Transfer Pricing:Its Interaction with
Multinationals’ Location,
Export and R&D Choices
Inauguraldissertation
zur Erlangung des Grades
Doctor oeconomiae publicae (Dr. oec. publ.)
an der Ludwig-Maximilians-Universität München

vorgelegt vonHirofumi Okoshi
2020

Referent: Prof. Dr. Andreas Haufler
Korreferent: Prof. Dr. Carsten Eckel
Promotionsabschlussberatung: 22. Juli 2020

Transfer Pricing:Its Interaction with
Multinationals’ Location,
Export and R&D Choices

Inauguraldissertation
zur Erlangung des Grades
Doctor oeconomiae publicae (Dr. oec. publ.)
an der Ludwig-Maximilians-Universität München

vorgelegt vonHirofumi Okoshi
2020

Referent: Prof. Dr. Andreas Haufler
Korreferent: Prof. Dr. Carsten Eckel
Promotionsabschlussberatung: 22. Juli 2020

Acknowledgements
First and foremost, I would like to thank my supervisor Andreas Haufler from the bottomof my heart. He was always available and spent much time for our research meetings.
Thanks to his extremely detail supervision, I have realized growth of my research skills
over time. In addition, his warmful words encouraged and directed me to work more in line
to my goal. I am also grateful to Carsten Eckel, my second supervisor, for his energetic
helps inside and outside my research. As he is a representative faculty of the GRK
programme to which I belong, my programme could not have been smoothly completed
without his support. I also thank Dominika Langenmayr for her willingness to join mythesis committee.
Across border, I am also extremely thankful to Jota Ishikawa, who was my supervisor in
the Master programme in Japan and recommended me to come to LMU for my Ph.D.
degree. Even after I moved to Munich, he sometimes visited and directed me to a rightway inside and outside research activities.
My deep thanks go to my coauthors, Hayato Kato (Chapter 1 and Chapter 2), and Hiroshi
Mukunoki (Chapter 3), both of whom have never hesitated to make time when I needed it.
Hayato Kato has always treated me as an equal partner and his continuous kind support
provided me with much energy in my daily work. Hiroshi Mukunoki has taken care of me
since the Bachelor programme, and provided me with chances to experience all research
processes.
As my research was highly supported by comments from participants of workshops andconferences, I am also thankful to them. Particularly, I am grateful to Taiji Furusawa,
Christian Holzner, Dominik Sachs, Dirk Schindler, Yoichi Sugita, and Eiichi Tomiura for
their insightful comments on my research.
I am also indebted to my colleagues at the Seminar for Economic Policy, Daniel Gietl, Ulrich Glogowsky, Tobias Hauck, Mandy Häusler, Bernhard Kassner, Florian Loipersberger,
Miriam Müting, Franz Reiter, Renate Schwirtz, and Davide Suverato. All of them gave
me a variety of academic, administrative and private supports. I enjoyed all events we
had inside and outside our chair. Furthermore outside the chair, I was fortunate to sharetime with the cohorts of 2017. Particularly, in the first year of my Ph.D programme, Lion
Henrich helped me a lot. Thank you all for your help and I will never forget what you
have done.
The biggest surprise to me was the presence of other Japanese at LMU München, Taisuke
Imai and Mina Taniguchi. Taisuke gave me many advices for spending time in the Ph.D
programme outside Japan based on his experience. Mina invited me to boardgames which
I liked a lot, and which kept my mental condition sound. As a visiting CES guest, Yukihiro

Nishimura also took care of me for the last six months. Yukihiro and his wife, Hsin-Jung
Ho invited me for dinner and other experiences. I appreciate all the interactions withthem.
My special thanks go to GRK 1928 for the generous financial support. As I spent a partof my Ph.D. period at Gakushuin University, I appreciated the hospitality by Hiroshi
Mukunoki, and the people there. In particular, I thank Daisuke Shimizu who was mymain advisor in the Bachelor programme for discussion about my research ideas during
the stay.
Last but not least, I show my most profound gratitude to my families. My parents,
Yoshiyuki and Ritsuko, believed in me and continuously supported me mentally andfinancially. My parents in law, Toshimasa Nakai and Masako Nakai, also constantly cared
for me a lot and gave me supportive advices on my career choice. My greatest appreciation
goes to my wife, Aina. She had cheered me a lot from Japan although she also had beenin very tough and lonely time. Your love and support are one and only! Thank you.
Hirofumi Okoshi
Munich, March 2020

To my love.

Contents

Preface1

1 Production Location of Multinational Firms under Transfer Pricing: The Impact of the Arm’s Length Principle
6
1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

1.2

Basic Setting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

1.3

Benchmark Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

1.3.1

Co-location Scheme . . . . . . . . . . . . . . . . . . . . . . .

13

1.3.2

Separate-location Scheme . . . . . . . . . . . . . . . . . . . .

14

1.3.3

Location Choice . . . . . . . . . . . . . . . . . . . . . . . . .

16Arm’s Length Principle (ALP) Case . . . . . . . . . . . . . . . . . .

19

1.4.1

Co-location Scheme . . . . . . . . . . . . . . . . . . . . . . .

19

1.4.2

Separate-location Scheme . . . . . . . . . . . . . . . . . . . .

20

1.4.3

Location Choice . . . . . . . . . . . . . . . . . . . . . . . . .

21

1.4.4

Extensions and Robustness . . . . . . . . . . . . . . . . . . .

22

1.4

1.5

The Impact of the ALP on Tax Revenues. . . . . . . . . . . . . . .

24

1.6

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

2 Economic integration and agglomeration of multinational production with transfer pricing
28
2.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

2.2

Basic setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

iContents

2.2.1

Optimal Prices in the Short-run Equilibrium . . . . . . . . .

37

2.3

Equilibrium allocation of production plants . . . . . . . . . . . . . .

40

2.4

Tax competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

2.5

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

3 Tariff Elimination versus Tax Avoidance: Free Trade Agreements
and Transfer Pricing
53
3.1

3.2

3.3

3.4

3.5

3.6

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3.1.1

Preview of the model and results . . . . . . . . . . . . . . . .

56

3.1.2

Relationship to the literature . . . . . . . . . . . . . . . . . .

57

Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

3.2.1

The equilibrium without ROO . . . . . . . . . . . . . . . . .

61

3.2.2

The welfare effects of FTA formation without ROO . . . . . .

62

Equilibrium with ROO . . . . . . . . . . . . . . . . . . . . . . . . .

63

3.3.1

The MNE’s decisions in each scheme . . . . . . . . . . . . . .

63

3.3.2

The MNE’s choice of scheme . . . . . . . . . . . . . . . . . .

65

Welfare effects with ROO . . . . . . . . . . . . . . . . . . . . . . . .

67

3.4.1

Consumer surplus . . . . . . . . . . . . . . . . . . . . . . . .

67

3.4.2

Tax revenue . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

3.4.3

Total welfare of member countries . . . . . . . . . . . . . . .

70Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

3.5.1

The optimal VA requirement . . . . . . . . . . . . . . . . . .

74

3.5.2

Partial procurement of inputs . . . . . . . . . . . . . . . . .

76

3.5.3

Concealment costs for transfer price manipulation. . . . . .

77

3.5.4

The role of profit shifting . . . . . . . . . . . . . . . . . . . .

78

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

ii

Contents

4 Innovation for Tax Avoidance: Product Differentiation and theArm’s Length Principle
82
4.1

4.2

4.3

4.4

4.5

4.6

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

4.1.1

Related literature . . . . . . . . . . . . . . . . . . . . . . . .

85

The benchmark model . . . . . . . . . . . . . . . . . . . . . . . . .

87

4.2.1

2nd stage: Market outcome . . . . . . . . . . . . . . . . . . .

89

4.2.2

1st stage: Investment decision . . . . . . . . . . . . . . . . .

90

Tax Haven and Globalization . . . . . . . . . . . . . . . . . . . . . .

90

4.3.1

Cost of profit shifting . . . . . . . . . . . . . . . . . . . . . .

91

4.3.2

Profit shifting . . . . . . . . . . . . . . . . . . . . . . . . . .

92

4.3.3

Investment decision with profit shifting . . . . . . . . . . . .

93

4.3.4

Globalization . . . . . . . . . . . . . . . . . . . . . . . . . .

94

Welfare effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

4.4.1

Welfare effects of lower profit shifting costs . . . . . . . . . .

95

4.4.2

Endogenous tax rate . . . . . . . . . . . . . . . . . . . . . .

100

Discussions and policy implications . . . . . . . . . . . . . . . . . .

104

4.5.1

Concealment cost . . . . . . . . . . . . . . . . . . . . . . . .

105

4.5.2

Product differentiation in inputs . . . . . . . . . . . . . . . .

105

4.5.3

Under or excess investment . . . . . . . . . . . . . . . . . . .

107

Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . .

109

Conclusion

111

Appendices

113

A

Appendix to Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . .

114

A.1

List of Key Variables . . . . . . . . . . . . . . . . . . . . . .

114

A.2

Proof of Proposition 1.3 . . . . . . . . . . . . . . . . . . . . .

114

A.3

A Local Firm in the Upstream Industry . . . . . . . . . . . .

116

A.4

Many Local Firms in the Downstream Industry . . . . . . . .

119

iii

Contents

B

C

D

A.5

Trade Costs . . . . . . . . . . . . . . . . . . . . . . . . . . .

121

A.6

Costs of Transfer Pricing . . . . . . . . . . . . . . . . . . . .

124

A.7

Differentiated Inputs . . . . . . . . . . . . . . . . . . . . . .

126

A.8

Endogenous Profits in the Parent Market . . . . . . . . . . .

129

A.9

Welfare Analysis . . . . . . . . . . . . . . . . . . . . . . . .

132

Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . .

136

B.1

Equilibrium Allocation of Production Plants . . . . . . . . .

136

B.2

Proof of Proposition 2.2 . . . . . . . . . . . . . . . . . . . . .

138

B.3

Conditions for Positive Profits . . . . . . . . . . . . . . . . .

140

B.4

Proof of Proposition 2.3 . . . . . . . . . . . . . . . . . . . . .

141

B.5

Proof of Lemma 2.1 . . . . . . . . . . . . . . . . . . . . . . .

142

B.6

Centralized decision making . . . . . . . . . . . . . . . . . .

142

B.7

Proof of Proposition 2.4 . . . . . . . . . . . . . . . . . . . . .

145

Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . .

149

C.1

Proof of Proposition 3.2 . . . . . . . . . . . . . . . . . . . . .

149

C.2

Proof of Proposition 3.3 . . . . . . . . . . . . . . . . . . . . .

150

C.3

Proof of Proposition 3.4 . . . . . . . . . . . . . . . . . . . . .

150

C.4

Key Symbols for Notations . . . . . . . . . . . . . . . . . . .

151

Appendix to Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . .

152

D.1

152

Proof of Proposition 4.5 . . . . . . . . . . . . . . . . . . . . .

Bibliography

153

iv

List of Figures
1.1

Model structure: (a) co-location scheme; (b) separate-location scheme

12

1.2

Production location choice in the benchmark case: (a) high T and (b)low T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

1.3

Production location choice in the ALP case . . . . . . . . . . . . . .

22

2.1

Profit share and manufacturing employment share of low-tax countries
in U.S. affiliates in Europe . . . . . . . . . . . . . . . . . . . . . . .

30

2.2

Share of production plants in the high-tax country 1 . . . . . . . . .

42

2.3

Revenue share and plant distribution . . . . . . . . . . . . . . . . . .

44

2.4

Profits and tax revenues: Country 1 on the left and country 2 on the right 45

2.5

Sustains points under tax competition . . . . . . . . . . . . . . . . .

49

3.1

Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

3.2

The equilibrium MNE’s choice . . . . . . . . . . . . . . . . . . . . .

66

3.3

The direction of the MNE’s shifted profits . . . . . . . . . . . . . . .

70

3.4

ROO and the feasibility of an FTA formation . . . . . . . . . . . . .

72

3.5

The welfare of member countries with the optimal level of α . . . . .

74

4.1

Welfare. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

4.2

Socially optimal d . . . . . . . . . . . . . . . . . . . . . . . . . . . .

108

A.1 Production location choice in the benchmark case: (a) high T and (b)low T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131

A.2 Production location choice in the ALP case: (a) high T and (b) low T

133

B.1 Equilibrium distribution of production plants under centralized decision making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

145v

Contents

B.2 Sustain points under tax competition . . . . . . . . . . . . . . . . .

148

D.1 MNEs’ profits under process innovation . . . . . . . . . . . . . . . .

152

vi

List of Tables
4.1

Optimal tax rate

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

A.1 List of Key Variables of Chapter 1 . . . . . . . . . . . . . . . . . . .

114

B.1 Key symbols for notations . . . . . . . . . . . . . . . . . . . . . . .

151

vii

Preface“Transfer pricing is not, in itself, illegal or necessarily abusive. What isillegal or abusive is transfer mispricing, also known as transfer pricing
manipulation or abusive transfer pricing”
Tax Justice Network1
In recent years, huge amount of corporate tax bases around the world have been untaxed. As multinational enterprises (MNEs), by definition, locate in several countries
and face different corporate tax rates, they have several chances to save their tax payments. One of the well-known methodologies is to concentrate MNEs’ profits in low
tax countries by manipulating the transfer price of either tangible or intangible intrafirm transactions. According to OECD’s estimates, around 4% to 10% of corporate
tax revenues disappear because of MNEs’ tax avoidance. An article in the Gurdianalso reports that “by the end of 2017, some of America’s most profitable companies,
including Apple, . . . had sequestered more than $1tn offshore, using the ‘double Irish’
to park billions in ‘ghost companies.’ ”2Globalization increases the possibility of the MNE to avoid taxes. First, the reduction
in trade costs in any forms such as trade agreements or technological improvementof transportation sector increases the volume of intra-firm transactions (Slaughter(2000), Hanson et al. (2005), Bernard et al. (2010), and Lanz and Miroudot (2011)).
Such an increase in intra-firm trade enables MNEs to transfer more profits even if thelevel of transfer prices keeps constant. Second, the use of tax havens is facilitatedas globalization progresses. According to Zucman (2014), the percentage of the U.S.
firms’ profits reported in tax havens grew over years. Hence, collecting tax revenue
from MNEs has become more difficult and becomes a serious problem around the1

Source: https://www.taxjustice.net/topics/corporate-tax/transfer-pricing/2
See https://www.theguardian.com/technology/2020/jan/01/google-says-it-willno-longer-use-double-irish-dutch-sandwich-tax-loophole.

1Prefaceworld.
Naturally, these trends have alerted governments to take necessary steps to keep
MNEs from international tax planning. Through the Organization for Economic
Co-operation and Development (OECD), countries have cooperatively dealt with tax
avoidance by enhancing the tax enforcement level. The most important rule in fighting tax avoidance is the arm’s length principle (ALP). The central idea of the ALP isthat the transfer price should be equal to arm’s length price of comparable transaction.
To evaluate the effects of the ALP, some papers explicitly introduce this principle intheir model (e.g. Bauer and Langenmayr (2013), Choe and Matsushima (2013), andChoi et al. (2019)).
This dissertation explores MNEs’ profit shifting behaviour in the wider context of
MNEs’ overall strategies. Traditionally, research in this field has focused on how MNEs
manipulate transfer price, and studied the impact of various policies on optimal transfer pricing. However, since tax avoidance decisions interact with other international
strategies of MNEs, ignoring these other decision margins of MNEs may lead to biased
conclusions. Therefore, incorporating other relevant decisions of MNEs is critical todesign or evaluate the right policies against profit shifting.
As a first example, an MNE’s location decision is influenced by tax factors such as
the level of corporate tax rate, or the tax enforcement level (Peralta et al. (2006)).
Therefore, designing policies that are based on an exogenously fixed MNEs’ location
may be pointless, because it is straightforward that MNEs which seek ways of tax
saving can change their global production or operation network in response to thesepolicy changes.
The interrelation with international trade rules is another important link to consider
since transfer prices are basically export prices. This interdependence is overlookedso far in academic works. Among trade policies, rules of origin (ROO) of free trade
agreements (FTAs) are highly related to export price. Reuter (2012) points out that
“Most of rules of origin are on a percent-of-value basis. . . . By overinvoicing the value
added, the MNE can more easily meet a rule-of-origin test and qualify for duty-freeentry for its products into another country in the free trade areas.” This implies that
MNEs’ transfer pricing may be motivated by not only tax avoidance but also tariff
reduction.
The implementation of the ALP causes another interaction between transfer pricing
and research and development (R&D) activities. The ideal way of implementing the
ALP is to compare the transfer price with an arm’s length price under similar conditions
2

Preface

which includes the characteristics of products and used technologies. This generates ahypothesis that tax avoidance incentivizes MNEs to conduct R&D to facilitate profit
shifting. Indeed this hypothesis is supported by empirical research which provides
robust evidence that profit shifting is frequently observed in R&D intensive sectors or
firms (Belz et al. (2017)).
Given the above discussions, all chapters in this dissertation consider MNEs’ profit
shifting from different angles: location choice, transfer pricing with a tariff avoidance
motive and innovation. All chapters are based on stand-alone papers and can be readseparately. In the followings, I will briefly give an overview of the lines of discussion
developed in each chapter.3
Chapter 1 studies the impact of the ALP on an MNE’s location choice. Traditional
empirical evidence shows that a low corporate tax rate attracts foreign direct investment. However, this chapter shows the possibility that an MNE prefers locating one of
its affiliates in a high tax country in the absence of the ALP. This is because geographically separated location of related entities makes profit shifting possible and thus the
MNE has a chance to transfer profits from other businesses as well. As this incentive
is stronger when the corporate tax gap between countries becomes larger, such a separate location is profitable when the tax gap is sufficiently large. The result is in linewith the empirical result of Overesch (2009). Overesch (2009) concluded that the investment level of subsidiaries in high-tax Germany is positively influenced by a rising
tax rate differential between Germany and the owner’s home country. In the presenceof the ALP, however, this location pattern disappears due to impossibility of price discrimination in intra-firm and inter-firm transactions. Hence, the model shows that
the ALP is able to prevent profit shifting via an MNE’s location choice. This paper isbased on joint work with Hayato Kato, Osaka University (Kato and Okoshi (2019b)),which is published in International Tax and Public Finance.
The second chapter also considers location choices of MNEs production. As globalization proceeds, relocation of MNEs’ plants from low tax countries to high tax countries
has been observed in reality. To address the relocation trend, the model investigates
the impact of a reduction in trade costs on the agglomeration patterns of MNEs’ affiliates. With high trade costs, profit shifting through intra-firm trade is inefficient andtherefore most MNEs gather their plants in a low tax country. However, this pattern
3

Some chapters are based on joint work with my co-authors. In all chapters, I use the pronoun”we” in the text, as it is used in the published and working paper versions with gratitude to theco-authors and those who gave me comments.

3Preface

reverses with low trade costs. This is because a lower transfer price caused by locating a plant in a high tax country makes a manager in a distribution branch in a low
tax country more aggressive in the market. This subsequently increases the market
share in a low tax country and intra-firm trade, and thus enhances the benefits of profit
shifting. Since low trade costs magnify these managerial and tax incentives, the agglomeration of MNEs’ plants in a high tax country only takes place when trade costs
are low enough. This paper is based on joint work with Hayato Kato, Osaka University(Kato and Okoshi (2019a)).
The third chapter considers multiple roles of transfer pricing for tax avoidance by considering ROO. The value added criterion of ROO requires exporters to add sufficiently
high value inside an FTA region, which implies that transfer pricing manipulation isrestricted as it also affects a value added ratio for a preferential tariff. To understandtransfer pricing decisions in a wider perspective, the model in this chapter studies the
optimal transfer pricing manipulation and the procurement strategies in the presenceof ROO. The results suggest that the value added criterion has an effect to restrict the
MNE’s abusive transfer pricing via either a change in input procurement or via transfer price adjustments. Thanks to this prevention of tax avoidance, ROO can transforma welfare-reducing FTA into a welfare-improving FTA. This chapter is based on joint
work with Hiroshi Mukunoki, Gakushuin University (Mukunoki and Okoshi (2019b)).
Chapter 4 analyzes MNEs’ incentives to invest in product differentiation in the presence of profit shifting. Recent empirical research provides evidence that transfer mispricing is intensively observed in differentiated product categories (Bernard et al.
(2006), Davies et al. (2018), and Liu et al. (2019)). An explanation for this stylized
fact is that such firms are likely to own intangible assets such as patents which are easy
to relocate to low tax countries, which provides them with more chances to engage
in profit shifting. This chapter, however, considers another possibility. I argue thatinvestment in differentiation makes it less costly for MNEs to conduct tax avoidance
because the ALP is difficult to apply. I incorporate an MNE’s decision in product differentiation investment which affects the cost of tax avoidance. The model shows that
MNEs have a stronger incentive to engage in product differentiation in the presenceof profit shifting, which benefits consumers and the MNEs, but reduces tax revenue.
Hence, it gives a new reason why transfer price manipulation is observed in R&D intensive firms.
The common novelty of the studies in the four chapters is to analyze MNEs’ tax avoidance behaviour by considering various forms of imperfect competition. By consider4

Preface

ing imperfect competition, we can investigate the interaction with other decisions of
MNEs. For example, the model in Chapter 3 analyzes the interaction of tax avoidancewith a trade policy by assuming a monopolistic MNE. Chapter 1 and Chapter 4 build
on duopoly environments and explore links of profit shifting with location and R&D
decisions, respectively. Chapter 2 employs a monopolistic competition with footloose
capital, also known as “new economic geography” model, to see the impact of transfer
pricing on MNEs’ agglomeration.
Traditionally, research in the public finance literature focuses on perfect competition
although markets in the globalized world are frequently characterized as international
oligopolies. Hence, results derived in each chapter reflect such realistic market structure. Moreover, most chapters overlap with other research fields, such as International
Economics, Industrial Organization, and Economic Geography. All chapters in thisdissertation study the MNEs’ tax avoidance decision in combination with other strategic choices. Our results therefore highlight that both researchers and policy makers
should pay more attention to the overall decisions setting in which MNEs operate.

5Chapter 1
Production Location ofMultinational Firms underTransfer Pricing: The Impact of
the Arm’s Length Principle
1.1

Introduction

The manner in which multinational enterprises (MNEs) organize their production
structure is essential for their international strategy. As MNEs can substantially benefit from the opportunity to locate their affiliates in several countries, their location
decisions depend on country-specific characteristics, such as the extent of competition and policies in host countries. Considerable research has been undertaken toinvestigate the determinants of MNEs’ locations from both theoretical and empiricalstandpoints.1 Among other factors affecting the location choice, the corporate taxation prevalent in both the host and parent countries is known to have a significant
This chapter is based on joint work with Hayato Kato (Kato and Okoshi, 2019b).
1
For comprehensive surveys, see Markusen (2004); Navaretti and Venables (2004); and Blonigen (2005).

6

Production Location and Multinational Firms under Transfer Pricing

impact.2
When considering a firm with a single plant, the consequence of corporate taxationis straightforward; the firm locates its production in a country with a lower tax rate
to save taxes. However, the impact of taxation on MNEs’ location choice is not thissimple. The striking difference between MNEs with multiple plants and single-plantfirms is that MNEs’ transactions may take place within their organization acrossborders. This means that MNEs can partly control prices of intermediate goods forforeign affiliates, which are known as transfer prices, through intra-firm trade in orderto reduce global tax payments. Thus, it is possible that using such a transfer pricing
strategy, MNEs locate their production in a high-tax country, while exporting inputs
to their affiliates located in a low-tax country.
The relationship between corporate tax rates and the location choice of MNEs usingtransfer pricing is not just a theoretical curiosity, but is of great importance to themodern economy. Along with the progress of economic integration, intra-firm trade hasgrown dramatically in recent years, which provides MNEs room for tax manipulations
through transfer pricing.34 Recently, the OECD launched a project involving over 80
countries to address the tax avoidance behavior of MNEs, including transfer pricing.5
According to the OECD, revenue losses from tax avoidance by MNEs are estimatedto be between 4% and 10% of global corporate income tax revenues.6 Despite thegrowing concern globally, limited work has been done on the interaction between
MNEs’ location choice and their transfer pricing strategy. The first aim of this paper
is to examine how corporate tax rates affect the production location decision of MNEs
2

Hebous et al. (2011) show that lower corporate tax induces inflows of foreign capital irrespective of the type of investment, such as greenfield foreign direct investment and cross-bordermergers and acquisitions. Voget (2011) finds that one percentage point decline in foreign effective
tax rate augments the likelihood of headquarters’ relocation by 0.22 percentage point. Karkinsky
and Riedel (2012) and Griffith et al. (2014) investigate the link between corporate taxation andpatent location.
3

Bernard et al. (2010) show that over 46 percent of U.S. imports composed of intra-firmtransactions in 2000. Lanz and Miroudot (2011) report that U.S. imports of intermediate products
score around 50 percent in 2009. See also Slaughter (2000) and Hanson et al. (2005) for theimportance of intra-firm trade.
4

For (in)direct evidence on transfer pricing, see Swenson (2001); Bartelsman and Beetsma(2003); Clausing (2003); Bernard et al. (2006); Cristea and Nguyen (2016); Gumpert et al. (2016);
Guvenen et al. (2017); and Davies et al. (2018).
5

The project is called “Base Erosion and Profit Shifting.” Further details can be found athttps:// www.oecd.org/g20/topics/taxation/beps.htm, accessed on 17 March 2017.
6

See http://www.oecd.org/ctp/oecd-presents-outputs-of-oecd-g20-beps-project-for-discussionat-g20-finance-ministers-meeting.htm, accessed on 17 March 2017.

7

Production Location and Multinational Firms under Transfer Pricing

using transfer pricing.
From the government’s perspective, there is no doubt that steps preventing MNEs
from tax manipulations are indispensable for collecting tax revenues. Many countries
adopt a transfer pricing tax system to infer whether MNEs avoid tax payments. The
key idea to appropriate the transaction price for related affiliates is the arm’s lengthprinciple (ALP) which is set out in Article Nine of the OECD Model Tax Convention.
The principle points out that conditions (e.g., price, markup or profit) of controlled
transactions between related firms should be similar to those of independent transactions.
Among several methods the application of the ALP follows in practice, we focus on
the comparable uncontrolled price (CUP) method, which compares the price charged
for goods in a controlled transaction with the price charged for comparable goods
in an uncontrolled transaction, called the arm’s length price.78 According to theOECD guideline on transfer pricing, the CUP method is to be preferred if this andother methods can be applied in an equally reliable manner (OECD, 2017, para. 2.3).
The second aim of this paper is to investigate the impact of the ALP on MNEs’ tax
avoidance and production location choice.
We present a simple two-country model with a vertically-related MNE and a local
downstream firm. The MNE has a headquarters in the parent country and a downstream affiliate in the host country. It locates an upstream affiliate in either the parent
or the host, which provides inputs to both the two downstream firms in the host. The
headquarters makes exogenous profits from different business in the parent. Corporate tax rates are exogenous and the parent’s tax rate is assumed to be higher than thehost’s.
We analyze the location pattern of upstream production under the cases with andwithout the ALP. If the ALP is imposed, the upstream affiliate must set equal prices
7

The CUP method is applied to tangible assets. The corresponding method for intangible
assets is called the comparable uncontrolled transaction (CUT) method. There are other methods
such as cost-plus method, resale price method, and profit split method. See OECD (2017, ch.2)
for details.
8

The uncontrolled transaction includes both a transaction of an MNE with an independent
firm (”internal comparables”) and a transaction between other independent firms (”external comparables”). Our framework captures the internal comparable transaction.

8

Production Location and Multinational Firms under Transfer Pricing

to the two downstream firms.9 We show that without the ALP, the MNE may locate
an upstream affiliate in the high-tax parent country. With the ALP, however, the
MNE simply locates it in the low-tax host country. There exist tax rates for which
the imposition of the ALP changes the location pattern. This location change leads
to smaller tax revenues in the host country, but greater revenues globally.
At first glance, it seems surprising that the upstream affiliate may be located in thehigh-tax country. The key is that the transfer price can be used as a profit shifting
device if the upstream and downstream affiliates are separately located. The upstream
affiliate located in the high-tax parent may set the transfer price low so as to shift theheadquarters’ exogenous profits to the low-tax host. The larger international tax
difference gives more room for profit shifting, likely leading to geographical separationof affiliates. The introduction of the ALP limits the ability to manipulate the transfer
price, so that the MNE simply prefers to locate its upstream affiliate in the low-tax
host.
It is not surprising that the imposition of the ALP removes the opportunity of profit
shifting and thus increases global tax revenues. However, even though the ALP encourages the co-location of affiliates in the host country, the host’s tax revenues decrease.
The ALP makes the transfer price of inputs higher, leading the downstream affiliate
to produce less. The reduction in the downstream affiliate’s profits is so huge that thehost country earns less tax revenues. Our result indicates that the ALP is certainly aneffective measure against worldwide profit shifting, but may cause a conflict of interest
between countries.
9
In our setting, the arm’s length price is the price that the upstream affiliate charged to
the local downstream firm. As MNEs are usually not price takers, the AL price in an internal
comparable transaction is more or less an MNEs’ choice variable and thus is subject to manipulation (Cristea and Nguyen (2016)). Although tax authorities recognize this possibility ofmanipulation (see e.g., IRS§1.482–1(d)(4)(iii)), they have to refer to internal comparable transactions in some cases due to limited information available. One recent example of such case is thetransfer pricing case of Medtronic, a medical device company based in the US, v. the Internal
Revenue Service (IRS) (see for details Global Tax Alert (News from Transfer Pricing), 21 June
2016: http://www.ey.com/gl/en/services/tax/international-tax/alert--us-tax-courtimposes-a-proper-arms-length-allocation-method-for-transfer-pricing, accessed on 2
June 2018). Medtronic US gave license to its Puerto Rican affiliate for production. The affiliate
purchased components from Medtronic US, manufactured finished medical devices, and sold themto the Puerto Rican market. Whereas the IRS accused Medtronic US of profit shifting for theyears at issue, 2005-06, Medtronic US argued that the royalty rates charged to the Puerto Rican
affiliate, which are a sort of transfer price of inputs, were the AL royalty rates in light of the CUT
method. The AL royalty rates calculated by Medtronic US came from several internal comparable
transactions, including a license agreement between Medtronic US and Siemens (German conglomerate company). In 2016, the US Tax Court accepted the royalty rates proposed by Medtronic USwith small adjustments. See Avi-Yonah (2007) for other applications of the CUP/CUT method.

9

Production Location and Multinational Firms under Transfer Pricing

Our contribution is to examine the location choice of MNEs using transfer pricing,to which most of the studies in the literature have provided limited attention. Theirmain interest is in how transfer prices are affected by international differences in, e.g.,
corporate tax rates, tax systems, and trade barriers.10 Nielsen et al. (2003) examine
how different corporate tax systems, separate accounting and formula apportionment,
affect transfer prices differently. Kind et al. (2005) ask the same question in a tax
competition framework and also look at the impact of a reduction in trade barriers.
However, the production location choice of MNEs is outside the scope of these papers.
There are a few papers that address the choice of organization structure of MNEs
with profit shifting motives. Nielsen et al. (2008) analyze the impact of different
decision structures on transfer prices; i.e., the decision on production is made either by
the headquarters of MNEs (centralization) or by the local affiliate (decentralization).
Unlike our model, their model fixes the location of affiliates. Using the property-rights
approach, Bauer and Langenmayr (2013) and Egger and Seidel (2013) investigate
the organization decision on whether to integrate local suppliers or import inputs
from independent foreign suppliers. Keuschnigg and Devereux (2013) ask the samequestion in a model with financial frictions. While they focus on sourcing decisions
across the boundaries of MNEs (”make or buy” inputs), we emphasize production
location decisions within the boundaries of MNEs.11 Closer to the interests of ourstudy, Yao (2013) analyzes the impact of the ALP on MNEs’ location choice in a
spatial competition model à la Hotelling. In his model, MNEs choose where to locate
within a host country, that is, they choose a point on the ”linear-city,” whereas in ourmodel an MNE chooses whether to locate in a host or parent country.12
Although the location choice of internationally-mobile firms is at the core of the literature on tax competition,13 the role of the transfer pricing and/or the ALP has notbeen addressed there. Haufler and Wooton (1999) consider tax competition between
potential host countries for a single MNE (or its affiliate) without profit shifting mo10

Earlier contributions include Copithorne (1971); Horst (1971); Samuelson (1982); and Kant
(1988b). In addition to the profit-shifting motive of transfer pricing mentioned in the text, studies
such as Elitzur and Mintz (1996); Schjelderup and Sørgard (1997); and Zhao (2000) point out astrategic motive. The strategic motive comes from MNEs’ incentive to make their downstream
affiliates competitive against rival firms. See Section 1.4.4. for more on this point.
11

In a related context, Choi et al. (2018a) find a possibility of dual sourcing where an MNEbuys inputs from both independent suppliers and related subsidiaries.
12

The role of the ALP on transfer prices is also studied by Gresik and Osmundsen (2008);
Bauer and Langenmayr (2013); Choe and Matsushima (2013); and Keuschnigg and Devereux(2013). However, they do not consider the location choice of MNEs.
13

See Keen and Konrad (2013) for a comprehensive survey.

10

Production Location and Multinational Firms under Transfer Pricing

tives.14 Based on their framework, Ma and Raimondos (2015) allow the MNE to use
transfer pricing and examine the effect of the market size of potential host countries.
They simplify the vertical structure within the MNE, and are thus unable to analyze
the impact of the ALP. In contrast, we take corporate taxes as given, and describe thevertical structure more precisely to address the ALP issue.
The rest of the paper is organized as follows. Section 1.2 describes the setup of themodel. The main analysis is presented in Sections 1.3 and 1.4 where the equilibriumoutcomes in the benchmark (no-ALP) and the ALP cases are derived. Section 1.5
analyzes the impact of the ALP on tax revenues. Section 1.6 concludes the paper.

1.2

Basic Setting

The economy consists of two countries, a host and a parent, with two vertically-linked
industries, an upstream industry (intermediate input) and a downstream industry(final good). Our focus is on the host country, where the consumption and productionof final goods take place. The headquarters of the MNE is located in the parent country
and makes exogenous profits π. In the host country, there are a downstream affiliateof the MNE and a local downstream firm. The two firms produce totally differentiatedgoods.
The MNE locates an upstream affiliate in either the parent country with tax rate T or
the host country with tax rate t (< T ). If the upstream affiliate is established in the host
together with the downstream affiliate, termed as a co-location scheme, it produces
and sells inputs to both the related and unrelated downstream firms. The price for the
related affiliate is called an internal price and the price for the independent local firm iscalled an arm’s length price. By contrast, if the upstream affiliate is established in theparent separate from the downstream affiliate, termed as a separate-location scheme,it produces in the parent and exports to the two downstream firms. The internal
price under this scheme can also be called a transfer price due to the cross-bordertransactions. The two schemes are illustrated in Figure 1.1.
The timing of the game is as follows. First, the MNE chooses the location of upstream
production (Figure 1.1 (a) or (b)). Second, it sets input prices to maximize the total
14

For subsequent development in the literature on bidding for a firm, see, e.g., Bjorvatn and
Eckel (2006); Haufler and Wooton (2006); Ferrett and Wooton (2010); and Furusawa et al. (2015).

11

Production Location and Multinational Firms under Transfer Pricing

Figure 1.1: Model structure: (a) co-location scheme; (b) separate-location scheme

post-tax profit, which is the sum of the post-tax profits of the upstream and the downstream affiliates. Third, the downstream affiliate and the local firm choose outputs
to maximize their own profits.15 We proceed by analyzing in turn the case where the
MNE is free from the arm’s length principle (ALP) and the case where it obeys the
ALP.

1.3

Benchmark Case

We first consider the case where the ALP is not imposed: the upstream affiliate can sellto the related downstream affiliate and the independent firm at different prices. The
equilibrium outcomes are derived in both the co-location and the separate-location
schemes. Comparing the equilibrium profits under the two schemes, we analyze inwhich country the MNE locates the upstream affiliate, given the tax rates of the hostand the parent countries.
15

We consider a decentralized decision structure where the MNE leaves quantity choice to thedownstream affiliate.

12

Production Location and Multinational Firms under Transfer Pricing

1.3.1

Co-location Scheme

Given the location of upstream production, the MNE first chooses input prices andthen the two downstream firms source the inputs to produce final goods. We solve theproblem backward.
The two downstream firms choose quantities to maximize their own pre-tax profits.
Let π and π∗ be respectively the pre-tax profits of the downstream affiliate and the
local firm; the maximization problems are formulated as
max π = (p − g)q,q

max π∗ = (p∗ − g∗ )q∗ ,q∗where p = 1 − q,p∗ = 1 − q ∗ .
p (p∗ ) is the final good’s price of the downstream affiliate (the local firm) and q (q∗ ) is
the quantity produced by the downstream affiliate (the local firm). The downstream
firms use linear production technology, resulting in a one-to-one transformation fromintermediate to final goods. g is the price of the intermediate inputs for the downstream
affiliate, called the internal price, and g∗ is the price for the local firm, called the arm’s
length price. Solving the maximization problems gives
1−g
2
1 − g∗
.
q∗ =
2
q=

(1.1)
(1.2)

Taking into account these demand schedules, the MNE sets input prices for the two
downstream firms. Letting πu be the pre-tax profits of the upstream affiliate and Π be
the total post-tax profit of the MNE, the MNE faces the following problem:max Π = (1 − T )π̄ + (1 − t)(πu + π)g,g∗

= (1 − T )π̄ + (1 − t)[(g − c)q + (g∗ − c)q∗ + (p − g)q],
where T and t are respectively the parent’s corporate tax rate and the host’s. It is

13

Production Location and Multinational Firms under Transfer Pricing

assumed that t < T throughout the analysis.16 c ∈ [0, 1) is the constant marginal costof the upstream production. π̄ is constant profits earned (from different business) inthe parent market.17
Deriving the two first-order conditions (FOCs) from the MNE’s problem (dΠ/dg = 0;dΠ/dg∗ = 0) and solving the system of equations for (g, g∗ ), we obtaing = c,
g∗ =

1+c
,
2

(1.3)
(1.4)

where the second-order conditions (SOCs) trivially hold. The equilibrium input prices
are independent of tax rates because both the upstream and downstream firms colocate in the host country and face the same tax rate. The MNE exercises monopoly
power against the local firm by setting g∗ greater than the marginal cost c. By contrast, it adopts marginal cost pricing for the downstream affiliate to avoid losses frominefficient markups.
Using equilibrium choices, the total post-tax profit Π is re-expressed as
Π = (1 − T )π̄ +

1.3.2

3(1 − t)(1 − c)2
.
8

(1.5)

Separate-location Scheme

In the separate-location scheme, where the upstream affiliate is located in the parent
country, the two downstream firms behave similarly to the co-location scheme. Suppose the superscript S denotes variables in the separate-location scheme. From Eqs.
16

If t ≥ T , the upstream affiliate is always located in the low-tax parent country (separate
location) in both the benchmark and ALP cases. Thus, our focus is on the range of t < T , where
the imposition of the ALP may change the location pattern.
17

It is common in the literature to assume exogenous profits or profits independent of transfer
price (Schjelderup and Sørgard, 1997; Nielsen et al., 2003, 2008; Haufler and Mardan, 2014). In
these studies, the tax-manipulation effect, which we will define shortly, is so strong that the pricecost margin (and thus profits) can be negative as in our analysis. To isolate the tax-manipulation
effect as clearly as possible, we follow the convention of the literature. In Appendix A.8, we
endogneize it by introducing a local downstream firm in the parent country.

14

Production Location and Multinational Firms under Transfer Pricing(1.1) and (1.2), the outputs of final goods can be written as
1 − gS,2
1 − g∗S
,
q∗S =
2
qS =

where g and g∗ have been replaced with g S and g∗S in Eqs. (1.1) and (1.2), respectively.
Given these demand schedules, the MNE chooses input prices to maximize the following total post-tax profit:max ΠS = (1 − T )(π̄ + πuS ) + (1 − t)π S
g S ,g∗S= (1 − T )[π̄ + (g S − c)q S + (g∗S − c)q∗S ] + (1 − t)(pS − g S )q S .
Our focus is on a certain range of tax rates where the maximization problem has aunique interior solution:t > t ≡ max{0, ta , tb },(A1)

where ta ≡ 2T − 1,tb ≡ [(3 + c)T − (1 + c)]/2.
If t and T satisfy (A1): t > t, equilibrium outputs and prices of intermediate and final
goods are positive, and the SOCs hold in all cases of the following analysis.18 The
regularity condition (A1) is assumed throughout the analysis.
The equilibrium input prices are given by
gS = c +(1 − c)(t − T ),| t − 2T{z + 1 }(1.6)

Tax-manipulation effect

g∗S =

1+c
,
2

(1.7)

where the SOCs are satisfied and t − 2T + 1 > 0 holds under (A1). The second term ofg S involves the tax difference, which is termed as a tax-manipulation effect of transfer
price. Its sign depends on the tax difference. If both countries had the same tax rate(t = T ), it would hold that g S = c (= g), meaning no room for tax manipulation.
18

More precisely, q S > 0 requires t > ta , while pS > 0 does t > tb .

15

Production Location and Multinational Firms under Transfer Pricing

Under our assumption that t < T , the second term of g S is negative and g S < c holds.
By making upstream profit negative, the MNE shifts exogenous profits from the hightax parent to the low-tax host country. A larger tax difference (t << T ) brings moreroom for profit shifting and thus lowers g S more.19
It is also noted that the arm’s length price g∗S is equal to the one in the co-location
scheme, and does not depend on tax rates. This is again because g∗S is used solely for
exploiting market power against the local firm.
The total post-tax profit evaluated at the equilibrium choices is given by(1 − c)2 (t − 4T + 3)
Π = (1 − T ) π̄ +,8(t − 2T + 1)


S

(1.8)

where the second term in the square bracket is positive under (A1): t > t.

1.3.3

Location Choice

Comparing the total post-tax profits in the two schemes, the MNE chooses a location
for upstream production. From Eqs. (1.5) and (1.8), the profit difference can becalculated asΠ − ΠS =(1 − c)2 (3t − 4T + 1)(T − t),8(t − 2T + 1)

where t − 2T + 1 > 0 holds under (A1). As the denominator is positive, the sign ofthe difference is determined by the numerator.
It can be seen that Π − ΠS = 0 holds at t ∈ {t∗ , T }, where t∗ is defined byt∗ ≡ (4T − 1)/3 (< T ).

(1.9)

t∗ is positive if the parent’s tax rate is sufficiently high, i.e., T > T ≡ 1/4.
The profits under the two schemes are illustrated in Figure 1.2.20 If the parent’s tax
rate is low (T ≤ T : Figure 1.2 (b)), t∗ becomes negative and Π − ΠS > 0 holds
19

Clausing (2003) empirically supports this result: she finds that MNEs in the U.S. tend to set
lower export prices, as tax rates in the trading partners are lower.
20

These figures are derived using the following parameter values: c = 0.3; π̄ = 3; (a)T = 0.35;(b)T = 0.2. In this numerical example, t = 0 holds. We note that the qualitative results stated in
Proposition 1.1 do not depend on these particular parameter values.

16

Production Location and Multinational Firms under Transfer Pricing

Figure 1.2: Production location choice in the benchmark case: (a) high T and (b)low T

for t < T . The MNE always co-locates the upstream affiliate with the downstream
affiliate in the host country.
If the parent’s tax rate is high (T > T : Figure 1.2 (a)), the location choice is more
complex. Π − ΠS > 0 holds if t is close to T (i.e., t ∈ (t∗ , T )), while Π − ΠS ≤ 0 holds
if t is far below T (i.e., t ∈ (t = 0, t∗ ]). The MNE chooses the co-location scheme, if
the two countries have similar tax rates. Otherwise, it prefers the separate-location
scheme.
If the two countries had equal tax rates, the tax manipulation effect would disappear
so that the location choice would not matter, i.e., Π = ΠS at t = T . Consider thena marginal decrease in the host’s tax rate from t = T . The MNE naturally benefits
from this reduction, but the degree of benefit varies from scheme to scheme. Indeed,17

Production Location and Multinational Firms under Transfer Pricing

we can confirm
−

dΠ
dΠS
>−
.
dt t=Tdt t=T

The marginal profit in the co-location scheme is higher than that in the separatelocation scheme. Having an upstream affiliate in the parent is beneficial to the MNE
trying to manipulate tax payments, but it comes at a cost of the higher tax rate in
the parent. Under small international tax differences, there is little room for manipulating tax payments. Thus, the low-tax host becomes more profitable for upstream
production than the high-tax parent.
Under fairly large tax differences, however, this is not necessarily the case. Let us
assume T > T and look at the marginal effects of taxes on the total post-tax profit att = t∗ > 0, where Π = ΠS holds. We can confirm
−

dΠS
dΠ
<−
.
dt t=t∗dt t=t∗In contrast to the previous case of t = T , a reduction in t increases total post-tax
profit in the separate-location scheme more than in the co-location scheme. A larger
tax difference strengthens the tax-manipulation effect and thus allows more profit
shifting. To exploit the profit-shifting opportunity, the upstream affiliate is separately
located from the downstream affiliate for t ≤ t∗ .
These results are summarized as follows.
Proposition 1.1 (No-ALP case).
Suppose the MNE can set different input prices for its downstream affiliate and the
local firm, and assume t < T and the regularity condition (A1): t > t. Two cases
may arise:(i) Suppose the parent country’s tax rate is sufficiently high (T > T ). If the hostcountry’s tax rate is not low enough (t ∈ (t∗ , T )), the MNE locates an upstream
affiliate in the low-tax host country (”co-location”). On the other hand, if it is
low enough (t ∈ (t, t∗ ]), the upstream affiliate is located in the high-tax parent
country (”separate location”).
(ii) Suppose the parent country’s tax rate is not sufficiently high (T ≤ T ). For
any host’s tax rate (t ∈ (t, T )), the MNE always locates an upstream affiliate
in the low-tax host country (”co-location”).
18Production Location and Multinational Firms under Transfer Pricing

1.4

Arm’s Length Principle (ALP) CaseLet us turn to the case where the MNE follows the ALP. It now sets equal prices toboth the downstream affiliate and independent local firm.21

1.4.1

Co-location Scheme

We first solve the third stage game, where the downstream firms choose quantities, andthen solve the second stage game, where the MNE chooses input prices. Maximization
problems facing the downstream firms are exactly the same as in the benchmark (noALP) case, except that both the affiliate and the local firm source inputs at the same
price, g̃, where the tilde (˜) represents the variable in the ALP case. Replacing g andg∗ with g̃ in Eqs. (1.1) and (1.2) givesq̃ = q̃∗ =1 − g̃
.
2

Noting the MNE is unable to discriminate prices, its maximization problem is formulated as
e = (1 − T )π̄ + (1 − t)(π̃u + π̃)
max Π
g̃

= (1 − T )π̄ + (1 − t)[2(g̃ − c)q̃ + (p̃ − g̃)q̃].
The profits from selling inputs, 2(g̃ − c)q̃, are doubled because prices and quantities
for the two downstream firms are the same.
From the FOC with respect to g̃, the following optimal input price is obtained:g̃ =1 + 2c,3(1.10)

where the SOC trivially holds. Comparing this with the input prices under the colocation scheme in the benchmark case, g and g∗ defined in Eqs. (1.3) and (1.4), we
find g < g̃ < g∗ . In the benchmark case, the MNE exercises market power against
the local firm and sets the arm’s length price higher than the marginal cost (g∗ > c).
21

We assume that the ALP applies to both cross-border transactions (i.e., separate location)and domestic transactions (i.e., co-location). Article Nine and the OECD guidelines are fully or
partly applicable to domestic transfer pricing in some member countries of the OECD such as the
U.K., Norway and Canada (Wittendorff, 2012).

19

Production Location and Multinational Firms under Transfer Pricing

For the downstream affiliate, the MNE sets the internal price to the marginal cost(g = c) so as to avoid inefficient markups between affiliates. The ALP, however, does
not allow for price discrimination so that the unique price reflects the two opposing
motives. Therefore, the input price in the ALP case falls between the two prices in thebenchmark case.
The total post-tax profit in equilibrium is given by2

e = (1 − T )π̄ + (1 − t)(1 − c) .
Π
3

1.4.2

(1.11)

Separate-location Scheme

The quantities that the downstream firms choose are the same as in the co-location
scheme:q̃ S = q̃∗S =1 − g̃ S,
2

where the superscript S represents the separate-location scheme as before. Given thesedemand schedules, the MNE chooses an input price to maximize the total post-tax
profit:e S = (1 − T )[π̄ + 2(g̃ S − c)q̃ S ] + (1 − t)(p̃S − g̃ S )q̃ S .
max Π
g̃ S

Solving the FOC yields the equilibrium input price:g̃ S =

1 + 2c2(1 − c)(t − T )+,33(t − 4T + 3){z}|

(1.12)

Tax-manipulation effectwhere the SOC is satisfied and t − 4T + 3 > 0 holds under the regularity condition(A1): t > t. The second term of g̃ S captures the tax-manipulation effect as seen in g S
defined in Eq. (1.6). Its sign depends only on the tax difference. The above input pricecan be reduced to the one under the co-location scheme (g̃ S = g̃) at t = T . For t < T ,the second term becomes negative, implying that the MNE reduces the input price tobring more profits to the downstream affiliate in the low-tax host country. Comparing

20

Production Location and Multinational Firms under Transfer Pricingg̃ S with g S reveals that the tax-manipulation effect is smaller in g̃ S than in g S .22 The
input price is no longer an effective device for shifting profits. As in the co-location
scheme, the input price in the ALP case falls between the transfer price and the arm’s
length price in the benchmark case, i.e., g S < g̃ S < g∗S .
The equilibrium total post-tax profit is calculated as(1 − c)2 (1 − T )SeΠ = (1 − T ) π̄ +.
t − 4T + 3

1.4.3(1.13)

Location Choice

From Eqs. (1.11) and (1.13), the profit difference is given by2e −Π
e S = (1 − c) (t − 3T + 2)(T − t) ,Π3(t − 4T + 3)
where t − 3T + 2 > 0 and t − 4T + 3 > 0 hold under (A1). The profits under thetwo schemes are illustrated in Figure 1.3.23 The sign of the profit difference dependse −Πe S ≥ 0 and thus
only on T − t. Under our assumption that t < T , it holds that Π
the MNE always prefers the co-location scheme. In contrast to the benchmark case,the separate-location scheme is never optimal even if T is much higher than t. The
input prices can neither be effectively used to exercise market power against the local
firm, nor to shift profits, thereby reducing the benefit of choosing the separate-location
scheme.
Proposition 1.2 (ALP case).
Suppose the MNE sets equal input prices for its downstream affiliate and the local
firm, and assume t ≤ T and the regularity condition (A1): t > t. For any host’s tax
22

To see this formally, we calculate the difference between the coefficient of t − T in g̃ S andthat in g S :
∂g̃ S
∂g S
2(1 − c)1−c−=−∂(t − T ) ∂(t − T )3(t − 4T + 3) 2(t − 2T + 1)=−

(t − 8T + 7)(1 − c)
< 0.
12(t − 4T + 3)(t − 2T + 1)

23

The parameter values are the same as those in Figure 1.2 (a): c = 0.3; π = 3; T = 0.35.
We note that the qualitative results stated in Proposition 1.1 do not depend on these particularparameter values.

21

Production Location and Multinational Firms under Transfer Pricing

Figure 1.3: Production location choice in the ALP caserate (t ∈ (t, T )), the MNE always locates an upstream affiliate in the low-tax hostcountry (”co-location”).

1.4.4

Extensions and Robustness

We have seen that the upstream affiliate may be located in the parent country (separate
location) even if the parent’s tax rate is higher than the host’s (Proposition 1.1), andthe imposition of the ALP may change the separate-location scheme to the co-location
scheme (Proposition 1.2). One may wonder these results crucially depend on oursimplified structure, where the intermediate inputs are supplied only by the upstream
affiliate, and there is only one local firm in the downstream market. We briefly discuss
the robustness of the results against three extensions: (i) imperfect substitutability
between the two final goods, (ii) a local upstream firm, and (iii) many downstream
firms.

Substitutability of the Final Goods. We allow for the two final goods to be substitutable. The transfer price has then a strategic effect as well as the tax-manipulation
effect. As the strategic effect reduces the transfer price to make the downstream affiliate competitive, it works in the same direction as the tax-manipulation effect.
Let b ∈ (0, 1) denote the degree of substitutability of the goods. If b is so high thatcompetition in the downstream industry is tough, the MNE prevents the local firmfrom doing business by stopping selling inputs to it. Unless such input foreclosure
occurs, we obtain the qualitatively same results as in Propositions 1.1 and 1.2. See our22

Production Location and Multinational Firms under Transfer Pricing

working paper (Kato and Okoshi, 2017) for details.
A Local Firm in the Upstream Industry. We add a local upstream firm in the hostcountry. The upstream firm has the same marginal cost of c, supplies the same type ofintermediate inputs as the upstream affiliate, and competes with it in prices. Bertrand
competition with homogeneous products leads both the two upstream firms to set theirprices equal to or lower than their marginal cost. The upstream firm cannot set its
price lower than the marginal cost in order to earn non-negative profits. On the other
hand, the upstream affiliate, if located in the parent country, can do so because its
negative profits are compensated by the profits from different business π̄. Thus, the
MNE locates the upstream affiliate in the high-tax parent country as in Proposition
1.1.
In the ALP case, if the MNE were to set the input price lower than the marginal costfor the downstream affiliate, the price would also be applied to the local firm andthus lead to negative profits from it. The introduction of ALP makes the separatelocation scheme less profitable than before and may change the location pattern as in
Proposition 1.2. See Appendix A.3 for details.
As we assume the two upstream firms produce the same type of inputs and have thesame marginal cost, the arm’s length price is uniquely identified. In practice, however,tax authorities may observe multiple uncontrolled comparable prices. The OECD
guideline suggests that the arm’s length price might be pinned down by statistical
tools to narrow the price range such as the interquartile range or other percentiles(OECD, 2017, para. 3.57). In Appendix A.7, we allow for the differentiation of inputs
and analyze the case where the arm’s length price takes a range of values.
Many Local Firms in the Downstream Industry. We allow for many local downstream
firms, each of which produces a differentiated variety of products. A greater number ofdownstream firms yields more input sales. This implies that the downstream affiliate’s
profits relative to profits from local downstream firms become less important in the
MNE’s total profits. The MNE now lays less emphasis on the role of transfer prices
and relies more on input sales from many local firms. Thus, it tends to prefer theco-location scheme simply for the low tax rate of the host country. However, if thenumber of downstream firms is not too large, Propositions 1.1 and 1.2 still hold. See
Appendix A.4 for details.
Furthermore, we extend our analysis to include (iv) extra costs of international trade,(v) extra costs of transfer pricing, and (vi) endogenous profits in the parent market.
In these generalized settings, we obtain the qualitatively similar results to those of23

Production Location and Multinational Firms under Transfer Pricing

Propositions 1.1 and 1.2. The detailed analysis can be found in the Appendix.

1.5

The Impact of the ALP on Tax Revenues

It has been shown that the imposition of the ALP may change the location of upstream
production from the parent to the host country. At first glance, this location change
seems to enhance production in the host and bring larger tax revenues. However, thisis not true.
It can be verified that for t ∈ (t, t∗ ), tax revenues under the separate-location scheme
in the benchmark case, denoted by T RH , are greater than those under the co-locationgscheme in the ALP case, denoted by T
RH :24g
T
RH < T RH ,gwhere T
RH = t(π̃u + π̃ + π̃∗ )= t · 2(p̃ − c)q̃,
T RH = t(π S + π∗S )= t[(pS − g S )q S + (pS∗ − g∗S )q∗S ],where it is noted that p̃ = p̃∗ and q̃ = q̃∗ . The tax base in the benchmark caseconsists of the profits of the two downstream firms (π S + π∗S ), while in the ALP casethe tax base includes the profits of the upstream affiliate (π̃u ) as well as the two profits(π̃ + π̃∗ ). In the benchmark case, the transfer price is set lower than the true marginalcost. As a result, the downstream affiliate significantly expands and more goods areproduced than in the ALP case, i.e., q S + q∗S > 2q̃.25 In fact, the imposition of the
ALP helps the local firm expand (q̃∗ = q̃ > q∗S ), but discourages the production of the24
For t∗ (defined in Eq. (1.9)) to be positive, we assume a sufficiently high T such that
T > T = 1/4.
25

To see this formally, we haveq S + q∗S − 2q̃ = [2g̃ − (g S + g∗S )]/2 > 0,
→ t < (4T + 1)/5 ≡ tq .

There exists t satisfying the above inequality because it holds that ta < tq < t∗ and t > t ≡max{0, ta , tb } from (A1): t > t.

24

Production Location and Multinational Firms under Transfer Pricing

downstream affiliate (q̃ < q S ) and reduces the price-cost margin (p̃ − g̃ < pS − g S ).26
The contraction of host production combined with the narrower price-cost marginresults in smaller tax revenues.
In contrast, it can be verified that in most cases, the location change induced by the
ALP increases tax revenues globally:g
T
RW > T RW ,gwhere T
RW = T π̄ + t(π̃u + π̃ + π̃∗ )= T π̄ + t · 2[(p̃ − g̃) + (g̃ − c)]q̃,
T RW = T (π̄ + πuS ) + t(π S + π∗S )= T [π̄ + (g S − c)q S + (g∗S − c)q∗S ] + t[(pS − g S )q S + (pS∗ − g∗S )q∗S ].
where tax revenues in the parent country are now included. In the benchmark case,the upstream affiliate sets the transfer price lower than the marginal cost (g S < c),and earns negative profits. The host country benefits from larger tax revenues at theexpense of the parent country, but the benefit of the host does not exceed the loss ofthe parent. By imposing the ALP, the internal price is set higher than the marginal
cost (g̃ > c), which brings positive profits to the upstream affiliate in the host country
and leads to greater tax revenues globally.
These results are summarized as follows (see Appendix A.2 for the proof).
Proposition 1.3 (Tax revenues).
The imposition of the ALP changes the location of upstream production from theparent to the host country (from ”separate location” to ”co-location”) if the international tax difference is large (t ∈ (t, t∗ )). This location change decreases tax revenues
in the host country, but increases those globally.
Considering the fact that countries adopt transfer pricing taxation to raise their tax
revenues, the implementation of the ALP may give rise to an unintended consequence
for countries with low corporate tax rates. Proposition 1.3 also suggests a conflict
26

Noting that g S < g∗S and g̃ > g∗S , we haveq̃ − q∗S = (g∗S − g̃)/2 > (g∗S − g)/2 > 0.

Combining this result with q S + q∗S > 2q̃ gives q̃ < q S . This also implies that the price-cost marginis smaller in the ALP case than in the benchmark case: q̃ = p̃ − g̃ < pS − g S = q S .

25

Production Location and Multinational Firms under Transfer Pricing

of interest in the ALP between low-tax and high-tax countries.27 In Appendix A.9,
we show that the results generally apply to social welfare. The ALP limits the use oftransfer price and thereby leads to higher prices of final goods, which reduces consumer
surplus in the host country. Thus the location change caused by the ALP would lower
not only tax revenues, but also social welfare (consumer surplus and profits as well
as tax revenues) in the host country. For a full analysis on welfare in a related model
but without location choice, we refer independent works by Choi et al. (2018a); andIshikawa et al. (2017).

1.6

Conclusion

We have analyzed how corporate tax rates affect the production location choice of
MNEs. One may think that internationally-mobile firms locate their production in
low-tax countries, but this simple reasoning may not hold true for MNEs with multiple
affiliates. MNEs attempt to reduce tax payments globally by manipulating transfer
prices for intra-firm trade. Thus, they have an incentive to locate their upstream anddownstream affiliates separately to exploit international tax differences. Contrary to
the conventional wisdom, this paper shows that the upstream affiliate is likely to belocated in the high-tax parent country, if its tax rate is much higher than that of thehost country where the downstream affiliate is located.
With a view to preventing tax manipulation, the transfer pricing tax system requires
MNEs to follow the ALP, where MNEs should not set different prices for related
affiliates and unrelated firms. We have also analyzed the impact of the ALP on thelocation choice of MNEs. With the ALP, MNEs are unable to fully utilize intra-firmtransactions across borders for profit shifting. The ALP makes the transfer pricing
strategy less effective, and thus may change the location pattern from a separatelocation to a co-location of upstream and downstream affiliates. This location change
seems to bring greater tax revenues to the country hosting the two affiliates, but we havedemonstrated that this is not true. In contrast to a separate location, a co-location in
the host country does not provide the scope of profit shifting from the parent country,
which leads to the loss of tax base in the host. Owing to this, the host government
may hesitate to implement the ALP strictly, although the ALP may increase global
tax revenues.
27

Similar results can be found in Yao (2013) in a different setting mentioned in the Introduction.

26

Production Location and Multinational Firms under Transfer Pricing

We conclude by proposing possible extensions worth investigating. One extension
is to allow taxes to be endogenously chosen by governments. In addition, one canthink of many other policies to attract MNEs such as production and entry subsidies.
Considering the importance of international tax planning, further analysis on different
national tax systems is also needed such as the impact of a change from the separate
accounting system to the formula apportionment system, or the role of the advancepricing agreement. These issues are left to future research.

27

Chapter 2
Economic integration andagglomeration of multinational
production with transfer pricing
2.1

Introduction

Continuing economic integration in the last few decades brought more international
mobility to multinational enterprises (MNEs) and allowed them to diversify activities across subsidiaries in different countries. Considering the complexity of multinational activities, governments today need to carefully design policies to attract MNEs.
Among many factors, corporate taxation is one of the essential determinants of foreign direct investment (FDI) (Navaretti and Venables, 2004, Ch.6; Blonigen and Piger,2014).1 One naturally expects that countries with a low corporate tax rate will succeed
in hosting more FDI inflow than those with a high tax rate.
However, the type of MNE activities that operate in such low-tax countries is not
obvious. Governments lower taxes with an aim of hosting production plants, which
contribute to local employment and tax revenues.2 Contrary to host governments’This chapter is based on joint work with Hayayo Kato (Kato and Okoshi, 2019a).
1

As other determinants of MNEs’ location decision, recent studies highlight agglomeration
economies arising from affiliates (Mayer et al., 2010) and financial development in the host country(Bilir et al., 2019).
2

The Irish government, for example, has explicitly stated its commitment to the low corporate
tax rate for attracting FDI. See the 2013 Financial Statement by the Minister for Finance: http://www.budget.gov.ie/Budgets/2013/FinancialStatement.aspx, accessed on 19 June 2019.

28

Economic Integration and Agglomeration of Multinational Production

expectations, MNEs reportedly establish affiliates in low-tax countries to save taxes
and do not engage in production (Horner and Aoyama, 2009).3
We can illustrate this point by looking at the profits and manufacturing activities of
U.S. affiliates in Europe. In Figure 2.1, we take U.S. affiliates in twelve European
countries and draw the share of their profits from two low-tax countries, Ireland andSwitzerland, over the last 15 years (thick line).4 The profit share of low-tax countries
is disproportionately large for their size and doubled from 17% in 1997 to 34% in
2012. The manufacturing employment share of low-tax countries (dotted line), on theother hand, has been less than their profit share, indicating that U.S. affiliates there
rely more on non-production activities such as distribution, than those in the othercountries. Although both the profit and manufacturing employment shares increased
over time, there is no clear sign of convergence between the two.
The diverging shares of profits versus manufacturing employment in low-tax countries
may be explained by profit shifting of MNEs. MNEs allocate their activities between
low-tax and high-tax countries and transfer profits by controlling prices for intra-firmtrade, known as transfer prices.5 For example, headquarters in high-tax countries
makes profits by producing goods and sells them to affiliates in low-tax countries by
setting low transfer prices to inflate the affiliates’ profits. As intra-firm trade enhancedby economic integration makes profit shifting easy, the geographical separation of
production and profits may continue to rise.
When firms can shift profits and relocate between countries with different tax rates,
it is no longer clear how MNEs optimally set up their firm structure. To answer thequestion, we extend a two-country spatial model developed by Martin and Rogers(1995) and Pflüger (2004) to incorporate MNEs with profit-shifting motives.
Specifically, we investigate in which country, the low-tax or the high-tax one, multinational production is agglomerated and how the location pattern changes as trade3

Horner and Aoyama (2009) provide a list of Irish company relocations, with several examples indicating that MNEs move production from Ireland—with the world’s lowest corporate tax
rate at the time—abroad while maintaining non-production activities such as service centers andmarketing. This implies that low-tax countries do not necessarily retain multinational production.
4

As noted in the caption of Figure 2.1, data on profit are from Zucman (2014), who relies on
the Bureau of Economic Analysis (BEA). Because recent studies point out that the BEA data
may overstate profits aboard (Blouin and Robinson, 2019), the figure should be interpreted withcaution.
5
Empirical evidence on transfer pricing can be found in many studies. See Swenson (2001);
Bartelsman and Beetsma (2003); Clausing (2003); Bernard et al. (2006); Cristea and Nguyen(2016); Gumpert et al. (2016); Guvenen et al. (2017); Bruner et al. (2018); and Davies et al.
(2018).

29

Economic Integration and Agglomeration of Multinational Production

Figure 2.1: Profit share and manufacturing employment share of low-tax countries
in U.S. affiliates in Europe

Sources: The U.S. Bureau of Economic Analysis (the BEA) and Zucman (2014).
Notes: Data on profit are from Zucman (2014) (“U.S. Direct Investment Abroad,
Direct Investment Income Without Current-Cost Adjustment”), who compiles data
originally from the BEA. Either Ireland or Switzerland had the lowest or the second
lowest corporate tax rates among the sample countries for most of the period from1997 to 2012: the average rates are 17.5% (Ireland), 23.3% (Switzerland), and 30.3%(overall) (source: OECD tax database). Data on employment are also from the BEA(“Employment of Affiliates, Country of UBO by Industry of Affiliate”). Because the
BEA reports employment data for only selected countries, we take twelve countries in
Europe with consistent reporting for 1997-2012: Belgium, Denmark, Finland, France,
Germany, Ireland, Italy, the Netherlands, Spain, Sweden, Switzerland, and the U.K.

30

Economic Integration and Agglomeration of Multinational Production

costs fall. There are monopolistically competitive firms producing different varietiesthat compete for consumers in two countries. A set of these firms are (the headquarters of) MNEs that can decide where to locate their production plants. Part of the
produced output will be sold in the country where the variety is produced, and somein a different country through a foreign affiliate that the MNE opens. With a foreign
affiliate present, the MNE can engage in intra-firm trade and use the transfer price for
profit shifting. However, due to trade costs, shipping goods from one country to another will be costly. Trade costs change the volume of intra-firm trade and thus theeffectiveness of profit shifting, which in turn affects MNEs’ location choice.
Our findings are as follows. In the beginning of economic integration marked by hightrade costs, the low-tax country attracts a higher share of multinational production
than the high-tax country. When high trade costs hamper intra-firm trade and thereby
limit the profit shifting opportunity, MNEs can sell little to their foreign affiliate. With
most of the profits made in the country where goods are produced, they simply prefer
to locate production in the low-tax country.
A further reduction in trade costs, however, reverses this location pattern, i.e., production plants agglomerating in the high-tax country. This result seems surprising,but it is indeed consistent with MNEs’ optimal location choice. The MNE with production in the high-tax country lowers the transfer price to shift its domestic plant’s
profits to its foreign affiliate in the low-tax country. The lowered transfer price reduces the affiliate’s marginal cost, which allows it to lower the price of goods and to
gain competitiveness against local plants. On the other, the MNE with productionin the low-tax country raises the transfer price to shift profits from its foreign affiliate in the high-tax country back to its domestic plant. Due to the high transfer price,
the affiliate sells goods at a high price and loses competitiveness against local plants.
The direction of profit shifting from the plant in the high-tax country to the affiliate in
the low-tax country makes the MNE competitive in both markets. When trade costs
are so low that this effect is significant, all MNEs choose to locate production in thehigh-tax country.
These results may explain the fact that U.S. affiliates in low-tax European countries
engage disproportionately more in non-production activities than those in high-tax
European countries do, as Figure 2.1 shows. In addition, Overesch (2009) provides
supporting empirical evidence. He finds that multinationals in high-tax Germany
increase real investments as the cross-country corporate tax difference between theirhome country and Germany is larger.
31

Economic Integration and Agglomeration of Multinational Production

The agglomeration of multinational production in the high-tax country, however, does
not necessarily bring greater tax revenues there, since a large portion of profits are
shifted to the foreign affiliates in the low-tax country. Amid growing concerns about
tax base erosion, the OECD recently reported that the estimated revenue losses from
MNEs’ tax avoidance is at most 10% of global corporate income tax revenues.6 Our
finding may justify the concern about low-tax countries attracting affiliates that receive
shifted profits from high-tax countries.
The basic framework is further extended to consider tax competition between two
unequal-sized countries. The main result goes through that profit shifting makes
more likely production agglomeration in the (large) high-tax country. We also findthat profit shifting makes tax competition tougher by reducing the large country’s tax
rate.
These results echo existing studies on tax competition in agglomeration economies,
telling that large countries set a higher tax rate, while keeping production agglomeration (Baldwin and Krugman, 2004; Borck and Pflüger, 2006).7 If transfer pricing
can be used, however, the large country may still keep the agglomeration, but set alower tax rate than it would if transfer pricing is impossible. A bigger tax difference
would bring more opportunities to manipulate transfer prices. To prevent an erosionof taxable profits, the large country is forced to lower its tax rate.

Relation to the literature. This paper fits into the literature on transfer pricing
pioneered by Copithorne (1971) and Horst (1971). The literature points out that
MNEs use transfer prices to make affiliates competitive as well as for shifting profits.
The former is called a strategic effect and the latter a tax manipulation effect. Earlier
studies examining the strategic use of transfer pricing include those by Elitzur and6
See http://www.oecd.org/ctp/oecd-presents-outputs-of-oecd-g20-beps-projectfor-discussion-at-g20-finance-ministers-meeting.htm, accessed on 20 February 2019. To
tackle this issue, the OECD set up a project called “Base Erosion and Profit Shifting” (BEPS),
involving over eighty countries. See http://www.oecd.org/tax/beps, accessed on 20 February
2019.
7

See also Kind et al. (2000); Ludema and Wooton (2000); Andersson and Forslid, 2003; andOttaviano and van Ypersele, 2005 for earlier contributions. Recent studies in the literature allow
for heterogeneity among firms (Davies and Eckel, 2010; Haufler and Stähler, 2013; Baldwin andOkubo, 2014), forward looking behavior by governments (Han et al., 2014; Kato, 2015), andlobbying by firms (Ma, 2017; Borck et al., 2012; Kato, 2018). See also Section 3.5.3 of Keen andKonrad (2013).

32

Economic Integration and Agglomeration of Multinational Production

Mintz (1996); Schjelderup and Sørgard (1997); Zhao (2000); and Nielsen et al. (2003).8
The literature looks only at profit shifting with a fixed location of each affiliate. Ourcontribution is to uncover how these two effects of transfer pricing affect the MNEs’
location choices.
Recent studies focus on the FDI decision of MNEs with profit-shifting motives; thatis, whether MNEs should undertake FDI to manufacture inputs within their firms, orsource inputs from independent suppliers, known as the make or buy decision (Bauerand Langenmayr, 2013; Egger and Seidel, 2013; Keuschnigg and Devereux, 2013;
Choi et al., 2018b).9 Egger and Seidel (2013), for example, theoretically predict andempirically confirm that larger tax differences are more likely to lead MNEs to engage
in FDI, rather than outsourcing. Choi et al. (2018b) find a possibility that MNEs
do both FDI and outsourcing to avoid regulations by tax authorities. While thesestudies fix the supplier’s location and look at MNEs’ organizational choices, we fix
the MNEs’ organization form and allow for the endogenous location of production.
Our companion study, Kato and Okoshi (2019b), focuses on the location decision
within MNEs, though accounts for neither MNEs’ various activities (production anddistribution), nor trade costs, unlike the present one.
Only a handful of studies examine tax competition for MNEs using profit-shifting
motives due to analytical inconvenience (Haufler and Schjelderup, 2000; Kind et al.,2005; Peralta et al., 2006; Stöwhase, 2005, 2013; Ma and Raimondos, 2015).10 In
models with two unequal-sized countries, Stöwhase (2005, 2013) find that introducing
profit shifting will not generally put downward pressure on tax rates, which is incontrast to our findings. These different results are mainly due to the strategic effectof transfer prices in our model, which strengthens profit-shifting incentives and thereby
leads to tougher tax competition.
In terms of setting, the closest studies to ours are Peralta et al. (2006); and Ma andRaimondos (2015), who allow for both trade costs and unequal-sized countries. In
8

See Nielsen et al. (2008); and Choe and Matsushima (2013) for subsequent development.
While these studies (and ours) deal exclusively with tangible assets, recent studies examine intangible assets (Juranek et al., 2018).
9

For studies on MNEs without profit shifting motives, see Antràs and Yeaple (2014); Section
3.6 of Costinot and Rodrı́guez-Clare (2014); and Shen (2018).
10

More recent studies introduce a low-tax country with no production or consumption, calling
it a tax haven country, and consider tax competition between a home country and the tax haven(Krautheim and Schmidt-Eisenlohr, 2011; Langenmayr et al., 2015; Hauck, 2019). This setting
greatly enhances analytical tractability but is not suitable to investigate the MNEs’ production
location.

33

Economic Integration and Agglomeration of Multinational Production

a tax-competition game over a single MNE’s plant, Peralta et al. (2006) show thepossibility that the large country may win the plant while setting a higher tax rate,
which is similar to our findings. However, the mechanism is crucially different from ours
because in their model countries use enforcement policy as well as corporate taxation.
Despite its higher tax rate, the large country can attract the plant if it adopts a loose
enforcement policy and thus its effective tax rate is lower. Moreover, in contrast to
our findings, they show that the large, high-tax country may win competition if trade
costs are high.
Ma and Raimondos (2015) also consider tax competition for a single MNE and obtainthe similar results.11 However, because of analytical inconvenience arising from thelocation discontinuities of a single MNE, their analysis relies heavily on numericalsimulations. It is thus unclear whether introducing profit shifting increases or decreases
equilibrium tax rates. By contrast, we can obtain sharp predictions in analytical form
by employing an economic geography model with a continuum of MNEs and focusing
on a fully agglomerated situation.
The rest of the paper is organized as follows. The next section develops the model.
Section 2.3 characterizes the equilibrium plant distribution in a situation where twocountries are equal-sized and taxes are given. It shows how allowing for transfer
pricing changes the plant distribution. Section 2.4 analyzes tax competition between
two unequal-sized countries and sees how the results change with and without profit
shifting. The final section concludes.

2.2

Basic setting

Consumers. We consider an economy with two countries, indexed by 1 and 2, andtwo goods, homogeneous and differentiated ones. Letting L be the world population,
country 1 has a population of L1 = s1 L, while country 2 has a population of L2 =s2 L = (1 − s1 )L, where s1 ∈ (0, 1) is country 1’s share of the world population. Eachindividual owns one unit of labor.
Following Pflüger (2004), each consumer has an identical quasi-linear utility function
with a constant-elasticity-of-substitution (CES) subutility. Consumers in country 1
11

In some of the numerical examples, they allow for both asymmetry in the leniency of enforcement policy and asymmetric market size, in which case the small country may win the MNE whilesetting a higher tax rate.

34

Economic Integration and Agglomeration of Multinational Production

solve the following maximization problem:max

q̃11 (ω),q̃21 (ω),q1O

where Q1 ≡u1 = µ ln Q1 + q1O ,
σ
# σ−1

" 2 Z
X

q̃i1 (ω)

σ−1
σ

dω

,

ω∈Ωi

i=1

subject to the budget constraint:
2 Z
X
i=1

pi1 (ω)q̃i1 (ω)dω + q1O = y1 + q O
1.

ω∈Ωi

µ > 0 captures the intensity of the preference for the differentiated goods. q1O andqO
1 are the individual demand for the homogeneous good and its initial endowment,
respectively. We assume that q O
1 is large enough for the homogeneous good to be
consumed. q̃i1 (ω) is the individual demand from consumers in country 1 for the varietyω ∈ Ωi , where Ωi is the set of varieties produced in country i ∈ {1, 2}. Q1 is the CES
aggregator of differentiated varieties with σ > 1 being the elasticity of substitution
over them.
Solving the above problem gives the aggregate demand for the variety ω produced incountry i ∈ {1, 2} and consumed in country 1:
qi1 (ω) ≡ L1 q̃i1 (ω) =where P1 ≡pi1 (ω)
P1

" 2 Z
X
i=1

−σ

µL1
.
P1
1
# 1−σ

pi1 (ω)1−σ dω

(2.1)

.

ω∈Ωi

P1 is the CES price index of the varieties. Although we will mainly present the results
for country 1 in the following, analogous expressions hold for country 2. As firms are
symmetric, we will suppress the variety index ω for notational brevity.

Homogeneous good sector. The homogeneous good sector uses a constant-returnsto-scale technology. That is, one unit of labor produces one unit of the good. The
technology leads to perfect competition, making the good’s price equal to its production cost, or the wage rate. Letting wi be the wage rate of country i ∈ {1, 2}, thecostless trade of the homogeneous good equalizes the wage rates between countries;

35

Economic Integration and Agglomeration of Multinational Productionthat is w1 = w2 . We choose the good as the numéraire such that w1 = w2 = 1.

Differentiated goods sector.
The differentiated goods sector uses an increasingreturns-to-scale technology. Each MNE needs f units of capital for a production plantin one country and another f units for a foreign affiliate in the other.12 Supposing
the world amount of capital is 2K, we choose f such that the world has 2K/(2f ) = L
MNEs, or f = K/L. We denote the number of production plants located in country 1(or country 2) by N1 = n1 L (or N2 = n2 L = (1 − n1 )L), where n1 ∈ [0, 1] is country
1’s share of production plants. Once established, each MNE needs a units of labor to
produce one unit of variety.
Consider an MNE with its production plant in country 1. The plant produces quantities
q11 and sells them at a price p11 to domestic consumers. In addition, it produces
quantities q12 and exports them at a transfer price g1 to its foreign affiliate in country
2. When exporting, due to iceberg trade costs τ > 1, 1/τ < 1 units of quantities
melt away, so the plant has to produce τ units to deliver one unit to the affiliate. The
affiliate sells the imported goods to consumers in country 2 at a price p12 .
MNEs have decentralized decision making. In other words, the headquarters (or the
production plant) of the MNE sets the transfer price to maximize global post-tax
profits, while the foreign affiliate sets the retail price to maximize its own profits.13 The
idea that the headquarters lets affiliates make decisions for strategic purpose is known
as the delegation principle, and is adopted by many studies in the literature (Zhao,
2000; Nielsen et al., 2003, 2008; Kind et al., 2005).14 In practice, it is sensible to delegate
decisions to local managers who are familiar with their local business environments.
In many cases, a company’s acquisition of a rival often involves the latter receiving
divisional autonomy (e.g., Volkswagen’s acquisition of Audi, Ford’s acquisition of
12

Similar specifications in the context of transfer pricing can be found in Kind et al. (2005);
and Matsui (2012), although they fix the location of plants and affiliates.
13

In the benchmark analysis, we do not consider the cost of profit shifting as in Nielsen et al.
(2003, 2008); Kind et al. (2005); Section 2.1.2 of Keen and Konrad (2013); and Agrawal andWildasin (2019). Introducing such costs does not affect the qualitative nature of our results. See
Appendix B.6.
14

It is worth noting that the strategic role of transfer pricing within multinationals should be
distinguished from strategic interactions across multinationals. As we employ the monopolisticallycompetitive framework, each plant/affiliate does not set a price strategically against others, leading
to the constant mark-up: σ/(σ −1), which we will see shortly (Matsuyama, 2000). But the transfer
price gi is strategically determined between the plant and its affiliate.

36Economic Integration and Agglomeration of Multinational Production

Volvo, and GM’s acquisition of Saab).15 We examine the case of centralized decision
making in Appendix B.6 and confirm the robustness of our results.
The timing of actions proceeds as follows. First, each MNE chooses the country inwhich to locate a production plant and a foreign affiliate, endogenously determining
the share of plants n1 . The decision is based on a comparison of the post-tax profits
in the two countries. Second, the MNE chooses the transfer price. Third, production
plants and foreign affiliates engage in price competition in each country. Finally,
production and consumption take place. We solve the game in a backward fashion.
For convenience, we refer to the results with fixed capital allocation as a short-run
equilibrium and refer to the results in the endogenous case as a long-run equilibrium.
We will examine the two situations in turn.

2.2.1

Optimal Prices in the Short-run Equilibrium

Let us derive the optimal prices given the distribution of plants and affiliates. The pretax profits of the production plant in country 1 (π11 ) and those of the foreign affiliate
in country 2 (π12 ) are, respectively,
π11 = (p11 − a)q11 + (g1 − τ a)q12 ,
{z
} |
{z
}
|
Domestic profit

Shifted profit

π12 = (p12 − g1 )q12 ,where q11 is given by Eq. (2.1) and q12 is defined analogously, and a is the unitlabor requirement. The second term in π11 represents the profits from intra-firm trade
subject to trade costs τ . As we will see shortly, this term captures profit shifting within
MNEs. At the third stage of the game, the production plant and the foreign affiliate
choose their prices to maximize their own profits. The optimal prices are
p11 =

σa
,
σ−1

p12 =

σg1
.
σ−1

At the second stage, the MNE with its production plant in country 1 sets the transfer
price to maximize the following global post-tax profits:
Π1 = (1 − t1 )π11 + (1 − t2 )π12 ,15See Ziss (2007) for more on this issue.

37

Economic Integration and Agglomeration of Multinational Production

where ti ∈ [0, 1] is the tax rate of country i ∈ {1, 2}. The optimal transfer price is16
g1 =

στ a
,
σ − ∆t1

where ∆t1 ≡t2 − t1,
1 − t1(2.2)

which is positive because σ − ∆t1 > 0. We can check that g1 decreases with t1 andincreases with t2 . As a higher tax rate in country 1 reduces the post-tax profit of the
production plant, the MNE tries to move profits from country 1 to 2 by lowering thetransfer price. When the tax rate in country 2 increases, the direction of profit shifting
reverses, and the MNE raises the transfer price.
Similarly, the MNE with its production plant in country 2 sets the optimal transfer
price as follows:
g2 =

στ a
,
σ − ∆t2

where ∆t2 ≡t1 − t2,
1 − t2(2.3)

which is also positive because σ − ∆t2 > 0.
To see the direction of profit shifting, we assume t1 > t2 and have ∆t1 < 0 < ∆t2 .
Using the optimal transfer prices, we can rewrite the profit from intra-firm trade as(g1 − τ a)q12 =(g2 − τ a)q21 =τ a∆t1
q12 < 0 for the MNE with production in country 1,
σ − ∆t1(2.4-1)
τ a∆t2
q21 > 0 for the MNE with production in country 2.
σ − ∆t2(2.4-2)The MNE with production in country 1 cuts the transfer price to below the true
marginal cost, making negative profits from intra-firm trade. In doing so, the plant
shifts profits made in the high-tax country 1 to the foreign affiliate in the low-tax
country 2. As for the MNE with production in country 2, the direction reverses: fromthe affiliate in country 1 to the plant in country 2.
16
We can confirm that the second order condition (SOC) is satisfied at the optimal point. The
SOC is ∂ 2 Π1 /∂g12 < 0, which reduces to (1 − t2 )g1 − (1 − t1 )[(σ + 1)τ a − σg1 ] < 0. This inequality
holds at g1 = στ a/(σ − ∆t1 ).

38

Economic Integration and Agglomeration of Multinational Production

We can rewrite the post-tax profit asΠ1 = (1 − t1 )π11 + (1 − t2 )π12
(σ − 1)∆t1
φγ1 µL2µL1+·= (1 − t1 )σ(N1 + φγ2 N2 )σσ(φγ N + N2 )|{z
} |{z 1 1}
Domestic profit+ (1 − t2 ) ·Shifted profit

φγ1 µL2,
σ(φγ1 N1 + N2 )(2.5-1)Π2 = (1 − t1 )π21 + (1 − t2 )π22
= (1 − t1 ) ·φγ2 µL1
σ(N1 + φγ2 N2 )(σ − 1)∆t2µL2
φγ2 µL1+,+ (1 − t2 )·σ(φγ1 N1 + N2 )σσ(N1 + φγ2 N2 )
|
{z
} |
{z
}
Domestic profit

Shifted profit(2.5-2)where φ ≡ τ 1−σ , γi ≡σσ − ∆ti

1−σ
,

∆ti ≡

tj − ti,
1 − tii 6= j ∈ {1, 2}.

The first and second terms in the square brackets in Π1 and Π2 are respectively the profit
from domestic market and the profit shifted through transfer pricing. φ = τ 1−σ ∈ [0, 1]
is an inverse measure of trade costs, or the freeness of trade. φ = 0 (i.e., τ = ∞)corresponds to a prohibitively high level of trade costs, while φ = 1 (i.e., τ = 1)
indicates zero trade costs.
If the tax difference is too large, profit shifting is so excessive that taxable profits canbe negative. To ensure positive profits, we assume the condition that 1 + ∆t1 > 0.
This simply requires that the tax difference should not be too large. See Appendix B.3
for details.
When the difference in the post-tax profits is positive, i.e., ∆Π ≡ Π1 − Π2 > 0, the
MNE prefers to locate its production plant in country 1, and vice versa. In the longrun equilibrium, the profit differential is zero and no MNEs are willing to change their
allocation of plants/affiliates.

39

Economic Integration and Agglomeration of Multinational Production

2.3

Equilibrium allocation of production plants

To highlight the role of tax difference, we suppose that the tax rate is higher in country
1 (t1 > t2 ), but the two countries are of the same size (s1 = 1/2).17 By solving thelong-run equilibrium condition (∆Π = 0) for the share of production plants in country
1, we obtain interior equilibria n1 ∈ (0, 1). If ∆Π = 0 does not have interior solutions,then we obtain corner equilibria in which all multinational production takes place in
one country, i.e., n1 ∈ {0, 1}.
To see how a reduction in trade costs affects the long-run equilibrium allocation, we
consider two extreme cases: prohibitive trade costs (φ = 0) and zero trade costs(φ = 1).
An extremely high level of trade costs does not allow for intra-firm trade, leaving noroom for profit shifting.18 As the MNEs earn profits only from the domestic sales of
their production plants, they prefer to locate them in the low-tax country 2. We notethat the equilibrium distribution involves a small but positive share of plants in thehigh-tax country 1, i.e., n1 |φ=0 ∈ (0, 1/2). Since competition in the domestic market
works as a dispersion force, the corner distribution where all plants are in country 2(n1 |φ=0 = 0) cannot be an equilibrium.
Zero trade costs, on the other, allow MNEs to engage in intra-firm trade fully, making
profit shifting through transfer pricing effective.19 In our model, transfer pricing does
not just shift profits between domestic plants and foreign affiliates, but also affects thecompetitiveness of the affiliates. As we showed, MNEs with production in the hightax country 1 set a low transfer price to shift profits to their affiliates in the low-tax
country 2 (see Eqs. (2.2) and (2.4-1)). Due to the low sourcing cost, the affiliates cansell varieties at a low price and become competitive against local plants. By contrast,
MNEs with production in the low-tax country 2 set a high transfer price (see Eqs. (2.3)
and (2.4-2)), which makes their affiliates in the high-tax country 1 less competitive.
They are at a disadvantage in both the domestic and foreign markets. Therefore,
MNEs prefer to locate production in the high-tax country so that the direction of
profit shifting makes affiliates competitive.
17

The assumption of symmetric market size is for simplicity and is not crucial for our main
result, which we will discuss after Proposition 2.1.
18
In Eqs. (2.5-1) and (2.5-2), the profits from intra-firm trade and those from the foreign
affiliate disappear if φ = 0.
19

We can confirm that the shifted profit increases with φ; that is, ∂[(gi − τ a)qij ]/∂φ > 0 for
i 6= j ∈ {1, 2}.

40

Economic Integration and Agglomeration of Multinational Production

From the results of the two polar cases, it is expected that more production plants
are in the low-tax country 2 if trade costs are high, whereas they are in the high-tax
country 1 if trade costs are low. We can prove that this is the case and summarize thefindings as follows (see Appendix B.1 for a proof).
Proposition 2.1 (Plant distribution).
Suppose that country 1 has a higher corporate tax rate than country 2. The equilibrium allocation of production plants is as follows:(i) With high trade costs such that φ ∈ [0, φ∗ ), the high-tax country 1 hosts a
smaller share of plants than the low-tax country 2, i.e., n1 < 1/2.
(ii) With low trade costs such that φ ∈ (φ∗ , 1], the high-tax country 1 hosts a
greater share of plants, i.e., n1 > 1/2.
At φ = φ∗ , the two countries have an equal share of plants, i.e., n1 = 1/2.
Figure 2.2 shows a representative pattern of equilibrium plant distribution for different
levels of the freeness of trade φ (thick curve), along with the equilibrium plant distribution under no profit shifting (dotted line).20 As φ increases from zero, the high-tax
country 1 decreases plants in both cases, with and without profit shifting. When hightrade costs prevent exporting, MNEs make profits mostly from their domestic plants
and thus prefer to locate them in the low-tax country. Along with a further increasein φ from φ# , however, the high-tax country 1 increases plants in the case with profit
shifting, whereas it continues to decrease plants in the case without profit shifting. Sufficiently low trade costs expand intra-firm trade and thus the opportunities for profit
shifting, leading to a sharp contrast in location patterns.
The result of the high-tax country 1 attracting more multinational plants for low
trade costs generally does not depend on the assumption of symmetric market size.
If country 1 is larger (s1 > 1/2), then the agglomeration incentive of plants to seek
country 1’s market is stronger (see also the tax-competition analysis in Section 2.4).
If country 1 is smaller (s1 < 1/2), then the agglomeration incentive is weaker but theshifted profits from country 2 to 1 are larger. We can numerically confirm that in both
20

The parameter values are σ = 5, t1 = 0.8, t2 = 0.7, L = 10, s1 = 0.5, µ = 1, and a = 1. The
qualitative feature of location pattern explained below (i.e., n1 first decreases and then increases
as φ rises) does not depend on specific parameter values. See Appendix B.1.

41

Economic Integration and Agglomeration of Multinational Production

Figure 2.2: Share of production plants in the high-tax country 1

cases multinational production is concentrated in country 1 for low trade costs if thesize asymmetry and the tax difference are not extremely large.
This finding seems consistent with the fact that in the last two decades marked by
globalization, U.S. affiliates in Europe make a disproportionate share of profits from
low-tax countries compared to manufacturing activities there, as Figure 2.1 shows.
Moreover, Overesch (2009) empirically finds that the cross-country tax difference between high-tax Germany and a low-tax home country increases German inbound investments.
Full agglomeration. If φ is sufficiently high such that φ > φS , which is called a sustain
point, then all production plants are located in country 1.21 It can be checked thatφS decreases with t1 − t2 . A larger tax difference offers more room for profit shifting
and thus leads to more aggressive transfer pricing (very low g1 or very high g2 ). This
strengthens the competitiveness of MNEs with production in country 1, since they
set a much lower price than their rivals in both the domestic and foreign markets, i.e.,p11 < p21 ; p12 < p22 . Consequently, full agglomeration in country 1 is more likely tooccur since the tax difference is larger. We summarize these findings as follows (seeAppendix B.2 for a proof).
Proposition 2.2 (Full agglomeration).
With sufficiently low trade costs such that φ ∈ [φS , 1], all production plants locate
21

Formally, a sustain point is the level of the freeness of trade above which full agglomeration
is sustainable.

42

Economic Integration and Agglomeration of Multinational Productionin the high-tax country 1: n1 = 1. As the tax difference increases, the sustain point
φS decreases, and thus full agglomeration is more likely to occur.
Tax revenues. The taxable base in country i consists of profits of production plantNi πii and those of distribution affiliate Nj πji . The tax revenue then becomes
T R1 ≡ t1 (N1 π11 + N2 π21 ),T R2 ≡ t2 (N2 π22 + N1 π12 ).
Figure 2.3 illustrates country 1’s share of tax revenues in the world along with its shareof plants.22 Naturally, with high trade costs (φ ' 0), the high-tax country 1 earns
greater tax revenues and its revenue share exceeds one-half.
The higher tax rate may not guarantee greater tax revenues, however, with low trade
costs (φ > φS ) such that production plants are agglomerated in country 1. In the fully
agglomerated situation, country 1 (country 2) collects taxes solely from the plants(affiliates). As a result of profit shifting, country 1 cannot fully enforce taxes on theplants, whereas country 2 can tax on shifted profits the affiliates receive. The profitshifting incentive of MNEs is stronger as a higher elasticity of substitution (high σ)
leads to tougher market competition.23 If σ is high enough such that σ > t1 /(2t1 − 1)and thus the loss from tax-base erosion is huge, country 1’s tax revenues are smaller
than country 2’s.
We can formally prove the above discussion and summarize the findings as follows (seeAppendix B.4 for a proof).

Proposition 2.3 (Tax revenues).
With high trade costs such that φ is close to zero, the high-tax country 1 earns
greater tax revenues than the low-tax country 2. This pattern reverses, however,with low trade costs such that φ ∈ (φS , 1] and a high elasticity of substitution suchthat σ > t1 /(2t1 − 1).
22

Parameter values are the same as those in Figure 2.2.

23

Given transfer prices, an increase in σ reduces the good’s price: ∂pii /∂σ < 0; ∂pij /∂σ < 0. It
also strengthens the profit shifting: ∂g1 /∂σ = −τ a∆t1 /(σ − ∆t1 )2 > 0; ∂g2 /∂σ = −τ a∆t2 /(σ −∆t1 )2 < 0.

43

Economic Integration and Agglomeration of Multinational Production

Figure 2.3: Revenue share and plant distribution

Figure 2.4 shows a further decomposition of tax revenues in each country.24 Let us firstlook at profits. The taxable profit, either of plant πii or affiliate πji , behaves similarly
in both countries. πii monotonically decreases with φ because a rise in φ exposes thedomestic market to more imports.25 On the other, πji exhibits an inverted-U shapein terms of φ. As φ rises, the affiliate can import goods at a lower cost and thus set
a lower selling price. This explains the increasing part of πji . A further decline in φ
induces the drastic relocation of plants from country 2 to 1. The massive inflow ofplants leads to tougher competition in country 1, reducing π21 . The relocated plants
in turn export goods at a lower transfer price, making tougher competition in country
2 and thus reducing π12 . These explain the decreasing part of πji .
The overall shape of tax revenues, T Ri , depends on the relative importance of πii
and πji , which is determined by the plant distribution Ni . Since N1 gets larger as φapproaches φS , T R1 and T R2 are respectively governed by N1 π11 and N1 π12 . Consequently, T R1 decreases with φ as π11 does, while T R2 exhibits an inverted-U shape in
24

The parameter values are the same as those in Figure 2.2. For φ ≥ φS , π21 and π22 are notdrawn because there are no multinationals with production in country 2, i.e., N2 = 0.
25

Strictly speaking, πii consists of the profit from domestic market and the profit from intra-firmtrade, which respectively corresponds to the “Domestic profit” term and the “Shifted profit” termin Eqs. (2.5-1) and (2.5-2). The domestic profit decreases with φ, while the shifted profit does notnecessarily so. Since the shifted profit is discounted by trade costs and is thus smaller than thedomestic profit in absolute terms, the overall shape of πii is determined by that of domestic profit.

44

Economic Integration and Agglomeration of Multinational Production

Figure 2.4: Profits and tax revenues: Country 1 on the left and country 2 on therightterms of φ as π12 does.
Centralized decision making. We assumed that MNEs have decentralized decision
making, where foreign affiliates choose prices to maximize their own profits. Our main
result holds true if MNEs have centralized decision making, in which the MNE chooses
all prices to maximize global profits. Note that the direction of profit shifting does
not change depending on the decision making style. That is, foreign affiliates source
goods from production plants by paying high (or low) transfer prices if they are in the
low-tax country (or the high-tax country). By locating in the low-tax country, foreign
affiliates enjoy a higher price-cost margin than those located in the high-tax country(p12 − g1 > p21 − g2 ) and earn larger profits. As in the decentralized decision making
case, profit shifting affects the profitability of foreign affiliates asymmetrically, leading
to agglomeration of production plants in the high-tax country. See Appendix B.6 fordetails.

2.4

Tax competition

We here allow countries to choose their tax rate non-cooperatively and compare theresults of tax competition with profit shifting to those without profit shifting.
If two countries with equal size compete with each other, they end up with having
equal taxes, resulting in the symmetric distribution of plants. To generate different
tax rates between countries, we introduce size asymmetry and assume that country 1
45

Economic Integration and Agglomeration of Multinational Production

is larger than country 2, i.e., L1 = s1 L > (1 − s1 )L = L2 , or s1 > 1/2. If there were
no tax differences, there would exist a sustain point above which level of trade freenessthe large country 1 would host all plants (see e.g., Chapter 3 of Baldwin et al., 2003).
Following Baldwin and Krugman (2004), the objective function of the government ineach country takes the form of
Gi = T Ri −βti,
1 − tiwhere T Ri ≡ ti (Ni πii + Nj πji ),i 6= j ∈ {1, 2}.

The first term represents tax revenues and the second term is a tax administration
cost, where β > 0 captures its inefficiency.26 The two governments simultaneously
and non-cooperatively decide their tax rates before the location decision of MNEs.
To make our results as comparable as possible to those of prior studies (Baldwin andKrugman, 2004, in particular), we analyze tax competition in the full-agglomerated
situation, known as the core-periphery situation. We focus on the situation where
φ is higher than a sustain point and country 1 hosts all plants (n1 = 1) before tax
competition.

No-transfer-pricing case. As a benchmark, we first derive the equilibrium tax rates
when transfer pricing is not allowed. The inability to manipulate transfer prices implies
that gi = τ a, resulting in zero profits from intra-firm trade: (gi − τ a)qij = 0 for
i 6= j ∈ {1, 2}. Government i maximizes
Gi =

βti
µLi ti−.
σ
1 − ti

Notice that Gi does not depend on trade freeness φ, which can be explained as follows.
The taxable base, Ni πii +Nj πji , is proportional to the sales of plant and affiliate locatedin the country, Ni pii qii + Nj pji qji . The sales must be in turn equal to the country’s
26
Tax administration cost is well recognized as an important determinant of raising revenues(OECD, 2017; Profeta and Scabrosetti, 2017). OECD (2017) states that “Even small increases
in compliance rates or compliance costs can have significant impacts on government revenues andthe wider economy.” (p.5) In addition, this objective function in general captures the fundamental
conflicts governments face: they attempt to raise tax revenues while maintaining a low tax rate,
which is thought of as a reduced-form objective that either selfish or benevolent government adopts(Baldwin and Krugman, 2004). See also Borck and Pflüger (2006); Han et al. (2014); and Kato
(2015) for similar specifications.

46

Economic Integration and Agglomeration of Multinational Production

expenditure, µLi , which is independent of φ.27
Solving the first-order condition gives the unique equilibrium tax rate in country i ∈{1, 2}:sbti = 1 −

βσ
,
µLi

(2.6)

at which the government objective is positive: Gi (ti = bti ) > 0. To exclude nonpositive taxes, we will assume that b
ti > 0, or β < β ≡ µL2 /σ. It can be verified thatthe large country 1 sets a higher tax rate than the small country 2, i.e., b
t1 > bt2 , because
its larger market size generates taxable agglomeration rents. This is in line with theresults in the literature (Baldwin and Krugman, 2004).
The equilibrium taxes are indeed consistent with the core-periphery situation. Thatis, there exists the sustain point φb ∈ (0, 1) above which level of φ plants are fully
agglomerated in country 1:
1 − s1 1 − b
t2
φbS =
b
s1 1 − t1r
1 − s1
=
,
s1

(2.7)

which lies in between zero and one.
These results are summarized as follows (see Appendix B.5 for a proof).
Lemma 2.1 (Tax competition without transfer pricing).
Assume that β < β ≡ µL2 /σ. Consider tax competition in the core-periphery situation without transfer pricing: φ ∈ [φbS , 1]; n1 = 1. The large country 1 maintains
the full agglomeration of production despite its higher tax rate: b
t1 > bt2 .
Transfer-pricing case.
We will see how the above results change if MNEs can use
transfer pricing. As in the previous case, we consider tax competition in the range of
trade freeness above the sustain point, where country 1 hosts all plants. The objective
27

The constant mark-up pricing implies that πii = (pii − a)qii = pii qii /σ and πji = (pji −τ a)qji = pji qji /σ. From the manufacturing good’s market clearing condition in country i, we haveNi pii qii + Nj pji qji = µLi or Ni πii + Nj πji = µLi /σ.

47

Economic Integration and Agglomeration of Multinational Production

functions become

µt1
G1 =
L1 +
σ

(σ − 1)∆t1
L2
σ{z
|
}


−

βt1
,
1 − t1

Erosion of taxable profits

G2 =µL2 t2βt2−.
σ1 − t2

Country 1’s objective now involves the tax difference, i.e., the second term in thesquare bracket of G1 , since plants in the high-tax country 1 move their profits to the
low-tax country 2. If country 1 keeps its tax rate as high as it does in the no-transferpricing case, then it earns less tax revenues. Thus, country 1 has an incentive to lower
its tax rate to prevent the erosion of taxable profits. On the other, as country 2 does
not have any plants that receive shifted profits, its tax revenue is the same as in the
no-transfer-pricing case.28
From the first-order conditions, we obtain the unique equilibrium tax rates:st∗1 = 1 −st∗2 = 1 −√βσ 2 + (σ − 1) βσµL2,µL(σ − s2 )(2.8-1)βσµL2(2.8-2)

(= b
t2 ),

which are positive and give positive government payoffs under β < β ≡ µL2 /σ.29 As
expected, we can check that introducing profit shifting pushes downward country 1’s
28

In the transfer-pricing case, the taxable profit in country i ∈ {1, 2} isNi πii + Nj πji =µLi(σ − 1)∆ti
φγj Nj+µLj ,σ
σσ(Ni + φγj Nj )where the first term in the right hand side is the taxable base in the no-transfer-pricing case. The
second term is zero when Nj = 0.
29

The condition for t∗1 > 0 reduces toσ 2 β + (σ − 1)

p

σµL2

p

β − µL(σ − s2 ) < 0,

t2 , we have
which holds under β < β. Noting that t∗2 = b
G1 (t1 = t∗1 , t2 = t∗2 ) > G1 (t1 = t∗2 , t2 = t∗2 ) = µL1 t∗2 /σ − βt∗2 /(1 − t∗2 )> µL2 t∗2 /σ − βt∗2 /(1 − t∗2 )= G2 (t2 = t∗2 ) > 0.

48

Economic Integration and Agglomeration of Multinational Production

Figure 2.5: Sustains points under tax competition

t1 (see Eq. (2.6)).
tax rate: t∗1 < b
Whether t∗1 is higher or lower than t∗2 depends on country 1’s market-size share s1 . We
can confirm that t∗1 is likely to be higher than t∗2 as s1 is higher (or s2 is lower). The
intuition is as follows. Profit shifting from country 1 to 2 is less effective when country
2’s market size is smaller and there are less exports to 2. Country 1 does not have tofear the erosion of taxable profits so that it can set t∗1 higher than t∗2 , while maintaining
production agglomeration.
As in the no-transfer-pricing case, the equilibrium taxes are consistent with the coreperiphery situation.30 We can further show that φS is smaller than φbS (see Eq. (2.7)),
implying that full production agglomeration is more likely to occur due to transfer
pricing, as illustrated in Figure 2.5.31
Thus, our main result in the exogenous-tax case, i.e., profit shifting making more
likely production agglomeration in the high-tax country, carries over when countries
30

Due to transfer pricing, φS takes a more complicated form than φbS defined in Eq. (2.7). See
Appendix B.7 for details.
This result is independent of whether t∗1 is higher or lower than t∗2 . For the MNE’s viewpoint,∗
if t1 > t∗2 , country 1 is attractive not just because of its large market size but also because of thedirection of profit shifting that makes their affiliates competitive. If t∗1 < t∗2 , on the other, the31

direction of profit shifting works against production agglomeration in country 1. But this effect isweaker than the effect of country 1’s large market size enhanced by its lower tax rate.

49

Economic Integration and Agglomeration of Multinational Production

are quite different in their market size.
These findings are summarized as follows (see Appendix B.7 for a proof).
Proposition 2.4 (Tax competition with transfer pricing).
Assume that β < β ≡ µL2 /σ. Consider tax competition in the core-periphery
situation with transfer pricing. The following holds:(i) (Country 1’s tax rate vs. country 2’s) Country 1’s tax rate is higher thancountry 2’s if country 1 is large enough: t∗1 > t∗2 if s1 > s∗1 , where s∗1 ∈ (1/2, 1)
is the solution of (σs1 −s2 )2 /s32 −µL(σ −1)2 /(βσ) = 0. Otherwise, country 1’s
equilibrium tax rate is equal to or lower than country 2’s: t∗1 ≤ t∗2 if s1 ≤ s∗1 .
(ii) (Tax rates with and without transfer pricing) Compared to the no-transferpricing case, country 1’s tax rate becomes low, whereas country 2’s tax ratet2 .
t1 ; t∗2 = b
remains unchanged: t∗1 < b(iii) (Sustain points with and without transfer pricing)Compared to the notransfer-pricing case, country 1 is likely to maintain the full agglomerationof production: φS < φbS .

The conclusion that profit shifting pushes taxes downward (Proposition 2.4 (ii)) can
be found in Haufler and Schjelderup (2000), who employ a framework of perfect competition with equal-sized countries.3233 Our result partly extends theirs to a settingwith imperfect competition and unequal-sized countries.
By contrast, Stöwhase (2005, 2013) obtain the opposite result: the presence of profit
shifting softens tax competition by increasing the equilibrium tax rates of both large
and small countries.34 Introducing profit shifting reduces MNEs’ tax payments andmakes them less sensitive to international tax differences; thus, tax competition becomes less severe. On the other, governments chase the shifted profits and intensify
tax competition. In Stöwhase (2005, 2013), the former effect dominates the latter,
32

Compared to the no-transfer-pricing case, the equilibrium tax difference always becomes small
as long as country 1’s tax rate is higher than country 2’s, i.e., 0 < t∗1 − t∗2 < bt1 − bt2 if s1 > s∗1 .
33

Agrawal and Wildasin (2019) also show that globalization, defined by a decline in relocation
costs, leads to tougher tax competition in a linear spatial model where agglomeration is exogenously
given.
34

Becker and Riedel (2013) also obtain the similar result, although MNEs in their model cannot
shift profits for tax-saving purposes.

50

Economic Integration and Agglomeration of Multinational Production

whereas the opposite is true in our model. These differing results are mainly because
our imperfectly competitive framework gives rise to the strategic purpose of transfer
pricing. The strategic effect strengthens profit-shifting incentives and increases the
tax-base sensitivity, leading to tougher tax competition.

2.5

Conclusion

Countries with lower corporate tax rates are expected to host more multinational production. Such a naive view may be challenged, however, because economic integration
marked by falling trade costs allows for profit shifting and may thus change the location incentive of multinationals. To investigate this, we have introduced transfer
pricing into a simple two-country model of trade and geography.
In the early stage of economic integration, the low-tax country attracts more production plants than the high-tax country. Further integration completely reverses thispattern and leads to the agglomeration of production in the high-tax country. With
low trade costs expanding intra-firm trade, transfer pricing can be used for strategic
motives as well as profit shifting. Shifting profits from the high-tax to the low-tax
country through low transfer prices makes distribution affiliates competitive, whereas
shifting profits the other way around does the opposite. MNEs thus prefer to locate
production in the high-tax country in the late stage of economic integration.
The similar result can be obtained in a tax-competition framework in which two countries differ in size. In addition, introducing profit shifting may make tax competition
fiercer by reducing the large country’s equilibrium tax rate. These findings may help
understand how economic integration shapes the distribution of multinational production and affects corporate tax policies.
Although our model is admittedly stylized, we believe that it is versatile enough toaccommodate several extensions. One interesting extension is to introduce tax havencountries. While we assume that MNEs shift profits between affiliates in two countries,
MNEs may do so using non-production affiliates in a third country with almost zerotaxes. The question is which non-tax haven country, the high-tax or the low-tax one,benefits from the presence of tax haven countries. Another extension is to examine
the impact of different international tax systems, such as separate accounting andformula apportionment. The system that prevents profit shifting effectively may differ
depending on the degree of economic integration. We leave these avenues for future51

Economic Integration and Agglomeration of Multinational Production

research.

52

Chapter 3
Tariff Elimination versus Tax
Avoidance: Free Trade
Agreements and Transfer Pricing
3.1

Introduction

For the past two decades, tax avoidance by multinational enterprises (MNEs) has
been a controversial topic as the world has become more globalized. According toestimates by the OECD, at least 4% of tax revenue in 2015 disappeared because of profit
shifting.1 One way to shift profits across countries is to manipulate the price of intrafirm trade (transfer price), which is known as abusive transfer pricing. Specifically,
because MNEs determine the prices of transactions between related companies, they
manipulate these prices to decrease profits in high-tax countries and increase profits inlow-tax countries. Some empirical research has provided evidence of transfer pricing
being used to save tax payments.2 As the taxes paid by firms are one of the main
sources of government revenues, tax avoidance by MNEs has become a serious issue,
as trade liberalization and the creation of global value chains increase intra-firm tradeand provide MNEs with greater opportunities to redistribute their tax base to low-tax
This chapter is based on joint work with Hiroshi Mukunoki (Mukunoki and Okoshi, 2019b).
1

See
www.oecd.org/tax/corporate-tax-remains-a-key-revenue-source-despitefalling-rates-worldwide.htm, accessed on November 14, 2019.
2

For instance, Swenson (2001), Clausing (2003), Cristea and Nguyen (2016), and Davies et al.
(2018) provided empirical evidence of transfer price manipulation. Blouin et al. (2018) found conflicting motives when MNEs use transfer pricing to lower corporate tax as well as tariff payments.

53

Tariff Elimination vs. Tax Avoidancecountries.
Our primary focus is on how such losses of tax revenues are linked to trade liberalization driven by trade agreements. Trade agreements among countries facilitate firms’
exports and imports; however, they also influence firms’ behaviors in other respects including transfer pricing and generate more complicated welfare effects. In particular,
the specific rules needed to implement trade agreements complicate the effects of tradeliberalization. Here, we focus on the rules of origin (ROO) of a free trade agreement(FTA), which require exporters in member countries making tariff-free exports to othermember countries to prove that the exported products originated within the FTA.3
To meet ROO, firms may change their strategies such as their input procurement. For
instance, Conconi et al. (2018) concluded that the ROO of the North-American Free
Trade Agreement (NAFTA) reduce imports of inputs from non-member countries,
suggesting that such rules cause input procurement to become inefficient. From theviewpoint of tax avoidance, this also implies that ROO can be an obstacle for MNEs toshift profits within the firm because they may need to consider whether their intra-firmtransactions satisfy the requirements of ROO.
One way to prove the origin is to satisfy a value-added (VA) criterion, which is closely
related to transfer price manipulation.4 The VA criterion requires firms to add asufficient value inside FTA member countries. Specifically, let p denote the export
price of the product and r denote the value of input materials, which are used perunit of final good production and do not originate in the FTA. Then, a VA criterion
typically requires that the VA ratio, (p−r)/p, is above the specified level. This methodof calculating the VA content is called the “transaction value method.” The value of
input materials depends on the transfer price if MNEs procure inputs from relatedcompanies outside FTA countries. Therefore, a VA criterion can be a constraint for
MNEs to engage in tax avoidance via abusive transfer pricing.
Although this possibility has been overlooked in the economic literature on transfer
3

Regional trade agreements in goods are classified into FTAs and customs unions. Unlike customs unions, member countries of an FTA can set their own tariff schedule against non-member
countries, which provides an opportunity for firms producing outside the FTA to save tariff payments by choosing as a transit country the member country whose tariff against non-member
countries is low and re-exporting from that country to other FTA member countries whose tariffs
against non-member countries are higher. See, for example, Stoyanov (2012) for evidence of firms’
incentive to transship a good through FTA members. To forestall firms from tariff avoidance, theWTO stipulates ROO.
4

Other ways to prove the origins of products include changing the tariff classification criterionand specific process criterion. Although the effects of these criteria are also important, this study
focuses only on the VA criterion.

54

Tariff Elimination vs. Tax Avoidance

pricing and that of FTA, it has been pointed out by some policy papers. For instance,
Eden (1998) examined the ROO of NAFTA and suggested that “. . . underinvoicing
parts coming outside North America and overinvoicing locally made parts would increase the North American content.” Falvey and Reed (1998) indicated that the VA
criterion “. . . allows room for [the] manipulation of prices as well as quantities, and may
generate additional incentives for transfer pricing by multinationals.” Reuter (2012)
also pointed out that “most rules of origin are on a percent-of-value basis. . . . By
overinvoicing the value added, the MNE can more easily meet a rule-of-origin test
and qualify for duty-free entry for its products into another country in the free tradearea.”5 Furthermore, the World Customs Organization suggests that one of the disadvantages of the VA criterion of ROO is possible exposure to transfer pricing.6 As
Estevadeordal and Suominen (2003) reported that 68 of the 87 FTAs they analyzed
employ a VA criterion at least in a particular product category, these statements tellus that investigating the role of ROO to restrict the abusive use of transfer pricing isimportant to understand the impact of FTAs on tax avoidance and welfare.
As countries have dealt with the tax avoidance problem, analyzing the anti-tax avoidance aspect of ROO is important for policymakers. In reality, different groups of policymakers, namely, customs and tax authorities, are responsible for designing trade
policies and regulations on transfer pricing. Therefore, the interaction between these
two authorities has been rare. According to WCO (2018), “. . . the WCO [World Customs Organization] is working with the OECD and World Bank Group to encourage
Customs and tax administrations to establish bilateral lines of communication in order to exchange knowledge, skills and data, where possible, which will help ensure thateach authority has the broadest picture of a MNE’s business, its compliance recordand can make informed decisions on the collect revenue liability.” Thus, as the number of FTAs and volume of intra-firm trade have increased, exploring the relationshipbetween transfer prices and ROO is an urgent issue.
Against this background, this study builds an international monopoly model to investigate an MNE’s response to an FTA formation with two new elements: transfer
pricing and ROO.
5

Some practitioners see the link as one factor to be considered and state that “if transfer pricing
changes the value of local content, then the ROO as applied may remove any FTA benefit thatwas previously available” (see https://www.expertguides.com/articles/oecd-beps-projectand-trade-new-perspectives/AREXIEUO, accessed on May 3, 2018).
6See
http://www.wcoomd.org/-/media/wco/public/global/pdf/topics/origin/overview/origin-handbook/rules-of-origin-handbook.pdf, accessed on May 3, 201855

Tariff Elimination vs. Tax Avoidance

3.1.1

Preview of the model and results

The MNE produces final goods within an FTA member country and exports the goods
to the other FTA member country. The MNE procures inputs from either an FTA
member country or a low-tax country outside the FTA. We assume input production isefficient in the outside country. Therefore, if the MNE procures inputs from a relatedcompany in a country outside the FTA, it can exploit efficient inputs as well as shiftprofits across countries by manipulating the transfer price.
In the absence of ROO, the MNE always prefers to produce inputs outside the FTA
by itself and engage in tax avoidance by setting a high transfer price. However, thepresence of ROO restricts the manipulation of the transfer price because a high transfer
price reduces the VA ratio of the final product inside the FTA. If the MNE procures
inputs inside the FTA, it always complies with the ROO and exports its productwithout paying a tariff, although it cannot save tax payments by transfer pricing. If
the MNE locates its upstream affiliate in a country outside the FTA, it either saves
corporate tax payments by setting a high transfer price or complies with the ROO
to avoid a tariff burden by setting a low transfer price. Thus, the MNE chooses oneof three options: (i) procuring inputs inside an FTA to comply with the ROO andeliminate tariffs, (ii) fully manipulating its transfer price to avoid tax payments at
the expense of the preferential tariff of the FTA, or (iii) adjusting its transfer priceto comply with the ROO to both eliminate tariffs and pursue partial tax avoidance.7
This model exhibits the MNE’s choice of “tariff elimination versus tax avoidance” via
its location choice of producing inputs and/or transfer price manipulation.
The third option, adjusting the transfer price to comply with the ROO, is the optimal
choice for the MNE when the stringency of the VA criterion is low and adjusting thetransfer price is less costly for the MNE. However, stricter ROO induce the MNE
to deviate more from the optimal abusive transfer price, which retains a part of the
MNE’s tax base in the high-tax country. Because of this inefficient tax avoidance, ahigher VA criterion changes the MNE’s optimal choice. When the tax differential ishuge and the MNE purchases inputs made in an FTA country, the MNE gives up the
FTA tariff but manipulates the transfer price to pursue tax avoidance. This is because
the tax avoidance motive is greater than the tariff avoidance motive.
7

Although the MNE uses its transfer price for ROO compliance, it can still shift profits fromone country to another to save tax payments when the VA requirement is less stringent and thetax gap is large. Nevertheless, the overall tax payments become larger because the transfer priceis suboptimal from the viewpoint of tax savings.

56

Tariff Elimination vs. Tax Avoidance

As ROO restrict the abusive use of transfer pricing by either a change in input procurement or an adjustment of the transfer price, tax revenues in a high-tax country
increase. Thus, the VA criterion works as an anti-tax avoidance policy. An interesting
result is that the direction of shifted profits can be from a low-tax country to a high-tax
country when the MNE adjusts the transfer price to meet the VA criterion. This is because the gain from efficient input production outside FTA countries becomes greater
as the tariff falls, and this outweighs the loss from more tax payments in a high-tax
country. This case is possible when the tax gap is small.
We also show that ROO transform an infeasible FTA into a feasible one. In theabsence of ROO, an FTA formation is harmful for member countries when the initial
tariff is small and the loss from the disappearance of tariff revenues exceeds consumers’
gains. In the presence of ROO, FTA countries can collect tax revenues from the MNE.
Although consumers’ gains from the FTA are smaller than those without ROO, tax
revenues from the MNE can cover the smaller consumers’ gains and the loss of tariff
revenues. Our results present a new role of ROO in preventing abusive transfer pricing
and making the FTA an welfare-improving one for member countries.
However, the country makes little tax revenue from the MNE when the absolute levelof the corporate tax in the high-tax country is low. In this case, ROO can deteriorate
total welfare inside FTA countries and make an initially feasible FTA infeasible.

3.1.2

Relationship to the literature

The welfare effects of FTAs with ROO have previously been analyzed, but such studies focus on intermediate goods markets.8 Krishna and Krueger (1995) showed that
ROO may work as a hidden protection against input suppliers outside the FTA. Ju
and Krishna (2005) showed that ROO increase the price of FTA-made inputs and reduce total output if they are not so stringent such that all firms comply with the ROO,
whereas they have the opposite effects if ROO are sufficiently stringent such that somefirms choose not to comply with them. In Ju and Krishna (2005), however, the output price is fixed and they did not consider how ROO affect consumers. Demidova
and Krishna (2008) extended Ju and Krishna (2005) to include the productivity heterogeneity of final good producers and showed that productivity sorting ensures the8More broadly, many studies have investigated the welfare effects of regional trade agreements
both theoretically and empirically. See Freund and Ornelas (2010) for a review of the literatureon regional trade agreements.

57

Tariff Elimination vs. Tax Avoidance

negative relationship between the stringency of ROO and demand for FTA-made inputs (i.e., wages). Ishikawa et al. (2007) focused on final good markets and showedthat ROO have a role to segment markets within the FTA and that both inside andoutside firms producing final goods may benefit from ROO at the cost of consumers.
Mukunoki (2017) showed that an FTA with ROO may harm consumers if it changes
outside firms’ location decisions. None of these papers, however, have consideredtransfer price manipulation to meet ROO. Mukunoki and Okoshi (2019a) investigateda firm’s export price manipulation to comply with ROO, particularly how an MNE’stransfer price manipulation affects inputs imported from outside FTA. Furthermore,
Felbermayr et al. (2019) suggested that there is little rationale for ROO because tariff
circumvention is not profitable for 86% of bilateral trade because of the small differences in external tariffs and non-negligible transport costs. This study thus provides
a new rationale for ROO from the viewpoint of tax avoidance by an MNE.
Specifically, this study examines the connection between transfer pricing and trade
policy. Some studies have investigated the relationship between transfer pricing andtrade barriers including tariffs. Horst (1971) showed that the optimal transfer priceis influenced by not only tax differentials but also tariffs. Schjelderup and Sørgard(1997) showed that if the importing country imposes an ad valorem tariff on inputs, an
MNE can save tariff payments by reducing its export price.9 Then, the optimal transfer
price is influenced by both corporate tax avoidance and tariff avoidance. Kant (1988b)
regarded the transfer price as a tool to repatriate profits when a foreign subsidiary is
not fully owned by the parent firm. With the partial ownership of the foreign affiliate,
the profit shifted from the home to the foreign country is partly distributed to otherowners. The study found that even when the tax rate in the home country is higher
than the tax rate in the host country, an MNE has an incentive to remit all the profit
earned in the low-tax host country if both the tariff and the proportion of the MNE’s
ownership shares in the foreign affiliate are low. This research, however, did not
explicitly consider trade liberalization by forming an FTA, let alone the effects of
ROO on transfer prices.
The presented model also contributes to the literature on transfer pricing policies since
MNEs have been accused of tax avoidance activities and how to regulate transfer prices
has been a central issue in policy debates. Several studies have examined the impactsof policies on transfer price manipulation. Elitzur and Mintz (1996) investigated9
Given the multiple roles of transfer prices, recent work has examined MNEs’ optimal strategies(Hyde and Choe, 2005; Nielsen et al., 2008; Dürr and Göx, 2011). None of them, however, linktransfer pricing and ROO.

58

Tariff Elimination vs. Tax Avoidance

the determinants of transfer prices when tax authorities use the cost-plus method
to infer the appropriate transfer price. Nielsen et al. (2003) compared the use oftransfer prices under two international tax systems, namely, separating account andformula apportionment.10 Choi et al. (2018b) examined the impact of the arm’s lengthprinciple, under which MNEs should set the same price for intra-firm transactions as
for the same transaction conducted between independent firms.11 As their focus wason direct regulation on transfer pricing, transfer pricing for meeting ROO has been
overlooked in the literature.
The rest of the paper is organized as follows. In Section 3.2, we set up the model andderive an equilibrium without ROO. Sections 3.3 and 3.4 investigate the effect of an
FTA with ROO. Section 3.5 discusses the robustness of the main results by relaxing
some key assumptions. The last section concludes.

3.2

Model

There are three countries, H, F , and O; countries H and F are potential FTA members.
Fig. 3.1 illustrates the model. A single firm, an MNE, produces a final good using
inputs and sells it in country F .12 For simplicity, the benchmark model ignores theoutput market in country H and focuses only on the consumers in country F .13 The
representative consumer’s utility in country F is given by U = ax − x2 /2, where x
is the consumption of the final good. By utility maximization, the inverse demand
function becomes p = a − x.
One of the two member countries, country H, has a location advantage for final good
production because of low factor prices, a large pool of skilled labor, and so on. There10

The traditional international corporate tax system is the separating account system thatcomputes MNEs’ national tax base by regarding intra-firm transactions as inter-firm transactions.
On the contrary, under the formula apportionment system, MNEs’ tax payments to one country
depend on their consolidated tax base and the proportion of activity operated in the country. See
more details in Chapter XVI, Article 86 of European Commission (2011).
11

Bauer and Langenmayr (2013), Choe and Matsushima (2013), and Kato and Okoshi (2019b)
also investigated the effect of the arm’s length principle on the input procurement decision, tacit
collusion, and input production location, respectively.
12

If we consider local firms in the FTA members and oligopoly in the final good market, thefundamental properties of our results remain unchanged, although the analysis becomes more
complicated. See Mukunoki and Okoshi (2019b) for an oligopoly version of the model.
13This assumption does not qualitatively change our main results as long as the two markets
are segmented in the sense that the MNE can make a separate decision in each market.

59

Tariff Elimination vs. Tax Avoidance

Figure 3.1: Model

fore, country H always hosts a downstream affiliate of the MNE (firm MH ). The
MNE’s headquarters (firm MO ) is located in country O.14 MO may also produce an
input for final good production, as explained below.
Firm MO has already operated in country O and makes positive profits, π, that areexogenously given. To produce the final product, firm MH needs to procure one unitof inputs for the production of one unit of final products.15 Firm MH can procure theinput from a perfectly competitive input market inside FTA countries, which supply
the input at the price of w. Alternatively, firm MO located in country O can produce
the input at the cost of w − ∆. We assume ∆ > 0 and ∆ ∈ [0, w]. Therefore, input
production in country O is more efficient than that in country H. This implies that the
self-production of the input in country O gives the MNE not only a lower input cost
but also a tax-saving opportunity via the manipulation of the transfer price, which is
14This type of foreign direct investment (FDI) is known as export platform FDI, where the
FDI firm exports from the host country to other countries. For example, see Tekin-Koru andWaldkirch (2010) for Mexican evidence of its increasing role as a host of export platform FDI.
Tintelnot (2017) showed the share of output exported to countries outside the host country by
U.S. MNEs. For instance, the share of exports located in Belgium was 63% in 2004.
15

We can consider a more general situation in which the MNE uses a continuum of inputs anddecides the extent to which it uses the intra-firm inputs for final good production. As explained in
Section 3.5.2, this modification does not change the qualitative results of the benchmark model.

60

Tariff Elimination vs. Tax Avoidance

denoted by r. We assume away transfer pricing that realizes negative reported profits
because tax authorities can audit tax avoidance.
Without the FTA, country F imposes a specific tariff, τ , on imports of the final good.
We consider the case in which τ < a − w + ∆ holds to rule out negative output inthe equilibrium. In addition, the governments in countries O and H respectively levyt and T as a corporate tax on reported profits.1617 To focus on the impact of FTA
formation on the final good market, tariffs on inputs are assumed away. Hereafter, we
focus on the case in which T ≥ t holds.18

3.2.1

The equilibrium without ROO

Let us first derive the market equilibrium without ROO in each scheme of the MNE
choice. In the inshoring scheme, denoted as scheme I, the MNE purchases the input
from local producers. Firm MH earns profits under the cost of inputs w and a tax rate
T . In the offshoring scheme, denoted as scheme O, the MNE’s headquarters in countryO, firm MO , produces the input at the production cost of w − ∆. Firm MO sells the
input to firm MH at the input price denoted by r. Thus, r is the transfer price of the
MNE.
The post-tax profits under the inshoring scheme are given by
2
a − w − λτ+(1 − t) |{z}π ,
Π = (1 − T )
2
I
|
{z
}
πO
I



(3.1)

I
πH

where λ is a state variable that takes zero if the MNE qualifies for an FTA tariff rate andunity otherwise. πis represents the reported profits of firm Mi under scheme s ∈ [I, O].
16

We use the terms “tax rate” and “tax revenue” to represent the corporate tax rate andcorporate tax revenue, respectively. Here, tax rate and tax revenue are distinguished from tariff
rate and tariff revenue.
17

In this model, we postulate that the governments in countries O and H adopt a territorial tax
system instead of a worldwide one. After the United States moved from a worldwide tax system toa territorial tax system in xxxx, most OECD countries have since adopted a territorial tax system.
18

This situation is consistent with the real-world observation. For instance, Mexico and Belgium
have higher corporate taxes than other countries and these countries are major host countries ofexport platform FDI. See also footnote 14.

61

Tariff Elimination vs. Tax Avoidance

In the offshoring scheme, the MNE maximizes
ΠO = (1 − T ) (p − r − λτ )x +(1 − t) [{r − (w − ∆)}x + π]
{z
}
{z
}
|
|
O
πH

O
πO

O
O
O
with respect to r and x, subject to πH≥ 0 and πO≥ 0. Since ∂Π= (T − t)x > 0∂ralways holds, the MNE is willing to set the optimal transfer price as high as possible.
Therefore, the optimal abusive transfer price is set at the level that transfers all the
profits earned in a high-tax country to a low-tax country, r = p − λτ .19 Thus, thepost-tax profits under the offshoring scheme are given byO

Π = (1 − t)a − w + ∆ − λτ22
+ (1 − t)π.

(3.2)

Irrespective of the formation of an FTA, the MNE always prefers the offshoring scheme
to the inshoring scheme asOIΠ − Π = (1 − t)a − w + ∆ − λτ22− (1 − T )a − w − λτ
2

2
≥0

(3.3)

holds. Intuitively, procurement from its upstream affiliate provides the MNE withboth efficient input production and the opportunity to shift profits.
For notational convenience, we use the superscript “∗” for the variables in the pre-FTA
case and “ b ” for the variables for post-FTA without ROO hereafter.

3.2.2

The welfare effects of FTA formation without ROO

To explore the welfare effects of FTAs, we focus on the total welfare of FTA countries.
If the redistribution of gains from the FTA is possible between member countries, theFTA is feasible if total welfare increases. The total welfare of FTA countries is the sumof the consumer surplus in country F (CS s ), tax revenues of country H paid by thes
MNE (T RH), and tariff revenues in country F (T RFs ):s
W s = CS s + T RH
+ T RFs =(xs )2s+ T πH+ λτ xs .
2

(3.4)

19
We assume there is no cost of shifting profits across countries. This is a conventional wayof determining the optimal transfer price in the literature, when cost-for-profit shifting is absent.
We relax this assumption by introducing a standard convex concealment cost in Section 3.5.3.

62

Tariff Elimination vs. Tax Avoidance

Total welfare does not include the post-tax profits of the MNE because it is owned byresidents outside the FTA.
Since member countries cannot collect tax revenues when the MNE chooses offshoring,
total welfare under offshoring becomesf − W O∗ = CS
c − CS O∗ − T RO∗
W
F=

2(a − w + ∆)−2(a − w + ∆) + 3τ
R 0 ⇐⇒ τ R
≡ τW.
8
3

(3.5)

As equation (3.5) shows, an FTA without ROO generates a trade-off between an
increase in the consumer surplus and disappearance of tariff revenues. When theinitial tariff rate is high, the consumers’ gains exceed tariff revenues and the FTA
formation increases the total welfare of member countries. This section concludes
with the following proposition.
Proposition 3.1 In the absence of ROO, the MNE always procures inputs fromits upstream affiliate outside FTA countries. Forming an FTA benefits member
countries when the initial tariff rate is high (τ > τ W ) and hurts them when it is low(τ < τ W ).

3.3

Equilibrium with ROO

In this section, we consider FTA formation with ROO. As stated in the Introduction,
our focus is on the VA criterion of ROO. Specifically, a VA criterion is applied to exportsof the final good in the FTA. For notational convenience, we use “ e ” as a circumflex
for the variables in the presence of ROO.

3.3.1

The MNE’s decisions in each scheme

After an FTA is formed, firm MH needs to meet the VA criterion to be eligible for theelimination of τ . Specifically, ROO require firm MH to add a proportion of at leastα(∈ [0, 1]) of the values of exported goods within the FTA. There are three cases,
which we explain sequentially below.
If firm MH chooses the offshoring of input production and sets an abusive transfer price,
rb = p, the VA ratio is always zero, which fails to meet the requirement of the ROO.
63

Tariff Elimination vs. Tax AvoidanceHence, the final good exports of the MNE incur the tariff, τ , even after the formation of
the FTA. We call this case scheme N (non-compliance).20 The equilibrium outcomesof this scheme are obtained by setting λ = 1 in equations (3.2) and (3.4), as well as in
the other corresponding welfare components.
For firm MH to utilize the FTA tariff, it has to comply with the ROO by either (i)inshoring the input procurement (scheme I) or (ii) setting r such thatpO − r
α≡
≥α
pO

(3.6)

is satisfied. We call this case scheme B (binding ROO). It is apparent that (pO − r)/pO
is decreasing in r and thereby the VA ratio, α, is more likely to exceed α as the MNE
O
sets a lower r. Remember that ∂Π> 0 holds. Then, the optimal transfer price is set∂rsuch that it binds equation (3.6), which is calculated as
reB = (1 − α)p.

(3.7)

As the ROO become stricter, the MNE needs to add more VA inside the FTA and thus
the optimal transfer price must decrease by αp, which is regarded as the adjustment
factor for meeting the ROO. We can easily see that reB is decreasing in α and is equivalent
to rb with α = 0.
Given the optimal transfer price, the post-tax profits of the MNE are given byΠB = (1 − T ) (p − reB )xB +(1 − t) [{erB − (w − ∆)}xB + π]
| {z }
|
{z
}
B
πH

B
πO

= {1 − t − α(T − t)}(p − cM )xB + (1 − t)π,(3.8)(1−t)(w−∆)
where cM = {1−t−α(T(≥ w−∆) represents the “perceived marginal cost” of produc−t)}
ing the final good.21 The perceived marginal cost is higher than the physical marginal
cost, w − ∆, as long as α is positive and T > t. Given the level of t, both an increasein the stringency of the ROO (α) and that in the tax differential (T − t) increase the20
Some empirical evidence shows that not all firms use FTA tariffs because of the existenceof ROO, which means the impacts of FTA formation are heterogeneous across firms. See, forexample, Takahashi and Urata (2010) and Hayakawa et al. (2013).
21

The terminology “perceived marginal cost” is often used in the analysis of vertically relatedindustries in the context of industrial organization. See Choi et al. (2018b) for an application ofthis terminology in the tax avoidance literature.

64

Tariff Elimination vs. Tax Avoidance

perceived marginal cost.
We can interpret the perceived marginal cost as follows. Without any ROO, the MNE
shifts all the profits to a low-tax country by setting re = p. From re = p, the introductionof the ROO decreases the transfer price by as much as αp and increases the per-unit tax
payments of the MNE by as much as α(T −t)p > 0. This means that the ROO decrease
the MNE’s post-tax profits of selling the final good and makes it less aggressive in the
product market under scheme B. The lower incentive to sell the final good is reflectedin the perceived marginal cost.
The output decision of the MNE is made with cM instead of w − ∆, generating thefollowing equilibrium profit:2e B = {(1 − t)(a − w + ∆) − α(T − t)a} + (1 − t)π.
Π
4{1 − t − α(T − t)}(3.9)

The post-tax profits under scheme B are a decreasing function of α because an increasein α induces the MNE to set a transfer price that deviates more from the level at which
it avoids tax payments in the high-tax country.

3.3.2

The MNE’s choice of scheme

Among the three possible schemes (I, N , and B), the MNE chooses the one that maxe I with Π
e N . Since both profits are independent
imizes its profits. Let us first compare Πof the VA threshold, α, the tariff level and tax differential determine which profit islarger. The MNE faces a trade-off between tax avoidance and tariff avoidance. If thetax differential is large, the MNE prefers scheme N to scheme I because of the stronger
incentive to avoid tax payments in country H. If the tax differential is small, scheme
I is more preferable for the MNE. Thus, there exists a unique threshold of T , Te, sucheI = Π
e N holds. As a larger tariff discourages the MNE from choosing scheme N ,that Π
∂ Te> 0 holds.22∂τLet us next compare the profits in scheme B with those in schemes N and I. SinceeB = Π
b holds at α = 0, which is larger than Πe N and Π
e I , and Πe B is decreasing in α, weΠ
can derive a unique threshold, αN (resp. αI ), above which the MNE prefers scheme
N (resp. scheme I) to scheme B. Intuitively, under less strict ROO, the MNE prefers2Formally, the threshold is calculated as Te = 1 − (1 − t) a−w+∆−τ< 1. We can confirma−wethat T is greater than t if and only if ∆ < τ holds. To secure the existence of the equilibrium with
scheme I, we additionally assume ∆ < τ hereafter.
22

65

Tariff Elimination vs. Tax Avoidance

Figure 3.2: The equilibrium MNE’s choice

scheme B to schemes N and I because adjusting the transfer price to comply withthose ROO becomes less costly as the VA criterion becomes less stringent.23 In otherwords, the MNE’s gains from tariff elimination by adjusting the transfer price become
smaller as the FTA is attached to more stringent ROO.
Putting the above comparisons together, we characterize the equilibrium outcomes asfollows, which is illustrated in Figure 3.2.
Proposition 3.2 After an FTA with ROO is formed, the MNE chooses (i) inshoring if T ≤ Te and α > αI hold, (ii) offshoring and its exports incur a tariff if
Te < T and α > αN hold, and (iii) offshoring and it adjusts its transfer price tomeet The ROO if α ≤ min{αI , αN } holds.
Proof. See Appendix C.1.
23

Here, the MNE meets the ROO by changing its transaction input price. An offshoring firm
may also adjust its export price p to meet the VA criterion. This possibility is analyzed by
Mukunoki and Okoshi (2019a).

66

Tariff Elimination vs. Tax AvoidanceRemember that the MNE always chooses the self-production of inputs before an FTA
is formed. After an FTA is formed, this proposition suggests that the MNE maychange its input procurement from self-production to the purchase of local inputs,
even though the production cost is higher. As Conconi et al. (2018) showed, ROO
lower the likelihood of input procurement from non-FTA countries. This “input trade
diversion” corresponds to the area of scheme I in Figure 3.2.
Further, as Takahashi and Urata (2010) and Hayakawa et al. (2013) pointed out, somefirms may not utilize FTA tariffs because of the burden of the ROO. This possibility
corresponds to the areas Te ≤ T and αN ≤ α in Figure 3.2. A standard explanationof the non-use of an FTA is that export firms must incur additional costs to meet
the ROO. Our model suggests another burden of meeting the ROO: it increases tax
payments by restricting the MNE’s freedom to adjust its transfer price.

3.4

Welfare effects with ROO

In this section, we explore the welfare effect of the FTA with ROO. As the FTA has
no effect if the post-FTA equilibrium scheme is scheme N , we investigate the welfare
effects in schemes I and B. Hereafter, we discuss the effect on each component ofwelfare and the total welfare of member countries. We also discuss the optimal levelof the ROO that maximizes members’ joint welfare.

3.4.1

Consumer surplus

Let us begin with the effect on consumers. Under scheme I, FTA formation increases
the marginal cost of production from w − ∆ to w because the MNE changes thelocation of its input procurement. However, the FTA formation also eliminates thetariff, τ , faced by the MNE. We can easily confirm that the MNE chooses scheme I
only if ∆ < τ holds (see footnote 22). Therefore, the FTA always decreases the MNE’s
marginal cost of exports whenever scheme I becomes the equilibrium outcome and it
always increases the exports of the MNE.24
Under scheme B, the MNE also faces a higher marginal cost because the perceived
marginal cost is higher than w − ∆. As in scheme I, however, the MNE chooses
24

Specifically, the change in exports becomes ∆xI∗ = x
eI − xO∗ = (τ − ∆)/2, which is positiveif ∆ < τ holds.

67

Tariff Elimination vs. Tax Avoidance

scheme B only if the cost reduction from tariff elimination dominates the increase in
the marginal cost of production (see the Appendix for details). Therefore, the FTA
always increases the exports of the MNE whenever scheme B becomes the equilibriumoutcome. Putting the two cases together, we have the following proposition.
Proposition 3.3 An FTA formation with ROO always benefits consumers if the
MNE utilizes an FTA tariff and has no effect on consumers otherwise. The presenceof ROO decreases consumers’ gains.
Proof. See Appendix C.2.
Although FTA formation is beneficial for consumers, ROO decrease consumers’ gains
because of the increase in the production cost due to the inefficient procurement of
inputs (scheme I) or increase in the perceived marginal cost (scheme B). Hence,
ROO have no effect on consumers’ gains in scheme B because the tariff is eliminatedand the MNE continues to produce the efficient input by itself. However, they actually diminish the increase in exports and consumers’ gains because giving up fulltax avoidance increases the MNE’s perceived marginal cost. We should recognize thisexport-decreasing effect of ROO driven by the change in the MNE’s transfer pricing.

3.4.2

Tax revenue

When the MNE engages in transfer pricing, an FTA with ROO enables member countries to recover some of the MNE’s tax base. When the MNE procures the input fromthe local input market (scheme I), there are no opportunities to shift profits and all
the tax base is retained in country H. When the MNE adjusts its transfer price tomeet the VA criterion of ROO, a part of the tax base is retained in country H becauseof the limited use of abusive transfer pricing.
Notably, we can confirm that ROO reverse the direction of profit shifting across countries. To see this point more clearly, it is useful to decompose the optimal transfer
prices into the “tax avoidance motive” and “tariff elimination motive.” In the preFTA equilibrium, the optimal transfer price is always above the marginal cost of input
production:a − w + ∆ − λτ.
(3.10)
r =w−∆+2|{z}
Tax avoidance motive

68

Tariff Elimination vs. Tax Avoidance

The second term of equation (3.10) represents the tax avoidance motive, which makes
the transfer price as high as making the profit of the downstream affiliate of the MNE
zero.
In scheme B of the post-FTA equilibrium, the tariff elimination motive counters thetax avoidance motive and the optimal transfer price is expressed as
reB = w − ∆ +

a−w+∆
2
| {z
}

Tax avoidance motive−α{(1 − t)a + (1 − T )(w − ∆) − α(T − t)a}.
2{1 − t − (T − t)α}|{z}
Tariff eliminative motive(3.11)The third term of equation (3.11) captures the tariff elimination motive, which is zeroat α = 0 and increasing in α. If the Tariff elimination motive is sufficiently large
such that reB is lower than w − ∆, the profits of the MNE are shifted from the low-tax
country to the high-tax country, which is in sharp contrast to the conventional effectof transfer pricing.
Therefore, the direction of profit shifting relies on the size of the two motives. Indeed,
we can derive a unique threshold of α, αr , such that reB < w − ∆ holds and profits shift
from a high-tax country to a low-tax country if α > αr holds. Figure 3.3 illustrates thereversal of profit shifting.25 The dotted line represents αr and the dotted area in the
figure is the case in which profits flow from a low-tax country to a high-tax country.
The following proposition summarizes the effect on tax revenue.
Proposition 3.4 An FTA formation with ROO reduces the profits of the MNE
shifted from a high-tax country to a low-tax country if the MNE utilizes an FTA
tariff. The MNE rather shifts its profits from a low-tax country to a high-tax country
if tariff elimination motive of transfer pricing is sufficiently large.
Proof. See Appendix C.3.
This proposition sheds new light on the role of ROO that has been overlooked in policy
debates. As Proposition 3.2 shows, an FTA formation with ROO can induce the MNE
to give up the self-production of inputs as well as the opportunity to avoid tax.26 This
result suggests that a VA criterion provides another channel to keep MNEs away from25

We use the following parameters for the figure: a = 1, w = 1/2, ∆ = 1/32, τ = 1/4, andt = 1/10.
26

This effect would be observed in the other two criteria of ROO, that is, the tariff classification
criterion and specific process criterion.

69

Tariff Elimination vs. Tax Avoidance

Figure 3.3: The direction of the MNE’s shifted profits

tax avoidance by restricting the extent of abusive transfer pricing. Thus, although themain purpose of imposing ROO is to prevent trade circumvention, ROO also play arole in preventing tax avoidance.
Furthermore, Proposition 3.4 provides a new empirical implication for estimatingtransfer pricing. As our model shows, the optimal transfer price depends on thestringency of the VA criterion, suggesting that the observed transfer prices can reflect
not only the tax avoidance motive but also the tariff elimination motive.27

3.4.3

Total welfare of member countries

Let us discuss how the presence of ROO changes the effect of FTA formation on the
total welfare of member countries. Remember that Proposition 3.1 suggests that an
FTA without ROO is feasible in the sense that it increases the total welfare of member
countries if and only if the initial tariff is sufficiently large (τ > τ W ).
As seen in this section, ROO reduce consumers’ gains from an FTA formation incountry F . However, ROO also help generate tax revenues in country H if the MNE
27

Although there are other ways of shifting profits such as using internal debt and making royalty payments, the tariff elimination motive behind the transfer pricing of tangible assets remains.

70

Tariff Elimination vs. Tax Avoidancechanges its input procurement or adjusts its transfer price to comply with the ROO.
This indicates that ROO can make an infeasible FTA without ROO feasible and they
can also make an initially feasible FTA without ROO infeasible.
Let us first discuss the welfare effect of an FTA formation in schemes I and B. In thecase of scheme I, total welfare is sum of the consumer surplus and tax revenue from
the MNE:22
f I = (a − w) + T (a − w) .
(3.12)
W
8
4
f I with W O∗ , we obtain the threshold of T , TeW , such that W
f I = W O∗
By comparing W
holds at T = TeW , which is given by2(a − w)(∆ + τ ) − (τ − ∆)(∆ + 3τ )TeW =.
2(a − w)2

(3.13)

f I > W O∗ for T > TeW and W
f I > W O∗ holds for T < TeW . An FTA withWe have W
ROO improves total welfare when the corporate tax in country H is sufficiently large
and the tariff revenue gains from the ROO dominate the loss of the consumer surplus.
Total welfare under scheme B also includes tax revenue from the MNE, given by2

f B = {(1 − t)(a − w + ∆) − αa(T − t)}W8{1 − t − α(T − t)}2
{(1 − t)(a + w − ∆) − αa(T − t)}{(1 − t)(a − w + ∆) − αa(T − t)}+ Tα.
4{1 − t − α(T − t)}2
(3.14)fB =At α = 0, regime B is identical to the post-FTA equilibrium without ROO (Wc ). Starting from α = 0, an increase in the stringency of ROO has two opposite
W
f B . On the one hand, a stricter VA requirement reduces the transfer
effects on W
price and thereby increases the tax revenue that country H collects. On the other
hand, it diminishes consumers’ gains from an FTA formation by increasing the MNE’s
perceived marginal cost and reducing the amount of exports. There is thus an inverted
f B and α. Specifically, the former effect dominates
U-shaped relationship between W
fB
the latter and ∂ W> 0 holds when α is small, whereas the latter effect dominates the∂αfB

former and ∂ W< 0 holds when α is large.28∂α
28

Let αx be the threshold of α such that the amount of exports is constant before and after
2 fB
fB
fB
W
W
x
the FTA is formed, x
eB = xO∗ . Since we have ∂ ∂α|α=0 > 0, ∂ ∂α
< 0, and W
2∂α |α=α < 0, therefBWxexists a unique threshold, αW= 0 holds.
0 ∈ [0, α ), such that ∂α |α=αW
071

Tariff Elimination vs. Tax Avoidance

Figure 3.4: ROO and the feasibility of an FTA formation

Because of the increased tax revenue, ROO can make an initially infeasible FTA feasible. Suppose τ < τW , with which an FTA without ROO reduces total welfare (seeProposition 3.1). Since stricter ROO improve post-FTA welfare in scheme B, postFTA welfare can be larger than pre-FTA welfare even with τ < τW . Specifically, we canf B = W O∗ holds.29 When αW < min[αI , αN ]specify a threshold of α, αW , at which W
holds, an FTA formation improves the total welfare of member countries in scheme
B for α > αW .30 The left figure of Figure 3.4 provides a numerical example that
αW < min[αI , αN ] holds.31 In the shaded area in scheme B, an FTA formation improves total welfare. Further, an FTA formation can improve total welfare in scheme
I. As shown above, an FTA formation improves total welfare in scheme I if T > TeW
holds. Therefore, ROO can transform an infeasible FTA into a feasible one because
the increased tax revenue from the MNE compensates for the tariff revenue loss.
Proposition 3.5 When τ < τ W holds and an FTA formation is infeasible without
29

At α = αx , an FTA formation does not change the MNE’s exports of the final good or the
consumer surplus. We can simplify the change in total welfare toof tax revenuenthe sum

 and
o the
T (1−t)a+w−∆+τ
B
x
B
O∗
O∗
f
loss of tariff revenue, W −WO∗ |α=αx = T α πeH −τ x = τ x
T −t2(w−∆+τ ) − 1 > 0.
f B = W O∗ .
This means that a threshold αW ∈ [0, αx ) exists that satisfies W
30
f B > W O∗ at α =f B is an inverted U-shaped curve in α, we always have W
Although W
I
N
I
N
x
min[α , α ] because min[α , α ] < α holds. This means that an FTA formation always improves
total welfare for αW < α ≤ min[αI , αN ].
31

The parameters are set as follows: a = 1, ∆ = 1/32, and τ = 1/4. The left figure is drawn
with w = 1/2 and t = 1/10, whereas the right figure uses w = 2/3 and t = 0.

72

Tariff Elimination vs. Tax Avoidance

ROO, an FTA formation with ROO improves the total welfare of member countries
if the MNE adjusts its transfer price to comply with the ROO and αW < α <min[αI , αN ] hold or if the MNE purchases local inputs and T < TeW holds. In thesecases, ROO make an initially infeasible FTA feasible.
However, ROO may negatively affect total welfare and make an initially feasible FTA
formation infeasible. The right figure of Figure 4 corresponds to the case with τ > τ W ,where the formation of an FTA without ROO is beneficial for member countries. The
dotted curve in scheme B represents αr , above which we see the reversal of profit
shifting discussed in the previous section. The figure shows that an FTA stays feasible
even if we take ROO into account, so that ROO increase the gains of forming an FTA
fB> 0|α=0 holds. If both α and T areunder scheme B in the equilibrium because ∂ W∂αhigh so that scheme N is the equilibrium outcome, there is no welfare change froman FTA formation. Moreover, if the equilibrium outcome is scheme I and T ≤ TeW
holds, the gains from increased tax revenue are smaller than the loss from the lower
consumer surplus. In this case, ROO transform a welfare-improving FTA formation
into a welfare-reducing one.
The next proposition summarizes these results.
Proposition 3.6 When τ ≥ τ W holds and an FTA formation is feasible without
ROO, an FTA formation with ROO deteriorates total welfare if it induces the MNE
to purchase local inputs to meet the ROO and T ≤ TeW holds. In this case, ROO
can make an initially feasible FTA infeasible.
From Propositions 3.3 and 3.4, we know that an FTA with ROO benefits consumers
and makes profit shifting difficult. Proposition 3.5 suggests that ROO with a certain
level of α can be necessary for FTA formation. A formation of an FTA with ROO works
as an effective policy not only to promote trade liberalization but also to prevent the
MNE from engaging in tax avoidance, and the latter effect is important to secure
welfare-improving FTA formation. Proposition 3.6 suggests, however, that ROO canalso deter the formation of an FTA if it is feasible without ROO.

3.5

Discussion

Our benchmark analysis provided a set of new results not thus far explored in the extant
literature. In this section, we discuss an extension of the model and the robustness of73

Tariff Elimination vs. Tax Avoidance

Figure 3.5: The welfare of member countries with the optimal level of α

the main results by relaxing some of the assumptions made in the benchmark model.

3.5.1

The optimal VA requirement

We showed that the MNE’s choice and welfare effect of an FTA critically depend on
the level of α. Here, we discuss how member countries choose α if it is endogenously
determined.
fB|> 0 holds, the optimal level of the VA ratio, which is denoted by αOpt , isAs ∂ W∂α α=0always positive. Under scheme B, total welfare is an inverted U-shaped curve in α, and
fB
∂W
W
I
N
it is maximized at α = αW
0 at which ∂α = 0 is satisfied. If α0 < min[α , α ] holds,
WIN
and the welfare-maximizing level within scheme B becomes αW
0 . If α0 ≥ min[α , α ]holds, however, it becomes the upper bound of α in scheme B, min[αI , αN ].
A further increase in α changes the equilibrium scheme from scheme B to either scheme
N or scheme I. The full tax avoidance in scheme N means that total welfare isindependent of the corporate tax in country H. Total welfare in scheme I, however, isincreasing in T because it generates more tax revenues.

74

Tariff Elimination vs. Tax Avoidance

Figure 3.5 illustrates a numerical example that shows maximized total welfare in eachscheme with optimal VA criterion, when τ < τ W holds.32 The solid curve is total
welfare in scheme B given that α is optimally set to maximize total welfare. The two
dotted lines illustrate total welfare in schemes I and N . In this example, we can see afB = WfI .
threshold of T , denoted as Teα , which satisfies W
If T < Teα holds, Scheme B realizes the highest total welfare. In this case, the optimal
VA criterion is the highest one that realizes scheme B, αOpt = min[1, αI ]. If Teα < T <Te holds, Scheme I brings the highest total welfare. In this range of T , the optimal
α is any α that induces the MNE to purchase local inputs within FTA countries, orαOpt ∈ (αI , 1]. If T > Te holds, scheme B again realizes the highest total welfare.
However, the optimal level is less than the highest one that realizes Scheme B, and itNis given by αOpt = αW
0 < α . This is easily understood by considering the perceived
marginal costs. Remember the perceived marginal cost rises as the tax gap widens
or the VA criterion becomes stricter. A higher perceived marginal cost decreases theamount of exports, x
eB , as the tax gap widens or the VA criterion becomes stricter.
Since the degree of the decrease in exports and its welfare cost are small when the tax
gap is small, the increase in tax revenues dominates when T < Teα holds. If the tax
gap is large, however, the optimal level of the VA requirement in scheme B balancesout the gains from the increased tax revenues and losses from the increased perceived
marginal cost.
This numerical analysis suggests that to determine the stringency of ROO, policymakers should take into account its effects on tax revenues. In reality, VA thresholds
are usually set between 30% and 60%.33 Our model predicts that the VA criterion of
ROO may play a positive role in preventing tax avoidance by MNEs and secure welfare
gains for member countries when the host countries of export platform MNEs impose
high tax rates. This is actually the case with NAFTA (now USMCA), where Mexico
attracts FDI and levies a high corporate tax. Moreover, as different VA thresholds are
imposed on different products, the design of a VA criterion or choice of ROO criteria
should differ across the products MNEs actively produce.
32
This figure is drawn with the following parameters: a = 1, w = 1/2, ∆ = 1/32, τ = 1/4, andt = 1/10.
33

See http://www.oecd.org/officialdocuments/publicdisplaydocumentpdf/?cote=TAD/
TC/WP(2015)28/FINAL&docLanguage=En.

75

Tariff Elimination vs. Tax Avoidance

3.5.2

Partial procurement of inputs

We have assumed that the MNE makes a binary choice about input procurement,that is, a “make all or buy all” choice. It would be more realistic to suppose that the
MNE purchases some proportion of parts from local suppliers and procures the rest
via intra-firm transactions, which we refer to as scheme P .
Suppose that the MNE uses a continuum of inputs indexed in the [0, 1] space. Letβ ∈ [0, 1] denote the proportion of inputs that firm MH procures from firm MO incountry O. This means that the 1 − β proportion of the input is procured within FTA
countries. The amount of intra-firm trade becomes βx and the modified VA ratio is. The MNE maximizes
given by p−βrp
Π = (1 − t)[β{r − (w − ∆)}x + π] + (1 − T )[{p − βr − (1 − β)w}x](3.15)≥ α.
with respect to x, r, β, which is subject to πH ≥ 0, πO ≥ 0, and p−βr
pSince ∂Π> 0 holds, the optimal transfer price, rP , is again set at the level such that∂r>0p − βrP − (1 − β)w = 0 is satisfied. Furthermore, we can also confirm that ∂Π∂βalways holds, which implies that the MNE sets β as high as possible. Formally, theoptimal β satisfies β = max{0, 1 − αp
≡ β P }. Let xP denote the correspondingw
optimal level of x. Then, the equilibrium post-tax profits in scheme P become



α∆
P
P
(p − cM )x + π ,Π = (1 − t) 1 −w
P(3.16)

where the modified perceived marginal cost is cPM = w(w−∆), which falls between w −∆w−α∆and w.
The reason why the optimal β can be zero is explained as follows. Given that the MNE. If
sets the abusive transfer price as rP , the VA ratio with r = rP becomes (1−β)w
pw
w≤ α holds, the MNE can never comply with the ROO when β > 0. Since p < 1,pthere exists a unique cutoff of α, αPβ=0 , above which the MNE sets β P = 0. In this case,
the MNE manipulates its transfer price to comply with the ROO (i.e., scheme B), or
it may choose scheme I or N . Thus, we can conclude that schemes N , I, and B are
still the equilibrium outcomes when α ≥ αPβ=0 holds, whereas the area of scheme B isreplaced with that of scheme P below α < αPβ=0 .
One notable difference from the benchmark model is that ROO can transform a feasible
FTA into an infeasible one in scheme P . This happens in the benchmark model when76

Tariff Elimination vs. Tax Avoidance

the equilibrium outcome is scheme I. However, in this modified setup, the MNE’s
tax base is zero and ROO reduce the gains from an FTA formation, which generates apossibility that ROO worsen total welfare if the required VA ratio is high. Specifically,f P = W O∗ holds. Then, an FTA formation islet αPW be the threshold such that W
infeasible when α > αPW holds.

3.5.3

Concealment costs for transfer price manipulation

In the benchmark model, the MNE can freely manipulate the transfer price. Here, weshow that the assumption of costless transfer pricing is not critical to obtain the main
results.
In practice, MNEs need to explain the plausibility of transfer pricing to shift profits
across countries. As MNEs shift more profits between countries, explaining the reasonsfor the greater deviation from the appropriate price, or the arm’s length price, becomes
more difficult. Following the literature on transfer pricing, we introduce the following“concealment cost” in the case of offshoring, which is increasing in the gap between
the transfer price and production cost of inputs:
C(r, xO ) =δ{r − (w − ∆)}2 xO.
2(3.17)In this concealment cost, the parameter δ captures the difficulty of concealing tax
avoidance, which reflects a well-enforced tax authority, for example. The post-tax
profits under offshoring are modified as
ΠO = (1 − t)[{r − (w − ∆)}xO π] + (1 − T )[(p − r − λM τ )xO ] − C(r, xO ),O= (1 − t)π + (1 − T )(p − cCM )x ,(3.18)
2(1−t)(w−∆)+(1−T )λτ −(T −t)r
where cC
+ δ{r−(w−δ)}is the effective marginal cost.
M =1−T
2(1−T )In this setup, the concealment cost can prevent the MNE from transferring all the
profits from country H to country O. In other words, the MNE can choose the transfer
price and final good price such that p > r + λM τ holds, even in the absence of ROO.
Given that some of the MNE’s tax base remains in country H, our welfare analysis has
several modifications.
First, an FTA formation in the absence of ROO now depends on the tax differential
between T and t. Substituting the optimal level of r that maximizes ΠO into cC
M , the77

Tariff Elimination vs. Tax Avoidance
2(T −t)
perceived marginal cost in the equilibrium is calculated as cC.
M = w − ∆ + λτ −2δThus, as the tax difference between countries widens, the perceived marginal costlowers. Since the MNE becomes less willing to increase r because of the concealment
cost, it has an incentive to increase xO and lower p, which saves the MNE’s tax payments
in country H by narrowing the gap between p and r + λM τ . This incentive is reflectedin the perceived marginal cost. Because the elimination of tariffs increases the gap
between p and r + λM τ , it gives the MNE an extra incentive to increase xO to avoid
tax payments. The increase in xO is advantageous for member countries because it
benefits consumers. Therefore, in the presence of concealment costs, an FTA formation
without ROO is more likely to benefit member countries as the tax gap widens.

Second, p > r + λM τ implies that the VA ratio is positive even in the absence of ROO.
In the benchmark model, the MNE always chooses a zero VA ratio in FTA countries
in the absence of ROO. This implies that the VA requirement of ROO affects neither
the MNE’s transfer pricing nor its location choice when α is sufficiently small because
the MNE has already satisfied the required VA ratio.
Even if we consider these new elements, the nature of our results does not change.
Specifically, an FTA formation without ROO may harm member countries, and ROO
can transform an infeasible FTA into a feasible one. The opposite case is also possible,
where ROO transform a feasible FTA into an infeasible one.

3.5.4

The role of profit shifting

So far, we have analyzed the impact of ROO given the MNE always has an option to
manipulate transfer price to shift profits. In the literature on tax avoidance, whether
profit shifting itself is harmful for high-tax countries is one of the main interests. Although profit shifting hurts high-tax countries by reducing tax revenues, the effect ismore complicated than it seems. For instance, Hong and Smart (2010) theoreticallyshowed that the use of tax havens is beneficial for a high-tax country because it stimulates the economic activities of MNEs and enables a high-tax country to set an evenhigher tax rate. Here, we provide another reason why MNEs’ profit shifting is beneficial for high-tax countries. To this end, we consider the situation in which the MNE
cannot manipulate transfer price.
In this alternative setup, the intra-firm transaction takes place at the price of w − ∆and all the tax base of the MNE remains in country H irrespective of whether an FTA
is formed. This means that scheme O is always the optimal choice for the MNE in the78

Tariff Elimination vs. Tax Avoidance

pre-FTA equilibrium. Once an FTA with ROO is formed, the VA ratio is calculated
as α = a−w+∆≡ αU B . Therefore, the MNE keeps producing its own inputs in countrya+w−∆
O as long as α ≤ αU B holds. If α > αU B holds, however, the MNE cannot comply
with the ROO on the self-production of inputs. In this case, the MNE always starts
procuring inputs inside the FTA (scheme I) because the gains from the eliminationof tariff is greater than the loss from the higher input cost (i.e., τ > ∆). From theviewpoint of welfare, FTA countries prefer the MNE to produce its own inputs (schemeO) and thus they set the optimal VA ratio below αU B .
Given this equilibrium property under no profit shifting, we compare the post-FTA
welfare of high-tax member countries with and without profit shifting. The required
VA ratio with profit shifting is also set at the level that maximizes the joint welfare ofmember countries. We find that if the corporate tax rate in the high-tax country, T , isrelatively small, profit shifting can improve the welfare of high-tax member countries.34
The intuition behind this outcome is explained as follows. Without profit shifting,country H can collect tax revenues from the MNE, but these are relatively small because T is not large. Thus, the welfare of high-tax member countries becomes relatively
small in these tax environments. With profit shifting, Proposition 3.4 suggests that
the MNE rather shifts its profits from a low-tax country to a high-tax country if τ is relatively high and the tariff elimination motive of transfer pricing is large. This implies
that allowing transfer pricing actually leads to larger tax revenues in high-tax countries because the MNE manipulates its transfer price to eliminate tariffs rather than
avoid tax. Thus, our analysis provides the possibility that transfer pricing benefits ahigh-tax country.

3.6

Conclusion

The recent proliferation of FTAs is playing a key role in advancing trade liberalization
between countries and the cross-border economic activities of MNEs prevail globally.
This study investigated a vertically integrated MNE’s input production and pricing
strategies to analyze the welfare effects of FTA formation when the MNE can manipulate its transfer price of intra-firm trade. As in previous studies, the MNE uses its
transfer price to avoid a high corporate tax. After the formation of an FTA, however,there emerges another reason for transfer price manipulation in the presence of ROO.
34

The detailed calculation of the numerical example in this case will be provided upon request.

79

Tariff Elimination vs. Tax AvoidanceSpecifically, if the ROO of the FTA employ a VA criterion, the FTA induces the MNE
to manipulate the transfer price to comply with the ROO and be eligible for tariffelimination.
When the VA criterion of the ROO is low, the MNE prefers transfer price manipulation
since adjusting the transfer price is straightforward. However, once the required VA
level is high, transfer price adjustment decreases the efficiency of tax avoidance sothat the manipulation of the transfer price for the ROO is suboptimal. If the tax gap
between a country outside the FTA and a member country is large, the MNE produces
a necessary input in the outside country at the expense of the FTA tariff rate because
the gain from tax avoidance is large. If it is small, the MNE procures the input inthe inside country to qualify for the FTA tariff. This result is in line with empiricaland anecdotal evidence that (i) FTAs sometimes induce input relocation to inside
FTA countries, (ii) not all firms export using the preferential tariffs of FTAs, and (iii)transfer price manipulation is a factor in the difference in corporate tax rates and therequired VA criterion of ROO.
Our model also showed the possibility that ROO can prevent profit shifting by an MNE
via either a change in procurement strategy or another use of transfer prices. Owing
to the emergence of the MNE’s tax base, ROO can transform an infeasible FTA intoa feasible one. Therefore, the formation of FTAs with ROO is expected to work as
an effective policy to not only induce trade liberalization but also keep MNEs awayfrom tax avoidance. A remarkable result is that the direction of the MNE’s shifted
profits is the opposite of that under common knowledge when the MNE manipulates
the transfer price for ROO.
The above argument does not indicate that the highest VA criterion is always optimal
because it deteriorates the efficiency of tax avoidance, increases the MNE’s perceived
marginal cost, and reduces the amount of exports to another FTA member country.
Our analysis showed that the optimal VA level depends on corporate tax rates. Thisimplies that policymakers should pay close attention to the link between tariffs andcorporate taxes even though cooperation between customs departments and tax authorities is rarely observed in reality.
There remains room for further research. We assumed that tax rates and tariff rates are
exogenously given. It would be intriguing to investigate how the formation of an FTA
affects the outcomes of tax competition among countries as well as the optimal tariffs
set by FTA members. Another direction in which to extend the model is to examine
the effects of regulations on transfer pricing, such as the arm’s length principle, in the80Tariff Elimination vs. Tax Avoidance

presence of ROO. Finally, further empirical investigation on the relationship between
ROO and transfer pricing is essential.

81

Chapter 4
Innovation for Tax Avoidance:
Product Differentiation and theArm’s Length Principle
4.1

Introduction

Investment in research and development (R&D) has been growing over years. According to the National Science Foundation, worldwide R&D expenditure rose from$336,571 million in 2009 to $451,831 million in 2016. Although these numbers do not
distinguish between R&D types, empirical evidence suggests that product differentiation is a core reason for R&D. According to Scherer and Ross (1990), three quarterof R&D expenditures by U.S. firms’ were used for product R&D. Bagwell (2007) also
reports examples of large spendings on advertisement by U.S. firms which serve to increase product differentiation. To give some examples, in 2003, $3.43 billion was spentby General Motors for cars and trucks, $3.32 billion was used for detergents and cosmetics manufactured by Protecter and Gamble, and Pfizer devoted $2.84 billion toadvertise its drugs. Such an investment in product differentiation is one of the mostimportant strategies of firms because it makes competition between firms gets lessfierce and firms are able to enjoy more market power by differentiating their products
from those of rival firms.
The increase in market power due to product differentiation is not always harmful
for consumers, once individuals’ preference over varieties are considered. This is supported by “love of variety” pioneered by Dixit and Stiglitz (1977) and Krugman (1980).
82

Product Differentiation and Profit Shifting

For example, Ardelean (2006) estimates the parameter of love of variety (see Table 1.
of her paper). Furthermore, Hotelling (1929) is a classical paper which introduces
heterogeneous preference on goods and concludes that the socially optimal level of
duopolists’ product differentiation is positive. These indicate higher degrees of product differentiation can benefit not only firms but also consumers and gives a rationale
for governments to design policies to promote product differentiation.
From the viewpoint of global taxation, however, product differentiation exacerbates
the difficulties of collecting corporate tax revenue, because of the tax avoidance behaviour of multinational enterprises (MNEs). MNEs exploit tax rate differentials
between countries by shifting their profits to low-tax environments by means such astransfer pricing. The transfer price is the price used in intra-firm transactions, onintermediate products and/or intangible assets such as trademarks. As OECD guidelines stipulate, such a price used in intra-firm transactions should be the one used ininter-firm transaction, or arm’s length (AL) price, which is known as the AL principle.
Based on the principle, tax authorities compare the transfer price used by an MNE
to the AL price from comparable uncontrolled transactions, so-called comparable uncontrolled price (CUP) method. However, product differentiation makes it difficult
to find comparable transactions, since characteristics of the comparable products ininter-firm transaction should be similar to the ones of the good traded in the intra-firmtransaction.1 Due to the difficulty, in practice, both consultant companies and tax
authorities frequently rely on other methodologies and a range of transfer prices, or
AL range, which provides MNEs with room to manipulate their transfer prices for the
purpose of profit shifting.2
This link between product differentiation and profit shifting is empirically supported
by academic literature as well. Bernard et al. (2006), Cristea and Nguyen (2016),
and Davies et al. (2018) used export price data in the U.S., Denmark, and France andshowed the significant difference between transfer prices and AL prices. Moreover,they categorized industry into homogeneous and differentiated sectors and conclude
1

AL principle is set in Article 9 of the OECD Model Tax Convention. the OECD guideline states thet “[T]here are some significant cases in which the arm’s length principle is difficultand complicated to apply, for example, in MNE groups dealing in the integrated prodution ofhighly specialised goods, in unique intangibles and/or in the provision of specialised services.”See
https://www.oecd-ilibrary.org/docserver/tpg-2017-en.pdf?expires=1580823209&
id=id&accname=ocid49014612&checksum=0465D173CEED90A136FA054047E36AB3 on page 36.
2

According to the Internal Revenue Service, the most frequently used method for transfer
pricing investigation was the comparable profits method or the transactional net margin method
in 2016. See https://www.irs.gov/irb/2017-15_IRB..

83

Product Differentiation and Profit Shiftingthat transfer prices are more sensitive to tax changes when the goods category isdifferentiated (e.g. Davies et al. (2018), Table 2).3 Liu et al. (2019) also investigates theinterrelation between them by employing U.K. data and shows that transfer mispricing
is concentrated in R&D intensive firms (see Table 3 of their paper). Even though
the empirical evidence points to a link between product differentiation and MNEs’
profit shifting, a theoretical approach that combines these two aspects has not beendeveloped so far. To the best of my knowledge, this is the first paper that studies thislink and analyzes its welfare effects.
Tax avoidance by MNEs has attracted global attention because of its sizable impact
on tax revenue losses.4 Especially, tax revenue losses are magnified by the use of tax
havens. Zucman (2014) shows that the share of U.S. corporate profits made in tax
havens has risen from 2% in 1983 to 17% in 2013. Tørsløv et al. (2018) also estimatethat more than $600 billion were shifted to tax havens. As governments sometimes
design policies such as R&D incentive tax and/or subsidy to induce firms to engage in
R&D activity, understanding the MNEs’ incentive to conduct tax avoidance and its
welfare effects is essential to make appropriate policies.
To this end, this paper incorporates tax avoidance behaviour into a model with endogenous product differentiation. To reflect the above argument, this paper introduces alink between product differentiation and the ease of profit shifting. When profit shifting is possible, MNEs benefit more from product differentiation because higher product differentiation makes shifting profits easier. Due to this additional incentive, wefind that the optimal investment in product differentiation in the presence of profit
shifting is higher than in the absence of profit shifting. We also analyze the impact of
globalization which is characterized as an increase in the mobility of tax bases. We
find that globalization results in greater post-tax profits of MNEs, higher consumer
surplus from the differentiated products, and lower tax revenues in a high tax country.
These results are robust even if we extend our model by endogenizing the corporate
tax rate. We confirm an emergence of a tax haven reduces the equilibrium tax rate.
Furthermore, our numerical example shows that globalization results in a further
3

See also Belz et al. (2017) that pointed out that tax avoidance is frequently observed in R&D
intensive industries. Traditional explanation is that R&D intensive MNEs shifts profits throughtransfer pricing on intangible assets such as patents by locating in low tax countries.
OECD stated that annual revenue losses from MNEs’ tax avoidance are estimated $100 billion
to $240 billion. See http://www.oecd.org/ctp/oecd-presents-outputs-of-oecd-g20-bepsproject-for-discussion-at-g20-finance-ministers-meeting.htm.
484

Product Differentiation and Profit Shifting

reduction in the equilibrium tax rate, which is known as “race to the bottom”.5
One intriguing result is that tax haven with a fixed tax rate can increase welfare ina non-tax haven country because the gains of product differentiation are more thanthe losses from tax revenue losses. Hence, welfare-improving globalization takes placewhen the relative importance from the tax revenue losses is small. Specifically, thisoccurs when either (a) marginal utility from the tax revenues is small or (b) a corporate
tax rate in a domestic country is low, which means tax revenue without profit shifting isalready small, and investment cost for product differentiation is small, which increases
consumers’ gains via more differentiation. However, our numerical examples with an
endogenous tax rate do not support the welfare-improving globalization in total.
We argue the optimal policy for product differentiation as well. In the absence of profit
shifting, the equilibrium investment in product differentiation is always the level below
the optimal. With a tax haven, tax revenue loss by profit shifting makes the optimal
investment level lower. Therefore, the excess product differentiation is possible if agovernment weights more on tax revenues.
As an extension, we also consider the case of differentiation on their production technologies, known as “process innovation”. Similar to product differentiation, developing their own technologies makes it difficult to find appropriate AL price since thesame logic of a link between differentiation and the AL principle is applicable while itdoes not affect consumers’ preference but decreases marginal cost of production. In
this case, the emergence of a tax haven is harmful for MNEs even though they engage
in tax avoidance. Note that more differentiation in final products boosts demands on
the products and this benefits are magnified by rival’s investments. In the case of process innovation, however, the rival’s investment makes the market competition fiercer
and the gains from process innovation are smaller. Due to these differences, the MNEs
benefit from the opportunities of tax avoidance in the case of product differentiation
while the impact of arising profit shifting hurts MNEs in the case of process innovation.

4.1.1

Related literatureThis paper contributes to several fields of research. The first strand of literaturestudies endogenous product differentiation. Lin and Saggi (2002) show a stronger
5This result is also in line with a stylized fact of a reduction in corporate tax rates over time.
According to OECD stat, the average statutory corporate tax rate in OECD countries dropped
from 32 % in 2000 to 23.51% in 2019. See https://stats.oecd.org/index.aspx?DataSetCode=TABLE_II1.

85

Product Differentiation and Profit Shifting

incentive to engage in more product differentiation in the presence of process R&D,
because innovation increases the benefit from product differentiation. A few papers
study endogeneous product differentiation in the open economy. Beladi et al. (2012)
incorporate an outsourcing firm in their analysis, but the focus is on differences in technology and wages across firms and countries. Ferguson (2015) analyzed the impact oftrade liberalization in a monopolistically competitive model with a constant elasticity
of substitution in consumption. For the papers closer to ours, Braun (2008) exploredthe impact of economic integration on product R&D and shows that economic integration increases operating profits from the export market and thus results in moreproduct differentiation. Bastos and Straume (2012) also consider a two-country modeland introduce per-unit tariffs on firms’ exports and. They conclude that economic integration leads to a stronger incentive to invest in product differentiation in order tomitigate market competition due to a intensified international competition driven by
economic integration. Therefore, their analysis does not allow to draw any conclusions
for product differentiation due to a tax motive, which is the focus of our paper.
Second, our model also contributes to the research on tax avoidance by MNEs. After
Copithorne (1971) and Horst (1971), a number of authors have studied transfer pricing
and profit shifting. Kant (1988a) first introduces legal or other costs of profit shifting
to obtain an interior solution. Traditionally, this field has been analyzed in a perfectcompetition setup but a few recent works also incorporated market imperfection in
their analysis. Some papers study AL regulation with taking MNEs’ strategies into
account. Among them, Choi et al. (2018b) and Choi et al. (2019) study the impact
of AL principle on an MNE’s sourcing and licensing strategies, respectively. As AL
regulation does not allow MNEs to discriminate input prices/royalty on patent between
related affiliate and independent firms, they show AL regulation distort an MNE’sstrategies (dual sourcing vs single sourcing and licensing to an unrelated firm or not,respectively). However, they do not consider the similarity of transactions whereas
our paper considers the link between product differentiation and profit shifting.
A few papers saw the link. Yao (2013) considers a spatial product differentiation modelwith profit shifting in a Hotelling fashion and shows that the opportunity of manipulating transfer price induces a wider distance of two MNEs’ location. Kato and Okoshi(2019b) incorporate the link between product differentiation and the ease of profit
shifting in their robustness analysis. In their analysis, an MNE sells differentiated inputs to a related affiliate and an independent firm so that transfer price manipulationis still possible with a limited degree but the degree of differentiation is fixed. Our pa-

86

Product Differentiation and Profit Shifting

per explicitly explores the interrelation between product differentiation and the easesof profit shifting by endogenizing investment in product differentiation. Therefore,
the contribution of this paper is to incorporate characteristics of products into thecost function of profit shifting, which plays a significant role in practice and provides
policy implications.
The rest of the paper is organized as follow. The next section explains the basic modeland derives the equilibrium in autarky situation where profit shifting is impossible.
Section 4.3 introduces profit shifting by incorporating a tax haven. Section 4.4 argues the welfare effects while section 4.5 discusses some extensions. The last section
concludes.

4.2

The benchmark model

Our benchmark model abstracts from profit shifting. Consider a domestic country(country D) where both consumption and production take place. In the economy,
there exist three sectors: an imperfect competition sector (sector X), a homogeneous
goods sector (sector Y ) and a public sector. In the Y sector, we assume perfectcompetition so that no positive profits accrue to any firm in the sector. The X sector
is characterized by an oligopolistic market structure and has only two operating firms
because of high entry cost. We refer to these firms as MNEs, labelled 1 and 2, since they
have a subsidiary in a tax haven (country H), which is introduced in the next section.

Consumers Individuals in country D are identical and share the same preferences
over consumption of the three types of goods provided by the MNEs, perfectly competitive firms and the government in country D. The preferences of a representative
individual are given by the following quasi-linear utility function;
U (xi , xj , y, G) = u(xi , xj ) + y + βG
where u(xi , xj ) = a(xi + xj ) −(xi )2 + (xj )2 + 2sxi xj
i ∈ {1, 2}, j 6= i, (4.1)
2

and xi is the consumption level of the product manufactured by the MNE i, y is theconsumption of the homogeneous good, and G is the quantity of the public good. aand β are parameters and exogenously given. β represents the marginal utility fromthe public good.

87

Product Differentiation and Profit Shifting

The parameter s ∈ [0, 1] represents the degree of substitutability between the two
products manufactured by the MNEs. The degree of substitutability is endogenously
determined by MNEs’ investments described below and the products are more differentiated as s approaches zero. At the other extreme case, the MNEs’ goods arehomogeneous if s is 1.
The utility function yields the following inverse demand function,pi = a − xi − sxj .
Note that our utility function has a property of “love of variety” and the inverse demand
function shifts outward as the degree of substitutability gets smaller.6 This is because
the more differentiated products increase the individuals’ willingness to pay for eachproduct.
Individuals own the MNEs and thus their income I consists of post-tax profits of the
MNEs. Therefore, utility maximization yields the optimal consumption level of the2Xnumeraire homogeneous good as yb = I −p i xi .
i=1

Government The government has only one tax instrument in order to finance theprovision of the public good: a proportional corporate tax rate on the reported profits
of the MNEs in country D. The government imposes a positive tax rate on firms’ profits(tD ∈ [0, 1]). Since the sector Y is perfectly competitive and makes zero profits, tax
revenue (T R) can be generated only from the sector X. The government can transform
one unit of the numeraire good into one unit of the public good, which means G = T R
holds.
In our benchmark model, we assume that the tax rate is exogenously given. Later, we
also argue the optimal tax rate and the effect of globalization on the tax rate.

Firms Our focus is on the differentiated sector. The MNEs produce their goods
with constant marginal cost c and compete over quantity. Before the MNEs produce
the goods, they also have a chance to invest in product differentiation. Following Lin
and Saggi (2002), at the first stage, they engage in investment to differentiate their
6

If the two goods are perfect substitute s = 1, the inverse demand function is linear, whichis the case that the elasticity of substitute is approaching to infinity, and love of variety effectvanishes. As the degree of product differentiation or the elasticity of substitute get smaller,
indifference curves become more convex with respect to origin.

88Product Differentiation and Profit Shifting 
goods from the one made by the rival MNE. Let di ∈ 0, 12 be the investment level by
MNE i and a measure of differentiation level. Then, the degree of substitutability isgiven by s = 1 − (d1 + d2 ). The investment cost is assumed to be F (di ) with F 0 (di ) > 0
and F 00 (di ) > 0. To secure interior levels of di , we assume that F 0 (0) = 0 and F 0 12 issufficiently large. Throughout the analysis, we assume that second order condition issatisfied.
The sequence of the game is as follow. At the first stage, both MNEs decide the investment level. Given the investment level, and hence the degree of product differentiation,
the MNEs compete in a Cournot fashion and make operating profits. We solve the twostage game by backward induction.

4.2.1

2nd stage: Market outcome

We denote the operating profits of MNE i by πi = (pi − c)xi and the post-tax profitsby Πi . As in standard Cournot competition, the equilibrium output and price level by
MNE i are
 


a−c
a + (2 − di − dj )c
a−c
.
(4.2)
=
, and, pbi =
x
bi =
2+s
3 − di − dj
3 − di − djEven though more product differentiation softens market competition between themand increases market power, it leads to more outputs by the MNEs because the (residual) demand expands. We can see this from the best response function of MNE i. Let
a−c−sxjR
xR. As s gets lower, meaning
i be the best response function, which is xi =2
their goods are more differentiated, MNE i increases its own output levels for any given
output of its rival. Although MNE i also negatively responds with such an increase in
MNE j’s output, the degree of its response declines because the substitutability of the
products gets less. In total, sxj decreases and thus, the best response xRi increases.
Due to this feature of market expansion, more outputs by MNEs do not mean a reduction in prices in this setup. Remember that the inverse demand function shifts
outward because of more product differentiation, which increases consumers’ willingness to pay and creates more demand. Formally, we can easily confirm the effect of
product differentiation on the price,
∂ pbi
a−c
=
> 0,
∂di
(3 − di − dj )2
so that more product differentiation always results in a higher price. As more product89

Product Differentiation and Profit Shifting

differentiation increases both supplies and prices, it obviously increases the operating
profits of MNEs.

4.2.2

1st stage: Investment decision

As more product differentiation results in greater operating profits, each MNE has anincentive to differentiate their product from the rival’s. For the purpose of identifying
variables, we use a superscript “O” for variables without profit shifting.
The MNEs maximize the following post-tax profits,ΠOi = (1 − tD )

a−c
3 − di − dj2
− F (di ).

(4.3)

Thus, the optimal investment level dO is characterized in symmetric equilibrium,∂ΠO
2(1 − tD )(a − c)2i− F 0 (dO ) = 0.
=
∂di di =dj =dO(3 − 2dO )3(4.4)

The first term is the (tax adjusted) marginal benefit from differentiation via market
expansion while the second term is marginal cost of the investment. Therefore, theoptimal investment level is the one which equates the marginal benefit and marginal
cost of investment.

4.3

Tax Haven and Globalization

Next, we consider the case where the MNEs have a possibility to shift profit into country H by some means such as transfer pricing on tangible/intangible assets. We assume
that country H is very small and there is no consumption in country H. This is a standard assumption in literature of tax havens because tax havens such as Caribbean
islands frequently have a relatively small county size but provide opportunities of tax
planning via non-production transaction such as patent royalty or internal debt.7 We
modify the game by introducing profit shifting stage after the first stage. In otherwords, the MNEs decide the amount of their supplies and shifted profits simultaneously.
7

Even if we introduce consumption in country H, the results are qualitatively robust.

90

Product Differentiation and Profit Shifting

4.3.1

Cost of profit shifting

In general, engaging in tax avoidance is costly. For example, MNEs need to hire specialists on accounting such as accountants or lawyers to justify shifted profits between
related companies. This cost is known as concealment cost in the literature. Therefore, irrespective of means of profit shifting such as transfer pricing or a licensing fee,the MNEs have to incur the cost.
In the literature of tax avoidance, the cost is assumed to increase as more profits are
shifted because experts in accounting branch or consulting firms have to exert much
effort to save tax and MNEs may need to pay more rewards to them so as to shift more
profits. We assume that the cost is formulated asC(η, πiS ) =η(πiS )2
2πi

(4.5)

where πiS represents the amount of shifted profits to country H and η is a measure ofdifficulty of profit shifting.8 This specification implies that a given amount of profit
shifting is easier to hide when total profits are large. Therefore, the marginal cost of
profit shifting is less as MNEs makes larger operating profits.
This traditional formulation of the cost function has one caveat that it does not reflectcomparability of an intra-firm transaction with another. In this model, it is straightforward to assume that the cost of profit shifting gets lower as the products are moredifferentiated. To capture this aspect, we decompose η into two elements. First partof η is factors that MNEs cannot change, which is denoted by θ. One example of thefactors is the prevalence of knowledge or information of using tax havens, which makes
it easy to shift profits into tax havens. As such knowledge and information prevail as
globalization proceeds, we interpret a reduction in θ as a measure of globalization.9
Second, the difficulty of profit shifting also depends on the degree of product differentiation between the MNEs. In any forms of intra-firm transactions, tax authorities
need to find appropriate comparable price or CUP. If the intra-firm traded assets either
tangible or intangible are differentiated, finding CUP is difficult for tax authorities.
8

This specification is also used in some empirical papers. See, for example, Hines Jr and Rice
(1994), Huizinga and Laeven (2008), Amerighi and Peralta (2010), and Gumpert et al. (2016).
We argue this specification of concealment costs more in detail in section 4.5.1.
9The existing literature also interprets this term as the degree of government’s attention toauditing profit shifting. In this case, higher θ can be interpreted as stricter policy or regulationsuch as worldwide cooperation, e.g. BEPS project or AL principle. For example, see Hindriks
et al. (2018) that incorporate governments’ effort on tax enforcement in their concealment cost.

91Product Differentiation and Profit ShiftingThus, shifting profits gets easier as products are more differentiated. To incorporate
these two properties, we assume η = θs.
We use a superscript “P” for the case with profit shifting.

4.3.2

Profit shifting

When profit shifting is possible, MNE i maximizes the following post-tax global profits,ΠPi = (1 − tD )(πi − πiS ) + πiS − F (di ) −θs(πiS )2,2πi

where the first term is post tax profits in country D and the second term is those incountry H. The first order condition provides the following optimal shifted profits,
π
biS =

tD
πi .
θs

(4.6)

To secure positive reported profits in country D, we assume tθsD ∈ [0, 1].
The optimal amount of shifted profits is determined by balancing the marginal benefit
with the marginal cost from profit shifting. Eq.(4.6) shows four determinants of profit
shifting. The MNEs shift more profits when tax gap gets wider, which increases thebenefit of saving tax payment, and when the world is well globalized, captured by lower
θ, which reduces the cost of profit shifting. Intuitively, the shifted profits are 0, whichcorresponds with the case of no profit shifting, when there is no tax gap, tD = 0, or
the world is not globalized, θ → ∞.
On top of these two determinants which are argued in the existing literature, two more
new channels caused by product differentiation appear in this model. First, as higher
product differentiation, captured by higher di or lower s, makes it difficult to find CUP,
it decreases the marginal cost of profit shifting. Second, as more operating profits
reduces the cost of shifting profits, the shifted profits are increasing in the operating
profits.10 As we saw above, product differentiation increases operating profits so thatboth of these new determinants positively affect the MNEs’ tax saving strategy.
10

In the transfer pricing literature, the amount of shifted profits is product of transfer priceand the amount of exports. Therefore, they also has a similar channel to ours that more exports(or more operating profits) leads to more shifted profits. Unlike our model, however, their channel
is related to benefit side since MNEs are able to shift more profits when they conduct intra-firmtrade more even if the same transfer price are set while our model indicates the channel throughcost side. For example, see Choi et al. (2018b).

92

Product Differentiation and Profit Shifting

Plugging in the optimal shifted profits, the maximized profits become,ΠPi = 1 − tD +

t2D
2θs
|{z}


 πi − F (di ).


(4.7)

Tax saving gains

The last term of the bracket appears in the presence of profit shifting, which captures
the net gains from tax savings. From the equation, we can see the decision on profit
shifting is independent from the quantity setting. Thus, the outcome of the quantity
decision is the same as in the benchmark.

4.3.3

Investment decision with profit shifting

In the presence of profit shifting, eq.(4.2) rewrites the post-tax profits of MNE i as,
ΠPi =



t2D
1 − tD +2θ(1 − di − dj )a−c
3 − di − dj2
− F (di ).

(4.8)

Similarly, the first order condition shows the condition that the optimal investment
level dP satisfies as,2(1 − tD )(a − c)2t2D (a − c)2∂ΠPi=+∂di di =dj =dP(3 − 2dP )3θ(1 − 2dP )(3 − 2dP )3|{z}
Tax avoidance effect+t2D(a − c)2−F 0 (dP ) = 0.
2θ(1 − 2dP )2 (3 − 2dP )2
|
{z
}

(4.9)

Concealment cost effect

The second and third terms appear as the additional incentives to capture marginal
benefits from tax savings since the term of tax saving gains exists in eq.(4.7). The
second term in eq.(4.9), we refer to this as “tax avoidance effect”, captures the marginal
benefit from the existence of profit shifting. As the more product differentiation resultsin the higher operating profits and shifted profits, the opportunity to shift profits ismore profitable as investment in product differentiation increases even with the fixed
tax saving term in eq.(4.7). Furthermore, the third term in eq.(4.9) captures thelink between product differentiation and the cost of profit shifting, we refer to this as“concealment cost effect”. More product differentiation benefits the MNEs via lesscost of profit shifting so that it increases tax saving gains even with fixed operating

93

Product Differentiation and Profit Shifting

profits. As the new terms are always positive, the chance to save tax payments provides
a stronger incentive to invest in product differentiation with the MNEs.
Note that the concealment cost effect is a specific term in this model as the effectreflects the determinant that more product differentiation leads to lower cost of profit
shifting. With a traditional concealment cost, product differentiation has no impacts
on the cost structure so that the term disappears once we ignore the relation between
product differentiation and the cost of profit shifting. To clarify this point, let dT be
the equilibrium investment level under the case of traditional concealment cost where
the concealment cost is unrelated to product differentiation. Then, dT < dP holds
because of disappearance of the positive concealment cost effect. These arguments
lead to the following proposition.
Proposition 4.1 The opportunity of profit shifting induces the MNEs to invest
more in product R&D, dO < dP . This effect is reinforced when product differentiation reduces the costs of profit shifting, dT < dP .

4.3.4

Globalization

In the last subsection, we see the impact of globalization on product differentiation
but this is one extreme example of globalization, that is, autarky to open economy.
Although the above analysis provides several arguments, considering marginal changes
in globalization is helpful to explain the reality since the recent world is featured notby drastic globalization. Thus, this section focuses on the effect of a reduction in θ.
By differentiating eq.(4.9) with respect to θ, we obtain



∂
∂θ



∂ΠPi
∂di


di =dj =dP


∝ −


1
P
|3 −{z2d }Via tax avoidance effect+1
2(1 − 2dP )| {z }

 < 0. (4.10)


Via concealment cost effectGlobalization reduces the cost of profit shifting, increases tax saving gains, and thusincreases the marginal benefit of the investment via both tax avoidance effect andconcealment cost effect. As the optimal level of the investment is determined so as tobalance the marginal benefit and the marginal cost of the investment, globalization
clearly induces the MNE to invest more in product differentiation. Thus, we have thefollowing proposition.
94

Product Differentiation and Profit Shifting

Proposition 4.2 Globalization induces the MNEs to invest more in product differP
entiation, ∂d< 0.
∂θPropositions 4.1 and 4.2 give a new rationale for current development of product differentiation from the tax avoidance angle. A common explanation on the development
is that relocating intangible assets is easy and provides MNEs with opportunities of
profit shifting across countries. Therefore, the intangible assets developed as outcomesof R&D investments enables MNEs to engage in tax avoidance. However, our modelshows another complementary channel which facilitates MNEs to invest more in product differentiation in the presence of interrelation between product differentiation andthe ease of profit shifting. In short, the model shows the potential incentives of obtaining more intangible assets for tax avoidance which is ignored by the conventional
explanation.

4.4

Welfare effect4.4.1

Welfare effects of lower profit shifting costs

Globalization has three effects on the post-tax global profits of the MNEs. Directly,
globalization magnifies the tax saving gains. On top of that, the more product differentiation via globalization increases not only operating profits but also tax saving
gains. Note that these indirect effects are reinforced by more investments of a rival’s
MNE. Clearly, the three effects augment the post-tax global profits. Formally, we canobtain the following inequality,t2∂ΠPi∝− 2 D P +∂θ2θ (1 − 2d )|{z}
Direct: Tax saving















∂dPj
t2D
2
t2D
+
1 − tD +< 0,
2θ(1 − 2dP )2
3 − 2dP
2θ(1 − 2dP ) 
∂θ



{z
} |
{z
}
|

Indirect: Tax saving

Indirect: Demand size

(4.11)
where the first term represents the direct effect of a marginal change in θ and the second
term captures indirect effects via a change in investment level of a rival firm. Thus,
95

Product Differentiation and Profit Shifting

globalization benefits the MNEs.
Next, we analyze the impact on a consumer surplus from the differentiated products.
Let CSX be denoted as the consumer surplus,
CSX = a(xPi + xPj ) −

xPi

2

2
X
+ xPi + 2sxPi xPj−
pPi xPi2i∈{1,2}= 2(2 − dPi − dPj )a−c
3 − dPi − dPj2(4.12)

As consumers love variety, there are two effects of more product differentiation on
consumer surplus. First, the volume of consumption is one of determinants which is
captured by the second term of eq. (4.12). More product differentiation results in moreconsumption and thus obviously has a positive effect on the consumer surplus via thevolume effect. In contrast to the positive effect, product differentiation has a negative
effect on the consumer surplus via price increases. Recall that product differentiation
increases the market demands for each product and thus increases the prices. This
aspect is captured by the first term of eq.(4.12). Irrespective of the counteracting
effects, the first derivative of the consumer surplus with respect to θ is,∂CSX ∂dPi∂CSX ∂dPj
4(1 − 2dP )(a − c)2 ∂dP
∂CSX
=
+
=
< 0.
∂θ
(3 − 2dP )3∂θ∂dPi ∂θ∂dPj ∂θ(4.13)

Therefore, the positive effect of product differentiation due to globalization always
exceeds the negative one.
In contrast to the positive effects on consumers and the MNEs, globalization can havea negative impact on tax revenues in country D which is formulated as,
P
T RD= tD X

πiP − πiS  = 2tD1−i∈{1,2}tD
θ(1 − dPi − dPj )a−c
3 − dPi − dPj2,(4.14)

which yields,P∂T RD
2tD (a − c)2=∂θ(3 − 2dP )22tD (5 − 6dP )−3 − 2dPθ(1 − 2dP )2 (3 − 2dP )


∂di
.
∂θ
(4.15)The direct effect is to induce outflows of tax base to country H, which is the first term of
the second parenthesis. The indirect effects via product differentiation, however, worktD+2θ (1 − 2dP )96Product Differentiation and Profit Shiftingin the opposite directions. On the one hand, more product differentiation also resultsin more outflows of tax bases as it increases tax saving gains. One the other hand, moreproduct differentiation also increases the operating profits of the MNEs. Therefore,
the overall impact of globalization on tax revenues in country D is not obvious.
With eq.(4.9), the implicit function theorem rearranges eq.(4.15) into,
∂T R
tD Γ
= 2
,
∂θ
θ (1 − 2dP )ΓSOC

2(a − c)2 t2D (5 − 6dP )2tD
where Γ ≡ ΓSOC +−,5 − 6dPθ(1 − 2dP ) 2(1 − 2dP )(3 − 2dP )4
t2D (5 − 6dP )6(a − c)22(1 − tD ) +and ΓSOC ≡(3 − 2dP )42θ(1 − 2dP )2−(a − c)2 t2D (13 − 18dP )− F 00 (di ).
θ(1 − 2dP )3 (3 − 2dP )3(4.16)(4.17)

As we assume the second order condition holds, ΓSOC is negative and thus,sign ∂T∂θR = sign (−Γ) holds. From eqs.(4.16) and (4.17), we have,(a − c)2∂T R
00> 0 ⇐⇒ Γ < 0 ⇐⇒ F (di ) > F ≡ΓF(4.18)∂θ(3 − 2dP )4
t2D (5 − 6dP )2
6(1 − tD ) +where ΓF ≡(3 − 2dP )1 − 2dPt2D(5 − 6dP ){6 − tD (5 − 6dP )} 13 − 18dP+−
θ(1 − 2dP )22(3 − 2dP )1 − 2dP
This sufficient condition means that globalization always leads to a reduction in tax
revenue in country D when the investment is sufficiently costly, or large F 00 (di ). Thisis because the net gains from the investment are small due to larger investment costs
and thus the investment level does not increase much, which implies the increase inoperating profits is also small.
The above discussions are summarized as the following proposition.
Proposition 4.3 Globalization, captured by a reduction in θ, always benefits consumers and MNEs. However, globalization decreases tax revenue from MNEs wheninvestment cost is sufficientyly large, or F 00 (di ) > F holds.
Given the effects on consumers, the MNEs and tax revenues, the overall effect onwelfare in country D is also ambiguous. We assume that the government’s objective
97

Product Differentiation and Profit Shifting

function is the welfare of consumers. Note that consumers own the MNEs so that
MNEs’ post-tax profits accrue to consumers. Thus, we can compute the objectivefunction of the government as,P
U (xP , y P , GP ) = CSX+XP
ΠPi + βT RD.

(4.19)i∈{1,2}

Obviously, globalization benefits country D when the weight on public goods is close
to zero.11
Even if β is large, however, welfare-improving globalization is possible when the tax
rate is low and thus tax revenue without profit shifting is small. This situation implies a reduction in tax revenue due to profit shifting is less significant. As the tax
revenue losses are relatively small, globalization can improve welfare when it increases
consumers’ and the MNEs’ gains a lot. This is most likely when profit shifting and investment in R&D are less costly, that is, θ and F 00 (di ) are small enough. Formally, we
can obtain at θ = tsD ,(a − c)2 (5 − 6dP )∂U∝ 2β − 1 +∂θ θ= tD
(1 − 2dP )(3 − 2dP )4 ΓSOC

tD β(1 + 2dP ) tDP−
+ 2(1 − d ) .
3 − 2dP2s(4.20)
Note that ΓSOC is negative and decreasing in F 00 (di ). Therefore, the second term getssmaller as F 00 (di ) becomes bigger, which makes eq.(4.20) likely to be positive. On thecontrary, the second term gets larger if F 00 (di ) is small enough. At an extreme point
F 00 (di ) = F ,1∂U= 2β−1+ 2∂θ θ= tD ,F 00 (di )=F
tD
s





2
tD {2β − 3 + 2tD (2β + 1)}
P+ 2(1 − d ) ,1 − 6dP2(3 − 2dP )
|
{z
}


<0 ∵ SOC(4.21)
which implies that ∂U< 0 likely holds when tD is closer to zero.
∂θThe above discussion is summarized as the next proposition.
Proposition 4.4 Globalization improves total welfare if either β is close to 0 or
11

Another situation corresponding with this situation is the one that government sector issufficiently inefficient to provide the public goods. In the literature of mixed oligopoly, it is wellknown that state-owned firms are relatively inefficient because of less incentive to improve theiroperation skills. In this model, we can capture this scenario by introducing cG as a marginal costof public goods provision and assuming cG is sufficiently large because G = TcGR holds. In thebenchmark model, we assume cG = 1.

98

Product Differentiation and Profit Shifting

Figure 4.1: Welfare

the triplet (tD , θ, F 00 (di )) is sufficiently small.
Figure 4.1 illustrates welfare in country D without and with profit shifting cases. The
dashed line represents welfare without profit shifting while the solid curve depicts thatwith profit shifting.12 The left figure is the case where β is low and corresponds to (a)of proposition 4.4. The solid curve in the figure is an inverse U-shape and globalization
improves welfare when θ is large. As β gets larger, the negative impact from tax revenue
loss becomes more important and the losses from tax revenue is likely to exceed thegains when tax avoidance is easy to conduct, or θ is low. As β increases, the curve
shifts toward downwardly and welfare improving globalization is less likely to happen.
Alternatively, the right figure shows the case where tD and F 00 (di ) are small and illustrates (b) of proposition 4.4. Unlike the case with low β, the shape of welfare curve is
U-shaped and globalization improves welfare when θ is low as proposition 4.4 predicts.
These figures provide us with two important policy implications. First, as another interpretation of θ is the degree of tax enforcement, we can see the effect of a stricter
enforcement, captured by a higher θ, which differs across the two cases. If a country imposes a high corporate tax but sees public goods provision less importantly, astricter enforcement tends to be beneficial when globalization proceeds well, or θ is12This figure is derived using the following parameter values and function: a = 2, c = 1, and
γd2
F (di ) = 2 i for both figures. For the left figure, β = 0.671, tD = 0.3 and γ = 1 are used while weuse β = 1, tD = 0.1 and γ = 0.615 for the right one.

99

Product Differentiation and Profit Shifting

low. However, engaging in more stringent enforcement likely to be welfare improving
when the world is less globalized if a country levies a low corporate tax.
Second and more importantly, the figures shed light on a new possibility of beneficial
tax havens. Although a traditional view of tax havens is negative because of lessprovisions of the public good (e.g. Slemrod and Wilson (2009)), Hong and Smart(2010) argued desirable aspect of tax havens because profit shifting makes MNEs’
investments in economic activity less sensitive to tax differentials and thus enables a
non-haven country to impose a high tax without keeping MNEs’ capital away. In ourmodel, however, the source of desirability stems from consumers’ and MNEs’ benefits
driven by product differentiation. This is the case with a large θ in the left figure anda low θ in the right figure.

4.4.2

Endogenous tax rate

So far, we fixed the corporate tax rate in country D. Hereafter, we endogenize the tax
rate. To assure that the government has an incentive to provide the public good, β isassumed to be greater than unity, β > 1.
In the absence of profit shifting, the first order condition for the tax rate is derived as,
∂U O
=
∂tD



2(a − c)2(3 − 2dO )2

∝β−1−





2{2(1 − dO ) + tD (2β − 1)} ∂dO
β−1+
3 − 2dO∂tD

4{2(1 − dO ) + (2β − 1)tD }(a − c)2.
F 00 (dO )(3 − 2dO )4 − 12(1 − tD )(a − c)2(4.22)

The first two terms in the square bracket are the direct effect that an marginal utility
from the public good and marginal (dis)utility from the homogeneous good. As we
assume β > 1, the government has an incentive to collect greater tax revenue on the
one hand. On the other hand, the rest term of the bracket is the net indirect effects via
a change in product differentiation. As an increase in tax rate discourages the MNEs toinvest in product differentiation because a higher corporate tax rate reduces the post
tax operating profits and thus gains from product differentiation. This negatively
affects consumer surplus, operating profits of the MNEs and tax revenue. Thus, thesign of eq.(4.22) is ambiguous. To see the impact of tax haven on the equilibrium tax
2 {2(1−2dO )+t }Drate, we assume β > 1 + (3−2dO )44(a−c)
and the equilibrium tax
F 00 (dO )−4(a−c)2 {3(1−tD )+2tD }rate without a tax haven is positive.

100

Product Differentiation and Profit Shifting

With profit shifting, the first order condition for the government is,

∂U P
=2
∂tD



a−c
3 − 2dP2β − 1(2β − 1)tD−
θ(1 − 2dP ){z}|

Net direct effect of tax avoidance

+






2{2(1 − dP ) + tD (2β − 1)}
3 − 2dP




−








∂dP 
t2D (5 − 6dP )(2β − 1),2θ(1 − 2dP )2 (3 − 2dP ) 
∂tD 

{z
}
|


Indirect effect via tax avoidance(4.23)
which shows two new effects via tax avoidance. First, as an additional direct effect, an
increase in tax rate gives the opportunity of profit shifting for tax savings. Even thoughsuch a tax avoidance contributes to an increase in consumption of homogeneous goods,
it reduces tax revenues and thus public good provision which is more valuable for the
consumer. Moreover, since such a tax avoidance behaviour entails concealment costs,
the net direct effect of the tax avoidance is negative. Second, a change in corporate
tax rate also affects the investment level, which influences the effectiveness of tax
avoidance as well.
Likewise the case without profit shifting, these effects make the sign of eq.(4.23) unPO< ∂d, which implies the MNEs’ response to a change
clear. However, we confirm ∂d∂tD∂tD
in the tax rate is less sensitive with profit shifting because they can shift some profits
to a haven country and the tax burden is mitigated.13 Hence, the optimal tax rate ismore influenced by the direct effects, which indicates that the government’s incentive
to impose a higher corporate tax rate for the public good provision is weakened.
Here, we rely on numerical calculation as it is impossible to derive analytical results ofglobalization. In Table 4.1, the numerical results are provided with β = 1.21 for theupper two tables and β = 1.01 for the bottom one.14 The top table shows outcomeswith endogenous tax rate while the middle one represents results with a fixed tax rateof the optimal one without profit shifting θ = ∞.

13O

Note that ∂d∂tD < 0 holds.

14
Other parameter values used in the table are: a = 2, c = 1, and γ = 0.8. “—” in the lower
Dtable represents the case where tθs> 1, which is outside our focus.

101

Table 4.1: Optimal tax rate

102

100.065240.1085125
0.15746
0.0951550
0.286430.07780100
0.461100.05629150
0.56760
0.04608200
0.637960.03637∞0.86033
0.013280.01671
0.71269
0.06470
0.99172

0.03958
0.712770.15623
0.992180.07033
0.712890.28449
0.993220.11004
0.71306
0.45871
0.994810.13333
0.713160.56525
0.995850.148390.71323
0.63577
0.99656

0.19461
0.713350.86033
1.0

II. Fixed tax at tD = 0.86033(= btD |θ=∞ )
θ
1
5
10
25
P
d
—
—
0.02314 0.01711
PTR——
0.17943 0.18865
UP——
0.70547 0.71026
ef f
t
—
—
0.78272 0.82967
tef f /tD——
0.90979 0.96436

50
0.015180.19165
0.711810.84506
0.98225100
0.01423
0.193140.71258
0.85271
0.991141500.01391
0.19363
0.712840.85525
0.99409200
0.01375
0.19388
0.71297
0.85652
0.99557∞
0.013280.19461
0.713350.86033
1.0

III. Fixed tax at tD = 0.1 if θ < ∞
θ
1
5
10
dP
0.22359 0.21184 0.21054
UP0.75593 0.75363 0.75339

50
0.20952
0.75320100
0.20938
0.753181500.20935
0.7531725
0.20977
0.75325∞ with b
tD = 000.77509

Product Differentiation and Profit Shifting

I. Endogenous tax
θ15b0.00657 0.03280
tDPbd0.11750 0.11343
Pd
T
R
0.00170 0.00846
Pb0.71263 0.71266
U
ef
f
b
t
0.00651 0.03252
ef f bbt /tD 0.99086 0.99146

Product Differentiation and Profit Shifting

As argued above, the equilibrium tax rate under profit shifting is lower than the one
without profit shifting and globalization lowers the optimal tax rate. This is in linewith the stylized fact known as “race to the bottom”. Moreover, most of propositions
under a fixed tax rate are carried over even if we endogenize the tax rate.
However, proposition 4.4 is the one which is not replicated. The middle table suggeststhat a reduction in welfare by globalization is not because we endogenize the tax
rate but because the optimal tax rate without profit shifting is sufficiently high. As
an increase in welfare is realized when the triplet (tD , θ, F 00 (d)) is small enough, theoptimal tax rate without profit shifting does not satisfy the statement of proposition
4.4 in this example.
To investigate the welfare-improving globalization, another numerical example isshown in the bottom table. As proposition 4.4 suggests, the bottom table represents acase that globalization improves welfare in country D under a fixed tax rate tD = 0.1
if profit shifting is possible, or θ < ∞. In the parameter values, globalization leads toan increase in welfare. However, the tax rate is not optimal without a tax haven andthe optimal tax rate is zero whose values of investment and welfare are shown in theright edge of the table. Immediately, we can see that the emergence of a tax haven isharmful for the domestic country.
The reason why welfare-improving globalization in the last subsection was observed is
obviously the tax rate was not the optimal both before and after a tax haven emerges.15
However, a tax rate is not always optimal industry-wide because of the nature ofcorporate taxation that a government imposes a unique corporate tax rate acrossindustries. Therefore, welfare-enhancing globalization occurs when the initial tax
rate is low enough due to , for example, other industries and adjustment of a tax rateis difficult to conduct.
By comparing the top and the middle tables, we can also see the impact of endogenizing
tax rate and the main source of welfare reduction because of globalization. As reduction
in tax revenue is dramatical with an endogenous tax rate compared to the one witha fixed tax rate, the primary reason of decline in welfare is drop of tax revenue when
tax is endogenized. To brake welfare reduction, the government gives the MNE more
incentive to conduct product differentiation that increases consumer surplus and the
MNEs’ profits by reducing a tax rate. This gives us an important implication that thebest tax policy is the one resulting in more product differentiation at the expense of
15

The equilibrium tax rate without a tax haven is relatively large when the cost of investment
is small or it is zero when the government weight a small weight on the public goods provision.

103

Product Differentiation and Profit Shifting

tax revenue. This seems surprising because the provision of the public good is morevaluable. As tax revenue is not reliable source to increase welfare under profit shifting,the government shifts main sources to maximize welfare to consumers’ gain and the
MNEs’ profits.
The last investigation of the endogenous tax rate is whether product differentiation
accelerates the efficiency of tax avoidance of the MNEs. A standard way of measuring
the efficiency of profit shifting is to compute effective tax rate, which is the ratio of tax
payments to operating profits. In this model, the effective tax rate is computed as,

ef f

t

=



tD 1 − tηD πi
πi


= tD

tD
1−
θ(1 − 2dP )
.

(4.24)

This indicates that the effective tax rate is determined by the tax rate and the effectiveness of profit shifting, captured by the second term of eq.(4.24).
Table 4.1 displays a case that globalization contributes to a decrease in the effective
tax rate for both an endogenous and a fixed tax cases but the decline is more prominent
under an endogenous tax. Notably, the main reason of the decline in the effective tax
rate is caused not by the efficiency of tax avoidance, but by a reduction in the tax rate.
We can see this by looking at the two bottom columns of the top and middle tables. The
bottom columns show the efficiency of tax avoidance and that profit shifting becomes
more efficient as globalization proceeds since the number of the columns decreases.
The smaller numbers under a fixed tax rate than those under an endogeneous tax rate
indicates that the MNEs’ tax avoidance is more effective under an exogenous tax ratein the sense that the proportion of the MNEs’ shifted profits is greater although theeffective tax rate is lower under a fixed tax rate. This alerts a simple comparison of theeffective tax rate over years as a measure of development of tax avoidance because thereduction may come from a direct reduction in tax rate and not from the efficiency oftax avoidance 1 − tηD .

4.5

Discussions and policy implications

This section discusses some key setups and assumptions.

104

Product Differentiation and Profit Shifting

4.5.1

Concealment cost

For simplicity, the benchmark model introduces a specific form of concealment costwhich is a function of lump sum shifted profits. Although this makes the modeltractable, it also makes the ways of profit shifting ambiguous. As one of the main
channel of profit shifting to tax haven is conducted with royalty payments on intangible
assets, this subsection assumes that the two MNEs have their own intangible asset suchas patent or trade marks in a tax haven to show robustness of the results.
Usually, royalty payments are based on proportional to sales. By assuming c = 0, theconcealment cost can be modified as;
C(αi , πi ) =ηα2 πi2where α ∈ [0, 1] represents the royalty rate. As the amount of shifted profits is πis = απiin this case, the optimal royalty rate is;
α
bi =

tD
,
η

which reduces the post-tax profits as;ηb
α 2 πiΠPi = (1 − tD )(πi − αb i πi ) + α
b i πi − i =
2



t2D
1 − tD +πi2ηwhich is the same as eq.(4.7) so that the following benchmark analysis and results holdin this modified setup.

4.5.2

Product differentiation in inputs

Another possibility on the source of differentiation is technological differentiation for
inputs rather than product differentiation of final products. In such a case, differentiation does not necessarily result in an increase in utility from the products in thesense of varieties. However, if an MNE develops its own technology to produce inputs in more efficient way, which is known as “process innovation”, the MNE produces
more products. In order to see the impact of types of R&D activities, this subsection
considers the case with process innovation.
As a source of differentiation comes from input, we assume homogeneous final products,
or s = 1, and the marginal cost of input is ci = c − di instead of c where di is105

Product Differentiation and Profit Shifting

the investment level for process innovation. Likewise, MNEs incur investment cost
γd2
F (di ) = 2 i to reduce marginal cost ci . We assume that this investment createsfirm specific technologies to reduce the marginal cost and more investment makes it
difficult for tax authorities to audit tax avoidance. Therefore, the coefficient of profit
shifting η is again a function of the investment levels.16 For simplicity, we specify theconcealment cost as;C(η, πiS ) =η(πiS )2,2πiwhere η =

θ.
di + dj(4.25)(d +d )t2
Then, the post tax profits for the MNEs become ΠPi = 1 − tD + i 2θj D πi −F (di ).
The tax avoidance gain captured by the third term exists and makes the investment
more than the case without profit shifting as proposition 4.1 suggests.
Notably, even though such additional investments reduce the marginal cost, the MNEs’
equilibrium post-tax profits can decrease because of fierce market competition. In theform of product innovation, an increase in firm j’s investment expands the demand of
MNE i so that an increase in investment costs of MNE i is covered by magnified market
expansion by MNE j. However, an increase in MNE j’s investment in process innovation shrinks the market share of MNE j, which means that an increase in investment
costs of MNE i dominates an increase in operating profits. Formally, we can see theeffect:t2 dP∂ΠPi= − D2∂θθ

a − c + dP
3

2+

∂ΠPi ∂dPi,∂dPi ∂θ t2 (a − c + dP )

 t2 dP (a − c + dP )D∝ − D
+
2

θ
|
{z
} 

|
Direct: Tax saving

2θ
{z







dP t2D  ∂dPi −2 1 − tD +
,

θ
∂θ 

}|

{z
}

Indirect: Tax saving

Indirect: Competition(4.26)
where the third effect is not indirect demand size effect as seen in eq.(4.11) but indirectcompetition effect. In the appendix, we show that total effects can be negative andglobalization hurts MNEs. Therefore, unlike product differentiation on final product,
16
Even though the subsequent marginal cost is the same across firm, it is plausible assumptionthat η is a function of investment levels. Suppose there are several tasks to produce the goods
and the total marginal cost without R&D investment is c. Each MNE decreases marginal costs ofdifferent tasks by investing in process innovation and the total reduction in marginal costs is di .
Note that the value of patents is not comparable as patents are task specific. Therefore, there arestill room for the MNEs to justify their transfer prices to some extent.

106

Product Differentiation and Profit Shifting

process innovation driven by tax avoidance hurts MNEs if eq.(4.26) is positive. This
new result is summarized as the following proposition.
Proposition 4.5 Suppose that investments in R&D are the form of process innovation. Then, globalization results in a reduction in the post-tax profits of the MNEs
if eq.(4.26) is positive.
Proof. See Appendix.
As a common anticipation of tax havens is to benefit MNEs by providing them with
tax avoidance opportunities, proposition 4.5 is an intriguing result. Even though thepost-tax profits without tax havens are greater than those with tax havens, conducting
more investments is a dominant strategy for each MNE, which results in the “prisoner’s
dilemma” outcome in a non-cooperative game.

4.5.3

Under or excess investment

We explore whether the equilibrium product differentiation are excess- or underinvestments in the benchmark model. Without a tax haven, it is easily obtained thatthe equilibrium degree of product differentiation is less than the optimal level of product differentiation that maximizes welfare in country D. This is because more productdifferentiation increases consumer surplus and tax revenue but such gains are out of
MNEs’ consideration. Formally,4(a − c)2 (1 − dO + 2βtD )
∂U O
=
> 0,
∂di di =dO(3 − 2dO )3(4.27)

is obtained.
With a tax haven, it is unclear whether the equilibrium level of product differentiation
is below the socially optimal level. At dP , the first derivative of welfare with respect
to d is;∂U (xPi , xPj , y P )∂di
t2D (5 − 6dP )(2β − 1)
2(1 − 2d ) + 2βtD −.
2θ(1 − 2dP )2
d=d(4.28)
The first and second terms in the parenthesis are the change in consumer surplus
from the differentiated products and the change in tax revenue from operating profits,
respectively, and the third term shows the net loss from tax avoidance. The loss term(a − c)2=(3 − 2dP )3
P



P

107

Product Differentiation and Profit Shifting

Figure 4.2: Socially optimal dbecomes greater as profit shifting is less costly, or low θ, and the marginal utility fromthe public goods β is large. Specifically, we can calculate,∂U (xPi , xPj , y P )
∂di

<0
d=dP

⇐⇒ β >

4(2 − 2dP − tD )θ(1 − 2dP )2 + t2D (5 − 6dP )P≡ βopt,2PP
22{tD (5 − 6d ) − 2tD θ(1 − 2d ) }(4.29)

as a condition where excess investment is realized.
Figure 4.2 shows the above discussions.17 In the figure, welfare in country D under thecase of profit shifting with two different β are depicted. The vertical solid line represents
the equilibrium investment level dP . A single-dot curve illustrates welfare with β = 2
and the single-dot vertical line shows the socially optimal level of investment, denoted
by dPβ=2 . As we can see the order dP < dbPβ=2 , the equilibrium investment is underinvestment. However, the double-dot curve and vertical line depict those with β =4, and the opposite order is observed dbPβ=4 < dP , which means the equilibrium ischaracterized as excess-investment. As mentioned above, if the country sees a larger
weight on the public good provision, an emergence of a tax haven can result in excessinvestment in product differentiation.
17

d2

The parameter values used for the figure is: a = 2, c = 1, tD = 0.3, θ = 0.6, and F (di ) = 2i .

108

Product Differentiation and Profit Shifting

The above argument is summarized as the following proposition.
Proposition 4.6 In the absence of profit shifting, the level of investment on
product differentiation is less than the optimal level. However, opportunities of
profit shifting makes the degree of investments in product differentiation greaterthan the optimal degree when the government weights tax revenue less, namely,
P P∂U (xPi ,xj ,y )Pholds.
< 0 holds if and only if β > βopt
∂dP
di =dj =dP

This proposition implies that policies to facilitate R&D investment in product differentiation does not necessarily lead to welfare improvement in the presence of profit
shifting although they are always welfare improving without profit shifting. Given thehuge tax revenue losses explained in the introduction, the currently arising competition for attracting R&D activities such as patent box may cause more R&D activities
and result in excess-investment.

4.6

Concluding remarks

In this paper, we have analyzed MNEs’ incentive to invest more in product differentiation in the presence of profit shifting. Product differentiation reduces the similarity
of MNEs’ products, which makes it difficult for tax authorities to find comparable orappropriate AL price and to audit MNEs’ tax avoidance behaviours. Based on thispractical difficulty, our model has shown a new rationale that MNEs engage in higher
product differentiation. We also have analyzed the impacts of globalization, captured
by a reduction in marginal cost of using a tax haven. Globalization reduces the costof profit shifting and increase a marginal benefit from product differentiation. As aresult, the further globalization leads to the more product differentiation.
The more product differentiation has counteracting effects. On the positive side,
consumers and MNEs benefit due to more product differentiation and less market
competition. On the negative side, tax revenue in a high tax country becomes smaller
and thus the provision of a public good is scarce. Our result showed that globalization
can improve welfare in a non-tax haven country when the tax revenue losses are notsignificant. Surprisingly, our numerical example showed that under such situations,an emergence of a tax haven can increase. This striking result does not appear once
we endogenized the tax rate of the non-tax haven country.
We have also considered some extensions and found several policy implications fromthe model. First, designing policies to promote product differentiation is not always
109

Product Differentiation and Profit Shifting

beneficial if profit shifting is taken into account. This is because product differentiation
magnifies profit shifting which reduces a public goods provision. As this loss is more
important when a country recognizes a higher weights on utility from the public good, a
policy reducing product differentiation is likely optimal. Second, our analysis predicts
that a type of differentiation is crucial for MNEs. Product differentiation always
benefits the MNEs thanks to the market expansion while product innovation canhurt them due to a fiercer competition effect. This implies policy makers should pay
attention to types of R&D when they design policies for R&D.
Even though this study found a set of new results, our analysis can be extended in several ways. First of all, although this study implicitly assumes that the world adopts
separate accounting system, MNEs’ incentive to invest in product differentiation candiffer under formula apportionment which allocates MNEs’ tax base across countries
based on real economic activities and is independent of product characteristics. As
introduction of formula apportionment is frequently argued, the effects of a change
in international tax scheme is important to understand. Furthermore, we postulated
that product differentiation takes place in the final product market but product differentiation is also seen in intermediate industries. Thus, investigation of a verticallyrelated industries can be interesting. Finally, governments’ behaviours should be analyzed more in detail in order to obtain richer policy implications. Especially, as globally cooperative actions such as BEPS project begins, interaction between countries
in non-cooperative and cooperative game can be one of the interesting extensions.

110Conclusion
This dissertation has considered MNEs’ tax avoidance strategies. All the chapters are
based on imperfect competition setups and have addressed specific questions which are
based on empirically observed relationship, such as transfer pricing for ROO (Chapter3), MNEs’ location in a high tax country (Chapter 1 and Chapter 2) and tax avoidanceby R&D intensive MNEs (Chapter 4). In this conclusion, I will draw some inferencesthat are common to all chapters although the main focuses are different.
The first three chapters have investigated how MNEs’ location choice is influenced by
tax regulation, economic integration and trade policy in the presence of profit shifting.
One of the common striking results is that locating an affiliate of MNEs in a high tax
country can be the optimal international organization structure, if profit shifting isallowed. This can be the opportunity of transferring profits being made from a hightax country (Chapter 1). Another rationale in Chapter 2 is that locating in a high tax
country lowers transfer prices, which makes its distribution branch more aggressive
in foreign markets. In addition, locating in a high tax country can be profitableby pursuing a preferential tariff, as we have seen in Chapter 3. As policy makers
expect that lowering their corporate tax rate attracts FDI, this result is surprising.
However, it is in line with several empirical findings (e.g. Overesch (2009) and Hornerand Aoyama (2009)). Moreover, Chapter 1 and 3 have shown that this pattern ofgeographically separated location is an outcome in the absence of regulations such as
the ALP and ROO. Although the primary reason of these rules is to prevent transfer
pricing manipulation and trade deflection, they may also contribute to prevent MNEs’
tax avoidance via location choices.
A major interest of both academics and policy makers is the effect of MNEs’ tax
avoidance decision on corporate tax revenue. Chapters 1 and Chapter 2 reveal that in
the presence of tax avoidance, attracting FDI does not necessarily lead to an increasein tax revenue. In Chapter 1, the tax base in a low tax country increases thanks to the
ALP but tax revenues in the low tax country declines. When the ALP does not exist,
111

Conclusiona large proportion of profits are shifted from a high tax country to a low tax country.
With the ALP, however, such inflows of profits no longer flows to a low tax country.
Additionally, in Chapter 2, a high tax country can attract MNEs’ production units if
trade costs are low. However, tax revenues fall nevertheless, because tax avoidance ishighly efficient under these conditions.
The last two chapters also indicate a positive side of profit shifting in a high tax
country. The traditional view of tax avoidance is negative because falling revenues
lead to less public good provisions (e.g. Slemrod and Wilson (2009)). In contrast to
this negative evaluation, Chapter 3 has argued that transfer pricing with ROO can
induce inflows of an MNE’s tax base into an FTA region and Chapter 4 has pointed outthat more product differentiation undertaken to avoid taxes can benefit consumers.
This highlights the importance of research across fields as MNEs’ business operations
are complex and there may exist hidden positive effects of profit shifting, even though
tax avoidance tends to hurt a high tax country.
In this dissertation, I have pointed out several effects of regulations (i.e. the ALP andROO) by combining profit shifting with other strategies of MNEs (namely location
choice and R&D activities), and some of the derived results contrast with common
knowledge. This clearly means that a further analysis is indispensable to get a fuller
understanding of the implications of tax avoidance. Furthermore, given the huge importance of tackling the issues of MNEs’ tax avoidance, worldwide political cooperation such as BEPS project is essential in the coming generation. Therefore, further
research in this direction remains an important topic for both academics and policy
makers.

112

Appendices113

Appendix to Chapter 1

A

Appendix to Chapter 1

A.1

List of Key Variables
Table A.1: List of Key Variables of Chapter 1

BenchmarkInternal price of the input
Arm’s length price of the input
Price of the affiliate’s final good
Price of the local firm’s final good
Quantity of the affiliate’s final good
Quantity of the local firm’s final good
Pre-tax profit of the upstream affiliate
Pre-tax profit of the downstream affiliate
Pre-tax profit of the local firm
Total post-tax profit of the MNE

Co-location
g
g∗
p
p∗
q
q∗
πu
π
π∗
Π

Separate locationg S (transfer price)
g∗S
pS
pS∗
qS
q∗S
πuS
πS
π∗S
ΠS

Arm’s Length Principle (ALP)
Arm’s length price of the input
Price of the affiliate’s final good
Price of the local firm’s final good
Quantity of the affiliate’s final good
Quantity of the local firm’s final good
Pre-tax profi of the upstream affiliate
Pre-tax profit of the downstream affiliate
Pre-tax profit of the local firm
Total post-tax profit of the MNE

Co-location
g̃
p̃
p̃∗
q̃
q̃∗
π̃u
π̃
π̃∗
e
Π

Separate location
g̃ S
p̃S
p̃S∗
q̃ S
q̃∗S
π̃uS
π̃ S
π̃∗S
eS
Π

We note that (i) in the ALP case, the internal price is equal to the arm’s length price,(ii) the downstream firms produce one unit of final goods using one unit of intermediate
inputs, and (iii) the pre-tax profits from the parent country π̄ are always constant.

A.2

Proof of Proposition 1.3

Tax Revenues in the Host Country. Assuming T > T = 1/4, we show that whent ∈ (t, t∗ ), tax revenues in the benchmark case, T RH , are greater than those in the114

Appendix to Chapter 1g
ALP case, T
RH . It suffices to check the difference of taxable profits:gT
RH − T RH = t[π̃u + π̃ + π̃∗ − (π S + π∗S )] < 0,→ π̃u + π̃ + π̃∗ − (π S + π∗S ) ≡ Γ < 0.
If it is shown that (i) Γ < 0 holds at t = t∗ and (ii) Γ is increasing in t, we can conclude
that Γ is negative for t ∈ (t, t∗ ). First we check (i):Γ|t=t∗ = −13(1 − c)2< 0.
72(ii) requires the following condition:dΓ∂(π S + π∗S ) dg S
=−
> 0,
dt
∂g S
dt
where

dg S
2(1 − c)(1 − T )
=
> 0,
dt
t − 2T + 1

noting that profits earned in the host under the ALP, π̃u + π̃ + π̃∗ , are independent oftransfer price and thus of tax rates. We only need to check that profits in the host in
the benchmark case, π S + π∗S , are decreasing in transfer price, g S :∂(π S + π∗S )5g S − 4
=
∂g S
8
<

g∗S − 1< 0,
2where we make use of g S < g∗S and g∗S < 1. Both (i) and (ii) are proved to be true andthus we complete the proof.

Tax Revenues in the World. We first show g S < c for t ∈ (t, t∗ ) while assuming
T > T = 1/4. g S < c requires the following condition:gS − c =(1 − c)(t − T )< 0,t − 2T + 1

which obviously holds under our assumption.

115

Appendix to Chapter 1
We then show the following:gT
RW − T RW = −T πuS + t[π̃u + π̃ + π̃∗ − (π S + π∗S )]= −T πuS + tΓ ≡ ∆ > 0,gwhere T RW and T
RW are world tax revenues in the benchmark and the ALP cases,
respectively.
Analogous to the previous case, if it is shown that (i) ∆ is positive at t = t∗ and (ii) ∆is decreasing in t, we can conclude that ∆ > 0 holds for t ∈ (t, t∗ ). First we see (i):∆|t=t∗ =(13 − 2T )(1 − c)2
> 0.
216

To prove (ii), it suffices to show
d∆
dπ S
dΓ
= −T u + Γ + t
dt
dt
dt


S
dΓ dπu
<t
−
+Γ
dt
dt
=t

∂(π S + π∗S − πuS ) dg S
+ Γ < 0,∂g S
dt

where from the first to the second line we make use of t < t∗ < T . As we have seen
dg S /dt > 0 and Γ < 0, we only need to checkc + 2 − 3g S∂(π S + π∗S − πuS )
=
−
∂g S
2
c + 2 − 3c<−2
= −(1 − c) < 0,noting that g S < c from the first to the second line. We complete the proof.

A.3

A Local Firm in the Upstream Industry

In the text, the upstream affiliate is the only supplier of inputs. One may wonder thissetting is crucial for the results, but it is not the case. We see that the upstream affiliate
116Appendix to Chapter 1
may be located in the high-tax parent country (“separate location”) in the benchmark
case (Proposition 1.1) and the imposition of the ALP may change this location pattern(Proposition 1.2). We introduce a local upstream firm in the host country. The local
upstream firm has the same marginal cost c as the MNE’s upstream affiliate andcompetes with the affiliate in a Bertrand fashion. The timing proceeds in the samemanner as in the text. First, the MNE chooses a location for upstream production.
Then the MNE and the local upstream firm set input prices. Finally the downstream
affiliate and the local firm source the inputs and produce final goods.
As inputs produced by the two upstream firms are homogeneous, the downstream firms
buy inputs from the lowest price supplier. Hence, the dominant strategy for the local
upstream is to set its input price equal to the marginal cost c. Considering this strategyof the local upstream, the MNE sets input prices equal or lower than c. We need tomodify the MNE’s maximization problem so as to include inequality constraints on
input prices.

Benchmark Case. Let us first look at the separate-location scheme. The maximization
problem for the MNE is modified as1
max ΠS = (1 − T )[π̄ + (g S − c)q S + (g∗S − c)q∗S ] + (1 − t)(pS − g S )q S ,g S ,g∗Ss.t. g S ≤ c, g∗S ≤ c,where the final good’s price pS and quantities (q S , q∗S ) are defined in Section 1.3 andwe assume that the MNE upstream affiliate takes all the input demand if its prices areequal to the ones of the local upstream.
Letting λ and µ be the Lagrange multipliers for the constraints of g S ≤ c and g∗S ≤ crespectively, we solve the above problem to get
gS = c +(1 − c)(t − T )< c,t − 2T + 1

λ = 0,g∗S = c,µ = (1 − c)(1 − T )/2 > 0,1
We do not distinguish the notation of variables between the unconstrained problem in the
text and the constrained problem here.

117

Appendix to Chapter 1
where we maintain the assumptions (A1): t > t and t < T . As the multipliers
are all non-negative, the equilibrium prices satisfy the Kuhn-Tucker conditions for
optimization. g S allows a similar interpretation to the one for the unconstrained
optimal transfer price defined in Eq. (1.6). The first term is the base price equal tothe arm’s length price. The second term represents the tax-manipulation effect.
The associated post-tax profits are then given by(1 − T )(1 − c)2.
Π = (1 − T ) π̄ +4(t − 2T + 1)
SUnder the co-location scheme in the benchmark case as discussed in Section 1.3, the
MNE sets input prices higher than c in the unconstrained maximization problem, i.e.,g > c and g∗ > c. Hence, in the constrained problem here, it can be confirmed that
the MNE sets input prices equal to c, i.e., g = c and g∗ = c, and obtains the following
post-tax profits:(1 − t)(1 − c)2.
Π = (1 − T )π̄ +4
As easily seen, Π is smaller than ΠS at t ∈ (t, T ). In other words, the MNE’s optimal
choice is that the upstream affiliate is always located in the parent country (separate
location). Even when considering the local upstream, our conclusion still holds; theupstream production may be located in the high-tax country for the tax-manipulation
purpose.

ALP Case. In the ALP case, the optimal input prices in the unconstrained problem
discussed in Section 1.4 are never below the marginal cost c under the two schemes,i.e., g̃ > c and g̃ S > c. By the same reasoning as before, it can be confirmed that theconstrained problem gives the input prices equal to the marginal cost, i.e., g̃ = c andg̃ S = c. Hence, the associated profits are identical with the one under the co-locatione =Π
e S = Π at t ∈ (t, T ). Unlike the benchmark
scheme in the benchmark case, i.e., Πcase, the tax-manipulation effect disappears and the two countries are indifferent as
to the location choice. In this generalized setting, we still see that the imposition of
the ALP may change the location pattern as argued in the text.

118

Appendix to Chapter 1

A.4

Many Local Firms in the Downstream Industry

As in A.3, we see here that our main conclusions are maintained in a more generalized
setting than in the text. Consider N local firms in the downstream industry. The local
firms are assumed to be symmetric and have the same marginal cost c. If N is set to
be unity, all the following results reduce to the corresponding results in the text.
The demand functions for the downstream affiliate and the local firm j are respectively
given by
p = 1 − q,p∗j = 1 − q∗j .
The following procedure is the same as in the text and we solve the problem backward.
Considering the above demand schedules, the downstream firms choose quantities tomaximize their own profits:
1−g,
2
1 − g∗j
q∗j =
.
2
q=

Benchmark Case. Given the optimal quantities the downstream firms choose, the
MNE sets input prices to maximize its post-tax profits. In the co-location scheme, theequilibrium input prices are given byg = c,
g∗ =

1+c
,
2

where g∗j = g∗ holds for all j and the SOCs trivially hold.
The total post-tax profits in equilibrium are calculated as
Π = (1 − T )π̄ +(1 − t)(1 − c)2 (2 + N )
.
8

119

Appendix to Chapter 1
The equilibrium input prices in the separate-location scheme are given by(1 − c)(t − T ),t − 2T + 1
1+c
g∗S =
,
2

gS = c +where t − 2T + 1 > 0 and the SOCs hold under (A1): t > t. Under t < T , the second
term of g S is negative so that the tax-manipulation effect works in the same way as in
Eq. (1.6).
The total post-tax profits in equilibrium are calculated as(1 − c)2 {N t − 2(1 + N )T + 2 + N }.
Π = (1 − T ) π̄ +8(t − 2T + 1)
STaking difference between the post-tax profits in the two schemes givesΠ − ΠS =Θ0 (1 − c)2 (T − t),16(t − 2T + 1)

where Θ0 ≡ 2(2 + N )t + 4(1 + N )T + 2N.
The profit difference becomes zero at t = T and t = t0 where t0 is the solution of Θ0 = 0.
It can be confirmed that t0 is in between (t, 1] if N is not sufficiently large.2 In this case,
we have Π − ΠS < 0 for t ∈ (t, t0 ) and Π − ΠS ≥ 0 for t ∈ [t0 , T ). We can conclude that
the MNE chooses the separate location if the tax difference is large as in Proposition
1.1.

ALP Case. Analogous to the benchmark case, the equilibrium input price under theco-location scheme becomesg̃ =c + N + cN,
1 + 2N

where the SOC trivially holds. It can be confirmed that g < g̃ < g∗ holds as in the
It always holds that t0 < T . t0 is decreasing in N if N is not sufficiently large, implying t0 > t
for not sufficiently large N .
2120

Appendix to Chapter 1
text. The total post-tax profits are given by22

e = (1 − T )π̄ + (1 − t)(1 − c) (1 + N ) .
Π4(1 + 2N )Turning to the separate-location scheme, the equilibrium input price becomesg̃ S =(1 − c)(1 + N )(t − T )c + N + cN+.
| 1 +{z2N } (1 + 2N )[t − 2(1 + N )T + 1 + 2N ]=g̃We can check that as long as N is not sufficiently large, g S < g̃ < g∗ holds as in the
text.
The total post-tax profits under the separate-location scheme are given bySeΠ = (1 − T ) π̄ +

(1 − T )(1 − c)2 (1 + N )2,4{t − 2(1 + N )T + 1 + 2N }where the SOC requirest − 2(1 + N )T + 1 + 2N > 0.
The profit difference then becomes
2

2

e −Π
e S = (T − t)(1 − c) (1 + N ) [t − (1 + 2N )T + 2N ] ,Π
4(1 + 2N )[t − 2(1 + N )T + 1 + 2N ]which is positive as long as the SOC holds. This implies that in the ALP case the MNE
always chooses the co-location scheme as in Proposition 1.2.

A.5

Trade Costs

We introduce here trade costs for inputs. If the upstream affiliate is located in the parent country, the downstream firms pay an extra unit trade cost τ > 0 when importing
inputs (Kind et al., 2005). If it is located in the host country, trade costs play no roleand the analysis is the same as in the text. Thus, we present only the results in theseparate-location scheme in the following.

Benchmark Case. The maximization problems of the downstream firms are modified
121

Appendix to Chapter 1asmax π S = (pS − g S − τ )q S ,qmax π∗S = (pS∗ − g∗S − τ )q∗S .
q∗Solving these gives
1 − gS − τq =,2
1 − g∗S − τ
.
q∗S =
2
S

The total post-tax profit of the MNE is also modified accordingly:ΠS = (1 − T )[π + (g S − c)q S + (g∗S − c)q∗S ] + (1 − t)(pS − g S − τ )q S .
The equilibrium input prices to maximize it are given by(1 − c − τ )(t − T ),t − 2T + 1
1+c−τ
g∗S =
.
2
gS = c +We impose an assumption of τ < 1 − c to ensure positive outputs. The equilibrium
total post-tax profit is calculated as(1 − c − τ )2 (t − 4T + 3)
Π = (1 − T ) π̄ +.
8(t − 2T + 1)
S

Taking difference between the post-tax profits in the two schemes givesΠ − ΠS =F (t),16(t − 2T + 1)

where F (t) ≡ −3(1 − c)2 t2 + [τ {2(1 − c) − τ } + (1 − c)2 (7T − 1)]t
+ τ [2(1 − c) − τ ](1 − T )(3 − 4T ) + T (4T − 1)(1 − c)2 .
We check (i) whether F (t) = 0 has two real roots and (ii) whether at least either ofthem falls into (t, T ).

122

Appendix to Chapter 1
F (t) = 0 has two real roots if its determinant D is positive:D(τ ) ≡ (1 − T )2 [τ 4 − 4(1 − c)τ 3 − 30(1 − c)2 τ 2 − 68(1 − c)3 τ + (1 − c)4 ] > 0,for τ ∈ [0, 1 − c).
We can verify this inequality by noting the following relations:
D(τ = 0) = (1 − T )2 (1 − c)4 > 0,
D(τ = 1 − c) = 36(1 − T )2 (1 − c)4 > 0,D0 (τ ) = −4(1 − T )2 (1 − c − τ )[τ 2 − 2(1 − c)τ − 17(1 − c)2 ] > 0.
Let t1 and t2 be respectively the smaller and the larger root of F (t) = 0. From thefacts that F (t) has a negative coefficient of the quadratic term and that ∂F (t; τ )/∂τ =2(1 − T )(1 − c − τ )(t − 4T + 3) > 0 holds, we see t1 is decreasing in τ while t2 isincreasing in τ . At τ = 0, t1 is reduced to t∗ = (4T − 1)/3 and t2 to T .
If T > 3/4 holds, t1 lies in (0, T ) regardless of τ so that the separate-location scheme
is chosen for t ∈ (0, t1 ). If T ≤ 3/4 holds, t1 may become negative at sufficiently hightrade costs. The maximum level of trade costs that allows for the separate-location
scheme is given bysτ = (1 − c) 1 −8T 2 − 8T + 3.
(1 − T )(3 − 4T )Even if T ≤ 3/4, we observe the separate-location scheme for t ∈ (0, t1 ] as long asτ < τ.
In sum, as in Proposition 1.1, assuming the parent’s tax rate is high enough (T > 3/4),
the MNE locates the upstream affiliate in the high-tax parent country if the host’s tax
rate is low enough (t ∈ (t, t1 ]) and otherwise locates it in the low-tax host country.
Higher trade costs reduce the range of tax rates where the separate-location scheme ischosen, i.e., dt1 /dτ < 0.

ALP Case. Analogously, the equilibrium input price to maximize the total post-tax

123Appendix to Chapter 1
profit is given byg̃ S =

1 + 2c − τ
2(1 − c − τ )(t − T )+.
33(t − 4T + 3)

The associated total post-tax profit becomes(1 − c − τ )2 (1 − T )Se.
Π = (1 − T ) π +t − 4T + 3
The profit difference is given by
2

2

e −Π
e S = (1 − c) (t − 3T + 2)(T − t) + 3τ [2(1 − c) − τ ](1 − T ) > 0,Π3(t − 4T + 3)
where we note that τ < 1 − c < 2(1 − c). This implies that with the ALP the MNE
always chooses the co-location scheme as in Proposition 1.2.

A.6

Costs of Transfer Pricing

Some studies in the literature assume that MNEs are subject to an extra concealment
cost of transfer pricing (e.g., Nielsen et al., 2003, 2008; Kind et al., 2005). We formulate
here the concealment cost as a quadratic function of the difference between the transfer
price and the arm’s length price, i.e., C(g, g∗ ) = δ(g − g∗ )2 /2 with δ ≥ 0. Following
the above-mentioned studies, we assume that the upstream affiliate bears this cost.
Thus, the concealment cost does not affect the optimal choices by the downstream
firms, which are the same as those given in the text.

Benchmark Case. In the co-location scheme, the total post-tax profit is modified as
Π = (1 − T )π + (1 − t)[(g − c)q + (g∗ − c)q∗ − C(g, g∗ ) + (p − g)q],
where C(g, g∗ ) = δ(g − g∗ )2 /2,

δ ≥ 0,

noting that the optimal outputs (q, q∗ ) chosen by the downstream firms are the sameas those in the text: q = (1 − g)/2; q∗ = (1 − g∗ )/2. The equilibrium input prices to124Appendix to Chapter 1
maximize it are given byδ + c(1 + 2δ),
1 + 3δ
1 + 2δ + c(1 + 4δ)g∗ =.
2(1 + 3δ)g=

The equilibrium total post-tax profit then becomesΠ = (1 − T )π +(1 − t)(1 − c)2 (3 + 8δ).
8(1 + 3δ)In the separate-location scheme, we can analogously define the total post-tax profit
and compute the equilibrium input prices as follows:gS = c +g∗S =(1 − c)[t − T + δ(t − 2T + 1)],
t − 2T + 1 + δ(t − 4T + 3)

(t − 2T + 1)(1 + c + 2δ) + 4cδ(1 − T ).
2[t − 2T + 1 + δ(t − 4T + 3)]

The equilibrium total post-tax profit is calculated as(1 − c)2 {t − 4T + 3 + 8δ(1 − T )}
Π = (1 − T ) π +.
8{t − 2T + 1 + δ(t − 4T + 3)}
S

Taking difference between the post-tax profits in the two schemes givesΠ − ΠS =G(t)(1 − c)2 (T − t),8(1 + 3δ)[t − 2T + 1 + δ(t − 4T + 3)]

where G(t) ≡ (1 + δ)(3 + 8δ)t − 8(3T − 2)δ 2 − (20T − 9)δ + 1 − 4T,
noting that its sign only depends on G(t). G(t) = 0 holds at t∗∗ , which is defined byt∗∗ =4T − 1 8δ(2 + 5δ)(1 − T )−.
3
3(1 + δ)(3 + 8δ)Without the concealment cost, t∗∗ is reduced to t∗ defined in Eq. (1.8). When T >T = 1/4 holds as in the text and δ is not too high, t∗∗ becomes positive.3 In this case,as in Proposition 1.1, we observe the separate-location scheme for t ∈ (t, t∗∗ ] and theˆˆδ is bounded above by δ ≡ min{δ̂, δ̂}, where δ̂ ≡ sup{δ : t∗∗ > 0} and δ̂ ≡ min{sup{δ : Π >S0}, sup{δ : Π > 0}}.
3

125Appendix to Chapter 1
co-location scheme for t ∈ (t∗∗ , T ). The more difficult concealment is, the less likely
we are to observe the separate-location scheme, i.e., dt∗∗ /dδ < 0.

ALP Case.
As the transfer price must be equal to the arm’s length price, theconcealment cost plays no role. The results in both schemes are the same as those in
the text.

A.7

Differentiated Inputs

In the text, the downstream affiliate and the local firm purchase the same input fromthe upstream affiliate. We consider here the situation where the two downstream firms
need a different type of inputs. The upstream affiliate produces the two different inputs
using different technology. That is, the marginal cost of input for the downstream
affiliate is c ∈ [0, 1), while that for the local firm is c∗ ∈ [0, 1).
As the input for the downstream firm is not perfectly comparable to that for the local
firm, tax authorities cannot require that the prices of the two inputs must be thesame. Instead, they allow for a certain range of arm’s length price. This arm’s length
range gives the MNE room for price differentiation even under the ALP. The partial
comparability of the two inputs implies that they are produced using more or less thesame technology. We thus assume the difference of marginal cost is not too large:|c∗ − c| < 1 − c.

Benchmark Case.
In the co-location scheme, the total post-tax profit isΠ = (1 − T )π + (1 − t)[(g − c)q + (g∗ − c∗ )q∗ + (p − g)q],
where the optimal outputs (q, q∗ ) chosen by the downstream firms are the same as
those in the text: q = (1 − g)/2; q∗ = (1 − g∗ )/2. The equilibrium input prices tomaximize it are
g = c,g∗ =1 + c∗,
2126

Appendix to Chapter 1
where we note g < g∗ . The equilibrium total post-tax profit then becomes(1 − c)2 (1 − c∗ )2Π = (1 − T )π + (1 − t)
+
.
4
8


In the separate-location scheme, the total post-tax profit is modified as follows:ΠS = (1 − T )[(g S − c)q S + (g∗S − c∗ )q∗S ] + (1 − t)(pS − g S )q S .
The equilibrium input prices are(1 − c)(t − T ),t − 2T + 1
1 + c∗,g∗S =2

gS = c +where we note g S < g∗S . The equilibrium total post-tax profit is calculated as(1 − c∗ )2 (1 − T )(1 − c)2
Π = (1 − T ) π ++.
84(t − 2T + 1)
SThe MNE prefers the co-location scheme if
S



Π−Π =

1
8(t − 2T + 3)

(T − t)[t{3 − 2c(2 − c) − c∗ (2 − c∗ )}
2

2

2



− 2T {(1 − c) + (1 − c∗ ) } + (1 − c∗ )→ t > t∗ ≡> 0,

2T [(1 − c)2 + (1 − c∗ )2 ] − (1 − c∗ )2.
3 − 2c(2 − c) − c∗ (2 − c∗ )where we can confirm t∗ ∈ (0, T ) if T is sufficiently large:
T > T ≡ max

1(1 − c∗ )2,
4 2[(1 − c)2 + (1 − c∗ )2 ]

.

The co-location scheme is chosen if the host’s tax rate is close to the parent’s(t ∈ (t∗ , T )) and the separate-location scheme is chosen otherwise (t ∈ (0, t∗ ]) as
in Proposition 1.1.

ALP Case. In the co-location scheme, the transfer price g̃ must be within the rangeof [g̃∗ − e, g̃∗ + e] with e > 0. We assume e is not too large, otherwise the situation
127

Appendix to Chapter 1
is reduced to the benchmark case. The MNE sets the price g̃∗ to the local firm andg̃ = g̃∗ + ẽ to the downstream affiliate, where ẽ ∈ [−e, e]. It chooses g̃∗ and ẽ tomaximize the total post-tax profit:e = (1 − T )π + (1 − t)[(g̃∗ + ẽ − c)q̃ + (g̃∗ − c∗ )q̃∗ + (p̃ − g̃∗ − ẽ)q̃],max Πg̃∗ ,ẽnoting that the optimal outputs (q̃, q̃∗ ) chosen by the downstream firms are the sameas those in the text.
As the fact that g < g∗ holds in the benchmark case suggests, the MNE tries to set g̃lower than g̃∗ and thus chooses ẽ = −e. The equilibrium input prices are
1 + c + c∗ + e,
3
1 + c + c∗ − 2e.
g̃ = g̃∗ − e =3g̃∗ =The total post-tax profit can then be rewritten as(2 − c − c∗ )2 e(1 − 2c + c∗ + e)e
Π = (1 − T )π + (1 − t)−.
126
In the separate-location scheme, we can analogously define the total post-tax profit
and compute the equilibrium input prices as follows:g̃∗S =

1 + c + c∗ + e (2 − c − c∗ + 2e)(t − T )+,33(t − 4T + 3)g̃ S = g̃∗S − e =1 + c + c∗ − 2e (2 − c − c∗ + 2e)(t − T )+,33(t − 4T + 3)

where the MNE sets ẽ = −e as implied by g S < g∗S . The equilibrium total post-tax
profit is calculated as(1 − T )(2 − c − c∗ )2 − 2e{e(t − 2T + 1) + κ}Se
Π = (1 − T ) π +,4(t − 4T + 3)
where κ ≡ (1 − c)(1 − t) − (c − c∗ )(t − 2T + 1).

128

Appendix to Chapter 1
Taking difference between the post-tax profits in the two schemes givese −Π
e S = H(e)(T − t) ,Π12(t − 4T + 3)
where H(e) ≡ −2(t − 6T + 5)e2 + 2[1 − t + 2c(t − 3T + 2) − c∗ (t − 6T + 5)]e
+ (2 − c − c∗ )2 (t − 3T + 2).
Since T − t > 0 and t − 4T + 3 > 0 hold, the inequality is positive if H(e) > 0 holds.
Noting that t − 6T + 5 > 0 and t − 3T + 2 > 0 hold because of (A1): t > t, we seethat H(e) has a negative coefficient of the quadratic term and that H(0) > 0. Theseobservations imply that H(e) > 0 holds if e ∈ (0, e2 ), where e2 is the larger root of
H(e) = 0. In other words, if the degree of input differentiation is so low that the arm’s
length range is narrow enough, the MNE always chooses the co-location scheme as in
Proposition 1.2.

A.8

Endogenous Profits in the Parent Market

In the text, we assume that the MNE earns exogenous profits π from different businessin the parent country. Here we endogenize it by introducing a local downstream firm in
the parent. The local firm is the monopolist facing the demand curve of P∗ = 1 − Q∗ .
It sources the same type of inputs as do the downstream firms in the host, from the
upstream affiliate at the price of G∗ . As the parent’s and the host’s markets aresegmented, the presence of the local firm does not affect the equilibrium outputs andinput prices for the downstream firms in the host. It only affects the location choice ofthe MNE, as we shall see below.

Benchmark Case. In the co-location scheme, the total post-tax profit is modified as
Π = (1 − t)[(g − c)q + (g∗ − c)q∗ + (G∗ − c)Q∗ + (p − g)q],
where the optimal outputs (q, q∗ ) chosen by the downstream firms are the same as
those in the text: q = (1 − g)/2; q∗ = (1 − g∗ )/2. We also note Q∗ = (1 − G∗ )/2. The

129

Appendix to Chapter 1
equilibrium input prices to maximize it are given byg = c,g∗ = G∗ =1+c.
2

The equilibrium total post-tax profit then becomesΠ=(1 − t)(1 − c)2.
2

In the separate-location scheme, the total post-tax profit is modified as follows:ΠS = (1 − T )[(g S − c)q S + (g∗S − c)q∗S + (GS∗ − c)QS∗ ] + (1 − t)(pS − g S )q S .
The equilibrium input prices are(1 − c)(t − T ),t − 2T + 1
1+cg∗S = GS∗ =.
2

gS = c +The equilibrium total post-tax profit is calculated asΠS =(1 − T )(1 − c)2 (t − 3T + 2).
4(t − 2T + 1)

The profit difference takes a complex form and is hard to characterize analytically.
We thus rely on numerical simulations. Figure A.1 draws the total post-tax profits inthe two schemes for different levels of the host’s tax rate.4 In Figure A.1 (a), where
the parent’s tax rate is high (T = 0.35), the separate-location scheme is chosen fort ∈ (0, t∗ ) and the co-location scheme for t ∈ [t∗ , T ). In Figure A.1 (b), where theparent’s tax rate is low (T = 0.2), the co-location scheme is chosen for the entire
range t ∈ (0, T ). We have experimented various parameter values and confirmed thequalitatively same results as in Proposition 1.1. That is, the higher the parent’s tax
rate is, the more likely we are to observe the separate-location scheme as Figure A.1(a) shows.
ALP Case.

Analogous to the benchmark case, the equilibrium input price in the4

The parameter values are the same as those in Figure. 1.1: c = 0.3; (a)T = 0.35; (b)T = 0.2.
In this numerical example, t = 0 holds.

130

Appendix to Chapter 1

Figure A.1: Production location choice in the benchmark case: (a) high T and (b)
low T

131

Appendix to Chapter 1
co-location scheme is derived as follows:g̃ = g̃∗ = G̃∗ =1 + 2c.
3

The associated total post-tax profit becomese = (1 − t)(1 − c)(5 − 8c) .
Π9e positive, we assume c < 5/8.
To make Π
In the separate-location scheme, the equilibrium input prices and the resulting total
post-tax profit areg̃ S = g̃∗S = G̃S∗ =1 + 2c 2(1 − c)(t − T )+.
33(t − 4T + 3)

The associated total post-tax profit becomes22

e S = 2(1 − T ) (1 − c) (t − 3T + 2) .
Π(t − 4T + 3)2
Because the profit difference is difficult to characterize analytically, we again use numerical simulations. Figure A.2 illustrates the total post-tax profits in the two schemes
for different levels of the host’s tax rate.5 Unlike the benchmark case, the co-location
scheme is chosen for the entire range even when the parent’s tax rate is high. We haveconducted many simulations and confirmed that the ALP prevents the MNE fromchoosing the separate-location scheme as in Proposition 1.2.

A.9

Welfare Analysis

We confirm here that the results on tax revenues stated in Proposition 1.3 carry overto social welfare. That is, the location change induced by the ALP decreases the hostcountry welfare, while increases global welfare.

Host Country Welfare. Assuming T > 1/4, we show that when t ∈ (t, t∗ ), the social
welfare of the host country in the benchmark case, WH , are greater than that in the5

The parameter values are the same as those in Figure 1.2: c = 0.3; (a)T = 0.35; (b)T = 0.2.

132Appendix to Chapter 1

Figure A.2: Production location choice in the ALP case: (a) high T and (b) low T

133

Appendix to Chapter 1
fH . WH and W
fH are defined as follows:
ALP case, W(q S )2 (q∗S )2
WH =++ (1 − t)(π S + π∗S ) + t(π S + π∗S ),{z} | {z }| 2 {z 2 } |Producer surplus

Consumer surplus

fH =
W

q̃ 2
2×
| {z 2}

Tax revenues+ (1 − t)(π̃u + 2π̃) + t(π̃u + 2π̃),|{z} | {z }Consumer surplus

Producer surplus

Tax revenues

where we note q̃ = q̃∗ and π̃ = π̃∗ .
Taking the difference of these two gives

S 2
S 2
)
(q
)
+
(q
∗
fH − WH = q̃ −W+ [π̃u + 2π̃ − (π S + π∗S )] .
|
{z
}
2


2

(−)

As we know from Proposition 1.3 that the second square bracket term is negative, itsuffices to check the first square bracket term is negative:q̃ 2 −(q S )2 + (q∗S )2(1 − c)2 f (t)=,2
288(t − 2T + 1)2

where f (t) ≡ 23t2 + 46(1 − 2T )t + 56T 2 − 20T − 13.
This is negative if f (t) < 0. We can confirm f (t) < 0 by noting that (i) f (t) ismonotonically increasing in t for t ∈ (t, t∗ ) and (ii) f (t) takes a negative value at thetwo endpoints of t and t∗ . The host country attains a higher consumer surplus underno regulation than under the ALP. Without the ALP, the lower transfer price helps
the downstream affiliate reduce its price, benefiting the host’s consumers more.
We can thus conclude that the location change triggered by the ALP reduces the hostcountry welfare.

Global Welfare. We show that global welfare under no regulation is higher than thatfP ) be the social
under the ALP for t ∈ (t, t̂), where t̂ is smaller than t∗ . Let WP (or W
welfare of the parent country under the regulation (or under the ALP), which are given

134Appendix to Chapter 1
by
WP = T (π + πuS ) + (1 − T )(π + πuS ),{z}| {z }|Tax revenues

Producer surplus

fP =
W

Tπ
|{z}

Producer surplus+ (1 − T )π .
| {z }Tax revenues

Global welfare is defined as the sum of the host’s and parent’s social welfare. Comparing
the global welfare under the ALP with that under no regulation yields(q S )2 + (q∗S )2
f
f+ πuS + π S + π∗S
WP + WH − (WP + WH ) = π + q̃ + π̃u + 2π̃ − π +
2


2

=

(1 − c)2 h(t),288(t − 2T + 1)2

where h(t) ≡ 97t2 + 2(25 − 122T )t + 136T 2 − 28T − 11.
This is positive if h(t) > 0. We can confirm h(t) = 0 at t = t̂ ∈ (t, t∗ ) by noting that(i) h(t) is monotonically decreasing in t for t ∈ (t, t∗ ), (ii) h(t) > 0, and (iii) h(t∗ ) < 0.
We can thus conclude that if the international tax difference is sufficiently large (t ∈fP +(t, t̂)), the location change induced by the ALP increases global welfare, i.e., W
fH − (WP + WH ) > 0.
W

135



Appendix to Chapter 2

B

Appendix to Chapter 2

B.1

Equilibrium Allocation of Production Plants

We first prove Proposition 2.1 by showing whether the equilibrium share of plants
n1 exceeds one-half depending on trade costs. Then, we further investigate how amarginal change in trade costs affects n1 .

Proof of Proposition 2.1.
differential as∆Π ≡ Π1 − Π2 =Using Eqs. (2.5-1) and (2.5-2), we can write the profitµ (1 − t1 )(1 − φγ2 ) − φγ2 (t1 − t2 )(σ − 1)/σ·2σ
n1 + φγ2 n2µ (1 − t2 )(1 − φγ1 ) − φγ1 (t2 − t1 )(σ − 1)/σ·.
2σ
φγ1 n1 + n2σ−1
σ − ∆titj − tiwhere γi ≡, ∆ti ≡
, for i 6= j ∈ {1, 2}.
σ
1 − ti−(B1)

We evaluate this at n1 = 1/2:
∆Π|n1 =1/2 =µ(t1 − t2 ) · F (φ),
2
σ (1 + φγ1 )(1 + φγ2 )where F (φ) ≡ γ1 γ2 (2 − σ)(t1 − t2 )φ2+ [2σ{γ1 (1 − t1 ) − γ2 (1 − t2 )} + (γ1 + γ2 )(t1 − t2 )]φ − σ(t1 − t2 ),The sign of the profit differential is determined by F (φ). At the level of φ that satisfies
F (φ) = 0, the equilibrium distribution of plants becomes one-half.
We denote this value of φ by φ∗ , and it is given by the larger (smaller) root of F (φ) = 0
under σ < 2 (σ > 2). We can confirm that φ∗ falls within (0, 1) from the facts that (i)F (φ) is a quadratic function of φ, (ii) f (0) < 0, and (iii) f (1) > 0.
If φ < φ∗ or F (φ) < 0, then the profit differential is negative, implying that MNEs withproduction in country 1 have an incentive to relocate. Thus, the long-run equilibrium
must be n1 < 1/2. Similarly, if φ > φ∗ or F (φ) > 0, then the positive profit differential
at n1 = 1/2 requires that the long-run equilibrium be n1 > 1/2. These findings
establish Proposition 2.1.
Equilibrium plant allocation and trade costs.
136

Here, we show that as trade costs

Appendix to Chapter 2
decline, the equilibrium share of production plants in country 1 first decreases, thenincreases. By solving the profit differential for n1 , we obtain(1 − t1 )(1 + φ2 Γ1 γ2 ) − φ(1 − t2 )(Γ2 + γ2 ), (B2)(1 − t1 )[1 − φ(Γ1 + γ1 ) + φ2 Γ1 γ2 ] + (1 − t2 )[1 − φ(Γ2 + γ2 ) + φ2 Γ2 γ1 ]σσ − ∆tiwhere Γi ≡
.
σ

n1 =

We differentiate this with respect to φ:
dn1
G(φ)
=
,
dφ
H(φ)
where
G(φ) ≡ [{t1 (2 − t1 ) − 1}Γ1 γ2 (Γ1 + γ1 ) − {t2 (2 − t2 ) − 1}Γ2 γ1 (Γ2 + γ2 )]φ2
+ 2(1 − t1 )(1 − t2 )(Γ1 γ2 − Γ2 γ1 )φ+ {t2 (2 − t2 ) − 1}(Γ2 + γ2 ) − {t1 (2 − t1 ) − 1}(Γ1 + γ1 ),H(φ) ≡ {Γ1 γ2 (1 − t1 ) + Γ2 γ1 (1 − t2 )}φ2
− {(Γ1 + γ1 )(1 − t1 ) + (Γ2 + γ2 )(1 − t2 )}φ + 2 − t1 − t2

2

> 0.

We note that (i) the numerator is a quadratic function of φ and that (ii) H(φ) > 0 for
any φ ∈ [0, 1]. Furthermore, we can verify that (iii) the slope is negative at φ = 0:dn1
t2 − t1'< 0,
dφ φ=0 σ(2 − t1 − t2 )where we use a Taylor approximation such that Γi ' 1 − ∆ti + [(σ − 1)/σ](∆ti )2 andγi ' 1 − [(σ − 1)/σ]∆ti + [(σ − 1)(σ − 2)/σ 2 ](∆ti )2 .
We then find φ# that satisfies dn1 /dφ = 0, or equivalently G(φ) = 0:
φ# '

σ
,
σ − (σ − 1)∆t1 ∆t2(B3)

where the approximation was used as before. We can confirm that φ# is within (0, 1).
From (i) and (iii), we observe that dn1 /dφ changes its sign at φ# from negative to137

Appendix to Chapter 2
positive. In sum,



<0




dn1 = 0
dφ 

>0




= 0

if φ ∈ [0, φ# )if φ = φ#
if φ ∈ (φ# , φS )

,

(B4)

if φ ∈ [φS , 1]

where φS is the sustain point, which will be discussed in detail in Appendix B.2.

B.2

Proof of Proposition 2.2

We first confirm that the high-tax country 1 hosts all production plants when the trade
costs are zero. Then, we show that there exists the level of trade freeness above which
the full agglomeration is realized; that is, the sustain point φS . Finally, we show thatφS decreases with t1 , but increases with t2
Full agglomeration at zero trade costs.
φ = 1 yields

Evaluating the profit differential (B1) atµ(t2 − t1 )(σ − 1)
∆Π|φ=1 =
2
2σ
|
{z
}



ω2
ω1
+
γ1 n1 + n2 n1 + γ2 n2


,

<0

where ωi ≡ γi +σ(1 − γi ),(σ − 1)∆tj

for i 6= j ∈ {1, 2},noting that ∆t1 < 0 < ∆t2 and γ1 > 1 > γ2 . The profit differential is positive(negative) if the big bracket term is negative (positive). We will check that the big
bracket term is indeed negative, the condition for which is
ω2
ω1
+
< 0,
γ1 n1 + n2 n1 + γ2 n2→ ω1 (n1 + γ2 n2 ) + ω2 (γ1 n1 + n2 ) < 0,
→ n1 [ω1 (1 − γ2 ) + ω2 (γ1 − 1)] +ω1 γ2 + ω2 < 0,
|
{z
}
>0

138

Appendix to Chapter 2
noting that n2 = 1 − n1 . The inequality holds for any n1 ∈ [0, 1] if the following holds
n1 [ω1 (1 − γ2 ) + ω2 (γ1 − 1)] + ω1 γ2 + ω2
< 1 · [ω1 (1 − γ2 ) + ω2 (γ1 − 1)] + ω1 γ2 + ω2 < 0,
→ ω1 + ω2 γ1 < 0.
Using a Taylor approximation such that γi ≡ (1 − ∆ti /σ)σ−1 ' 1 − [(σ − 1)/σ]∆ti ,we can confirm that the inequality holds:(t1 − t2 )2< 0.
ω1 + ω2 γ1 ' − 2
σ (1 − t1 )(1 − t2 )Hence, the profit differential at φ = 1 is positive for any n1 ∈ [0, 1]. All MNEs arewilling to establish production plants in the high-tax country 1, that is, n1 |φ=1 = 1.
Sustain point. Evaluating the profit differential (B1) at n1 = 1 gives∆Π|n1 =1 =µ · I(φ),
2σ 2 φγ1

where I(φ) ≡ −γ1 γ2 (1 − t2 )(σ − ∆t2 )φ2 + γ1 (1 − t1 )(2σ − ∆t1 )φ − σ(1 − t2 ).
Since the denominator is positive, the sign of the profit differential is determined by
I(φ). Solving I(φ) = 0 for φ ∈ [0, 1] gives the sustain point φS (if any).
We observe that I(φ) is a quadratic function of φ with a negative coefficient of φ2 . A
further inspection reveals that
I(0) = −σ(1 − t2 ) < 0,
I(1) = σ[2γ1 (1 − t1 ) − (1 + γ1 γ2 )(1 − t2 )] + γ1 (1 + γ2 )(t1 − t2 ) > 0,
noting that 2γ1 (1 − t1 ) − (1 + γ1 γ2 )(1 − t2 ) > 2γ1 (1 − t1 ) − (1 + γ1 )(1 − t2 ) =(γ1 − 1)(1 − t1 ) > 0 holds because γ1 > 1 > γ2 .
These observations imply that (i) the sustain point φS ∈ (0, 1) always exists and isgiven by the smaller root of I(φ) and that (ii) I(φ) or the profit differential is negativefor φ ∈ [0, φS ) but positive for φ ∈ (φS , 1].
Sustain point and taxes.

As Figure 2.2 and Eq. (B4) clearly show, a higher φ# ,139

Appendix to Chapter 2
defined in Eq. (B2), makes φS higher. A close inspection of φ# reveals thatdφ#σ(σ − 1)(1 − t2 )(2 − t1 − t2 )(t2 − t1 )
=
< 0,
dt1
[(σ − 1)(t1 − t2 )2 + σ(1 − t1 )(1 − t2 )]2σ(σ − 1)(1 − t2 )(2 − t1 − t2 )(t1 − t2 )
dφ#
=
> 0,
dt2
[(σ − 1)(t1 − t2 )2 + σ(1 − t1 )(1 − t2 )]2
implying that φS also decreases (increases) with t1 (t2 ). As the tax difference is larger,
multinational production is more likely to be agglomerated in the high-tax country 1.

B.3

Conditions for Positive Profits

The taxable profits are π11 , π12 , π21 , and π22 , but only π11 can be negative:(σ − 1)∆t1
φγ1
µ
1
+
π11 =
,
2σ n1 + φγ2 n2 |
σ
φγ
n
+
n
1
1
2
{z
}
<0

because of ∆t1 < 0. Note also that π11 > 0 at φ = 0. We check whether π11 remains
positive if the following assumption holds:
1 + ∆t1 > 0.

(B5)

Differentiating π11 with respect to φ yields
dπ11(1 − φ)(2 − t1 − t2 )[φ(−∆t1 )(σ − 1)(σ − ∆t2 ) − σ 2 ]',dφ2(1 − t1 )[φ2 (σ − ∆t1 )(σ − ∆t2 ) − σ 2 ]where we use Eq. (B2) and a Taylor approximation such that γi ' 1 − [(σ − 1)/σ]∆ti .
The numerator is always negative:φ(−∆t1 )(σ − 1)(σ − ∆t2 ) − σ 2 ≤ 1 · (−∆t1 )(σ − 1)(σ − ∆t2 ) − σ 2= −(1 + ∆t1 )σ 2 + ∆t1 (1 + ∆t2 )σ − ∆t1 ∆t2 < 0,because of −(1 + ∆t1 ) < 0 and σ > 1.
The sign of the derivative is determined by the square bracket term in the denominator.

140

Appendix to Chapter 2
We can see thate
> 0 if φ ∈ [0, φ)


dπ11
,
= 0 if φ = φedφ < 0 if φ ∈ (φ,e 1]σwhere φe ≡ p∈ (0, 1).
(σ − ∆t1 )(σ − ∆t2 )(B6)This result and π11 |φ=0 > 0 imply that π11 takes the minimum value at φ = 1:µ(σ − 1)∆t1
π11 |φ=1 =
1+
,
2σ
σ
noting that n1 = 1 at φ = 1. The inequality holds under Ineq. (B5).

B.4

Proof of Proposition 2.3

Tax revenues in the two countries can be re-expressed asµLt1(σ − 1)∆t1 φγ1 n1
T R1 =
1+,2σσ
φγ1 n1 + n2
(σ − 1)∆t2 φγ2 n2
µLt2
1+
.
T R2 =2σσ
n1 + φγ2 n2Taking the difference yields




µL
σ−1
t1 γ1 n1 ∆t1
t2 γ2 n2 ∆t2∆T R ≡ T R1 − T R2 =t1 − t2 + φ−.
2σσφγ1 n1 + n2 n1 + φγ2 n2
At φ = 0, we see ∆T R|φ=0 = µL(t1 − t2 )/(2σ) > 0.
If φ is below the sustain point φS , the tax-revenue differential becomes




σ−1
µL
t1 − t2 +t1 ∆t1 .
∆T R|n1 =1 =2σσBecause of t1 > 1/2, this is negative if σ(1 − 2t1 ) + t1 < 0, i.e., σ > t1 /(2t1 − 1).
These results establish Proposition 2.3.

141

Appendix to Chapter 2

B.5

Proof of Lemma 2.1

In the transfer-pricing case, the profit differential at n1 = 1 isb n1 =1 =∆Π|bµ · Θ(φ),σφ

bwhere Θ(φ)≡ −s1 (1 − bt1 )φ2 + [s1 (1 − bt1 ) + (1 − s1 )(1 − bt2 )]φ − (1 − s1 )(1 − bt2 ),bClearly, the sign of the profit differential is determined by Θ(φ),
which is a quadratic
function of φ. We note thatthe sign of the coefficient of φ2 : −s1 (1 − bt1 ) < 0,b
Θ(0)= −(1 − s1 )(1 − bt2 ) < 0,b 0 (0) = s1 (1 − bΘt1 ) + (1 − s1 )(1 − bt2 ) > 0,
b
Θ(1)
= 0.
b
Θ(φ)
= 0 has two solutions, φ = 1 and φ = φbS :1 − s1 1 − b
t2
φbS ≡
=
s1 1 − bt1r

1 − s1∈ (0, 1).
s1

bb n1 =1 are non-positive if φ ∈ [0, φbS ], while they are
These imply that Θ(φ)
and thus ∆Π|positive if φ ∈ (φbS , 1]. That is, if φ ∈ [φbS , 1], then all multinational production takes
place in the large, high-tax country 1.

B.6

Centralized decision making

In the main text, we considered the case of decentralized decision making, in which theforeign affiliate chooses a price to maximize its own profit. Here, we will examine thecase of centralized decision making, in which the MNE chooses all prices to maximize
its total profit, using the same framework as in the main text. As we will show, thetwo different organizational forms give qualitatively similar results.

142

Appendix to Chapter 2
An MNE with production in country 1 solves the following problem:max Π1 = max (1 − t1 )π11 + (1 − t2 )π12 ,p11 ,g1 ,p12

p11 ,g1 ,p12

where π11 = (p11 − a)q11 + (g1 − τ a)q12 − C(g1 , q12 ),π12 = (p12 − g1 )q12 .
In contrast to decentralized decision making, p12 is chosen to maximize Π1 rather thanπ12 . C(·) is the concealment cost specified as C(gi , qij ) = δ(gi − τ a)2 qij with δ ≥ 0 (seeNielsen et al., 2003; Kind et al., 2005; Haufler et al., 2018 for similar specifications).
The first order conditions give the following optimal prices:∆t1
σag1 = τ a +, p12 =2δσ−1
tj − tiwhere ∆ti ≡, i 6= j ∈ {1, 2}.
1 − ti
σa
,
p11 =
σ−1



∆t1 ∆t2τ+,
4aδ

Mirror expressions hold for MNEs with production in country 2:
σa
,
p22 =
σ−1

∆t2
g2 = τ a +
,
2δ

σa
p21 =
σ−1



∆t1 ∆t2
τ+
4aδ


.

As in the decentralized case, gi decreases with ti , while it increases with tj . Since
p12 = p21 and g1 < g2 hold, we see p12 − g1 > p21 − g2 , implying a higher profitabilityof the affiliate in country 1 than that of the affiliate in country 2. As trade costs decline
and the shifted profits are larger, more MNEs are likely to locate their affiliate incountry 2 to exploit the higher price-cost margin. As a result, plants are agglomerated
in country 1 for low trade costs. The mechanism here that transfer pricing does notjust shift profits but affects profitability is very close to the one in the decentralizeddecision case we show in the text.

143

Appendix to Chapter 2
Using the optimal prices, we can rewrite the post-tax profit asΠ1 =(1 − t1 )µL/2
σ(N1 + γN2 )σ(2σ − 1)∆t1 ∆t2 − 2(σ − 1)(∆t1 + ∆t2 )γ σ−1 µL/2
+ (1 − t2 ) τ +,4aδσ(γN1 + N2 )(1 − t2 )µL/2
σ(γN1 + N2 )σ(2σ − 1)∆t1 ∆t2 − 2(σ − 1)(∆t1 + ∆t2 )γ σ−1 µL/2
+ (1 − t1 ) τ +,4aδ
σ(N1 + γN2 )1−σ
∆t1 ∆t2
where γ ≡ τ +
.
4aδ

Π2 =

The equilibrium distribution of plants is interior if Π1 − Π2 = 0 has a solution for
n1 ∈ (0, 1). If Π1 − Π2 > 0 (Π1 − Π2 < 0), then the economy reaches the corner
equilibrium of n1 = 1 (n1 = 0). We obtain1(γ + 1)(t1 − t2 )+
if τ ∈ (τ S1 , ∞) (i)
2 2(γ − 1)(2 − t1 − t2 )0if τ ∈ (τ S2 , τ S1 ] (ii)
n1 =
,

S2
[0, 1]
if τ = τ
(iii)




1
if τ ∈ [1, τ S2 ) (iv)1−σ∆t1 ∆t2
tj − tiwhere γ ≡ τ +, ∆ti ≡
, i 6= j ∈ {1, 2},4aδ
1 − ti 1
1 − t1 1−σ ∆t1 ∆t2∆t1 ∆t2
S1
τ ≡−, τ S2 ≡ 1 −,1 − t24aδ
4aδ
which is illustrated in Figure B.1. The horizontal dotted line represents the share atwhich the equilibrium share converges as trade costs go to infinity:nb1 ≡ lim n1 =τ →∞1t2 − t1+.
2 2(2 − t1 − t2 )If trade costs are high such that τ ∈ (τ S1 , ∞), then the low-tax country hosts moreproduction plants than the high-tax country does. If trade costs are low such that τ ∈[1, τ S1 ), on the other hand, then the high-tax country attracts all production plants.
The result is qualitatively the same as that under decentralized decision making.

144

Appendix to Chapter 2
Figure B.1: Equilibrium distribution of production plants under centralized decision making

B.7

Proof of Proposition 2.4(i) Country 1’s tax rate vs. country 2’s. We derive the condition under which in thetransfer-pricing case the equilibrium tax in country 1 is higher than that in country 2,
i.e., t∗1 > t∗2 :s√
2 + (σ − 1) βσµL
βσβσ2t∗1 = 1 −>1−
= t∗2 ,µL(σ − s2 )
µL2
s
s
√
βσ
βσ 2 + (σ − 1) βσµL2
→
>
,
µL2
µL(σ − s2 )hip
→ βσµL(σ − s2 ) > µL2 βσ 2 + (σ − 1) βσµL2 ,p→ βσ(s1 σ − s2 ) > s2 (σ − 1) βσµL2 ,s→ (σs1 − s2 )2 /s32 − µL(σ − 1)2 /(βσ) ≡ Ω(s1 ) > 0.

145

Appendix to Chapter 2
Inspections of Ω(s1 ) revealΩ(1/2) = (σ − 1)2 [2 − (µL)/(βσ)] < 0,lim Ω(s1 ) = ∞,s1 ↑1

Ω0 (s1 ) = 2(σ + 1)[s1 (σ + 1) − 1]/s32 + 3[s1 (σ + 1) − 1]2 /s42 > 0,
while noting that β < β ≡ µL2 /σ < µL/(2σ) and s1 (σ + 1) − 1 > (σ − 1)/2 > 0. AsΩ(s1 ) monotonically increases with s1 , Ω(s1 ) = 0 has a unique solution in s1 ∈ (1/2, 1),
which is denoted by s∗1 . If s1 > s∗1 or Ω(s1 ) > 0, we have t∗1 > t∗2 . If s1 ≤ s∗1 or Ω(s1 ) ≤ 0,
we have t∗1 ≤ t∗2 .
(ii) Tax rates with and without transfer pricing. We check that country 1’s equilibrium tax rates in the case without transfer pricing is higher than that in the case withtransfer pricing: b
t1 > t∗1 :√
2 + (σ − 1) βσµL
βσ2bt1 = 1 −= t∗1 ,µL(σ − s2 )ss√
βσ 2 + (σ − 1) βσµL2
βσ,>→µL(σ − s2 )
µL1
h
i
p
2
→ µL1 βσ + (σ − 1) βσµL2 > βσµL(σ − s2 ),ih p→ (σ − 1) s1 βσµL2 − βσs2 > 0,
s

→β<

βσ
>1−
µL1

s

s21 µL,s2 σwhich always holds under β < β ≡ µL2 /σ.
(iii) Sustain points with and without transfer pricing. In the transfer-pricing case,the profit differential at n1 = 1 is∆Π|n1 =1 =µ · Θ(φ),σφ

where Θ(φ) ≡ −γ2∗ s1 (1 − t∗2 )[(σ − ∆t∗2 )/σ]φ2+ (1 − t∗1 )[{σ − (1 − s1 )∆t∗1 }/σ]φ − (1 − s1 )(1 − t∗2 )/γ1∗ ,where ∆t∗i and γi∗ respectively correspond to ∆ti and γi evaluated at the equilibriumtax rates: t∗i . The sign of the differential is determined by Θ(φ), which is a quadratic146

Appendix to Chapter 2function of φ. As in the previous case, we note thatthe sign of the coefficient of φ2 : −γ2∗ s1 (1 − t∗2 )(σ − ∆t∗2 )/σ < 0,
Θ(0) = −(1 − s1 )(1 − t∗2 )/γ1∗ < 0,
Θ0 (0) = (1 − t∗1 )[σ − (1 − s1 )∆t∗1 ]/σ > 0,(σ − 1)(t∗1 − t∗2 )[σ(2s1 − 1) − s∆t∗2 ]> 0,
σ 2 (1 − t∗2 )(σ − ∆t∗2 )−10Θ (1) ' 2
(2s1 − 1)(1 − t∗1 )(1 − t∗2 )σ 2
σ (1 − t∗2 )Θ(1) '− (t∗1 − t∗2 )[s1 (3t∗2 − 2t∗1 − 1) + 1 − t∗2 ]σ − 2s1 (t∗1 − t∗2 )2
Θ(φbS ) '
< 0,

t2 − ∆t∗2 )Υ
(1 − s1 )(1 − bt2 )(1 − t∗2 )(σ∆b> 0,s1 σ 2 (1 − bt1 )2 (1 − t∗2 )2 (σ − ∆t∗2 )where Υ ≡ σ 2 (1 − t∗1 )(1 − t∗2 )[s1 (2 − bt1 − bt2 ) − (1 − bt2 )]− s2 (σ − 1)(1 − bt2 )(bt1 − bt2 )2 > 0,
and where the inequalities in the third to fifth lines hold due to the Taylor approximation such that γi ' 1 − [(σ − 1)/σ]∆ti and Ineq. (B5). On the fifth line, we noticethat ∆bti is the corresponding ∆ti evaluated at b
ti and σ∆bt2 − ∆t∗2 holds because ofbt1 − bt2 > t∗1 − t∗2 .
b
From these observations, we can illustrate Θ(φ)
and Θ(φ) as in Figure B.2. The sustain
S
point in the case with transfer pricing φ is the smaller root of Θ(φ) = 0. We can thus
conclude that the sustain point in the case with transfer pricing, φS , is lower than thatin the case without transfer pricing, φbS .

147

Appendix to Chapter 2

Figure B.2: Sustain points under tax competition

148

Appendix to Chapter 3

CAppendix to Chapter 3

C.1

Proof of Proposition 3.2

The post-tax profits of the MNE under schemes N and I are given by2

e N = (1 − t)(a − w + ∆ − τ ) + (1 − t)π,Π
4(1 − T )(a − w)2Ie+ (1 − t)π.
Π =
4

(C-1)
(C-2)

The condition under which the MNE prefers scheme I to scheme N is given byeI − Π
e N > 0 ⇐⇒ T < 1 − (1 − t)Π

a−w+∆−τ
a−w

2
≡ Te.

(C-3)

From equation (3.9), we can easily confirm that the following inequality holds:
2

e B |α=0 = (1 − t)(a − w + ∆) + (1 − t)π > max{ΠeN, Πe I }.
Π4(C-4)

e B with respect to α is
Further, the first derivative of ΠeB∂Π(T − t){(1 − t)(a − w + ∆) − (T − t)aα}ξ
=
< 0,
∂α
4{1 − t − (T − t)α}(C-5)

where ξ ≡ [−{1 − t − (T − t)α} − (1 − t)(w − ∆)]Let αx denote the cutoff level of αx such that x
eB = xO∗ (= xeN ) holds. Specifically, wehave(1 − t)τ
x
eB R xO∗ ⇐⇒ α Q≡ αx .
(C-6)(T − t)(w − ∆ + τ )If evaluated at α = αx , equation (3.9) becomes2e B |α=αx = (1 − t)(w − ∆)(a − w + ∆ − τ ) + (1 − t)π < ΠeN .
Π4(w − ∆ + τ )(C-7)

This implies that there exists the unique cutoff level of α, αN ∈ (0, αx ), such thateN ≥ Π
e N holds with α ≤ αN and T ≥ Te. Moreover, remember that ∂ Πe I < 0 andΠ
∂TeI = Π
e N holds at T = Te. Then,ΠeI > Π
eI| e = Π
eN > Π
e B |α=αx
Π
T =T
149

(C-8)

Appendix to Chapter 3
eB > Π
e I holds if the following condition is satisfied:holds for any T ∈ [t, Te]. Note that Π
eB



eI

Π |α=1 > Π ⇐⇒ T < 1 − (1 − t)

w−∆
w


.

(C-9)

This implies that there exists the unique cutoff level of α, αI ∈ (0, αx ), such thateB ≥ Π
e I holds with α ≤ αI and 1 − (1 − t) w−∆ ≤ T < Te.
Π
w

C.2

Proof of Proposition 3.3

Under scheme I, the changes in the amount of supplies from the pre-FTA equilibrium
to the post-FTA equilibrium without ROO are
τ −∆
> 0,
2
−∆
< 0,
x
eI − xbO =2

xeI − xO∗ =(C-10)(C-11)

because τ > ∆ holds. Under scheme B, the FTA formation increases the amount ofexports to country F when α < αx holds. From Proposition 3.2, we know that α < αx
holds under scheme B and we always have x
eB > xO∗ . In addition, we can easily confirm
that−(T − t)(w − ∆)αxeB − xbO =<0(C-12)
2{1 − t − (T − t)α}holds.

C.3

Proof of Proposition 3.4

From equation (3.11), we obtain∂erB{1 − t − (T − t)α}2 + (1 − T )(1 − t)(w − ∆)
=−
< 0.
∂α
2{1 − t − (t − t)α}2(C-13)

Therefore, reB = w − ∆ + a−w+∆> w − ∆ holds at α = 0 and reB takes the minimum
2
value at α = 1, which is given by
reB |α=1 = 0 < w − ∆.

(C-14)

Scheme B is the equilibrium at any α if T < Te holds. Therefore, there exists a uniqueαr such that reB < w − ∆ holds when α > αr holds.
150

C.4

Key Symbols for Notations
Table B.1: Key symbols for notations
λExportTransfer price

MNE’s post-tax profits

FTA Welfare

1

xO∗

r∗

ΠO∗

W O∗

0

x
bO

rb

bO
Π

cO
W

0
1
0

x
eI
x
eN
x
eB

reI
reN
reB

eI
Π
eN
Π
eB
Π

fI
W
fN
W
fB
W

Appendix to Chapter 3

151

SchemeNo FTA (w/ “∗”)Offshoring (s = O)
FTA w/o ROO (w/ “ b ”)
Offshoring (s = O)
FTA w/ ROO (w/ “ e ”)
Inshoring (s = I)
Non-compliance (s = N )Binding ROO (s = B)

Appendix to Chapter 4

D

Appendix to Chapter 4

D.1

Proof of Proposition 4.5

By the implicit function theorem, eq.(4.26) is rewritten as,∂ΠPi∝∂θ d= dP P  2  2dtD (a − c + 3dP )tD (a − c + dP )−+− 2(1 − tD ) Ξ R 0
θ
θ
2θ


(a − c + 9dP )where Ξ ≡2{4θ(1 − tD ) + t2D (5(a − c) + 9dP ) − 9θγ⇐⇒

4θ(1 − tD )(a − c + 13dP ) + t2D {−(a − c)2 + 14(a − c)dP + 71d2 }≡ γP 5 R γ.
36dP θ

Thus, globalization reduce the MNEs’ post tax profits if γ < γP 5 holds. This concludes
proposition 4.5. Figure D.1 shows two patterns of the MNEs’ post tax profits withdifferent γ, γ = 1.3 for the left figure and γ = 1.5 for the right one by using thefollowing set of parameter values: a = 2, c = 1, and t = 0.3.
Figure D.1: MNEs’ profits under process innovation

152

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Eidesstattliche Versicherung
Ich versichere hiermit eidesstattlich, dass ich die vorliegende Arbeit selbständig undohne fremde Hilfe verfasst habe. Die aus fremden Quellen direkt oder indirektübernommenen Gedanken sowie mir gegebenen Anregungen sind als solche kenntlich
gemacht. Die Arbeit wurde bisher keiner anderen Prüfungsbehörde vorgelegt undauch noch nicht veröffentlicht. Sofern ein Teil der Arbeit aus bereits veröffentlichten
Papers besteht, habe ich dies ausdrücklich angegeben.

Datum: 20. Marz. 2020

Unterschrift:
Hirofumi Okoshi