thatdB1∗
1
⋛ 0 if s ⋛ .
dϕ ϕ=02

In addition, we obtain that B1∗ = 0 for all s ∈ (0, 1) if ϕ = 0 according to (40). The
proposition is proved.
□
Intuitively, the developed country has a large share of MNEs (s > 1/2). When trade
opens, the developed country’s export affiliates become more profitable and hence shift
more profits into the tax haven compared with the developing country’s, which generates
a positive (negative) profit-reallocation effect in the developed (developing) country. Furthermore, the impact of concealment costs and the rate-reducing effect are negligible when
trade freeness is small. Therefore, The profit-reallocation effect dominates, and hence thedeveloped (developing) country benefits (hurts) from the presence of a tax haven when
trade freeness is small.
Proposition 2 From the free trade, a country is better off with a small reduction in trade
freeness if it has a large headquarters share (s > sb ), otherwise the country suffers, where
0 < sb < 1/2.
Proof: See Appendix A.

□

The intuition for Proposition 2 is simple. When trade freeness is very large (ϕ → 1),
the rate-reducing effect and profit-reallocation effect in a developing (developed) country
decrease (increase) with trade liberalization, which affects the developed country’s welfare
positively and the developing country’s welfare negatively. Meanwhile, the shifting costs
in a developed (developing) country increase (decrease) with trade liberalization, which
affects the developed country’s welfare negatively and the developing country’s welfare
positively. Consequently, the positive (negative) effect dominates, leading to welfare gains
from profit shifting in a country with a small share of MNEs.
Proposition 1 and 2 indicate that the impact of trade liberalization on the gains(or losses) from profit shifting is non-monotonic in some situations. For a developed
country (s > 1/2), trade liberalization increases the gains when trade freeness is small
22and decreases the gains when trade freeness is large. Furthermore, for a developing country
and in the case of a small s (s < sb < 1/2), trade liberalization decreases the net benefits
when trade freeness is small and increases the net benefits when trade freeness is large.
Benefit

Benefit
0.2

s=0.5

0.4

0.6

0.8

1.0



0.08

s=0.6

-0.02

s=0.7

0.06

-0.04

s=0.8
s=0.9

0.04

-0.06

s=0.5
0.02

-0.08

0.2

0.4

0.6

0.8

1.0

s=0.4
s=0.3

 -0.10

s=0.2
s=0.1

-0.02

-0.12

(a) the developed country: s > 1/2(b) the developing country: s < 1/2

Figure 1: The net benefits (B ∗ ) from the tax haven
Figure 1 shows how the headquarter share s changes the net benefits using the following
parameters:
σ = 4, γ = 9, cM = 0.01, f = 0.2, α = 0.8, ϕ = 0.3.

(56)

Panel (a) and (b) show the cases of developed countries (s > 1/2) and developing countries(s < 1/2), respectively. We observe a bell shape for a large s and a “U” shape for a verysmall s. Therefore, these numerical results are consistent with Proposition 1 and 2.

4.2

Welfare analysis

According to (39), taking the derivative of W1∗ with respect to ϕ leads to
dW1∗
=
dϕ

dW o∗
dϕ
| {z }+

gains from trade

dB1∗
dϕ
|{z}

.

(57)

impacts of shifting(57) shows that the effect of trade liberalization on the non-haven country’s welfare isdivided into two parts: gains from trade and impacts of shifting. The first term of (57) is
positive for all ϕ ∈ (0, 1) according to (19), which indicates that without profit shifting,non-havens always benefit from trade liberalization. However, according to proposition
1 and 2, the impact of trade liberalization on the net benefits of profit shifting is nonmonotonic. In other words, the sign of the second term of (57) can be positive or negative.

Proposition 3 The non-havens benefit from trade openness when MNEs shift profits.
23

WelfareWelfare

3.80

3.7

3.6
3.75

3.5
3.70

s=0.5

s=0.5

3.4

s=0.4

s=0.6

3.65

s=0.7

s=0.3

3.3

s=0.2

s=0.8
3.60

s=0.9

0.2

0.4

0.6

0.8

s=0.1

3.2
ϕ

1.0

0.2

(a) the developed country

0.4

0.6

0.8

1.0

ϕ

(b) the developing country

Figure 2: Welfare (large f , f = 0.2)
WelfareWelfare

3.90
3.7
3.85
3.6
3.80
3.5
3.75

3.4

s=0.5

s=0.5

3.70

s=0.6

s=0.4

s=0.7

s=0.3

3.3

3.65

s=0.8

s=0.2

s=0.9

s=0.1
3.2

3.60

0.2

0.4

0.6

0.8

ϕ

1.0

0.2

3.55

(a) the developed country

0.4

0.6

0.8

1.0

ϕ

(b) the developing country

Figure 3: Welfare (small f , f = 0.0001)
proof: From (57), we can easily verify that
dW1∗
dW o∗
dB1∗
α[(1 − s)2 + (σ − 1)s2 ]=+=>0
dϕ ϕ=0dϕ ϕ=0dϕ ϕ=0(1 − s)s(σ − 1)σholds for all s ∈ (0, 1).

□

Proposition 4 In the case of free trade, a small reduction of trade freeness decreases thenon-havens’ welfare when MNEs shift profits.

24

proof: From (57), we can easily verify that
dW1∗
dW o∗
dB1∗
=
+
dϕ ϕ=1dϕ ϕ=1dϕ ϕ=1"
1−s 1/ϵ1−s+ϵs(ϵ + 1) s+ϵ−1−s+ϵ(s + ϵ)2
"
 #
s 1/ϵ
(ϵ
+
1)
α(1 − s)s+ϵ
− f N (1 − s)s(ϵ + 1)>
(σ − 1)(s + ϵ)2


1/ϵ



sϵ(ϵ + 1)sϵ + s(32) α(1 − s)  σ
 > 0.
−
×
>


2
σ
σ
−
1
(s
+
ϵ)
s
+
ϵ
| {z } | {z } |{z}α(1 − s)=+ f N (1 − s)s(ϵ + 1)
(σ − 1)>1<11/ϵ #<1□
Proposition 3 and 4 indicate that trade liberalization increases non-havens’ welfare
when trade freeness is very small or very large. Without profit shifting, non-havens
always benefit from trade liberalization, which is regarded as gains from trade. However,
the impact of trade liberalization on the net benefits of profit shifting is non-monotonic
and can be positive or negative. The part of gains from trade dominates and leads to a
positive effect of trade liberalization on welfare when trade freeness is very small or verylarge.
Figure 2 and 3 show how the trade freeness ϕ changes a non-haven country’s welfare
using the parameters of (56) except for f . Figure 2 plots a non-haven country’s welfare in
the case of a very small f (f = 0.0001), and Figure 3 plots a non-haven country’s welfare
in the case of a large f (f = 0.2). Panels (a) and (b) in both figures show the cases ofdeveloped countries (s > 1/2) and developing countries (s < 1/2), respectively. In mostcases, trade liberalization leads to higher welfare in the non-havens. However, the effectof trade liberalization is non-monotonic in a country with a very large share of MNEs
(e.g., s = 0.9) when the concealment costs f is very small (f = 0.0001). Our numericalresults show a non-monotone impact of gradual trade liberalization, which indicates thatemerging trade might be harmful to developed countries under some conditions in thepresence of tax havens.
Some previous literature also demonstrates the harmful trade under non-CES demand
structures and explains it by the market distortions due to incomplete pass-through anddumping (e.g., Bykadorov et al., 2015; Chen and Zeng, 2018; Kokovin et al., 2022). In
contrast, this paper indicates that harmful trade occurs even under the CES demand
structure and due to the non-monotonic impact of profit shifting.

25

5Inequality of asymmetric countries

Before analyzing the general cases of the MNE share s, we examine some primary resultsof the value of B1∗ by considering the special cases where s = 0, s = 1/2, and s = 1. In
the case of s = 0, there are no MNEs headquartered in country 1 and all varieties areproduced by country 2. From (40), the net benefits are given by
B1∗ |s=0 = −(1 − ∆21 )Πt21 < 0.
This indicates that country 1 incurs a loss from the presence of the tax haven because it
cannot benefit from tax avoidance by its export affiliates (Πt12 = 0 ) and experiences areduction in the effective tax rate, and hence, in tax revenue from foreign affiliates.
s∗
In the case of s = 1/2, the two non-havens are symmetric. This means Πs∗
12 = Π21 ,t∗t∗1 = t∗2 , and Πt∗
12 = Π21 . The net benefits therefore become
B1∗ |s=1/2 = −C < 0.
Here, the only negative effect comes from the concealment costs (C) paid by country 1’s
firms engaging in profit-shifting. Since both countries are symmetric, there is no net gainor loss from the rate-reducing effect or tax-avoiding effect.
In the case of s = 1, Country 1 owns all MNEs and produces all varieties. Wet∗immediately know that Πs∗
21 = 0 and Π21 = 0. The net benefits then are
B1∗ |s=1 = (1 − ∆12 )Πt12 − C
ϵ+1α= − f N (ϵ + 1)− ϵ (ϵ + 2) > 0,σwhere the inequality is ensured by (32). This indicates a positive net benefit for country
1. It benefits from the reduction in the effective tax rates faced by its exporting affiliates,
while the concealment costs (C) are not large enough to outweigh these gains.
The following lemma summarizes the above discussions.
Lemma 5 (a): A non-haven incurs a loss (gain) from the presence of a tax haven if no(all) MNEs are located in this country; and(b): when both non-havens are symmetric, the presence of a tax haven harms both countries.
Lemma 5 highlights the varying impacts of profit-shifting by MNEs on non-havens
depending on the distribution of MNEs across these countries.

26

5.1

Aggregate impact of MNEs’ share

Using (40), the derivative of B1∗ , with respect to s is given by
dB1∗
d∆12
d∆21
dΠt
dΠt
dC
= − Πt12+ (1 − ∆12 ) 12 + Πt21
− (1 − ∆21 ) 21 −
ds
ds
ds
ds
ds
ds
= C(s) − D(s)f

(58)

where


1
αϕ
1
> 0,
C(s) =+σ (s + ϕ − sϕ)2 (1 − s + sϕ)2
 1ϵ sϕ[s(ϵ + 1)ϕϵ+1 − sϵ + 2ϵ + 1] [1 − s (1 − ϕϵ+1 )]D(s) =N
1+(1 − s)ϵ + s(ϵ + 1)ϕϵ+1[(1 − s)ϵ + s(ϵ + 1)ϕϵ+1 ]2 1ϵ 
(1 − s)ϕ
1
+N
1+
> 0.
sϵ + (1 − s)(ϵ + 1)ϕϵ+1
sϵ + (1 − s)(ϵ + 1)ϕϵ+1
It is easy to verify that C(s) > 0 and D(s) > 0 for all s ∈ [0, 1].
Proposition 5 (a) : When s = 0, a small increase in the MNEs’ share generates more
losses if f is large enough (f > f1 ), otherwise it leads to less losses.
(b) : When s = 1, a small reduction in the MNEs’ share generates more gains if f is large
enough (f > f2 ), otherwise it leads to fewer gains, where f1 and f2 are given by11α(ϵ + 1) ϵ +1 (ϕ2 + 1) ϕϵ
f1 ≡,N σ [(ϵ + 1)ϕϵ+1 + 1]α(ϵ + 1) ϵ +1 (ϕ2 + 1) ϕϵ
f2 ≡.
N σ [(ϵ + 2)ϕϵ+1 + 1]

(59)

Proof: Using (58), the derivative of B1∗ with respect to s at s = 0 is
dB1∗
N [(ϵ + 1)ϕϵ+1 + 1]=
×(f1 − f ),ϵ+1
ds s=0(ϵ + 1) ϵ ϕϵ+2
|
{z
}
+

which proves (a). The derivative of B ∗ with respect to s at s = 1 isdB1∗N [(ϵ + 2)ϕϵ+1 + 1]=
×(f2 − f ),ϵ+1
ds s=1(ϵ + 1) ϵ ϕϵ+2
|
{z
}
+

which proves (b).

□According to Lemma 5, we easily obtain that B1∗ |s=1 > 0 > B1∗ |s=0 . Meanwhile,
Proposition 5 (a) and (b) show that when the concealment costs for profit shifting f are
27

B
0.2

f=0.2
0.1

f=0.1
f=0.0001

s
0.2

0.4

0.6

0.8

1.0

-0.1

-0.2

Figure 4: Impacts of headquarter share (s) on net benefits (B ∗ )large, the net benefits B1∗ decrease with s in the cases of a very small s (s → 0) or a verylarge s (s → 1). Therefore, we immediately know that the relationship between B1∗ ands is non-monotonic if f is large (f > f1 ). Building from this discussion, we now establish
a simple corollary to Proposition 5:
Corollary 1 A developed country (with a very large s) benefits from the MNEs’ profit
shifting. A developing country (with a very small s) suffers from the MNEs’ profit shifting.
Figure 4 shows how the MNEs’ share s changes the net benefits using the parametersof (56). The dashed curve is the case of f = 0.0001, whose monotonicity shows thatraising the headquarters share s improves the net benefits of profits shifting if f is smallenough. The solid and dotted curves are the cases of f = 0.2 and f = 0.1, respectively,
whose non-monotonicity is consistent with Proposition 5 (a) and (b).

6

Endogenous tax rate in the tax haven

Following Krautheim and Schmidt-Eisenlohr (2011) and Pan and Zeng (2023), we assume
the tax rate is ts > 0, which is endogenously determined by the haven government.
Therefore, the tax difference between the tax haven and the non-havens and the marginal
cost jointly determine an affiliate’s decision on profit shifting. Similar to the baselinemodel, we obtain the cutoffsc∗ii =Af (si + (1 − si )ϕ)

1
 σ−1

(ti − ts )1
σ−1c∗ji =,Aϕf (si + (1 − si )ϕ)

1
 σ−1

1

(ti − ts ) σ−1 ,where ti − ts is the tax difference between non-haven i and tax haven. Similar to Pan
and Zeng (2023), we also assume that three countries set tax rates simultaneously in a
one-shot game. The non-havens set tax rates t1 and t2 to maximize their own welfare asin the baseline model. The optimal problem of the tax-haven government is to maximize
the total tax revenue Ts = ts Πs , where Πs = Πs1 + Πs2 is the total shifted profits. See
28

the details in Appendix B. Our simulations confirm the non-monotonic impacts of tradeliberalization on gains (or losses) from profit shifting and on welfare in some situations.
We also show the non-monotonic relationship between MNE share (s) and benefits ofprofit shifting (B ∗ ) In summary, our main results remain true when the tax rate in thehaven is endogenously given.

7

Conclusion

This paper establishes a three-country model of heterogeneous firms and a monopolisticcompetition goods market to explore the welfare impact of the profit shifting on developed and developing non-havens in an open economy. Furthermore, we also examine how
trade liberalization changes the impact of profit shifting. First, we show that the impactof trade liberalization on the gains (or losses) from profit shifting is non-monotonic insome situations. For a developed country (s > 1/2), trade liberalization increases thegains when trade freeness is small and decreases the gains when trade freeness is large.
Furthermore, for a developing country and in the case of a small s (s < sb ), trade liberalization decreases the net benefits when trade freeness is small and increases the net
benefits when trade freeness is large.
Second, we find that trade liberalization increases non-havens’ welfare when trade
freeness is either very small or very large. Without a tax haven, trade liberalization
generates welfare gains by reducing the price indices in the New Trade Theory models
measured by ACR. Our paper shows that the part of gains from trade dominates when
trade freeness is very small or very large. By simulation, we also indicate that the welfare
effect of trade liberalization, including gains from trade part and the impact of profit
shifting part, is non-monotonic in a country with a very large share of MNEs, and theconcealment costs are very small.
Thirdly, we find that developing countries (with a small share of MMEs) are worse
off, and highly developed countries (with a very large share of MNEs) may be better off
with the presence of a tax haven. However, we disclose that the relationship between thewelfare impact of profit shifting and the MNEs’ share is non-monotonic if the concealment
costs are large enough.

References
Arkolakis, C., Costinot, A., & Rodrı́guez-Clare, A., 2012. New trade models, same oldgains. American Economic Review 102(1), 94-130.

29

Arkolakis, C., Costinot, A., Donaldson, D., & Rodrı́guez-Clare, A., 2019. The elusive
pro-competitive effects of trade. The Review of Economic Studies 86(1), 46-80.
Buettner, T., Wamser, G., 2007. Intercompany Loans and Profit Shifting—Evidence from
Company-Level Data. CESifo Working Paper Series No. 1959. Available at SSRN:
https://ssrn.com/abstract=981120
Buettner, T., Overesch, M., Schreiber, U., Wamser, G., 2012. The impact of thincapitalization rules on the capital structure of multinational firms. Journal of Public
Economics 96, 930-938.
Bykadorov, I., Gorn, A., Kokovin, S., & Zhelobodko, E. (2015). Why are losses from trade
unlikely?. Economics Letters 129, 35-38.
Chen, C. M., & Zeng, D. Z. (2018). Mobile capital, variable elasticity of substitution, andtrade liberalization. Journal of Economic Geography, 18(2), 461-494.
Choi, J. P., Furusawa, T. & Ishikawa, J. (2020) Transfer pricing regulation and tax
competition. Journal of International Economics ,127, 103367.
Desai, M.A., Foley, C.F., Hines, J.R., 2006. The demand for tax havens. Journal of Public
Economics 90, 513-531.
Gao, W., Lu, Y. & Shi, X., 2019. Trade liberalization and corporate income tax avoidance.
Economic Inquiry, 57(4), 1963-1980.
Garcia-Bernardo, J., Janský, P., & Tørsløv, T. (2022). Decomposing multinational corporations’ declining effective tax rates. IMF Economic Review 70(2), 338-381.
Garretsen, H., & Peeters, J. (2007). Capital mobility, agglomeration and corporate tax rates: is the race to the bottom for real?. CESifo Economic Studies 53(2), 263-293. https://www.taxjustice.net/wp-content/uploads/2014/04/Price of Offshore Revisited 120722.pdf
Hong, Q., Smart, M. 2010. In praise of tax havens: international tax planning and foreign
direct investment. European Economic Review 54(1), 82-95
Kato, H., and H. Okoshi (2022), ‘Economic integration and agglomeration ofmultinational production with transfer pricing.’ International Economic Review,doi.org/10.1111/iere.12569.
Keen, M., & Konrad, K. A. (2013). The theory of international tax competition andcoordination. Handbook of public economics, 5, 257-328.
Kokovin, S., Molchanov, P., & Bykadorov, I. (2022). Increasing returns, monopolisticcompetition, and international trade: Revisiting gains from trade. Journal of International Economics 137, 103595.
Krautheim, S. & Schmidt-Eisenlohr, T. (2011) Heterogeneous firms, ‘profit shifting’ FDI
and international tax competition. Journal of Public Economics, 95(1-2), 122-133.
Kind, H. J., Midelfart, K. H., & Schjelderup, G., 2005. Corporate tax systems, multinational enterprises, and economic integration. Journal of International Economics30

65(2), 507-521.
Johannesen, N., Tørsløv, T., Wier, L., 2020. Are less developed countries more exposed
to multinational tax avoidance? Method and evidence from micro-data, The WorldBank Economic Review 34(3), 790-809.
Johannesen, N. 2010. Imperfect tax competition for profits, asymmetric equilibrium andbeneficial tax havens. Journal of International Economics 81(2), 253-264.
Nielsen, S. B., P. Raimondos-Møller, and G. Schjelderup, 2003. Formula Apportionment
and Transfer Pricing under Oligopolistic Competition. Journal of Public Economic
Theory 5 , 419–37.
Nielsen, S. B., P. Raimondos-Møller, and G. Schjelderup, 2008. Taxes and Decision Rights
in Multinationals. Journal of Public Economic Theory10, 245–58.
OECD, 1998. Harmful tax competition: an emerging global issue. Organisation for Economic Co-operation and Development, Paris, France.
OECD, 2013. Addressing Base Erosion and Profit Shifting. Available athttps://www.oecd-ilibrary.org/taxation/addressing-base-erosion-and-profit-shifting 9789264192744-en https:/http://www.oecd.org/daf/inv/
mne/investmentnews.html
Pan, R., and Zeng, D. Z. (2023). The effects of trade liberalization on tax avoidance.
International Journal of Economic Theory 19(4), 898-932.
Phillips, R., Gardner, M., Robins, A., Surka, M., 2017. The Use of Offshore Tax Havens
by Fortune 500 Companies. Available at https://itep.org/wp-content/uploads/
offshoreshellgames2017.pdf
Slemrod, J., Wilson, J. D., 2009. Tax competition with parasitic tax havens. Journal of
Public Economics 93, 1261-1270.
Tørsløv, T., Wier, L., & Zucman, G. (2023). The missing profits of nations. The Review
of Economic Studies, 90(3), 1499-1534.
Zhao, L.,2000. Decentralization and Transfer Pricing under Oligopoly. Southern Economic
Journal 67 , 414–26.

AppendixA

Proof of Proposition 2

Using (55), the derivative of B1∗ with respect to ϕ at ϕ = 1 is
dB1∗
= f N (1 − s)s(ϵ + 1)H(s),dϕ ϕ=131

where
1−s 1/ϵ1−s+ϵs(ϵ + 1) s+ϵ
H(s) =−1−s+ϵ(s + ϵ)2

1/ϵ
.

∗

is the sign of H(s).
Therefore, the sign of dBdϕ ϕ=1
We first consider the case of s > 1/2. Define1h(x) =
x+ϵ



x
x+ϵ

 1ϵ
.

Then, given s < 1, we can obtain that
H(s) < h(1 − s) − h(s).
The derivative of h(x) with respect to x gives
 1ϵ −1x(1 − s) x+ϵ
∂h(x)
=
> 0,
∂x
(x + ϵ)3
which indicates h(x) is strictly increasing. Therefore, for all s ∈ (1/2, 1], we haveH(s) < h(1 − s) − h(s) < 0.
∗

Therefore, for all s > 1/2, the sign of dB
is negative.
dϕ ϕ=1
We now consider the case of s ≤ 1/2. Taking the derivative of H(s) with respect s,
we obtain that 1ϵ −1s
1−s 1/ϵ(1 − 2s)(ϵ + 1) s+ϵs 1−s+ϵ
∂H(s)
=−
−
.
∂s
(s + ϵ)4(1 − s)(1 − s + ϵ)2
It is easy to see that ∂H(s)< 0 for all s ≤ 1/2. In addition, we have∂s
 1ϵ +1
1
H(0) => 0,ϵ+1
 1ϵ +2
1
H(1/2) = −2
< 0.
2ϵ + 1Hence, there is a sb ∈ (0, 1/2), which is the root for H(sb ) = 0. For all s < sb , we have
dB ∗
dB ∗
H(s) > 0, and hence dϕ1 ϕ=1 > 0. For all s > sb , we have dϕ1 ϕ=1 < 0. Thus, theproposition is proved.

32

B

Endogenous tax rate in the tax haven

Here, we assume that the tax haven also endogenously determines its tax rate,ts . Moreover, as in Krautheim and Schmidt-Eisenlohr (2011) and Pan and Zeng (2023), both thetax haven and the non-havens set tax rates simultaneously in a one-shot game.
The cutoff cost levels are determined by(1 − ti )πii (ceii ) = (1 − ts )πii (ceii ) − f,
(1 − ti )πij (ceji ) = (1 − ts )πij (ceij ) − f.
The cutoffs are then given byc∗ii =Af (si + (1 − si )ϕ)

1
 σ−1

(ti − ts )1
σ−1c∗ji =,Aϕf (si + (1 − si )ϕ)

1
 σ−1

The masses of profit-shifting domestic and exporting affiliates are calculated asneiis = H(ceii ) = (ceii )γ c−γ
M ,neijs = H(ceij ) = (ceij )γ c−γ
M .

The tax-base loss in country i is
α si + (1 − si )ϕϵ+1
Πeis = Πsii + Πsji =σ si + (1 − si )ϕ



α
1
ϵ
σN f si + (1 − si )ϕ ϵ + 1

The total tax-base loss in the two non-havens is given byΠes = Πe1s + Πe2s
The remaining tax base in country i is
Πei = Πti − Πeis .
The aggregate income of individuals in country i isIie = 1 + (1 − ti )Πei + (1 − ts )Πeis − (neiis + neijs )f.
The optimal problems of non-haven i and the tax haven are given byα− α + Iie + ti Πei ,P
eemax Ts =ts Πs ,max Wie =α ln
ti

ts

33

1

(ti − ts ) σ−1 .

ϵ(ti − ts )ϵwhose FOCs are∂Wi∂I e ∂Ti
= i +
= 0.
∂ti
∂ti
∂ti


∂Ts
∂Π1s ∂Π2s= Π1s + Π2s + ts
+
= 0.
∂ts
∂ts
∂ts

(C.1)
(C.2)

Equilibrium tax rates t∗1 , t∗2 , and t∗s are determined by (C.1) and (C.2).
Benefit

Benefit
0.2

s=0.5

0.4

0.6

0.8

1.0



0.08

s=0.6

-0.02

s=0.7

0.06

-0.04

s=0.8
s=0.9

0.04

-0.06

s=0.5
0.02

-0.08

0.2

0.4

0.6

0.8

1.0

s=0.4
s=0.3

 -0.10

s=0.2
s=0.1

-0.02

-0.12

(a) the developed country: s > 1/2(b) the developing country: s < 1/2

Figure 5: The net benefits (B ∗ ) from the tax havenTwo panels of Figure 5 illustrate the effects of trade liberalization on the benefits ofprofit shifting when the endogenous tax rate in the haven is incorporated. Parameters
are given by (56) in the main text. Panel (a) and (b) illustrate how trade liberalization(rising ϕ) affects the net benefits (B ∗ ) in developed and developing countries, respectively.
We observe a bell shape for a large s and a “U” shape for a very small s. Therefore, thesenumerical results are consistent with Proposition 1 and 2 and Figure 1 in the main text.
Two panels of Figure 6 illustrate the welfare impact of trade liberalization in the presenceof a tax haven. We find that the effect of trade liberalization is non-monotonic in acountry with a very large share of MNEs (e.g., s = 0.9) when the concealment costs f is
WelfareWelfare

3.80

3.7

3.6

3.75

3.5
3.70

s=0.1

s=0.9
3.4

s=0.2

s=0.8
3.65

s=0.7

s=0.3

3.3

s=0.4

s=0.6

3.60

3.2

s=0.5

s=0.5
0.2

0.4

0.6

0.8

1.0

ϕ

(a) the developed country

0.2

0.4

0.6

0.8

(b) the developing country

Figure 6: Welfare impact

34

1.0

ϕ

very small (f = 0.0001). these numerical results are consistent with Figure 2 in the maintext. Similarly, the non-monotonicity is observed in Figure 7, which is consistent with
B
0.2

f=0.2
0.1

f=0.1
f=0.0001

s
0.2

0.4

0.6

0.8

1.0

-0.1

-0.2

Figure 7: Impacts of headquarter share (s) on net benefits (B ∗ )Proposition 5 (a) and (b) and Figure 4.

35