Economic Integration and Agglomeration ofMultinational Production with Transfer Pricing ∗Hayato Kato †Hirofumi Okoshi ‡January 25, 2021

Abstract
Do low corporate taxes always favor multinational production in the course of economic integration? We propose a two-country model in which multinationals choose
the locations of production plants and foreign distribution affiliates and shift profits
between home plants and foreign affiliates by manipulating transfer prices in intra-firmtrade. We show that when trade costs are high, plants are concentrated in the low-tax
country, but surprisingly this location pattern reverses when they are low. Unlike existing models with single-plant firms, the impact of economic integration is non-monotonic,
which we empirically confirm: a fall in trade costs first decreases and then increases
the share of plants in the high-tax country. We also analyze tax competition and findthat allowing for transfer pricing makes competition tougher, indicating a possibility ofinternational coordination on transfer-pricing regulation making the world better off.

Keywords: Profit shifting; Multinational firms; Intra-firm trade; Trade costs; Foreign direct
investment (FDI).
JEL classification: F12; F23; H25; H26.
∗
This paper is a much-revised version of Chapter 2 of Okoshi’s Ph.D. thesis submitted to the Universityof Munich (Okoshi, 2020). Helpful discussions with the committee members, Carsten Eckel, Andreas Haufler
and Dominika Langenmayr are greatly appreciated. We are grateful to Cristina Angelico, Tsung-Yu Ho, Yukio
Karasawa-Ohtashiro and Dirk Schindler for acting as discussant. Thanks also to participants of seminars andconferences at Kagawa U, Kochi U, U of Munich, IIPF (U of Tampere), 2019 Symposium of Public Economics(Osaka U), APTS (U of Tokyo), Osaka U (ISER and OSIPP), U of Tokyo, ERSA (U. of Lyon), MYEM
Conference (U of Munich), Chulalongkorn U and Kobe U for useful comments. Financial supports fromthe Japan Society for the Promotion of Science (Grant Numbers: JP16J01228; JP17K03789; JP18H00866;
JP19K13693; JP99K13693; JP20K22122), the German Research Foundation through GRK1928, the Nomura
Foundation, and the Obayashi Foundation are gratefully acknowledged.
†
Corresponding author. Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka,
Osaka, 560-0043, Japan. E-mail address: hayato.kato@econ.osaka-u.ac.jp‡
Munich Graduate School of Economics, University of Munich, Seminar for Economic Policy,
Akademiestr. 1/II, D-80799 Munich, Germany; Faculty of Economics, Okayama University, 3-1-1 Tsushima,
Kita-ku, Okayama, 700-8530, Japan E-mail address: hirofumi.okoshi1@gmail.com

1

Introduction

Progressive economic integration in the last few decades brought more international mobility
to multinational enterprises (MNEs), allowing 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, Chapter 6; Blonigen and Piger, 2014). 1 One naturally expects thatcountries with a low corporate tax rate would succeed in hosting more FDI inflow than thosewith a high tax rate. Earlier empirical studies confirmed this using data on FDI in all sectors(e.g., Bénassy-Quéré et al., 2005; Egger et al., 2009).
However, the type of activities of multinationals that operate in such low-tax countries
is not obvious. Governments reduce taxes to attract production plants, which contribute to
local employment and tax revenues. 2 Contrary to host governments’ expectations, MNEs may
establish affiliates in low-tax countries just to save taxes and may not engage in production(Horner and Aoyama, 2009). 3 As economic integration has dismantled barriers to goods’ andfactors’ mobility in recent years, MNEs may put more emphasis on other barriers such as
high taxes when choosing a location.
The point that countries with lower taxes do not necessarily attract more multinational
production can be illustrated using Fig. 1. In Fig. 1(a), we take 23 Organisation for Economic
Co-operation and Development (OECD) countries and draw the relationship between eachcountry’s average corporate tax rate from 2008 to 2016 and the average number of foreign
affiliates in all sectors coming from the other OECD countries in the same periods. 4 To control
for the host country’s size, the average number of affiliates is divided by the average GDP ofthe host country. The fitted line with a clear downward slope tells us that countries with a1

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
to attract FDI. See the 2013 Financial Statement by the Minister for Finance: http://www.budget.gov.
ie/Budgets/2013/FinancialStatement.aspx, accessed on 25 November 2020.
3
Horner and Aoyama (2009) provide a list of Ireland-based MNEs’ relocations. There are several examples
where some MNEs moved production from Ireland abroad while maintaining non-production activities suchas service centers and marketing in Ireland.
4
The sample countries do not include four European countries identified as tax havens by Zucman (2014),
i.e., Ireland, Luxembourg, the Netherlands, and Switzerland. The patterns laid out in Fig. 1 are unchanged
if we include these four countries.

1lower tax rate tend to attract more MNEs. Fig. 1(b) shows the type of MNEs’ activities byplotting the share of affiliates in manufacturing sectors out of those in all sectors. The fitted
line has little explanatory power with R-squared being 0.088, suggesting that multinationals
locating in low-tax countries do not necessarily engage in production.

Fig. 1. Corporate tax rates and foreign affiliates in 2008 to 2016
Sources: Centre for Business Taxation Tax Database 2017 (Habu, 2017); Corporate Outward activity ofmultinationals by country of location–ISIC Rev 4. In OECD Statistics: https://stats.oecd.org/
Notes: The horizontal axis is the average statutory corporate tax rate of a country in 2008 to 2016. In
panel (a), the vertical axis is the average number of foreign affiliates in all sectors (per USD 1 billion GDPof the host country) coming from the other sample countries in 2008 to 2016. In panel (b), it is the average
share of foreign manufacturing affiliates out of those in all sectors. Foreign affiliates in 2008 to 2016. See also
Appendix 1 for details.

The fact that low taxes do not necessarily attract multinational production can be explained by profit shifting of MNEs. MNEs allocate their activities between low-tax andhigh-tax countries and transfer profits by controlling prices for intra-firm trade, known astransfer prices. 5 For example, headquarters in high-tax countries make profits by selling
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).

2

goods to affiliates in low-tax countries by setting low transfer prices to inflate the affiliates’
profits. Such profit shifting through intra-firm trade has been made easy by the recent
proliferation of trade liberalization and the advancement of transportation technology.
When profits can be transferable between countries with different tax rates, it is no longer
clear where MNEs optimally set up their plants and affiliates. To answer the question, we
extend a two-country spatial model developed by Pflüger (2004) to incorporate MNEs withprofit-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 trade costs fall. Thereis a fixed mass of monopolistically competitive MNEs in the world, each of which locates aplant (or the headquarters) for production in one country and an affiliate for distribution in
the other. The MNE engages in intra-firm trade by exporting the output produced in homecountry to the affiliate in foreign country. It can use the transfer price of the output 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 affect the effectiveness of
profit shifting, which in turn affects the choice of MNEs’ location.
Based on this setting, we obtain the following results. With a low level of economic
integration marked by high trade costs, the low-tax country attracts a higher share of multinational production than the high-tax country. When high trade costs hamper intra-firmtrade, thereby limiting the profit shifting opportunity, MNEs can sell little to their foreign
affiliate. As most of the profits are made in the country where goods are produced, they
simply prefer to locate production in the low-tax country.
With a high level of economic integration marked by low trade costs, however, this location
pattern reverses: production plants agglomerate in the high-tax country. This result seems
surprising, but it is indeed consistent with MNEs’ optimal location choice. The MNE withproduction in the high-tax country lowers the transfer price to shift its home 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 gain competitiveness against
local plants. Conversely, the MNE with production in the low-tax country raises the transfer
price to shift profits from its foreign affiliate in the high-tax country back to its home plant.
Due to the high transfer price, the affiliate sells goods at a high price and loses competitivenessagainst local plants. Thus, transfer pricing favors the MNE with production in the high-tax
country in a way such that makes them competitive in both home and foreign markets. When
trade costs are so low that this effect is significant, all MNEs strategically choose to locate

3

production in the high-tax country.
Moreover, the location pattern of multinational production is indeed non-monotonic.
That is, a fall in trade costs first decreases and then increases the share of production plants
in the high-tax country. A simple intuition that production is agglomerated in the low-tax
country to save both taxes and trade costs holds under high trade costs, but it does not apply
under low trade costs where transfer pricing crucially affects the strategic location choice of
MNEs that seek price competitiveness.
These results may explain the fact that low-tax countries do not necessarily attract manufacturing affiliates compared with high-tax countries, as Fig. 1 suggests. In addition,
Overesch (2009) provides empirical evidence that multinationals in high-tax Germany increase real investments as the cross-country corporate tax difference between their homecountry and Germany is larger. Our own empirical exercise using the same data as those in
Fig. 1 also confirms the non-monotonic impact of economic integration on the distributionof multinational production.
As a result of transfer pricing, the high-tax country attracts more multinational production but does not enjoy greater tax revenues than it would without transfer pricing. The
opposite is true for the low-tax country. In fact, allowing for transfer pricing lowers global
tax revenues. Amid growing concerns about tax base erosion, the OECD recently reported
that the estimated revenue losses from MNEs’ tax avoidance are about 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 model is further extended to consider tax competition between two countries
that differ in tax-administration efficiency. The main result is carried over that transfer
pricing leads to production agglomeration in the high-tax country with more efficient tax
administration. Contrary to existing studies telling that agglomeration generates taxable
rents (Baldwin and Krugman, 2004), agglomeration in our model leads to tax-base erosion. A
bigger tax difference would bring more opportunities to manipulate transfer prices, triggering
greater tax-base erosion. To prevent this, the high-tax country is forced to lower its tax
6

See http://www.oecd.org/ctp/oecd-presents-outputs-of-oecd-g20-beps-project-for-discussion-at-g20-fin
htm, accessed on 25 November 2020. 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, accessedon 20 February 2019. Recent empirical studies estimate the magnitude of revenues losses from BEPS (e.g.,
Dharmapala, 2014; Janskỳ and Palanskỳ, 2019; Beer et al., 2020; Tørsløv et al., 2018), among which Blouin
and Robinson (2020) caution against the possibility of overestimation due to double counting of foreign
income. The estimated magnitude of revenue losses depends on how pre-tax profits respond to corporate
taxes. Heckemeyer and Overesch (2017) suggest that one of the dominant channels of profit shifting istransfer pricing, which our model highlights.

4

rate. In addition, transfer pricing makes tax competition tougher and the countries worse
off by narrowing the equilibrium tax difference. Although the governments have difficulty
coordinating their tax rates, they agree on tightening transfer-pricing regulation to achievea Pareto improvement.
Relation to the literature.

Our main contribution to the literature on transfer pricing

pioneered by Copithorne (1971) and Horst (1971) is to examine the impact of economic
integration on the location choice of MNEs using transfer pricing. Earlier studies in theliterature points out that transfer prices are used to make affiliates competitive as well as toshift profits (Elitzur and Mintz, 1996; Schjelderup and Sørgard, 1997; Zhao, 2000; Nielsen
et al., 2003). 7 The former is called a strategic effect and the latter a tax manipulation
effect. They assume the fixed location of affiliates, unlike our study. In our monopolisticallycompetitive model à la Dixit and Stiglitz (1977), optimal transfer prices themselves are notchosen strategically in the sense that they do not depend on the number of rival firms asa result of the constant elasticity of substitution between varieties. However, our model
shares the strategic aspect of transfer pricing in the sense that MNEs choose their location ofplants/affiliates to make them competitive in their markets. We allow for the flexible locationof affiliates and show that it is in fact chosen strategically due to transfer pricing.
Although there are a number of studies examining the production location choice of MNEs
with profit-shifting motives, they focus on symmetric tax rates (e.g., Haufler and Schjelderup,
2000; Kind et al., 2005; Slemrod and Wilson, 2009). Some studies highlight asymmetric tax
rates resulting from tax competition between symmetric or asymmetric countries (Stöwhase,
2005, 2013; Johannesen, 2010). 8, 9 Stöwhase (2013) studies tax competition between two
unequal-sized countries and finds that the large country sets a higher tax rate while attracting
a plant. By contrast, Stöwhase (2005) and Johannesen (2010) obtain the opposite result that
low-tax countries attract more plants (or a higher capital-labor ratio) than high-tax countries.
7

See Nielsen et al. (2008); Choe and Matsushima (2013); and Yao (2013) for subsequent development.
In many studies dealing with asymmetric tax rates, country asymmetry results from difference in market
size (Stöwhase, 2005, 2013). In other tax competition models without profit-shifting MNEs, countries are
assumed to be asymmetric due to inequality in public infrastructure (Han et al., 2018), hub-and-spoke
structure of jurisdictions (Janeba and Osterloh, 2013; Darby et al., 2014), and heterogeneous efficiency in
tax administration (Han et al., 2014) as in ours.
9
There are studies introducing a low-tax country with no production and/or no consumption, calling it
a tax haven country (Slemrod and Wilson, 2009; Johannesen, 2010; Krautheim and Schmidt-Eisenlohr, 2011;
Langenmayr et al., 2015; Hauck, 2019). Underlying channels through which profits are shifted to tax havens
include royalty payments for intangible assets (Juranek et al., 2018; Choi et al., 2020b) and the financial
choice between debt and equity (Fuest et al., 2005; Haufler and Runkel, 2012). However, we do not consider
tax havens because our main focus is on the MNEs’ production location.
85

These studies, however, do not consider trade costs, which is our primary interest. Tradecosts are important for profit-shifting patterns among MNEs because they significantly affectintra-firm trade, one of the main channels of profits shifting (Heckemeyer and Overesch, 2017).
The location choice of MNEs’ production plants is sometimes associated with the choice of
their organizational form (Bauer and Langenmayr, 2013; Egger and Seidel, 2013; Keuschnigg
and Devereux, 2013). 10 Specifically, firms choose whether they should undertake FDI to
manufacture inputs within their firms (i.e., vertical integration), or source inputs from independent suppliers (i.e., outsourcing), known as the make or buy decision. 11 This typeof FDI can be considered as a vertical FDI in the sense that different stages of bringing a
product on to the market are organized across borders (Antràs and Helpman, 2004). Using amonopolistically competitive trade model, Egger and Seidel (2013) theoretically predict andempirically confirm that larger tax differences are more likely to encourage MNEs to engage
in vertical FDI, rather than outsourcing. Bauer and Langenmayr (2013) develop a similar
model with contracting frictions between headquarters and suppliers and show that vertical integration is desirable for high-productive MNEs. To highlight MNEs’ organizational
choices, whether vertical integration or outsourcing, these studies fix the headquarters’ location, either a high-tax or a low-tax country. The location of input production is determined
not only by international tax differences but also by organizational differences such as bargaining positions of headquarters and suppliers. By contrast, we isolate the pure effect oftaxes on MNEs’ location choice by fixing their organization form, i.e., vertical integration
only. 12 Moreover, we emphasize the role of economic integration, which is not explored by
the aforementioned studies. Furthermore, we extend the basic model to incorporate a flexible
choice of organizational form and confirm the robustness of our main results (see Section 4.2).
Among studies on internationally mobile MNEs with profit-shifting motives, Peralta et al.
(2006); and Ma and Raimondos (2015) are the closest to ours in that they allow for bothtrade costs and asymmetric tax rates. In a tax-competition game over a single MNE witha plant and an affiliate, Peralta et al. (2006) show the possibility that the large, high-tax
10

See also Amerighi and Peralta (2010); Behrens et al. (2014); Bond and Gresik (2020); and Choi et al.
(2020a) for related studies on organizational choice of MNEs with profit-shifting motives. As in studies
cited above, they only deal with a single MNE and/or do not consider trade costs, unlike our model. Our
companion study investigates the location of input production within the boundaries of MNEs (Kato andOkoshi, 2019).
11
For quantitative studies on MNEs and taxes but without transfer pricing, see Shen (2018); and Wang(2020).
12
Strictly speaking, the function of foreign affiliate in our model is the distribution of final goods, whilethat in the aforementioned models is the production of intermediate good. Nonetheless our model shares thevertical nature of FDI with the aforementioned models in that different stages of value-added processes arelocated across borders.

6country wins the MNE’s plant when trade costs are high, which is similar to but different
from our findings. Moreover, the mechanism crucially differs from ours because in their model
countries use regulation policy on transfer pricing as well as corporate taxation. 13 Despite
its higher tax rate, the large country can attract the plant by adopting a loose regulation
policy and thus its effective tax rate is lower. Ma and Raimondos (2015) also consider tax
competition for a single MNE and obtain similar results. The crucial difference of our modelfrom theirs is that we consider a continuum of MNEs and allow them to compete in the final
good’s market. In doing so, we can shed light on the strategic aspect of transfer pricing,which cannot be captured by the aforementioned models with a single MNE. In our model,
MNEs strategically choose the location of their plants/affiliates such that transfer pricing
contributes to competitiveness as well as to tax saving, leading to the non-monotonic impactof economic integration on MNEs’ plant share. This new finding in the literature is indeed
empirically confirmed (see Section 3.3) and helps understand the fact shown in Fig. 1 that
low-tax countries do not necessarily attract a higher share of multinational production.
We also contribute to the literature on new economic geography (NEG) that examines theimpact of economic integration on firm location (Fujita et al., 1999). To our knowledge, ourstudy is the first to introduce transfer pricing into a NEG model, specifically one developedby Martin and Rogers (1995) and Pflüger (2004). An important insight from NEG models
is that countries with large home market hosts a greater share of firms than their marketsize share for all levels of trade costs except for prohibitive and zero levels, known as thehome market effect (Helpman and Krugman, 1985). Our model also inherits this effect inthe sense that the low-tax country offers a greater profit potential for MNEs than the hightax country. Indeed, the low-tax country attracts a higher plant share when trade costs arehigh. By contrast, when trade costs are low making profit shifting through intra-firm tradeeffective, the home-market effect is no longer dominant so that the location pattern reverses(Propositions 1 and 2).
In the analysis of tax competition using NEG models, the home-market effect allows thecountry where firms are agglomerated to set a higher tax rate without losing firms (Baldwin
and Krugman, 2004; Borck and Pflüger, 2006). 14, 15 Introducing transfer pricing does not
13

Some studies analyze competition for capital between governments using both taxes and other policy
instruments such as public infrastructure (Hindriks et al., 2008; Han et al., 2014), though they do not consider
MNEs with profit-shifting motives.
14
See also Kind et al. (2000); Ludema and Wooton (2000); Andersson and Forslid (2003); and Ottaviano
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 and Okubo, 2014), forward looking
behavior of governments (Han et al., 2014; Kato, 2015). See also Keen and Konrad (2013, Section 3.5.3).
15This result is in contrast with that of perfectly competitive models of tax competition between asym-

7

alter this location pattern, but drastically changes the implication of agglomeration. Thatis, agglomeration of production plants in the high-tax country does not bring such taxable
rents, but, on the contrary, induces tax-base erosion and thus puts a downward pressure on
its tax rate (Proposition 3).
The rest of the paper is organized as follows. The next section develops the model.
Section 3 characterizes the equilibrium plant distribution when taxes are given. It shows
how allowing for transfer pricing changes the plant distribution. Section 4 discusses several
extensions of the basic model. Section 5 deals with tax competition between two countries
and examines how the results change with and without profit shifting. The final section
concludes.

2

Basic setting

We consider an economy with two countries (country 1 and 2), two goods (homogeneous anddifferentiated goods), and two factors of production (labor and capital). Letting L be theworld population, there are L1 = s1 L of population in country 1 and L2 = s2 L = (1 − s1 )Lin country 2, where s1 ∈ (0, 1) is country 1’s world share. Likewise, the amount K of world
capital is distributed such that country 1 (or country 2) is endowed with K1 = s1 K (orK2 = s2 K = (1 − s1 )K). An individual in each country owns one unit of labor and two unitsof capital, implying that K = 2L. To highlight corporate tax difference, we assume away
the difference in market size, i.e., s1 = 1/2, throughout the paper except for Section 4.3.
There are two types of MNEs, one with a production plant (the headquarters) in country 1
and a foreign distribution affiliate in country 2; and the other with a production plant (theheadquarters) in country 2 and a foreign distribution affiliate in country 1. MNEs use laborand capital supplied by individuals. The government in each country taxes on operating
profits, sales minus labor/input costs, of plants and affiliates there. We interpret capital as
equity and assume that capital costs are non-deductible, while labor costs are deductible. 16
In this and the next sections, we fix the tax rates of countries and assume that country 1’s
tax rate is higher than that of country 2, t1 > t2 , without loss of generality.
The timing of actions proceeds as follows. First, each MNE chooses in which country
metric countries (Bucovetsky, 1991; Wilson, 1991; Stöwhase, 2005). In these models, diminishing returns tomarginal capital investment imply that smaller countries face a higher outflow of capital when raising theirtax rate than larger countries, unlike NEG models. As a result, smaller countries set a lower tax rate andachieve a higher capital-labor ratio.
16
We thank two referees for pointing this out.

8

to locate a production plant and in which country to locate a foreign distribution affiliate,
endogenously determining the share of plants n1 . Second, the MNE chooses transfer prices, gi .
Third, production plants and distribution affiliates set selling prices, pij . 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 theresults in the endogenous case as a long-run equilibrium.
Consumers.

Following Pflüger (2004), each consumer has an identical quasi-linear utility

function with a constant-elasticity-of-substitution (CES) subutility. Consumers in country 1
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 = w1 + q O
1.

ω∈Ωi

µ > 0 captures the intensity of the preference for the differentiated goods. q1O and q O
1 are
respectively the individual demand for the homogeneous good and its initial endowment. We
assume that q O
1 is large enough for the homogeneous good to be consumed. w1 is the wage
rate. q̃i1 (ω) is the individual demand from consumers in country 1 for the variety ω ∈ Ωi ,where Ωi is the set of varieties produced in country i ∈ {1, 2}. Q1 is the CES aggregator ofdifferentiated 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

(1)

.

ω∈Ωi

P1 is a 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 will9

suppress the variety index ω for notational brevity.
Homogeneous good sector.

The homogeneous good sector uses a constant-returns-to-scaletechnology. 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}, the costless trade of the homogeneous
good equalizes the wage rates between countries; that is w1 = w2 . 17 We choose the good as
the numéraire such that w1 = w2 = 1.
Differentiated goods sector.

The differentiated goods sector uses an increasing-returns-

to-scale technology. Each MNE needs one unit of capital for a production plant serving
as the headquarters in one country and another unit for a foreign affiliate in the other. 18
Once established, the plant needs a units of labor to produce one unit of variety. Since theworld amount of capital is K = 2L, the mass of (the headquarters of) MNEs in the world is
K/2 = L. We denote the mass of production plants located in country 1 by N1 = n1 L andthat in country 2 by N2 = n2 L = (1 − n1 )L, where n1 ∈ [0, 1]. There are 100 · n1 % of allplants in the world in country 1, while the remaining 100·(1−n1 )% of plants are in country 2.
The symmetric organization structure of MNEs implies that there are N2 (or N1 ) distributionaffiliates in country 1 (or country 2). Put differently, 100·n1 % of all establishments in country
1 are the production plant, while the remaining 100 · (1 − n1 )% establishments in country 1
are the distribution affiliate.
Consider a MNE with production plant (i.e., the headquarters) in country 1. The plant
produces quantities q11 using aq11 units of labor and sells them at a price p11 to homeconsumers. In addition, it produces quantities q12 and exports them at a transfer price g1
to its distribution 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 pricep12 .
MNEs have decentralized decision making following previous studies on transfer pricing(Zhao, 2000; Nielsen et al., 2003, 2008; Kind et al., 2005). In other words, the headquarters(i.e., the production plant) of the MNE sets the transfer price to maximize global post-tax
17

We assume the costless trade of the homogeneous good to highlight the role of differentiated sector while
cutting the complicated general-equilibrium channel of wages. This is common in the NEG models, but is
not totally innocuous. See, for example, Fujita et al. (1999, Chapter 7) for more on this point.
18
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.

10

profits, while the foreign affiliate sets the retail price to maximize its own profits. In practice,
it is sensible to delegate decisions to local managers who are familiar with their local businessenvironments. In many cases, a company’s acquisition of a rival often involves the latterreceiving divisional autonomy (e.g., Volkswagen’s acquisition of Audi, Ford’s acquisition of
Volvo, and GM’s acquisition of Saab). 19 We examine the case of centralized decision making
in Appendix 9 and confirm the robustness of our results.

2.1

Short-run equilibrium

Let us derive the optimal prices given the location of plants and affiliates (see Appendix 2 fordetailed derivations). The initial share of production plants is assumed to be equal to thatof capital share, i.e., n1 = s1 = 1/2. 20 The MNE with production in country 1 makes profits
from a home plant and a foreign distribution affiliate in country 2. The pre-tax operating
profits of the plant, π11 , and that of the affiliate, π12 , are respectively,
π11 = (p11 − a)q11 + (g1 − τ a)q12 − δ|g1 − τ a|q12 ,
|
{z
} |
{z
} |
{z
}
Domestic profits

Shifted profits

Concealment cost

π12 = (p12 − g1 )q12{z}|
Foreign profits= (p12 − τ a)q12 −(g1 − τ a)q12 ,|{z}
Shifted profits

where q11 is given by Eq. (1), q12 is defined analogously, a is the unit-labor requirement,
and R1 is the reward to capital invested in the MNE. The second term in π11 represents the
profits from intra-firm trade subject to trade costs τ . The MNE may choose the transfer pricedifferently than the true marginal cost: gi 6= τ a. For profits to move from high-tax country 1
to low-tax country 2, the second term must be negative: (g1 − τ a)q12 < 0 or g1 < τ a, which
we will see shortly. This term captures profit shifting within MNEs, appearing in π12 withthe opposite sign. The third term in π11 is a concealment cost associated with the deviationof the transfer price from the true marginal cost (Haufler and Schjelderup, 2000; Kind et al.,2005). As the deviation is larger, it is more costly for MNEs to conceal the transfer pricing
activity from tax authorities. High δ makes profit shifting more costly, implying that δ canbe interpreted as the stringency of transfer price regulation.
19
20

See Ziss (2007) for more on this issue.
As we shall see, the allocation of plants does not affect optimal selling prices or transfer prices.

11

At the third stage of the game, the production plant and the foreign affiliate choose theirprices to maximize their own profits. The optimal prices are
p11 =

σa
,
σ−1

p12 =

σg1
.
σ−1

(2)

At the second stage, the MNE with a plant in the high-tax country 1 sets the transfer
price to maximize the following global post-tax profits Π1 :
Π1 ≡ (1 − t1 )π11 + (1 − t2 )π12 − 2R1 ,(3)

where ti ∈ [0, 1] is the tax rate of country i ∈ {1, 2}. We again note that labor/input costs are
deductible, while capital costs are non-deductible. Suppose that the MNE with production incountry 1 tries to shift profits of its home plant to its foreign affiliate in the low-tax country 2,
i.e., (g1 −τ a)q12 < 0, where the concealment cost is given by δ|g1 −τ a|q12 = −δ(g1 −τ a)q12 > 0.
It chooses the transfer price to maximize the post-tax profit, Eq. (3):g1 =(1 + δ)στ a,
σ − ∆t1 + δ(σ − 1)

where ∆t1 ≡t2 − t1< 0,
1 − t1(4-1)

where g1 decreases with t1 , while it increases with t2 , implying that a greater tax difference
leads to a more aggressive transfer-pricing behavior. 21 Similarly, supposing that the MNEwith production in country 2 tries to shift profits from its foreign affiliate in country 1 backto its home plant, it incurs the concealment cost of δ|g2 − τ a|q21 = δ(g2 − τ a)q21 > 0. The
optimal transfer price maximizing the MNE’s post-tax profit isg2 =(1 − δ)στ a,
σ − ∆t2 − δ(σ − 1)

where ∆t2 ≡t1 − t2> 0,
1 − t2(4-2)

where g2 decreases with t2 , while it increases with t1 . The optimal transfer prices gi do notdepend on the plant share ni because of the constant elasticity of substitution σ, implyingthat gi s entail only tax-saving motives, not strategic ones. As will be clear in the next section,
however, MNEs make a strategic location choice such that they use gi s to make their affiliatescompetitive.
For the optimal transfer prices to be consistent with the direction of profit shifting, theoptimal transfer price from country 1 to 2 (or from country 2 to 1) must be set lower (or21

The result that a larger tax difference leads to a lower export price from the high-tax to low-tax country
is in line with empirical findings by Clausing (2003).

12

higher) than the true marginal cost:t1 − t2,
1 − t1t1 − t2
g2 > τ a → δ <.
1 − t2
g1 < τ a → δ <These conditions reduce to δ < (t1 − t2 )/(1 − t2 ) = δ, which also satisfies the second-ordercondition for maximization (δ < 1). Under δ < δ, profits net of concealment cost shiftedfrom country 1 to 2 are negative: (1 + δ)(g1 − τ a)q12 < 0, while those shifted from country 2
to 1 are positive: (1 − δ)(g2 − τ a)q21 > 0. If the tax difference is too large, the total pre-tax
profits of the plant in country 1 could be negative: π11 < 0 (see Appendix 3 for details).
To exclude this possibility, we further assume (t2 <)t1 < 1/2, which is plausible considering
the highest corporate tax rate being 0.4076 in 23 OECD countries in 2010 to 2016 (Japan in2010 to 2012).
Using the demand function, Eq. (1), and optimal prices, Eqs. (2) and (4), we rearrange
the post-tax profit, Eq. (3), asΠ1 = (1 − t1 )π11 + (1 − t2 )π12 − 2R1µL1
φγ1 µL2(σ − 1)(∆t1 + δ)
= (1 − t1 )·+σ(N1 + φγ2 N2 )σσ(φγ1 N1 + N2 )
|
{z
} |
{z
}
Domestic profits+ (1 − t2 ) ·Shifted profits (net of concealment cost) <0φγ1 µL2−2R1 ,σ(φγ1 N1 + N2 )
{z
}
|

(5-1)

Foreign profits

Π2 = (1 − t1 )π21 + (1 − t2 )π22 − 2R2
φγ2 µL1= (1 − t1 ) ·σ(N1 + φγ2 N2 )|{z}
Foreign profitsµL2(σ − 1)(∆t2 − δ)φγ2 µL1+ (1 − t2 )+− 2R2 , (5-2)·σ(φγ1 N1 + N2 )σσ(N1 + φγ2 N2 )
|
{z
} |
{z
}
Domestic profits

Shifted profits (net of concealment cost) >0

tj − tiwhere φ ≡ τ 1−σ , ∆ti ≡, i 6= j ∈ {1, 2},
1 − ti

1−σ

1−σ
σ(1 + δ)σ(1 − δ)γ1 ≡, γ2 ≡.
σ − ∆t1 + δ(σ − 1)σ − ∆t2 − δ(σ − 1)
The first and second terms in the square brackets in Π1 and Π2 are respectively the profit

13

from domestic market and the profit shifted through transfer pricing. φ = τ 1−σ ∈ [0, 1] is aninverse measure of trade costs, or the openness of trade. φ = 0 (i.e., τ = ∞) corresponds toa prohibitively high level of trade costs, while φ = 1 (i.e., τ = 1) indicates zero trade costs.
We assume as in standard NEG models the free entry and exit of potential MNEs (orequivalently the arbitrage behavior of capital owners), so that excess profits are driven to
zero. This zero profit condition implies that, for given MNEs’ locations, the return to capital,
Ri , is determined at the point where Πi = 0 holds. In the short-run equilibrium where
capital is immobile, the return to capital in general differs between countries. The capitalreturn differential generates a relocation incentive which guides us to analyze the long-run
equilibrium where capital is mobile.

3Long-run equilibrium

To highlight the role of tax difference, we assume that the two countries are of equal size
(s1 = 1/2). When the difference in the capital return is positive: R1 − R2 > 0 (or negative:
R1 − R2 < 0), capital owners invest in the MNE with production in country 1 (or the MNEwith production in country 2). In the long-run equilibrium, the return differential is zero
where no capital owners change their investment behavior. This also means that no MNEs
are willing to change their location of plants/affiliates. By solving the long-run equilibrium
condition (R1 − R2 = 0) for the share of production plants in country 1, we obtain interior
equilibria n1 ∈ (0, 1). If R1 − R2 = 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}.

3.1

Plant distribution and the non-monotonic impact of economic
integration

Location incentives of MNEs depend on the ease of intra-firm trade, which is subject totrade costs. A high level of trade costs τ (or lower trade openness φ) does not allow formuch intra-firm trade, leaving little room for profit shifting. 22 As the MNEs earn profits
mostly from home production plants, they prefer to locate them in the low-tax country 2.
The low-tax country offers a greater profit potential for MNEs and thus it can be considered
as a country with a large home market. The concentration of production in country 2 results
22

In Eqs. (5-1) and (5-2), the profits from intra-firm trade and those from the foreign affiliate disappear
if φ = 0.

14

from the well-known home-market effect common in NEG models (Helpman and Krugman,1985). We note that there is a small but positive share of plants in the high-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 the low-tax country 2 cannot be an equilibrium,i.e., (n1 |φ=0 6= 0.
By contrast, smaller τ (or higher φ) allows MNEs to engage in intra-firm trade fully,
making effective profit shifting through transfer pricing. 23 Transfer pricing does not justshift profits between home plants and foreign affiliates, but also affects the competitivenessof the affiliates. As we showed, MNEs with production in the high-tax country 1 set a
low transfer price to shift profits to their affiliates in the low-tax country 2 (see Eq. (41)). Due to the low input cost, the affiliates can sell at a low price and become competitive
against local plants. Conversely, MNEs with production in country 2 set a high transfer price(see (4-2)), which makes their affiliates in country 1 less competitive against local plants.
MNEs with production in country 1 have a competitive advantage in both the domestic
and foreign markets against MNEs with production in country 2. Therefore, MNEs prefer
to locate production in the high-tax country 1 so that transfer-pricing makes their affiliatescompetitive. In fact, if φ is sufficiently high such that φ > φS , which we call an agglomerationthreshold, all production plants are located in country 1. 24
Assuming away transfer-pricing regulation (δ = 0), we can formally prove the following
proposition by applying Taylor approximations at zero tax difference.

23

We can confirm that given the plant share n1 , the shifted profit increases with φ; that is, ∂(|gi −τ a|qij )/∂φ > 0 for i 6= j ∈ {1, 2}.
24
The agglomeration threshold is called the sustain point in the literature in the sense that full agglomeration is sustainable when trade openness is higher than the point (Fujita et al., 1999). It can be checkedthat φS decreases with t1 − t2 (see Appendix 4). 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 against MNEs in both the domestic and foreign markets.
Consequently, the larger tax difference lowers φS , making full production agglomeration in country 1 more
likely.

15

Proposition 1 (Plant distribution).

Assume that two countries are of equal size (s1 =1/2) and that country 1 has a higher corporate tax rate than country 2 (t2 < t1 < 1/2), butthat the tax difference is small enough (t1 − t2 ≈ 0), and that there is no transfer-pricing
regulation (δ = 0). 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 shareof 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 shareof plants, i.e., n1 > 1/2.
(ii-a). With sufficiently low trade costs such that φ ∈ [φS , 1] where φS (> φ† ) is the agglomeration threshold, all production plants are located in the high-tax country ,i.e., n1 = 1.
At φ = φ† , the two countries have an equal share of plants, i.e., n1 = 1/2.
We do not report here the lengthy expressions of φ† and φS , which are implicitly definedas φ† ≡ argφ {n1 = 1/2} and φS ≡ min argφ {n1 = 1}, respectively. See Appendix 4 for the
proof.
It is worth noting that full production agglomeration in country 1 occurs even at zero
trade costs (τ = 1 or φ = 1). In the case without transfer pricing, MNEs are indifferent to
the location of plants at φ = 1. The selling price for the foreign market is equal to that for
the home market, i.e., pij = pii = σa/(σ − 1), so that MNEs make the same profits fromthe two markets. They cannot avoid high taxes in country 1 by changing the location ofplants/affiliates and thus do not have a strong location preference. In the transfer-pricing
case, however, the selling prices for the two markets are not equalized even at φ = 1, i.e.,pij 6= pii , because they reflect transfer prices that are not equal to the true marginal cost(gi 6= τ a) but are dependent on the tax difference (see Eqs. (4-1) and (4-2)). To fully
utilize transfer pricing for saving taxes and enhancing competitiveness, MNEs have a strong
preference for production location even at φ = 1.
Fig. 2 shows a representative pattern of long-run equilibrium plant share for different
levels of trade openness φ (solid curve), along with the long-run equilibrium plant share in
the case without transfer pricing (dashed curve). 25 As φ increases from zero, the share of
For clarity, φ† is not shown in Fig. 2, at which n1 = 1/2 holds. Parameter values are given in Appendix
12. Specifically, we set the elasticity of substitution σ to five, which is the lower bound of the range estimatedby Lai and Trefler (2002). We set tax rates to (t1 , t2 ) = (0.3, 0.2), which seem plausible considering the fact
25

16

plants in the high-tax country 1 decreases in both cases with and without profit shifting.
When high trade costs prevent exporting, MNEs make profits mostly from their home plants
and thus prefer to locate them in the low-tax country. Along with a further increase in φfrom 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 increase the opportunities for profit shifting,leading to a sharp contrast in location patterns.
This finding is summarized in the following proposition:
Proposition 2 (Non-monotonic impact of economic integration).

Under the same

assumptions as in Proposition 1, the impact of economic integration on the plant share in
the high-tax country 1, n1 , is non-monotonic. That is, a fall in trade costs first decreases
and then increases the plant share, i.e., dn1 /dφ ≤ 0 for φ ∈ [0, φ# ) and dn1 /dφ > 0 forφ ∈ (φ# , 1].
The exact expression of φ# and the proof are given in Appendix 5.

Fig. 2. Share of production plants in the high-tax country 1that the average tax rate is 0.274 and the average tax difference is 0.077 in our sample of 23 OECD countries
in 2008 to 2016. We experimented with different values of σ and ti s and obtained similar patterns to thosein Fig. 2. In the special case where σ is extremely low, it is possible that as trade costs fall, full production
agglomeration in country 2 occurs before full production agglomeration in country 1 is achieved. But ourqualitative results are unchanged in this special case.

17

3.2

Tax revenues

The tax base in country 1, denoted by T B1 , consists of profits of both home production
plants and foreign distribution affiliates. Using Eqs. (5-1) and (5-2), we can rewrite T B1 as
T B1 =Nπ| 1{z 11}+

Profits of home plants=Profits of foreign affiliates

N1 (p11 − a)q11|{z}

Domestic profits of home plants+

N2 π21| {z }N2 (p21 − τ a)q21
|
{z
}



N1 (1 + δ)(g1 − τ a)q12
|
{z
}

+

Shifted profits of home plants (net of concealment cost) <0

Domestic profits of foreign affiliates

N2 (τ a − g2 )q21
|
{z
}

+



Shifted profits of foreign affiliates <0

"

#
µL1
(σ − 1)(∆t1 + δ)
φγ1 µL2+ N1= N1
σ(N1 + φγ2 N2 )σσ(φγ1 N1 + N2 )#"φγ2 µL1φγ2 µL1(σ − 1)(∆t2 − δ)(σ − 1)(∆t2 − δ)
+ N2
1+
− N2
σ(N1 + φγ2 N2 )σ(1 − δ)σ(1 − δ)σ(N1 + φγ2 N2 )
=

µL
+
2σ

N1
|

φγ1 µL(σ − 1)(∆t1 + δ)σ
2σ(φγ1 N1 + N2 )
{z
}

,

(6-1)

Shifted profits of home plants (net of concealment cost) <0

where L1 = L2 = L/2; ∆t1 + δ < 0; and ∆t2 − δ > 0. Tax revenues are then given by
T R1 ≡ t1 · T B1 . The first term of the last line, µL/(2σ), is the total profits made in country
1 and turns out to be the tax base in the no-transfer-pricing case. The constant first term
corresponds to the tax base in the case without transfer pricing (see Section 5.1 for moredetails). It is clear from the second negative term of the last line, the shifted profits of home
plants, that allowing for transfer pricing always reduces tax revenues in country 1.
As shown in the second and third lines, there are two types of shifted profits, one by
the plants of MNEs headquartered in country 1 (i.e., home plants) and the other by theaffiliates of MNEs headquartered in country 2 (i.e., foreign affiliates). It turns out, however,that the shifted profits of foreign affiliates do not explicitly show up in the last line. This isbecause the lost tax base is compensated by an increase in domestic profits of home plants
and is implicitly included in the first term of the last line: µL/(2σ). More specifically, foreign
affiliates in the high-tax country 1 pay a high input/transfer price g2 for moving profits totheir plants in the low-tax country 2. They pass on the high-input price to the selling priceP1
1−σ 1−σp21 , raising the price index (higher P1 = ( 2i=1 Ni pi1) ) and thus the demand for all−σ σ−1varieties in country 1 (larger qi1 = pi1
P1 µL1 ). Home plants increase their domestic profits

such that the loss from profit shifting is cancelled out.
18

Similarly, the tax base in country 2 isT B2 =Nπ| 2{z 22}+

Profits of home plants=Profits of foreign affiliates

N2 (p22 − a)q22|{z}

Domestic profits of home plants+

N1 π12| {z }N1 (p12 − τ a)q12
|
{z
}



N2 (1 − δ)(g2 − τ a)q21
|
{z
}

+

Shifted profits of home plants (net of concealment cost) >0

Domestic profits of foreign affiliates

N1 (τ a − g1 )q12
|
{z
}

+



Shifted profits of foreign affiliates >0

"

#
µL2
(σ − 1)(∆t2 − δ)φγ2 µL1= N2+ N2
σ(φγ1 N1 + N2 )σσ(N1 + φγ2 N2 )"#φγ1 µL2(σ − 1)(∆t1 + δ)(σ − 1)(∆t1 + δ)
φγ1 µL2
+ N1
1+
− N1
σ(φγ1 N1 + N2 )σ(1 + δ)σ(1 + δ)σ(φγ1 N1 + N2 )
=

µL
+
2σ

N2
|

(σ − 1)(∆t2 − δ)φγ2 µLσ
2σ(N1 + φγ2 N2 )
{z
}

,

(6-2)

Shifted profits of home plants (net of concealment cost) >0

noting that ∆t2 − δ > 0. Due to the inflow of profits made in the high-tax country 1 (i.e.,the second positive term of the last line), tax revenues, defined by T R2 ≡ t2 · T B2 , are higher
in the transfer-pricing case than those in the no-transfer-pricing case except when φ = 0. As
in the case of T B1 , the shifted profits of foreign affiliates do not explicitly enter the last line.
By sourcing inputs at a low transfer price g1 , foreign affiliates in country 2 set a low selling
price p12 and thus push the price index there P2 downward. The lowered price index reduces
the domestic profits of home plants, eroding the tax-base inflow that foreign affiliates bring.
These findings are summarized as follows.
Lemma 1 (Tax revenues). Under the same assumptions as in Proposition 1, tax revenues
in the high-tax country 1 (or the low-tax country 2) in the transfer-pricing case are always
lower than or equal to (or higher than or equal to) those than in the no-transfer-pricing case.
Fig. 3(a) illustrates the total profits shifted from the high-tax country 1 to the low-tax
country 2, N1 (τ a − g1 )q12 + N2 (g2 − τ a)q21 , for different levels of trade openness φ. 26 The
dashed horizontal lines are the corresponding values in the no-transfer-pricing case. Naturally,
more profits are transferred as trade gets more open. Tax revenues in each country are drawn
in Fig. 3(b). It is worth noting that both curves exhibit an inverted-U shape when φ is high.
26

Parameter values are the same as those in Fig. 2. See Appendix 12 for details.

19This can be explained from the U-shaped relationship between φ and country 1’s plant sharen1 . As Fig. 2 and Proposition 2 suggest, a rise in φ below φ# (< φS ) decreases n1 and increases
n2 = 1 − n1 . This change in the plant share is likely to suppress the tax-base outflow fromcountry 1 (smaller N1 (τ a − g1 )q12 ) and encourage the tax-base inflow to country 2 (larger
N2 (g2 − τ a)q21 ), contributing to greater tax revenues in both countries. 27 Conversely, a risein φ above φ# increases n1 and decreases n2 = 1 − n1 , changing tax revenues in the opposite
direction to the one before.

Fig. 3. Shifted profits (a) and tax revenues (b)3.3

Empirical evidence

Proposition 2 gives an empirical implication on the relationship between bilateral FDI flows,
tax differential and trade openness. That is, given the tax differential between two countries, there is a non-monotonic effect of economic integration on the share of manufacturingmultinationals out of multinationals in all sectors. To empirically test this prediction, we canthink of the following regression:(Manufacturing-affiliate share)h,s = β1 ∆T AXh,s · φh,s + β2 ∆T AXh,s · φ2h,s + x0h,s β + εh,s ,27

It can be readily verified that ∂[N1 (τ a − g1 )q12 ]/∂n1 > 0 and ∂[N2 (g2 − τ a)q21 ]/∂n1 < 0.

20

where the variables are defined as(Manufacturing-affiliates share)h,s :the share of manufacturing affiliates out of all affiliates in country h from country s,∆T AXh,s = T AXh − T AXs : corporate tax rate differential between h and s,
φh,s : trade openness,
xh,s : vector of control variables,
εh,s : error term,
and where the time subscript is omitted for brevity. Supposing that the host country h setsa higher tax rate than the source country s, i.e., ∆T AXh,s > 0, the theory predicts< 0 if φh,s < −β1 /β2∂(Manufacturing-affiliate share)h,s= ∆T AXh,s ·(β1 + β2 φh,s )∂φh,s| {z }|{z} > 0 if φ++h,s > −β1 /β2which states that an increase in trade openness has a negative (or positive) effect on the
manufacturing-affiliate share in country h coming from country s if trade openness is low(or high). The sign of the derivative flips in the case of ∆T AXh,s < 0. Because φh,s takes
positive values, the theory-consistent signs are β1 < 0 and β2 > 0.
We test this using the same affiliate data as those used in Fig. 1. To construct thetrade openness, φh,s ∈ (0, 1), we take the inverse of the log of the bilateral distance measureconstructed by Mayer and Zignago (2011). Besides the two interaction terms of our interest,
we include as control variables (xh,s ) a simple tax differential; a common-language dummy;a colony dummy; a host country-year dummy; and a source country-year dummy, following
the empirical literature on the determinants of FDI (e.g., Egger et al., 2009; Choi et al.,2020c). 28 In addition to the statutory tax rates, we use as a robustness check the effective
average tax rates (Devereux and Griffith, 1998), which are calculated from data on profits
and investment. The sample is an unbalanced panel of 23 OECD countries, covering theperiod of 2008-2016. We exclude observations with missing values and/or zero affiliates fromthe sample. See Appendix 1 for details.
The regression results are summarized in Table 1. In columns (1) and (2) the statutory
tax rates are used, while in columns (3) and (4) the effective average tax rates are used. In
28

We cannot include variables varying only in host/source country-year level such as host/source country
GDP because their effects are absorbed by the host/source country-year dummy.

21,

columns (2) and (4), the tax differential is lagged by one year. The theoretical predictionthat β1 < 0 and β2 > 0 is strongly supported with a 1% significance in all columns. We canalso confirm that the infection point of trade openness is actually in between zero and one(e.g., in column (1): 74/270 ' 0.27).

Table 1Non-monotonic effect of economic integration on multinational production
Dependent variable: (foreign manufacturing affiliates)/(foreign affiliates in all sectors)∆T AXh,s,t · φh,s∆T AXh,s,t · φ2h,sStatutory tax rate

Effective tax rate

(1)

(3)

−71.93∗∗∗(23.07)259.43∗∗∗(82.38)∆T AXh,s,t−1 · φ2h,s
Yes
1,845
0.516

(4)

−83.86∗∗∗(25.09)305.51∗∗∗(90.16)−71.70∗∗∗(24.87)267.32∗∗∗(88.65)∆T AXh,s,t−1 · φh,sControl variables
Observations
R2

(2)

Yes
1,596
0.491

−83.14∗∗∗(26.45)315.41∗∗∗(94.29)
Yes
1,845
0.516

Yes
1,596
0.491

Notes: The dependent variable is the share of foreign manufacturing affiliates outof those in all sectors in a host country. All regressions include a host country-year
dummy; a source country-year dummy; and other control variables mentioned in the
text. Robust-standard errors in parentheses are clustered at the host country-year level.
***Significant at the 1% level; **Significant at the 5% level; *Significant at the 10%
level.

Supporting evidence can also be found in existing studies such as Overesch (2009) andGoldbach et al. (2019). Using firm-level panel data of German inward FDI from 1996 to
2005, Overesch (2009) finds that domestic investment by foreign affiliates located in Germany increases as the corporate tax difference between Germany and their source country
gets higher. Goldbach et al. (2019) also employ similar data of German outward FDI andfind that the complementarity between domestic and foreign investment by German-based
MNEs is higher as the tax difference between Germany and their destination country gets
22

wider. Considering the fact that important source/destination countries of German FDI are
Germany’s neighboring ones such as France and Austria, their empirical results are consistent with our prediction that the high-tax country attracts multinational production fromthe low-tax country when the bilateral trade openness is high. 29

4Extensions

This section discusses four extensions of our main model.

4.1

Transfer-pricing regulation

We established Propositions 1 and 2 under no transfer-pricing regulation, i.e., δ = 0. A
tighter regulation (higher δ) limits the effectiveness of profit shifting in a way such thatmakes smaller the deviation of the transfer price from the true marginal cost. Thus, MNEs
find less profitable to move to country 1, where there is a higher tax rate but little scope
for transferring profits. In fact, we can numerically confirm in Fig. 4 that higher δ makes
less likely the concentration of production in the high-tax country 1. 30 When δ is sufficiently
high such that δ = (t1 − t2 )/(1 − t1 ) = (0.3 − 0.2)/(1 − 0.3) = 0.143 (dashed curve), there is
no room for profit shifting (gi = τ a) so that the plant share in country 1 coincides with thatin the case without transfer pricing (dashed curve in Figure 2) and never exceeds one-half.
29

Strictly speaking, Overesch (2009) and Goldbach et al. (2019) consider a different mechanism than oursin that they consider incremental investment by a representative MNE, while we consider discrete investment
by a continuum of MNEs. In the theoretical model of Overesch (2009), the amount of shifted profits is
assumed to be related to that of capital invested by the affiliate. Profit shifting from an affiliate in high-tax
Germany to its parent in a low-tax source country reduces the required rate of return to the affiliate, leading
to an increase in investment by the affiliate. Goldbach et al. (2019) apply the same argument to the case ofGerman-based parents.
30
Parameter values are the same as those in Figs. 2 and 3 except for δ. See Appendix 12.

23

Fig. 4. Impact of transfer-pricing regulation

4.2

Pure exporters

In the main analysis, we excluded the possibility of pure exporters, who export varieties
without using distribution affiliates. However, one may expect that it would be profitable for
production plants in the low-tax country to serve the high-tax country by exporting directly to
consumers, rather than via distribution affiliates. Exporting while locating production in the
low-tax country would save taxes and avoid the negative aspect of strategic transfer pricing.
To consider this, we endogenize whether each firm becomes a MNE or a pure exporter. The
MNE establishes a plant in one country and a distribution affiliate in the other, as in themain model. The pure exporter locates two plants in the same country, one for the homemarket and the other for the foreign market. Specifically, the timing of actions is modified
as follows. Firms first decide the location of a plant for the home market and then choose
their organization form, either a MNE or a pure exporter. The subsequent actions proceed
as in the main analysis.
We also assume that MNEs face a lower level of trade cost than pure exporters. The easeof communication within a MNE reduces costs related to intra-firm trade. In fact, Ramondo
and Rodrı́guez-Clare (2013) report that what they call multinational production costs, which
are similar to intra-firm trade costs here, are more sensitive to changes in distance than arm’s
length trade costs. Let τ M and τ E be intra-firm trade costs and arm’s-length trade costs
respectively. The corresponding measures of openness are denoted by φM ≡ (τ M )1−σ andφE ≡ (τ E )1−σ , where η ≡ φE /φM ∈ [0, 1] represents the (inverse of) difficulty of arm’s length
trade relative to intra-firm trade.
24This extended model is fully analyzed in Appendix 6, where we confirm the aforementioned expectation; given the location of production (i.e., first plant), firms in the high-tax
country 1 always become MNEs, while firms in the low-tax country 2 always become pure exporters. Given production in the high-tax country, there is no point becoming pure exporters
because in doing so firms would dismiss the opportunities of profit-shifting. Conversely, given
production in the low-tax country, it makes no sense becoming MNEs because their distribution affiliates are imposed on high-taxes and are less competitive due to a higher transfer
price of inputs.
Considering these decisions of organization form, firms choose production location. Fig.
5 shows the world share of MNEs with production in country 1 in the long-run equilibrium,
denoted by n1 ∈ [0, 1], for different levels of intra-firm trade openness φM . 31 We note that theremaining share, 1 − n1 , represents the world share of pure exporters in country 2. There arethree ηs, each of which has different φE /φM . All n1 s decrease with φM for low φM , but they
behave differently for high φM . When arm’s length trade is about as open as intra-firm trade(φE /φM = 0.882: the bottom dashed curve), most firms choose the low-tax country 2 for
production and become pure exporters, i.e., n1 ' 0. When arm’s length trade is subject tomore difficulties than intra-firm trade (φE /φM = 0.88135, 0.88: the dotted and solid curves),
more firms become MNEs and seek to utilize transfer pricing. Thus the location patterns
are similar to those in the basic model (see Fig. 2). In sum, if we allow for the pure export
solution, our main results of (i) agglomeration of MNEs’ production plant in the high-tax
country (Proposition 1) and (ii) the non-monotonic impact of economic integration on theplant share (Proposition 2) are unchanged as long as intra-firm trade costs are sufficiently
lower than arm’s length trade costs.
31

Parameter values are the same as those in Figs. 2 and 3 except for φE /φM = η. See Appendix 12 fordetails.

25

Fig. 5. MNEs vs. pure exporters

4.3

Asymmetric country size

The result of the high-tax country 1 attracting more multinational production for low trade
costs, in general, does not depend on the assumption of symmetric market size. Our model
inherits a common feature of NEG models that firms try to locate in large countries tosave trade costs when exporting. Thus, if country 1 is larger (s1 > 1/2), the larger market
size strengthens the incentive of MNEs to locate production there. If country 1 is smaller(s1 < 1/2), MNEs have less incentive to choose it for production. Even in this case, however,the small high-tax country 1 may achieve full production agglomeration for low trade costs,
where the trade-cost-saving motive is weak. In Appendix 7, we confirm that production
plants are always agglomerated in the high-tax country 1 at zero trade costs except in thecase where country 1 is extremely large. 32

4.4

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 thatthe direction of profit shifting does not change depending on the decision making style. That
32

In the special case where s1 > s1 ≡ σ/(2σ − ∆t2 ), full production agglomeration in the large, high-tax
country 1 does not occur, because the transferable profits, which depend on the sales of distribution affiliates
in country 2, are very small. This exceptional case implies that the very small, low-tax country, which canbe roughly considered as a tax-haven, may host a greater share of plant than its market-size share: n2 > s2 .

26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 toagglomeration of production plants in the high-tax country. See Appendix 8 for details.

5

Tax competition

We here allow countries to choose their tax rate non-cooperatively and compare the resultsof tax competition in the case with and without transfer pricing. Throughout this section
except for Section 5.3, we cast aside transfer-pricing regulation, i.e., δ = 0. The timing ofactions is modified such that the government in each country sets its tax rate before all theactions of multinationals and individuals. The objective function of government i ∈ {1, 2}
takes the form of
Gi = T Ri −αi ti,
1 − tiwhere T Ri ≡ ti · T Bi ,T Bi ≡ Ni πii + Nj πji ,i 6= j ∈ {1, 2},As we saw in Section 3.2, the tax base for government i, T Bi , consists of profits of home
production plants, Ni πii , and those of foreign distribution affiliates, Nj πji . The second term
is a tax administration cost, where αi > 0 captures its inefficiency. We assume that government 1 is more efficient in tax administration than government 2: α1 < α2 . 33 The two
governments simultaneously and non-cooperatively decide their tax rates before the location
MNEs’ decision.
33
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 and the 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 deemed 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.

27

5.1

No-transfer-pricing caseAs a benchmark, we derive the equilibrium tax rates when transfer pricing is not allowed.
The inability to manipulate transfer prices implies that the transfer price must be equal to
the true marginal cost: gi = τ a, in which case γi = 1 holds. This leads to zero profits fromintra-firm trade: (gi − τ a)qij = 0 for i 6= j ∈ {1, 2}. Combining these results with Eq. (6-1)
yield tax revenues for government 1:
T R1 = t1 T B1
= t1 [N1 π11 + N2 π21 ]


µL1
φµL1
= t1 N1 ·+ N2 ·σ(N1 + φN2 )σ(N1 + φN2 )µL1 (N1 + φN2 )= t1 ·σ(N1 + φN2 )µL= t1 ·,
2σwhere L1 = L2 = L/2. Using Eq. (6-2), we can analogously derive tax revenues for government 2 as T R2 = t2 T B2 = t2 µL/(2σ). It is worth noting that T B1 depends on neither
the share of plants (ni ), trade openness (φ), nor taxes (ti s). The tax base independent of ni ,φ and ti s can be explained by the two facts. 34 First, the total mass of plants and affiliates
generating country 1’s tax base is constant and is given by N1 + N2 = n1 L + (1 − n1 )L = L.
Second, the transferable profits of foreign affiliates depend on their sales in country 1 andP
are thus limited by its residents’ expenditure on manufacturing goods ( 2i=1 Ni pi1 qi1 = µL1 ).
The constant tax base then implies that governments do not benefit from full agglomerationof plants. Put differently, the concentration of multinational production in a country does
not generate taxable agglomeration rents there, which sharply contrasts with the implicationof the existing NEG models (Baldwin and Krugman, 2004).
Government i thus maximizes
Gi =

αi ti
µLti
−
.
2σ
1 − ti34
The constant tax basenot result from the quasi-linear utility function with constant expenditure
Pdoes
2
on manufacturing goods:N
i=1 i pij qij = µLj . In Appendix 12, we confirm that the Cobb-Douglas utility
function also yields a constant tax base.

28

Solving the first-order condition gives the equilibrium tax rate in country i:rbti = 1 −

2αi σ
,
µL

(7)

where we use xb to represent the equilibrium value of x in tax competition without transfer
pricing. We can check that the government payoff is positive: Gi (ti = bti ) = [µL/(2σ)−αi ]2 >0. The equilibrium tax rate decreases with αi , reflecting the fact that a government with aninefficient tax-administration finds it costly to raise taxes. In fact, government 1 sets a lower
tax rate than government 2, i.e., b
t1 > bt2 , because more efficient tax administration allows
government 1 to do so. Because the government objective functions depend on neither theplant share (ni ) nor trade openness (φ), the equilibrium tax rates given in Eq. (7) are uniquefor any ni and φ. A too high (or low) α1 makes the equilibrium tax rate too low (or high).
To ensure bti ∈ (0, 1/2), we will assume αi ∈ (µL/(3σ), µL/(2σ)).
Without transfer pricing, the higher tax rate of a country discourages production plants
to locate there, as discussed in Section 3. This tendency is more pronounced when trade
costs are low, or equivalently, trade openness is high. In particular, when the level of trade
openness is smaller than the agglomeration threshold (φ > φbS ), all plants are located in the
low-tax country 2:
1−b
t1
φbS =
∈ (0, 1),
1−b
t2

(8)

The situation of full production agglomeration in country 2 (bn1 = 0) is shown in Fig. 6(dashed line). 35 We note that MNEs are indifferent to production location at zero trade costs(bn1 ∈ [0, 1]) because they cannot differentiate selling prices for home and foreign markets tosave taxes (see Section 3.1).
These results are summarized as follows (see Appendix 9 for the proof).
Lemma 2 (Tax competition without transfer pricing). Assume that two countries
are of equal size (s1 = 1/2) and that government 1 has a more efficient tax administration
than government 2: α1 < α2 , where αi ∈ (µL/(3σ), µL/(2σ)). As a result of tax competition
without transfer pricing, government 1 always sets a higher tax rate than government 2(bt1 > bt2 , given in Eq. (7)). If trade costs are small enough such that φ ∈ [φbS , 1), where φbS
is given in Eq. (8), all MNEs locate their production plants in the low-tax country 2, i.e.,nb1 = 0. At zero trade costs (φ = 1), all MNEs are indifferent to the location of plants, i.e.,
35

Parameter values are given in Appendix 12.

29

nb1 ∈ [0, 1].

Fig. 6. Plant share under tax competition

5.2

Transfer-pricing case

We examine how the above results change if MNEs can use transfer pricing. The analyses ofSection 3 indicate that when trade costs are low such that φ ∈ [φS , 1], all production plants
are agglomerated in country 1, as long as its tax rate is higher than that of country 2, evena little (t1 > t2 ). This situation is illustrated in Fig. 6. 36 We here derive conditions underwhich this situation emerges as a result of tax competition.
Suppose that all plants are in country 1 (n1 = 1). From Eq. (6-1), we derive tax revenues
for government 1 asT R1 = t1 T B1µL(σ − 1)∆t1
φγ1 µL
= t1
+ N1
2σ
σ
2σ(φγ1 N1 + N2 )#"µL(σ − 1)∆t1 µL
= t1
+
,
2σ
σ{z 2σ}|Shifted profits of home plants <036
We obtain the agglomeration threshold φS∗ in Figure 6 by evaluating φS∗ at the equilibrium tax rate{t∗i }2i=1 , which will be discussed shortly. Parameter values are given in Appendix 12.

30

where L1 = L2 = L/2; N1 = n1 L = L; and N2 = (1 − n1 )L = 0. By contrast, tax revenues forgovernment 2 are unchanged because there are no production plants there (N2 = 0), whichtransfer profits. From Eq. (6-2), we obtain
T R2 = t2 T B2µL (σ − 1)∆t2
φγ2 µLN2
= t2
+
2σ
σ
2σ(N1 + φγ2 N2 )µL
= t2 ·.
2σ
The governments’ payoffs then becomeµLt1(σ − 1)∆t1
α1 t1
G1 =
,
1+
−
2σ
σ
1 − t1
µLt2
α2 t2
G2 =
,
−
2σ
1 − t2where G1 now involves the tax difference due to the presence of shifted profits of home plants.
To prevent this tax-base erosion, government 1 has a stronger incentive to lower its tax rate
than it does in the no-transfer-pricing case. By contrast, as country 2 does not have any
plants that receive shifted profits, G2 is the same as in the no-transfer-pricing case. As notedin Section 3.2, profits shifted by foreign affiliates are included in the first term of T Bi anddo not show up explicitly.
From the first-order conditions, we obtainst∗1 = 1 −t∗2 = 1 −r√
2α1 σ (σ − 1)( 2α2 σµL − 2α1 σ)+,µLµL(2σ − 1)

(8-1)

2α2 σ
µL

(8-2)

(= b
t2 ),

where we use x∗ to represent the equilibrium value of x in tax competition with transfer pricing. t∗1 and t∗2 are in (0, 1/2) under our assumptions: α1 < α2 , where αi ∈ (µL/(3σ), µL/(2σ)).
To be consistent with the full agglomeration of plants in country 1, t∗1 must be higher thant∗2 . This requires sufficiently low α1 such that α1 < α∗ , implying that government 1 is efficient enough in tax administration (see Appendix 10). As expected, t∗1 is also lower than theequilibrium tax rate without transfer pricing b
t1 . Introducing profit shifting intensifies tax
competition in the sense that the tax difference gets narrower.
If instead α1 is lower than α2 but is high enough such that α1 ∈ [α∗ , α2 ), t∗1 is equal31

to or lower than t∗2 and full production agglomeration in country 1 does not occur. In thiscase, government 1 chooses to mimic government 2’s tax rate (t∗1 = t∗2 ) and government 2t2 ), giving rise tochooses the same tax rate as it does in the no-transfer-pricing case (t∗2 = b
the symmetric distribution of plants (n∗1 = 1/2).
Thus, our main result that profit shifting leads to production agglomeration in the hightax country for low trade costs (Proposition 1(ii)) carries over to a tax-competition framework
when countries are quite different in their efficiency in tax administration. We can formally
prove the following proposition by assuming that the elasticity of substitution is slightly
higher than one: σ > 3/2.
Proposition 3 (Tax competition with transfer pricing). Assume that s1 = 1/2, α1 <α2 , where αi ∈ (µL/(3σ), µL/(2σ)) as in Lemma 2, and σ > 3/2. Consider tax competition
with transfer pricing under sufficiently low trade costs such that φ ∈ [φS , 1], where φS is theagglomeration threshold. Then there exists a unique pair of equilibrium tax rates, {t∗i }2i=1
given in Eqs. (8-1) and (8-2), which satisfy the following:(i). (Country 1’s tax rate vs. country 2’s) Country 1’s tax rate is higher than country
2’s (t∗1 > t∗2 ) if the level of tax-administration efficiency of government 1 is low enough:α1 < α∗ . All production plants are located in country 1 (n∗1 = 1) for φ > φS∗ , whereφS∗ is the agglomeration threshold evaluated at the equilibrium tax rates.
(ii). (Tax rates with and without transfer pricing)

Assume α1 < α∗ and φ > φS∗ .

Compared to the no-transfer-pricing case, country 1’s tax rate and payoff decrease (t∗1 <bt2 ;t1 )), whereas country 2’s tax rate and payoff are unchanged (t∗2 = b
t1 ; G1 (t∗1 ) < G1 (bG2 (t∗2 ) = G2 (bt2 )). That is, introducing transfer pricing makes tax competition tougher(0 < t∗1 −t∗2 < bt1 − bt2 ) and leaves the world worse off (G1 (t∗1 )+G2 (t∗2 ) < G1 (bt1 )+G2 (bt2 )).

See Appendix 10 for the proof. We note that unlike the no-transfer-pricing case full production agglomeration occurs even at zero trade costs (φ = 1) because MNEs can differentiate
the two selling prices using transfer prices dependent on international tax difference. In Appendix 11, we also confirm that qualitatively the same results as Proposition 3 hold when
the utility function takes the Cobb-Douglas form.
The conclusion that profit shifting pushes taxes downward (Proposition 3 (ii)) can befound in Haufler and Schjelderup (2000), who employ a framework of perfect competition

32

with symmetric countries. 37 By contrast, Stöwhase (2005, 2013) obtain the opposite result:introducing profit shifting softens tax competition by increasing the equilibrium tax rates
of countries. 38 In the presence of profit shifting, governments chase the shifted profits andintensify tax competition. At the same time, MNEs’ can save tax payments regardless of
their locations and become less sensitive to international tax differences, thereby making tax
competition less severe. In Stöwhase (2005, 2013), the latter effect dominates the former,
whereas the opposite is true in our model. These differing results seem to come from thefact that while Stöwhase (2005, 2013) consider a representative firm or a monopoly firm, weconsider a continuum of MNEs competing with each other. The competitive environment
strengthens the tax-saving incentive and thus increases the tax-base sensitivity in the high-tax
country hosting full production agglomeration.
Although the result that the high-tax country achieves full production agglomeration(Proposition 3(i)) resembles the one in Baldwin and Krugman (2004) and other NEG models,
their mechanism crucially differs from ours. In Baldwin and Krugman (2004), production
agglomeration generates taxable rents, which are non monotonic in terms of the degree of
economic integration. A higher degree of integration may expand the rents and soften tax
competition. To the contrary, in our model with profit shifting, production agglomerationis harmful to the country by inducing the erosion of tax base there. One government sets ahigher tax rate than the other, not because it wants to tax agglomeration rents, but because
it has a more efficient tax administration.

5.3

Coordination of transfer-pricing regulation

Based on Proposition 3(ii) stating that introducing transfer pricing leaves the world worse
off, one may think that international coordination of transfer-pricing regulation would makethe world better off. We show that this is indeed possible as a result of mutual agreement
between the two governments. We note that international coordination of tax rates is difficult
because both governments set the dominant-strategy equilibrium tax rate and thus do nothave any incentive to change it.
37

Agrawal and Wildasin (2020) 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.
38
Becker and Riedel (2013) obtain a similar result, although MNEs in their model cannot shift profits for
tax-saving purposes.

33

Adding transfer-pricing regulation δ modifies the governments’ payoffs asµLt1(σ − 1)(∆t1 + δ)
α1 t1
G1 =
1+
−
,
2σ
σ
1 − t1µL2 t2
α2 t2
G2 =
−
,
σ
1 − t2where government 2’s payoff, G2 , is unchanged since there is no plant in country 2. The
associated equilibrium tax rates are
s√2α1 σ (σ − 1)[ 2α2 σµL − 2α1 σ(1 + δ)]+,µLµL[2σ − 1 + δ(σ − 1)]

r

2α2 σ
µL

t∗∗
1 = 1−t∗∗
2 = 1−(= t∗2 = bt2 ).

A tighter regulation (higher δ) increases t∗∗
1 and thus raises government 1’s payoff. Since δdoes not enter G2 , government 2 is indifferent to the degree of regulation. These observations
suggest a possibility of a Pareto improvement through the coordination of transfer-pricing
regulation. Both governments agree on tightening the regulation to make transfer pricing
impossible, i.e., ∆t1 + δ = 0 or δ = (t1 − t2 )/(1 − t2 ). This result is summarized as follows.
Proposition 4 (Transfer-pricing regulation). Consider tax competition with transfer
pricing, as described in Proposition 3. International coordination of regulation that prohibitstransfer pricing, i.e., δ = (t1 − t2 )/(1 − t2 ), makes the world better off and is possible basedon mutual agreement between the two countries.

6

Conclusion

Countries with lower corporate tax rates are expected to host more multinational production.
Such a simplistic view may be challenged, however, because economic integration marked byfalling trade costs allows for profit shifting and may thus change the location incentive ofmultinationals. To investigate this, we introduced transfer pricing into a simple two-country
model of trade and geography.
With high trade costs, a low-tax country attracts more production plants than a high-tax
country. With low trade costs, this pattern completely reverses and production is agglomerated in the high-tax country. When low trade costs expand intra-firm trade, MNEs can use
34

transfer pricing as both a strategic and a profit-shifting device. To shift profits, the transfer
price from the high-tax to the low-tax country is set high, whereas that from the low-tax
to the high-tax country is set low. This transfer-pricing strategy lowers the input cost of
distribution affiliates in the low-tax country and thus makes them competitive. In contrast,
distribution affiliates in the high-tax country become less competitive due to the high input
cost. Therefore, MNEs prefer to locate production in the high-tax country and distribution
in the low-tax country.
The main results carry over to a tax-competition framework where countries non-cooperatively
choose their tax rates. The difference in equilibrium tax rates between countries results fromthe difference in the level of efficiency in tax administration. Unlike standard NEG models,the country hosting all production plants does not enjoy agglomeration rents from it; rather,
it faces tax-base erosion due to profit shifting. Another finding is that introducing profit
shifting makes tax competition fiercer by reducing the high-tax country’s equilibrium tax
rate.
We test our prediction using bilateral FDI data on 23 OECD countries in 2008 to 2016.
The empirical exercise supports the non-monotonic effect of economic integration on theshare of production affiliate out of affiliates in all sectors. Furthermore, supporting evidence
can be found in existing studies such as Overesch (2009) and Goldbach et al. (2019). For
example, Overesch (2009) confirms that foreign affiliates in Germany invest more, as the
cross-country tax difference between their source countries and high-tax Germany increases.
Although our model is admittedly stylized, we believe that it is versatile enough to accommodate further extensions. An interesting extension is to consider various ways of profit
shifting, besides transfer pricing, such as licensing fees for intellectual property rights andthe choice between equity and debt financing. While we solely focus on the transfer pricingof tangible goods, these alternative ways are equally important in reality. Adding anotherchannel of profit shifting into our model would yield different implications for production
location and tax revenues. Another extension is to examine the impact of different international tax systems, such as separate accounting and formula apportionment. The system
which prevents profit shifting more effectively may differ depending on the degree of economic
integration. We leave these avenues for future research.

35

Appendices
Appendix 1. Data sources
Foreign affiliates: We take bilateral outward “Number of enterprises” data from Corporate
Outward activity of multinationals by country of location–ISIC Rev 4. in OECD Statistics,
covering the period 2007 to 2017. Although the data is available by sector, we only use dataon “TOTAL BUSINESS SECTOR” and “MANUFACTURING” because many of sector-level
data are missing. The sample consists of 23 OECD counties: Australia, Austria, Belgium,
Canada, Czech Republic, Germany, Finland, France, Greece, Hungary, Israel, Italy, Japan,
South Korea, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, United Kingdom,
United States. We exclude observations with missing values and/or zero affiliates from thesample, so that the sample period is reduced to the period 2008 to 2016. Note that four
European countries identified as tax havens by Zucman (2014), i.e., Ireland, Luxembourg,
the Netherlands, and Switzerland, are not included in the sample.
Corporate tax rates: Data on statutory corporate tax rates and effective average tax
rates are from Centre for Business Taxation Tax Database 2017 (Habu, 2017).
Trade openness: We take the bilateral distance measure from Mayer and Zignago (2011)
and define the trade openness as the inverse of the log of the distance measure.
Other variables: Data on real GDP are from OECD statistics. A common-language
dummy and a colony dummy are from Mayer and Zignago (2011).

Appendix 2. Derivations
Optimal transfer price.
We here derive the optimal transfer price given the allocationof plants. As in the text, we focus on the case where profits are shifted from high-tax
country 1 to low-tax country 2, i.e., g1 < τ a and g2 > τ a, which is equivalent to assume
δ < (t1 − t2 )/(1 − t2 ). The post-tax profit of the MNE with a plant in country 1 is
Π1 = (1 − t1 )[(p11 − a)q11 + (g1 − τ a)q12 − δ|g1 − τ a|q12 ] + (1 − t2 )(p12 − g1 )q12 − 2R1
#
" 
 −σ
 1−σ
1−σ
µL1
p12
µL2
p12
µL2
p11
= (1 − t1 )+ (1 + δ)(g1 − τ a)
+ (1 − t2 )− 2R1 ,
P1
σ
P2
P2
P2
σ
 −σ
µLj
p1j
σa
σg1
where q1j =, p11 =
, p12 =, j ∈ {1, 2}.
Pj
Pj
σ−1
σ−1

36

The optimal transfer price is obtained from taking the first derivative with respect to g1 :
"
#
−σ

−σ
∂Π1
σg1 1
µL2
σ
1
µL
2
= (1 − t1 )(1 + δ)
− τ a(−σg1−σ−1 )∂g1
σ − 1 P2
P2
σ − 1 P2
P2

1−σ
σ 1
µL2
−σ
+ (1 − t2 )(1 − σ)g1
= 0,
σ − 1 P2σ
(1 + δ)στ a,→ g1 =σ − ∆t1 + δ(σ − 1)
where it is assumed as usual in monopolistic competition that individual firms take the priceindex as given: ∂Pj /∂g1 = 0. The second-order condition for the post-tax profit maximization
problem requires−σ∂ 2 Π1σ 1στ a(1 + δ)(1 − t1 ) · SOC1
−σ−2
= g1
< 0,
2
∂g1
σ − 1 P2(σ − 1)[1 − t2 + (1 − t1 )(σ − 1)(1 + δ)]
where SOC1 ≡ −(1 − t1 )2 (σ − 1)2 δ − (1 − t2 )σ 2 + (2t2 − 3t1 + 1)σ + t1 − t2 ,This inequality holds because SOC1 is negative while noting that δ > 0; σ > 1; ti ∈ [0, 1];
and t1 > t2 .
Similarly, we can derive the optimal transfer price for the MNE with a plant in country 2.
Supposing that profits are shifted from high-tax country 1 to low-tax country 2, i.e., g2 > τ a,
the MNE’s post-tax profit isΠ2 = (1 − t2 )[(p22 − a)q22 + (g2 − τ a)q21 − δ|g2 − τ a|q21 ] + (1 − t1 )(p21 − g2 )q21 − 2R2
#
" 
 −σ
 1−σ
1−σ
p21
p21
p22
µL2
µL2
µL1
+ (1 − δ)(g2 − τ a)
+ (1 − t1 )− 2R2 ,= (1 − t2 )
P2
σ
P1
P2
P1
σ
 −σ
p2j
σg2
µLj
σa
where q2j =, p21 =, j ∈ {1, 2}.
, p22 =
Pj
Pj
σ−1
σ−1
The first-order condition is
#
−σ

−σ
σg2 1
µL1
σ
1
µL
1
− τ a(−σg2−σ−1 )σ − 1 P1
P1
σ − 1 P1
P1
1−σ

σ 1
µL1
−σ
+ (1 − t1 )(1 − σ)g2
= 0,
σ − 1 P1σ
(1 − δ)στ a→ g2 =.
σ − ∆t2 − δ(σ − 1)

∂Π2
= (1 − t1 )(1 − δ)
∂g2

"

37

The second-order condition requires−σ∂ 2 Π2σ 1
στ a(1 − δ)(1 − t1 ) · SOC2
−σ−2
= −g2
< 0,
2
∂g2
σ − 1 P2(σ − 1)[1 − t1 + (1 − t2 )(σ − 1)(1 − δ)]
where SOC2 ≡ −(1 − t2 )2 (σ − 1)2 δ + (1 − t1 )σ 2 + (3t2 − 2t1 − 1)σ + t1 − t2 .
The sufficient condition for this inequality is δ < 1, in which case SOC2 is positive. To beconsistent with both the direction of profit shifting and the second-order conditions, we needto assumeδ<t1 − t2(< 1).
1 − t2

Post-tax profit.
rewritten as

The post-tax profit of the MNE with a plant in country 1 can be


p1−σ
p1−σ
g1 − τ a
12 µL211 µL1Π1 = (1 − t1 )1−σ + (1 + δ)
1−σ
p12 N1 p1−σσ(N1 p1−σ
11 + N2 p21 )12 + N2 p22
p1−σ
12 µL2− 2R1+ (1 − t2 )1−σσ(N1 p12 + N2 p1−σ
22 )


µL1
g1 − τ a (p12 /p22 )1−σ µL2= (1 − t1 )+ (1 + δ)σ(N1 + N2 (p21 /p11 )1−σ )p12 N1 (p12 /p22 )1−σ + N2
(p12 /p22 )1−σ µL2+ (1 − t2 )− 2R1 ,σ(N1 (p12 /p22 )1−σ + N2 )noting that the price index reduces to Pi1−σ = Ni pii1−σ + Nj p1−σbecause symmetric firms set
ji
the same price for each market. We use the results of optimal prices to obtainσ(1 − δ)σg2 σ − 1
p21
=τ·
,
=
p11
σ − 1 σaσ − ∆t2 − δ(σ − 1)
 1−σ1−σ
p21
σ(1 − δ)1−σ→=τ·
= φ · γ2 ,p11
σ − ∆t2 − δ(σ − 1)p12
σg1 σ − 1σ(1 + δ)
=
=τ·
,
p22
σ − 1 σaσ − ∆t1 + δ(σ − 1)
 1−σ1−σ
p12
σ(1 + δ)1−σ→=τ·
= φ · γ1 ,p22
σ − ∆t1 + δ(σ − 1)
g1 − τ aσ − 1 ∆t1 + δ=,
p12
σ2 1 + δ

1−σ

1−σ
σ(1 + δ)σ(1 − δ)1−σwhere φ ≡ τ , γ1 ≡, γ2 ≡.
σ − ∆t1 + δ(σ − 1)σ − ∆t2 − δ(σ − 1)38We substitute these results into the above to obtainµL1(σ − 1)(∆t1 + δ)
φγ1 µL2Π1 =(1 − t1 )+σ(N1 + φγ2 N2 )σσ(φγ1 N1 + N2 )φγ1 µL2+ (1 − t2 )− 2R1 ,σ(φγ1 N1 + N2 )which is Eq. (5.1) in the text. The post-tax profit of the MNE with a plant in country 2 canbe derived analogously.
For later reference, we provide Taylor approximations of γi as a function of ∆ti . Applying
a Taylor approximation at ∆ti = 0 to γi gives∂γ1(∆t1 − 0)∂∆t1 ∆t1 =0
1−σ 

σ−1σ(1 + δ)1−
∆t1 ,=σ + δ(σ − 1)σ + δ(σ − 1)∂γ2γ2 ' γ2 |∆t2 =0 +(∆t2 − 0)∂∆t2 ∆t2 =01−σ σ(1 − δ)
σ−1
=
1−
∆t2 .
σ − δ(σ − 1)σ − δ(σ − 1)
γ1 ' γ1 |∆t1 =0 +These approximations are justified when ∆ti = (tj − ti )/(1 − ti ) is sufficiently small. As far
as our sample of 23 OECD countries in 2008 to 2016 is concerned, this is plausible because|average tax differential| / [1−(average tax rate)] = 0.077/(1 − 0.2747) = 0.1061. If δ is set
to zero, we can further simplify these expressions as
γi ' 1 −σ−1∆ti , i ∈ {1, 2}.
σ(A1)

Appendix 3. Conditions for positive profits
We here derive sufficient conditions under which operating profits are positive. The operating
profits are π11 , π12 , π21 , and π22 , but only π11 can be negative:
π11 =

µL1
(σ − 1)(∆t1 + δ)
φγ1 µL2+
σ(N1 + φγ2 N2 ) |σ{z} σ(φγ1 N1 + N2 )
<0

=

µL/2
(σ − 1)(∆t1 + δ)
φγ1 µL/2+,
σ(n1 + φγ2 n2 ) |σ{z} σ(φγ1 n1 + n2 )<0

where L1 = L2 = L/2; Ni = ni L; and n2 = 1 − n1 . Note that ∆t1 + δ < 0, or equivalently,δ < (t1 − t2 )/(1 − t1 ) because we assumed δ < δ ≤ (t1 − t2 )/(1 − t2 ) < (t1 − t2 )/(1 − t1 ). We

39

can check that π11 decreases with n1 :∂π11µγ2 n2µγ1 n2 (σ − 1)[t1 − t2 − δ(1 − t1 )]
=−
−
< 0,
2
∂φ
2σ(n1 + φγ2 n2 )2σ 2 (1 − t1 )(φγ1 n1 + n2 )2where σ > 1 and δ < δ ≤ (t1 − t2 )/(1 − t2 ) < (t1 − t2 )/(1 − t1 ). Since π11 takes the minimum
value at φ = 1, in which case n1 must be one according to Proposition 1(ii-a), the sufficientcondition for it to be positive is
π11 ≥ min π11 = π11 |(n1 ,φ)=(1,1)φµ[σ(1 + t2 − 2t1 ) + t1 − t2 + δ(σ − 1)(1 − t1 )]'2σ 2 (1 − t1 )µ[σ(1 + t2 − 2t1 ) + t1 − t2 ]≥> 0,
2σ 2 (1 − t1 )→ 1 + t2 − 2t1 > 0,
where we used the Taylor approximation (A1). The sufficient condition for this inequality
is (t2 <)t1 < 1/2, which is close to 0.4076, i.e., the highest corporate tax-rate in 23 OECD
countries in 2010 to 2016 (Japan in 2010 to 2012).

Appendix 4. Proof of Proposition 1
Proof of Propositions 1(i) and 1(ii).
tionals requires

The zero-profit conditions for both type of multina-

Π1 = (1 − t1 )π11 + (1 − t2 )π12 − 2R1 = 0,
→ R1 = [(1 − t1 )π11 + (1 − t2 )π12 ]/2,
Π2 = (1 − t1 )π21 + (1 − t2 )π22 − 2R2 = 0,
→ R2 = [(1 − t1 )π21 + (1 − t2 )π22 ]/2.
The capital-return differential is∆R ≡ 2(R1 − R2 )µs1 σ(1 − t1 )(1 − φγ2 ) − φγ2 (σ − 1)[t1 − t2 − δ(1 − t2 )]= 2 ·σn1 + φγ2 n2µs2 σ(1 − t2 )(1 − φγ1 ) − φγ1 (σ − 1)[t2 − t1 + δ(1 − t1 )]− 2 ·. (A2)
σφγ1 n1 + n2
tj − tiwhere φ ≡ τ 1−σ , ∆ti ≡, for i 6= j ∈ {1, 2},
1 − ti

1−σ

1−σ
σ(1 + δ)σ(1 − δ)γ1 ≡, γ2 ≡.
σ − ∆t1 + δ(σ − 1)σ − ∆t2 − δ(σ − 1)
We here show that there exists a level of trade openness, denoted by φ† , which satisfies40

∆R|n1 =1/2 = 0 and that the long-run equilibrium becomes n1 < 1/2 (or n1 > 1/2) if φ < φ†(or φ > φ† ).
Assuming symmetric country size: s1 = 1/2, we evaluate the capital-return differential
at n1 = 1/2:
∆R|n1 =1/2 =µ · F (φ)σ 2 (1 + φγ1 )(1 + φγ2 )

,

where
F (φ) ≡ γ1 γ2 [(2 − σ)(t1 − t2 ) + δ(σ − 1)(2 − t1 − t2 )]φ2
+ [2σ{γ1 (1 − t1 ) − γ2 (1 − t2 )} + (γ1 + γ2 )(t1 − t2 ) + δ(σ − 1){γ1 (1 − t1 ) + γ2 (1 − t2 )}]φ−σ(t1 − t2 ),The sign of the capital-return differential is determined by the quadratic function of φ: F (φ).
At the level of φ that satisfies F (φ) = 0, the equilibrium distribution of plants becomes
one-half.
We readily observe that (i)F (φ) is a quadratic function of φ and (ii)F (φ = 0) = −σ(t1 −t2 ) < 0. When δ = 0, we can also confirm (iii)F (φ = 1) < 0:
F (φ = 1) '2(σ − 1)(t1 − t2 )3> 0,
σ 2 (1 − t1 )(1 − t2 )where the Taylor approximation (A1) is used. From these three observations, we can conclude
that there exists φ† ∈ (0, 1) that satisfies F (φ) = 0 (or equivalently ∆R|n1 =1/2 = 0), as canbe seen in Fig. A1. Regardless of the sign of the coefficient of φ2 , F (φ) has a unique solution
in φ ∈ (0, 1). In addition, if φ < φ† , F (φ) < 0 and thus ∆R|n1 =1/2 < 0 holds, implyingthat MNEs with production in country 1 have an incentive to relocate. Thus, the long-run
equilibrium must be n1 < 1/2. Similarly, if φ > φ† , F (φ) > 0 and thus ∆R|n1 =1/2 > 0
holds. The positive return differential at n1 = 1/2 requires that the long-run equilibrium ben1 > 1/2. These findings establish Propositions 1(i) and 1(ii).

Fig. A1. Function F (φ)
41Proof of Proposition 1(ii-a).
We first confirm that all MNEs prefer to locate theirproduction plant in the high-tax country 1 when trade costs are zero. In other words, capitalreturn differential ∆R is positive irrespective of plant share n1 at τ = 1 (or φ = 1). Then,
we show that there exists a level of trade openness above which the full agglomeration isachieved; that is, the agglomeration threshold, or also known as the sustain point, denotedby φS . Finally, we show that φS decreases with t1 , but increases with t2
Full agglomeration at zero trade costs.
We set δ to zero and evaluate the capital-return
differential (A2) at φ = 1 to obtain


ω1
ω2
µ(t2 − t1 )(σ − 1)+,
∆R|φ=1 =
2
2σ
γ
n
+
n
n
+
γ
n
1
1
2
1
2
2
{z
}
|
<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 capital-return differential is positive (ornegative) if the big bracket term is negative (or positive). We check that the big bracket
term is indeed negative. The condition for this 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

noting that n2 = 1 − n1 and γ1 > 1 > γ2 . The inequality holds for any n1 ∈ [0, 1] if thefollowing holds:
n1 [ω1 (1 − γ2 ) + ω2 (γ1 − 1)] + ω1 γ2 + ω2
< 1 · [ω1 (1 − γ2 ) + ω2 (γ1 − 1)] + ω1 γ2 + ω2
= ω1 + ω2 γ1 < 0.
Using the Taylor approximation (A1), we can confirm that the inequality holds:
ω1 + ω2 γ1 ' −(t1 − t2 )2< 0.
2σ 2 (1 − t1 )(1 − t2 )Hence, it holds that ∆R|φ=1 > 0 for any n1 ∈ [0, 1]. All MNEs are willing to establish
production plants in the high-tax country 1; that is, n1 |φ=1 = 1 is achieved in the long-run
equilibrium.
Agglomeration threshold (or sustain point).
Evaluating the capital-return differential42(A2) at n1 = 1 givesµ · I(φ),
2σ 2 φγ1
where I(φ) ≡ −γ1 γ2 (1 − t2 )(σ − ∆t2 )φ2 + γ1 (1 − t1 )(2σ − ∆t1 )φ − σ(1 − t2 ).
∆R|n1 =1 =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 agglomeration threshold φS (if any).
We observe that I(φ) is a quadratic function of φ with a negative coefficient of φ2 . Further
inspections reveal thatI(φ = 0) = −σ(1 − t2 ) < 0,I(φ = 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 agglomeration threshold φS ∈ (0, 1) always exists
and is given by the smaller root of I(φ) = 0 and that (ii) I(φ) or the capital-return differential
is negative for φ ∈ [0, φS ) but positive for φ ∈ (φS , 1].
Agglomeration threshold and taxes.
As Fig. 2 clearly shows, higher φ# , which will beSgiven in Eq. (A3) in Appendix 5, makes φ 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 )]2dφ#
σ(σ − 1)(1 − t2 )(2 − t1 − t2 )(t1 − t2 )
=
> 0,
dt2
[(σ − 1)(t1 − t2 )2 + σ(1 − t1 )(1 − t2 )]2
implying that φS also decreases (or increases) with t1 (or t2 ). As the tax difference is larger,
multinational production is more likely to be agglomerated in the high-tax country 1.

Appendix 5. Proof of Proposition 2
We here show that as trade costs decline, the equilibrium share of production plants incountry 1 first decreases, then increases. By solving the capital-return differential for n1 , weobtainΥ − φγ2 Υ0,(1 − φγ1 )Υ + (1 − φγ2 )Υ0
where Υ ≡ (σ − φγ2 )(1 − t1 ) − φγ2 (1 − δ)(σ − 1)(1 − t2 ),Υ0 ≡ (σ − φγ1 )(1 − t2 ) − φγ1 (1 + δ)(σ − 1)(1 − t1 ).

n1 =

43

We differentiate this with respect to φ:
dn1
G(φ)
=
,
dφ
H(φ)2
where
G(φ) ≡ G2 φ2 + G1 φ + G0 , Gi s are bundles of parameters of γi , ti , σ and δ ,H(φ) ≡ γ1 γ2 [σ(2 − t1 − t2 ) − δ(σ − 1)(t1 − t2 )]φ2−[2σ{γ1 (1 − t1 ) + γ2 (1 − t2 )} + (γ1 − γ2 )(t1 − t2 ) + δ(σ − 1){γ1 (1 − t1 ) − γ2 (1 − t2 )}]φ+σ(2 − t1 − t2 )2 > 0.
Because H(φ)2 > 0, the sign of the derivative, dn1 /dφ, is determined by G(φ). We assume
δ = 0 in what follows.
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:
G(φ = 0) = G0 ' −σ(t1 − t2 )(2 − t1 − t2 ) < 0,where we used the Taylor approximation (A1). We then solve for φ# that satisfies dn1 /dφ = 0,or equivalently G(φ) = 0, while assuming δ = 0:
φ# '

σ2
,
(σ − ∆t1 )(σ − ∆t2 )(A3)

where the Taylor approximation (A1) is used. It can easily be confirmed that φ# ∈ (0, 1).
We know from Proposition 1(ii-a) that if δ = 0, country 1 achieves full agglomeration
with sufficiently low trade costs such that φ ∈ [φS , 1], in which case the slope becomes zero:
dn1 /dφ = 0. Combining this with observations (i) to (iii), we can summarize the sign of
dn1 /dφ as follows: In sum,

<0




dn1 = 0
dφ 
>0



=0

if φ ∈ [0, φ# )if φ = φ#,
if φ ∈ (φ# , φS )if φ ∈ [φS , 1]

where φS is the agglomeration threshold, which was discussed in detail in Appendix 4.

Appendix 6. Pure exporters
We here introduce pure exporters into the main model, who serve foreign market throughdirect exporting. Pure exporters use two units of capital as fixed inputs, one for producing
goods for home market and the other for producing goods for foreign market. We assume thatarm’s length trade is subject to a higher level of trade costs than intra-firm trade. Letting τ E
44and τ M be arm’s length trade costs and intra-firm trade costs, this implies τ E > τ M . In termsof trade openness, we have φE /φM = η ∈ [0, 1], where φE ≡ (τ E )1−σ and φM ≡ (τ M )1−σ .
Whether a firm becomes a MNE or a pure exporter is endogenously determined. The timingof actions is modified as follows. First, each firm chooses the location of a production plantin one country. Second, they decide whether to establish a export plant in the same country
or to set up a distribution affiliate in the other country. The one using a distribution affiliate
is called a MNE and the one not using it is called a pure exporter. Third, MNEs set transfer
prices. Fourth, distribution affiliates and production plants of both MNEs and pure exporters
set selling prices. Finally, production and consumption take place.
In what follows, there are three things we want to show. First, (i) given the location of
production, all firms producing (or headquartered) in the high-tax country 1 become MNEs,
while those producing in the low-tax country 2 become pure exporters. Second, (ii) at theprohibitive level of intra-firm trade costs (τ M = ∞ or φM = 0), a fall in τ M decreases theplant share in country 1. Third, (iii) at zero intra-firm trade costs (τ M = 1 or φM = 1), allfirms become MNEs and are agglomerated in country 1 if the difference between intra-firm
and arm’s length trade costs is sufficiently large such that η < η ∗ .
We solve the problem from the fourth stage. The superscript M (or E) stands for MNEs
(or pure exporters). For a MNE with production in country 1, the pre-tax operating profits
of a production plant and a distribution affiliate are
M
M
M
M
M
M
π11
= (pM
11 − a)q11 + (g1 − τ a)q12 − δ|g1 − τ a|q12 ,
M
M
π12
= (pM
12 − g1 )q12 , M −σ M −σ
µL1
p12
p11
M
M
,
, q12 =
where q11 =
P1
P1
P2
1
" 2
# 1−σ
X
1−σ
1−σ
Pj =
, j ∈ {1, 2},
NiM (pM+ NiE (pE
ij )
ij )
i=1

and where NiM is the mass of MNEs with production in country i and NiE the mass of pureexporters in country i. We note that pure exporters in country i locate their two production
plants in the same country i. The optimal prices are
pM
11 =

σa
,
σ−1

pM
12 =

σg1
.
σ−1

For a pure exporter in country 1, the pre-tax operating profits consist of
E
E
π11
= (pE
11 − a)q11 ,
E
E
E
= (pE
π12
12 − τ a)q12 , E −σ E −σ
p11
µL1
p12
µL2
E
E
where q11 =, q12 =
.
P1
P1
P2
P2

45

The optimal prices are
pE
11 =

σa
(= pM
11 ),
σ−1

pE
12 =

στ E a.
σ−1

We can similarly derive optimal prices of MNEs with production in country 2 and pureexporters in country 2.
In the third stage, MNEs with production in country 1 set transfer prices to maximize
the following post-tax profits:
M
M
M
M
M
M
M
ΠM
1 = (1 − t1 )[(p11 − a)q11 + (g1 − τ a)q12 − δ|g1 − τ a|] + (1 − t2 )[(p12 − a)q12 ] − 2R1 .

The optimal transfer price is the same as in the text:
g1M =(1 + δ)στ M a.
σ − ∆t1 + δ(σ − 1)

Similarly, MNEs with production in country 2 sets the transfer price as
g2M =(1 − δ)στ M a.
σ − ∆t2 − δ(σ − 1)

We substitute these optimal prices into the post-tax profit of MNEs to obtainMMΠM
1 = (1 − t1 )π11 + (1 − t2 )π12 − 2R1
φM γ1 µL2
(σ − 1)(∆t1 + δ)
µL1·+
= (1 − t1 ) ·σσ(N1 + φM γ2 N2M + φE N2E )σ(φM γ1 N1M + φE N1E + N2 )φM γ1 µL2
− 2R1 ,+ (1 − t2 ) ·σ(φM γ1 N1M + φE N1E + N2 )MMΠM
2 = (1 − t1 )π21 + (1 − t2 )π22 − 2R2

φM γ2 µL1
σ(N1 + φM γ2 N2M + φE N2E )µL2(σ − 1)(∆t2 − δ)φM γ2 µL1
+ (1 − t2 )+·σσ(φM γ1 N1M + φE N1E + N2 )σ(N1 + φM γ2 N2M + φE N2E )− 2R2 ,= (1 − t1 ) ·where φM ≡ (τ M )1−σ ; φE ≡ (τ E )1−σ ; and Ni = NiM + NiE is the total mass of production
plants in country i ∈ {1, 2}. Note that pure exporters in country i locate their two plants
there. The above expressions reduce to Eqs. (5-1) and (5-2) if NiE = 0. We set δ to zero inwhat follows.

46

Similarly we use the optimal prices to write the post-tax profits of pure exporters as
EE
ΠE
1 = (1 − t1 )(π11 + π12 ) − 2R1
µL1
φE µL2= (1 − t1 )+− 2R1 ,σ(N1 + φM γ2 N2M + φE N2E ) σ(φM γ1 N1M + φE N1E + N2 )EEΠE
2 = (1 − t2 )(π21 + π22 ) − 2R2
φE µL1µL2= (1 − t2 )+− 2R2 .
σ(N1 + φM γ2 N2M + φE N2E ) σ(φM γ1 N1M + φE N1E + N2 )In the second stage, given the location of production, firms choose their way of serving theforeign market, either through distribution affiliates or through exporting. A firm with plantEin country i choose to use distribution affiliates if ΠM
i > Πi . Noting that L1 = L2 = L/2
E
M
and φ = ηφ , we haveEΠM
1 − Π1 =φM µL[σ(ηγ1 − 1)(1 − t1 ) + ηγ1 (t1 − t2 )],2σ 2 (φM γ1 N1M + ηφM N1E + N2 )which is positive because the numerator is positive:σ(ηγ1 − 1)(1 − t1 ) + ηγ1 (t1 − t2 ) '(1 − t1 )(1 + t2 − 2t1 )σ 2 + (t1 − t2 )2 (σ − 1)
> 0,
2σ(1 − t1 )where σ > 1; 1/2 > t1 > t2 ; δ ∈ [0, δ); γ1 > 1; and we used the Taylor approximation (A1)from the first to the second line. This inequality implies that a firm with plant in country
1 always prefers serving the foreign market through its distribution affiliate. On the other
hand, a firm with plant in country 2 always prefers direct exporting:EΠM
2 − Π2 = −φM µL[σ(1 − ηγ2 )(1 − t2 ) + ηγ2 (t1 − t2 )]< 0,
2σ 2 (N1 + φM γ2 N2M + ηφM N2E )noting that 0 < η < 1; 0 < γ2 < 1. In sum, (i) all firms with plant in country 1 choose to use
distribution affiliate and thus there are no pure exporters’ plants in country 1, i.e., N1E = 0;
those with plant in country 2 choose direct exporting and thus there are no MNEs’ plants incountry 2 and no distribution affiliates in country 1, i.e., N2M = 0.

47

In the first stage, free entry and exit of firms drives the post-tax profits to zero:MMΠM
1 = (1 − t1 )π11 + (1 − t2 )π12 − 2R1 = 0,MM
→ 2R1 = (1 − t1 )π11
+ (1 − t2 )π12,
(σ − 1)∆t1µL
φM γ1 µL+
= (1 − t1 )·σ
2σ(N1M + ηφM N2E )2σ(ηφM γ1 N1M + N2E )φM γ1 µL
+ (1 − t2 ) ·,σ(φM γ1 N1M + N2E )EE
ΠE
2 = (1 − t2 )(π11 + π12 ) − 2R2 = 0,EE
→ 2R2 = (1 − t2 )(π11
+ π12
)


µL
ηφM µL+.
= (1 − t2 )2σ(N1M + ηφM N2E ) 2σ(φM γ1 N1M + N2E )The world capital-market clearing requires that the total mass of plants/affiliates of both
MNEs and pure exporters must be equal to the mass of world capital endowment: 2(N1M +N2E ) = K = 2L or N1M + N2E = L. Letting n1 ∈ [0, 1] be the world share of (the headquartersof) MNEs with production in country 1, there are N1M = n1 L MNEs in country 1 andN2E = (1−n1 )L pure exporters in country 2. 39 Capital owners invest in MNEs/pure exporters
who guarantee higher return: Ri > Rj . Solving ∆R ≡ 2(R1 − R2 ) = 0 gives, if any, theinterior long-run equilibrium n1 ∈ (0, 1), which we do not show here for brevity.
We first check that (ii) a fall in intra-firm trade costs τ M (or an increase in intra-firmtrade openness φM ) from the prohibitive level τ M = ∞ (or zero openness φM = 0) decreases
the share of MNEs in country 1:
dn1(t1 − t2 )[2η(1 − t2 )σ 2 + {1 − t2 − 2η(t1 − t2 )}σ + η(t1 − t2 )]< 0,'−
dφM φM =0
σ 2 (2 − t1 − t2 )2where 0 < η < 1; σ > 1; and we used the Taylor approximation (A1). We then derive theconditions under which (iii) all capital owners invest in MNEs with production in country
1 at zero intra-firm trade costs (φM = 1). Inspections of the capital-return differential at(n1 , φM ) = (1, 1) revealµ · Λ(η),
2ηγ1 σ 2Λ(η) ≡ −σγ1 (1 − t2 )η 2 + γ1 [σ(1 + t2 − 2t1 ) + t1 − t2 ]η + σ(γ1 − 1)(1 − t2 ),Λ(η = 0) = σ(γ1 − 1)(1 − t2 ) > 0,
(t1 − t2 )[(1 − t2 )σ 2 − (t1 − t2 )(2σ − 1)]
Λ(η = 1) ' −< 0,σ(1 − t1 )∆R|(n1 ,φM )=(1,1) =where γ1 > 1; σ > 1; and we used the Taylor approximation (A1). The sign of the capitalreturn differential ∆R|(n1 ,φM )=(1,1) is determined by that of Λ(η). From the facts that (iii-a)
39

In terms of plants/affiliates, country 1 has N1M production plants of MNEs, while country 2 has N1M
distribution affiliates of MNEs and 2N2E production plants of pure exporters.

48

Λ(η) is a quadratic function of η with a negative coefficient of η 2 ; (iii-b) Λ(η = 0) < 0; and(iii-c) Λ(η = 1) > 0, we can conclude that Λ(η) = 0 has a unique solution of η ∈ (0, 1), which
we denote as η ∗ , and that ∆R|(n1 ,φM )=(1,1) is positive if η ∈ [0, η ∗ ).

Appendix 7. Asymmetric country size
We here allow countries to have unequal size, i.e., s1 6= 1/2, and derive conditions underwhich all production plants are agglomerated in the high-tax country 1 at zero trade costs(τ = 1 or φ = 1). We set δ to zero and evaluate the capital-return differential (A2) at φ = 1
to obtain
s1 ω2µ(t2 − t1 )(σ − 1)
s2 ω1
+
,
∆R|φ=1 =2σ|{z} γ1 n1 + n2 n1 + γ2 n2<0where ωi ≡ γi +σ(1 − γi ),(σ − 1)∆tj

for i 6= j ∈ {1, 2},noting that ∆t1 < 0 < ∆t2 and γ1 > 1 > γ2 . The capital-return differential is positive (ornegative) if the big bracket term in the first line is negative (or positive). The condition forthe big bracket term to be negative is
s1 ω2
s2 ω1
+
< 0,
γ1 n1 + n2 n1 + γ2 n2→ s2 ω1 (n1 + γ2 n2 ) + s1 ω2 (γ1 n1 + n2 ) < 0,
→ n1 [s2 ω1 (1 − γ2 ) + s1 ω2 (γ1 − 1)] +s2 ω1 γ2 + s1 ω2 < 0,
|
{z
}
>0

noting that n2 = 1 − n1 and γ1 > 1 > γ2 . The inequality holds for any n1 ∈ [0, 1] if thefollowing holds
n1 [s2 ω1 (1 − γ2 ) + s1 ω2 (γ1 − 1)] + s2 ω1 γ2 + s1 ω2< 1 · [s2 ω1 (1 − γ2 ) + s1 ω2 (γ1 − 1)] + s2 ω1 γ2 + s1 ω2= s2 ω1 + s1 ω2 γ1(t1 − t2 )[σ(2s1 − 1)(1 − t2 ) − s1 (t1 − t2 )]< 0,'
σ 2 (1 − t1 )(1 − t2 )where we used the Taylor approximation (A1) from the second last to the last line. Thisinequality holds if the following holds:
σ(2s1 − 1)(1 − t2 ) − s1 (t1 − t2 ) < 0,σ1
→ s1 <≡ s1 ∈,1 .
2σ − ∆t2249

As long as the high-tax country is not too large such that s1 < s1 , the capital-return differential at φ = 1 is positive for any n1 ∈ [0, 1]. In this case, production plants are agglomerated
in the high-tax country 1 in the long-run equilibrium: n1 |φ=1 = 1.

Appendix 8. Centralized decision making
In the text, we considered the case of decentralized decision making, in which the foreign
affiliate chooses a price to maximize its own profit. We here examine the case of centralized
decision making, where the MNE chooses all prices to maximize its total profit, using thesame framework as in the text. As we shall see, the two different organization forms givequalitatively similar results.
A MNE with a plant in country 1 solves the following problem:max Π1 = max (1 − t1 )π11 + (1 − t2 )π12 − 2R1 ,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 than π12 .
C(·) is the concealment cost specified as C(gi , qij ) = δ(gi − τ a)2 qij with δ ≥ 0 (see Nielsen
et al., 2003; Kind et al., 2005; Haufler et al., 2018 for similar specifications).
The first order conditions give the following optimal prices:


∆t1
σa
∆t1 ∆t2
σa, g1 = τ a +, p12 =
τ+
,
p11 =
σ−1
2δ
σ−1
4aδ
tj − tiwhere ∆ti ≡, i 6= j ∈ {1, 2}.
1 − ti
Mirror expressions hold for MNEs with production in country 2:


σa
∆t2
σa
∆t1 ∆t2
p22 =, g2 = τ a +, p21 =
τ+
.
σ−1
2δ
σ−1
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 profitability of the affiliate incountry 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 in country 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 not just shift profits but affects profitability isvery close to the one in the decentralized-decision case in the text.

50

Using the optimal prices, we can rewrite the post-tax profit asσ(1 − t1 )µL/2(2σ − 1)∆t1 ∆t2 − 2(σ − 1)(∆t1 + ∆t2 )γ σ−1 µL/2
Π1 =
+ (1 − t2 ) τ +− 2R1 ,σ(N1 + γN2 )4aδ
σ(γN1 + N2 )σ(1 − t2 )µL/2(2σ − 1)∆t1 ∆t2 − 2(σ − 1)(∆t1 + ∆t2 )γ σ−1 µL/2
Π2 =+ (1 − t1 ) τ +− 2R2 ,
σ(γN1 + N2 )4aδσ(N1 + γN2 )
1−σ∆t1 ∆t2
where γ ≡ τ +.
4aδFree entry and exit of firms drive these post-tax profits to zero (Πi = 0), determining thecapital-return, Ri .
As in the decentralized-decision case, the long-run equilibrium distribution of plants isinterior if R1 − R2 = 0 has a solution for n1 ∈ (0, 1). If R1 − R2 > 0 (or R1 − R2 < 0) for
any n1 ∈ [0, 1], then the economy reaches the corner equilibrium of n1 = 1 (or n1 = 0). We
obtain(γ + 1)(t1 − t2 )1
+if τ ∈ (τ S1 , ∞) (i)


2
2(γ
−
1)(2
−
t
−
t
)

1
2

if τ ∈ (τ S2 , τ S1 ] (ii) ,n1 = 0[0, 1]
if τ = τ S2
(iii)




S2
1
if τ ∈ [1, τ )
(iv)

1−σ
∆t1 ∆t2
tj − tiwhere γ ≡ τ +, i 6= j ∈ {1, 2},, ∆ti ≡
4aδ
1 − ti
1

 1−σ
1
−
t
∆t1 ∆t2∆t1 ∆t21
τ S1 ≡−, τ S2 ≡ 1 −,1 − t24aδ
4aδ
which is illustrated in Fig. A2 (see Appendix 12 for parameter values). The horizontal
dashed line represents the share at which 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, the high-tax country attracts all production plants. The result
is qualitatively the same as that under decentralized decision making.

51

Fig. A2. Plant share under centralized decision making

Appendix 9. Proof of Lemma 2
In the no-transfer-pricing case, the capital-return differential at n1 = 0 isb n1 =0 =∆R|bµ · Θ(φ),
2σφbwhere Θ(φ)≡ (1 − φ)[1 − t1 − φ(1 − t2 )].
b
Θ(φ)= 0 has two solutions, φ = 1 and φ = φbS :
1−b
t1
φbS ≡
∈ (0, 1),b
1 − t2bb n1 =0 are negative if φ ∈ (φbS , 1). That is, if φ ∈ (φbS , 1),
noting b
t1 > bt2 . Clearly, Θ(φ)
or ∆R|
then all production plants are located in low-tax country 2: n2 = 1 − n1 = 1, or n1 = 0.

Appendix 10. Proof of Proposition 3
We first check the second-order condition (SOC) for the maximization problem. For government 2, we have
2α2
∂ 2 G2
< 0.
=−
2
∂t2
(1 − t2 )3
Evaluating the SOC of government 1 at t2 = t∗2 = b
t2 gives√√√∂ 2 G12α2 σ[ 2α2 σ 3 + (σ − 1) µL]< 0.
=−∂t21 t2 =t∗σ(1 − t1 )3
2

52

We then confirm that t∗i lies in (0, 1/2) and the government payoffs are positive. From theanalysis of no-transfer-pricing case, we know that t∗2 = bt2 ∈ (0, 1/2) and G2 (t2 = t∗2 ) > 0 holdbecause α1 < α2 and αi ∈ (µL/(3σ), µL/(2σ)). We only have to confirm t∗1 ∈ (0, 1/2). The
condition for t∗1 > 0 iss√
2 + (σ − 1) 2α σµL
2ασ1
2t∗1 = 1 −> 0,µL(2σ − 1)√µL(2σ − 1) − (σ − 1) 2α2 σµL→ α1 <≡ α† .
2
2σ
As we assumed α1 < α2 , it suffices to check α2 ≤ α† :√µL(2σ − 1) − (σ − 1) 2α2 σµL†
α2 ≤ α ≡,2σ 2p→ 2α2 σ 2 + (σ − 1) 2α2 σµL ≤ µL(2σ − 1).
This inequality always holds because α2 < µL/(2σ):
r
p
µL
µL
+ (σ − 1) 2σµL ·= µL(2σ − 1).
2α2 σ 2 + (σ − 1) 2α2 σµL ≤ 2σ 2 ·2σ
2σThe condition for t∗1 < 1/2 iss√
1
2α1 σ 2 + (σ − 1) 2α2 σµL∗
t1 = 1 −< ,µL(2σ − 1)2√µL(2σ − 1)/4 − (σ − 1) 2α2 σµL→ α1 >≡ α‡ .
2
2σ
As we assumed µL/(3σ) < α1 , it suffices to check α‡ < µL/(3σ):√µLµL(2σ − 1)/4 − (σ − 1) 2α2 σµL
<
,
2
2σ
3σ
p
→ µL(2σ − 3) + 12(σ − 1) 2α2 σµL > 0,
which holds as we assumed σ > 3/2.
We can see that the government 1’s payoff in equilibrium is positive:


µLt∗1
(σ − 1)∆t∗1
α1 t∗1∗∗G1 (t1 = t1 , t2 = t2 ) =
1+
−
2σ
σ
1 − t∗1µLt∗2
α1 t∗2> G1 (t1 = t∗2 , t2 = t∗2 ) =−2σ
1 − t∗22µLt∗2α2 t∗2µL∗> G2 (t2 = t2 ) =
−
=
− α2
2σ
1 − t∗2
2σ
> 0,

53

p
where we used t∗2 = b
t2 = 1 − 2α2 σ/(µL) and α1 < α2 .
(i) Country 1’s tax rate vs. country 2’s.
We check the condition under which in
the transfer-pricing case the equilibrium tax in country 1 is higher than that in country 2(t∗1 > t∗2 ):sr√
2 + (σ − 1) 2α σµL
2α
σ
2α2 σ
1
2
t∗1 = 1 −>1−
= t∗2 ,µL(2σ − 1)
µL
s
r
√
2α2 σ
2α1 σ 2 + (σ − 1) 2α2 σµL→>,µLµL(2σ − 1)p
→ 2α2 σ(2σ − 1) > 2α1 σ 2 + (σ − 1) 2α2 σµL,√
2α2 σ(2σ − 1) − (σ − 1) 2α2 σµL→ α1 <≡ α∗ .
22σ
We can further check that α∗ ∈ (µL/(3σ), α2 ) hold in a similar manner. When φ is smaller
than φS , all production plants are located in the high-tax country (n∗1 = 1) as long ast2 ) hold. The equilibrium is unique because both government do
α1 < α∗ and thus t∗1 > t∗2 (= b
not benefit from changes in the tax rate from the equilibrium one.
Conversely, if α ≥ α∗ and thus t∗1 ≤ t∗2 hold, the lower tax rate of country 1 is inconsistent
with the presumption that all production plants are in country 1. In this case, government
1 sets a tax rate equal to government 2’s, and the plants are equally distributed between
the two countries: n∗1 = 1/2. As both governments try to avoid tax-base erosion from fullt2 )is unique one.
agglomeration of plants, the equal equilibrium tax rate of t∗1 = t∗2 (= b(ii) Tax rates with and without transfer pricing. Assume δ = 0 and α1 < α∗ . Supposing
t1 > t2 , the objective function of government 1 under the case with and without transfer
pricing is summarized as
G1 =

µLt1
µLt1 (σ − 1)∆t1
α1 t1
+1
−
,
2σ
| 2σ {z σ} 1 − t1
<0(
1 transfer-pricing casewhere 1 =,0 no-transfer-pricing casewhere the second negative term represents tax-base erosion. A higher t1 increases the tax-baseerosion:µL(2σ − 1) t1 (2 − t1 ) − t2
∂ µLt1 (σ − 1)∆t1
=−
·
< 0.
∂t1 2σσ2σ 2(1 − t1 )2Using this, we can compare the marginal effect of tax on the objective with and without

54

transfer pricing:
∂G1 (1 = 1)
α1 t1
∂ µLt1 (σ − 1)∆t1∂ µLt1−+=∂t1∂t1 2σ1 − t1 ti =bti ∂t1 2σ
σ
ti =b
ti
ti =b
ti


∂ µLt1 (σ − 1)∆t1∂G1 (1 = 0)+=
∂t1
∂t1 2σ
σ
ti =b
ti
ti =b
ti
b
b
b
µL(2σ − 1) t1 (2 − t1 ) − t2
=0−
·
2σ 2
(1 − bt1 )2<0=∂G1 (1 = 0)
,
∂t1
ti =b
ti

where taxes are evaluated at the equilibrium under no transfer pricing: (t1 , t2 ) = (bt1 , bt2 ).
Government 1 has an incentive to reduce its tax rate from b
t1 . Since the concave objectivefunction has a unique maximizer, government 1 sets a lower tax rate in the transfer-pricing
t1 . Under our assumption of α1 < α∗ , t∗1 > t∗2case than in the no-transfer-pricing case: t∗1 < bactually holds.

Appendix 11.
ences

Tax competition under the Cobb-Douglas prefer-

We here check the robustness of our result that introducing transfer pricing makes the tax
difference narrower using the Cobb-Douglas utility function. The main model assumed thequasi-linear utility function such that u1 = µ ln Q1 + q1O , implying that expenditures for
manufacturing varieties are fixed. To see this first, let E1 be the total expenditure for
manufacturing varieties in country 1. Using Eq. (1), we calculate the goods-market clearing
condition as
E1 =
=

2 Z
X

pi1 (ω)qi1 (ω)dωi=1 ω∈Ωi

1−σ
2 Z
X
pi1 (ω)i=1

ω∈Ωi= µL1 P1σ−1

P1
2 Z
X

µL1 dω

pi1 (ω)1−σ dω

i=1 ω∈Ωiσ−1= µL1 P1 · P11−σ= µL1 ,
which is exogenously given.
We instead adopt the Cobb-Douglas utility function such that u1 = Qθ1 (q1O )1−θ withθ ∈ (0, 1) being the weight attached to the manufacturing goods. We also assume that tax
revenues in each country are repatriated to its residents. The aggregate demand for variety55ω defined in Eq.(1) is modified aspi1 (ω)P1

qi1 (ω) =−σθ(L1 + T R1 ),P1

where L1 (= w1 L1 ) is labor income and T R1 is tax revenues. The total expenditure is nolonger constant:
E1 =

2 Z
X
i=1

ω∈Ωi



pi1 (ω)P1

1−σ
θ(L1 + T R1 )dω= θ(L1 + T R1 ).
We note that optimal prices are the same as those derived in the text. Using the results of
optimal prices, we rearrange tax revenues as
T R1 = t1 · T B1 ,T B1 = N1 π11 + N2 π21= N1 [(p11 − a)q11 + 1(g1 − τ a)q12 ] + N2 (p21 − g2 )q21
= N1 [(p11 − a)q11 + N2 (p21 − g2 )q21 ] + 1N1 (g1 − τ a)q12= (N1 p11 q11 + N2 p21 q21 )/σ + 1N1 (g1 − τ a)q12= E1 /σ + 1N1 (g1 − τ a)q12
θ(L1 + t1 T B1 )(σ − 1)∆t1 φγ1 θ(L2 + t2 T B2 )
=
+ 1N1
σ
σ
σ(φγ1 N1 + N2 )(1 transfer-pricing casewhere 1 =.
0 no-transfer-pricing case(A4-1)

Similarly, tax revenues in country 2 are given by
T R2 = t2 · T B2 ,T B2 = N2 π22 + N1 π12θ(L2 + t2 T B2 )(σ − 1)∆t2 φγ2 θ(L1 + t1 T B1 )
+ 1N2
.
=
σ
σ
σ(N1 + φγ2 N2 )(A4-2)The tax bases of the two countries are obtained by solving the system of equations: (A4-1)
and (A4-2). In the following, we derive Nash-equilibrium tax rates in the case with andwithout transfer pricing.
No-transfer-pricing case.
In the case without transfer pricing, government i ∈ {1, 2}’spayoff becomes
αi ti
1 − tiθLi tiαi ti=−,
σ − θti 1 − ti

Gi (1 = 0) = ti T Bi −56

where α1 < α2 . Solving the first-order conditions give the equilibrium tax rates:
√
(σ
−
θ)
2αi θ
b
ti = 1 − √,√σL − 2αi θnoting that the tax base does not depend on the plant distribution ni . We assume thatσ > 2α2 θ/L and α1 > L/2 to ensure positive tax rates: bti > 0, in which case the secondorder conditions also hold. Clearly, bti decreases with αi . Government 1 with a more efficient
tax administration sets a higher tax rate than government 2 with a less efficient one.
Transfer-pricing case.
In the case with transfer pricing and full production agglomeration in country 1, government 1’s payoff becomes
α1 t1
θt1
(L1 + X) −,σ − θt1
1 − t1(σ − 1)∆t1
where X ≡· (L2 + t2 T B2 )σθL2 t2(σ − 1)∆t1· L2 +=< 0.
σ
σ − θt2

G1 (1 = 1) =X is a negative term accruing from the profits that the MNEs with production in country 1
transfer to their affiliates in country 2. It increases with t1 :θL(σ − 1)[σ(1 − t1 ) + θ{t2 (2t1 − 1) − t21 }]
∂X
< 0,
=−
∂t1
2(1 − t1 )2 (σ − θt1 )2 (σ − θt2 )noting that σ > 1; θ ∈ (0, 1); and ti ∈ [0, 1].
Government 2’s payoff is the same as that in the no-transfer-pricing case and thus its
equilibrium tax rate, denoted by t∗2 , is unchanged: t∗2 = b
t2 . Using this, we can compare themarginal effect of tax on government 1’s payoff with and without transfer pricing:




∂
αi ti
∂
θLi tiθt1∂G1 (1 = 1)
=
−
+
X
∂t1
∂t1 σ − θti 1 − ti ti =bti ∂t1 σ − θt1
ti =b
ti
ti =b
ti


∂G1 (1 = 0)
θt1
∂
=
+
X
∂t1
∂t1 σ − θt1
b
ti =b
ti

 ti =tiσθθt1 ∂X=0+X+(σ − θt1 )2
σ − θt1 ∂t1 ti =bti
<0=

∂G1 (1 = 0)
.
∂t1
ti =b
ti

where taxes are evaluated at the equilibrium under no transfer pricing: ti = b
ti . Governmentb
1 has an incentive to reduce its tax rate from t1 . Since the concave objective function has
a unique maximizer, government 1 sets a lower tax rate in the transfer-pricing case than in
the no-transfer-pricing case: t∗1 < bt1 . To be consistent with full production agglomeration incountry 1, we choose the range of parameters such that t∗1 > t∗2 holds.

57

Appendix 12. Parameter values
The figures in the text were produced using the following parameter values:
Figs. 2 and 3: σ = 5, t1 = 0.3, t2 = 0.2, δ = 0, L = 20, s1 = 0.5, µ = 1, a = 1.
Fig. 4: Parameter values are the same as those in Figs. 2 and 3 except for δ ∈ {0, 0.07, 0.143}.
Fig. 5: Parameter values are the same as those in Figs. 2 and 3 except for η ∈ {0.88, 0.88135, 0.882}.
Fig. 6: σ = 5, α1 = 0.3, α2 = 0.25, δ = 0, L = 20, s1 = 0.5, µ = 1, a = 1.
Fig. 7: σ = 5, α1 = 0.3, α2 = 0.25, δ = 0, L = 20, s1 = 0.5, µ = 1, a = 1.
Fig. A1 does not depend on specific parameter values.
Fig. A2: σ = 5, t1 = 0.3, t2 = 0.267, δ = 0.1, L = 20, s1 = 0.5, µ = 1, a = 1.

References
Agrawal, D. R. and Wildasin, D. E. (2020). Technology and tax systems. Journal of Public
Economics, 185:104082.
Amerighi, O. and Peralta, S. (2010). The proximity-concentration trade-off with profit shifting. Journal of Urban Economics, 68(1):90–101.
Andersson, F. and Forslid, R. (2003). Tax competition and economic geography. Journal of
Public Economic Theory, 5(2):279–303.
Antràs, P. and Helpman, E. (2004).
112(3):552–580.

Global sourcing.

Journal of Political Economy,

Baldwin, R. E. and Krugman, P. R. (2004). Agglomeration, integration and tax harmonisation. European Economic Review, 48(1):1–23.
Baldwin, R. E. and Okubo, T. (2014). Tax competition with heterogeneous firms. Spatial
Economic Analysis, 9(3):309–326.
Bartelsman, E. J. and Beetsma, R. M. (2003). Why pay more? Corporate tax avoidance
through transfer pricing in OECD countries. Journal of Public Economics, 87(9):2225–
2252.
Bauer, C. J. and Langenmayr, D. (2013). Sorting into outsourcing: Are profits taxed at agorilla’s arm’s length? Journal of International Economics, 90(2):326–336.
Becker, J. and Riedel, N. (2013). Multinational firms mitigate tax competition. Economics
Letters, 118(2):404–406.
Beer, S., De Mooij, R., and Liu, L. (2020). International corporate tax avoidance: A reviewof the channels, magnitudes, and blind spots. Journal of Economic Surveys, 34(3):660–688.
Behrens, K., Peralt, S., and Picard, P. M. (2014). Transfer pricing rules, OECD guidelines,
and market distortions. Journal of Public Economic Theory, 16(4):650–680.
Bénassy-Quéré, A., Fontagné, L., and Lahrèche-Révil, A. (2005). How does FDI react tocorporate taxation? International Tax and Public Finance, 12(5):583–603.

58

Bernard, A. B., Jensen, J. B., and Schott, P. K. (2006). Transfer pricing by US-based
multinational firms. NBER Working Paper, 12493.
Bilir, L. K., Chor, D., and Manova, K. (2019). Host-country financial development andmultinational activity. European Economic Review, 115:192–220.
Blonigen, B. A. and Piger, J. (2014). Determinants of foreign direct investment. Canadian
Journal of Economics, 47(3):775–812.
Blouin, J. L. and Robinson, L. A. (2020). Double counting accounting: How much profit ofmultinational enterprises is really in tax havens? mimeo.
Bond, E. W. and Gresik, T. A. (2020). Unilateral tax reform: Border adjusted taxes, cash
flow taxes, and transfer pricing. Journal of Public Economics, 184:104160.
Borck, R. and Pflüger, M. (2006). Agglomeration and tax competition. European Economic
Review, 50(3):647–668.
Bruner, J., Rassier, D. G., and Ruhl, K. J. (2018). Multinational profit shifting and measuresthroughout economic accounts. In The Challenges of Globalization in the Measurement of
National Accounts. University of Chicago Press.
Bucovetsky, S. (1991). Asymmetric tax competition. Journal of Urban Economics, 30(2):167–
181.
Choe, C. and Matsushima, N. (2013). The arm’s length principle and tacit collusion. International Journal of Industrial Organization, 31(1):119–130.
Choi, J. P., Furusawa, T., and Ishikawa, J. (2020a). Transfer pricing regulation and tax
competition. Journal of International Economics, 127:103367.
Choi, J. P., Ishikawa, J., and Okoshi, H. (2020b). Tax havens and cross-border licensing.
RIETI Discussion Paper Series 19-E-105.
Choi, S., Furceri, D., and Yoon, C. (2020c). Policy uncertainty and foreign direct investment.
Review of International Economics.
Clausing, K. A. (2003). Tax-motivated transfer pricing and US intrafirm trade prices. Journalof Public Economics, 87(9):2207–2223.
Copithorne, L. W. (1971). International corporate transfer prices and government policy.
Canadian Journal of Economics, 4(3):324–341.
Cristea, A. D. and Nguyen, D. X. (2016). Transfer pricing by multinational firms: New
evidence from foreign firm ownerships. American Economic Journal: Economic Policy,
8(3):170–202.
Darby, J., Ferrett, B., and Wooton, I. (2014). Regional centrality and tax competition for
FDI. Regional Science and Urban Economics, 49:84–92.
Davies, R. B. and Eckel, C. (2010). Tax competition for heterogeneous firms with endogenous
entry. American Economic Journal: Economic Policy, 2(1):77–102.
Davies, R. B., Martin, J., Parenti, M., and Toubal, F. (2018). Knocking on tax haven’s door:
Multinational firms and transfer pricing. Review of Economics and Statistics, 100(1):120–
134.
59

Devereux, M. P. and Griffith, R. (1998). The taxation of discrete investment choices. Working
Paper Series No. W98/16, The Institute for Fiscal Studies.
Dharmapala, D. (2014). What do we know about base erosion and profit shifting? A reviewof the empirical literature. Fiscal Studies, 35(4):421–448.
Dixit, A. and Stiglitz, J. (1977). Monopolistic competition and optimum product diversity.
American Economic Review, 67(3):297–308.
Egger, P., Loretz, S., Pfaffermayr, M., and Winner, H. (2009). Bilateral effective tax rates
and foreign direct investment. International Tax and Public Finance, 16(6):822–849.
Egger, P. and Seidel, T. (2013). Corporate taxes and intra-firm trade. European Economic
Review, 63:225–242.
Elitzur, R. and Mintz, J. (1996). Transfer pricing rules and corporate tax competition.
Journal of Public Economics, 60(3):401–422.
Fuest, C., Huber, B., and Mintz, J. (2005). Capital mobility and tax competition. Foundations and Trends in Microeconomics, 1(1).
Fujita, M., Krugman, P. R., and Venables, A. J. (1999). The Spatial Economy. MIT Press,
Cambridge, MA.
Goldbach, S., Nagengast, A. J., Steinmüller, E., and Wamser, G. (2019). The effect ofinvesting abroad on investment at home: On the role of technology, tax savings, andinternal capital markets. Journal of International Economics, 116:58–73.
Gumpert, A., Hines Jr, J. R., and Schnitzer, M. (2016). Multinational firms and tax havens.
Review of Economics and Statistics, 98(4):713–727.
Guvenen, F., Mataloni Jr, R. J., Rassier, D. G., and Ruhl, K. J. (2017). Offshore profit
shifting and domestic productivity measurement. NBER Working Paper, 23324.
Habu, K. (2017). Centre for business taxation tax database 2017. University of Oxford.
Han, Y., Pieretti, P., Zanaj, S., and Zou, B. (2014). Asymmetric competition among nation
states: A differential game approach. Journal of Public Economics, 119:71–79.
Han, Y., Pieretti, P., and Zou, B. (2018). Does tax competition increase infrastructural
disparity among jurisdictions? Review of International Economics, 26(1):20–36.
Hauck, T. (2019). Lobbying and the international fight against tax havens. Journal of Public
Economic Theory, 21(3):537–557.
Haufler, A., Mardan, M., and Schindler, D. (2018). Double tax discrimination to attract
FDI and fight profit shifting: The role of CFC rules. Journal of International Economics,
114:25–43.
Haufler, A. and Runkel, M. (2012). Firms’ financial choices and thin capitalization rules
under corporate tax competition. European Economic Review, 56(6):1087–1103.
Haufler, A. and Schjelderup, G. (2000). Corporate tax systems and cross country profit
shifting. Oxford Economic Papers, 52(2):306–325.

60

Haufler, A. and Stähler, F. (2013). Tax competition in a simple model with heterogeneousfirms: How larger markets reduce profit taxes. International Economic Review, 54(2):665–
692.
Heckemeyer, J. H. and Overesch, M. (2017). Multinationals’ profit response to tax differentials: Effect size and shifting channels. Canadian Journal of Economics, 50(4):965–994.
Helpman, E. and Krugman, P. R. (1985). Market Structure and Foreign Trade. MIT Press,
Cambridge, MA.
Hindriks, J., Peralta, S., and Weber, S. (2008). Competing in taxes and investment underfiscal equalization. Journal of Public Economics, 92(12):2392–2402.
Horner, R. and Aoyama, Y. (2009). Limits to FDI-driven growth in Ireland: A newspaper
content analysis for investment, upgrading and divestment. Irish Geography, 42(2):185–
205.
Horst, T. (1971). The theory of the multinational firm: Optimal behavior under different
tariff and tax rates. Journal of Political Economy, 79(5):1059–1072.
Janeba, E. and Osterloh, S. (2013). Tax and the city—A theory of local tax competition.
Journal of Public Economics, 106:89–100.
Janskỳ, P. and Palanskỳ, M. (2019). Estimating the scale of profit shifting and tax revenue losses related to foreign direct investment. International Tax and Public Finance,
26(5):1048–1103.
Johannesen, N. (2010). Imperfect tax competition for profits, asymmetric equilibrium andbeneficial tax havens. Journal of International Economics, 81(2):253–264.
Juranek, S., Schindler, D., and Schjelderup, G. (2018). Transfer pricing regulation andtaxation of royalty payments. Journal of Public Economic Theory, 20(1):67–84.
Kato, H. (2015). The importance of government commitment in attracting firms: A dynamic
analysis of tax competition in an agglomeration economy. European Economic Review,
74(C):57–78.
Kato, H. and Okoshi, H. (2019). Production location of multinational firms under transfer
pricing: The impact of the arm’s length principle. International Tax and Public Finance,
26(4):835–871.
Keen, M. and Konrad, K. A. (2013). The theory of international tax competition and coordination. In Auerbach, A. J., Chetty, R., Feldstein, M., and Saez, E., editors, Handbook of
Public Economics, volume 5, pages 257–328. Elsevier, Oxford.
Keuschnigg, C. and Devereux, M. P. (2013). The arm’s length principle and distortions tomultinational firm organization. Journal of International Economics, 89(2):432–440.
Kind, H. J., Knarvik, K. H. M., and Schjelderup, G. (2000). Competing for capital in a‘lumpy’ world. Journal of Public Economics, 78(3):253–274.
Kind, H. J., Midelfart, K. H., and Schjelderup, G. (2005). Corporate tax systems, multinational enterprises, and economic integration. Journal of International Economics,
65(2):507–521.

61

Krautheim, S. and Schmidt-Eisenlohr, T. (2011). Heterogeneous firms, profit shifting of FDI
and international tax competition. Journal of Public Economics, 95(1):122–133.
Lai, H. and Trefler, D. (2002). The gains from trade with monopolistic competition: Specification, estimation, and mis-specification. NBER Working Paper, 24884.
Langenmayr, D., Haufler, A., and Bauer, C. J. (2015). Should tax policy favor high-or
low-pproductivity firms? European Economic Review, 73:18–34.
Ludema, R. D. and Wooton, I. (2000). Economic geography and the fiscal effects of regional
integration. Journal of International Economics, 52(2):331–357.
Ma, J. and Raimondos, P. (2015). Competition for FDI and profit shifting. CESifo Working
Paper Series, 5153.
Martin, P. and Rogers, C. A. (1995). Industrial location and public infrastructure. Journalof International Economics, 39(3):335–351.
Matsui, K. (2012). Auditing internal transfer prices in multinationals under monopolisticcompetition. International Tax and Public Finance, 19(6):800–818.
Mayer, T., Méjean, I., and Nefussi, B. (2010). The location of domestic and foreign production
affiliates by French multinational firms. Journal of Urban Economics, 68(2):115–128.
Mayer, T. and Zignago, S. (2011). Notes on CEPII’s distances measures: The GeoDist
database. CEPII Working Paper 2011-25.
Navaretti, G. B. and Venables, A. (2004). Multinational Firms in the World Economy.
Princeton University Press, Princeton, NJ.
Nielsen, S. B., Raimondos-Møller, P., and Schjelderup, G. (2003). Formula apportionment
and transfer pricing under oligopolistic competition. Journal of Public Economic Theory,5(2):419–437.
Nielsen, S. B., Raimondos-Møller, P., and Schjelderup, G. (2008). Taxes and decision rights
in multinationals. Journal of Public Economic Theory, 10(2):245–258.
OECD (2017). Tax Administration 2017: Comparative Information on OECD and Other
Advanced and Emerging Economies. OECD, Paris.
Okoshi, H. (2020). Transfer Pricing: Interaction with Multionationals’ Location, Export andR&D Choices. Ph.D. dissertation submitted to the University of Munich.
Ottaviano, G. I. and van Ypersele, T. (2005). Market size and tax competition. Journal ofInternational Economics, 67(1):25–46.
Overesch, M. (2009). The effects of multinationals’ profit shifting activities on real investments. National Tax Journal, 62(1):5–23.
Peralta, S., Wauthy, X., and van Ypersele, T. (2006). Should countries control international
profit shifting? Journal of International Economics, 68(1):24–37.
Pflüger, M. (2004). A simple, analytically solvable, Chamberlinian agglomeration model.
Regional Science and Urban Economics, 34(5):565–573.

62

Profeta, P. and Scabrosetti, S. (2017). The political economy of taxation in Europe. HaciendaPública Española, 1(220):139–172.
Ramondo, N. and Rodrı́guez-Clare, A. (2013). Trade, multinational production, and thegains from openness. Journal of Political Economy, 121(2):273–322.
Schjelderup, G. and Sørgard, L. (1997). Transfer pricing as a strategic device for decentralized
multinationals. International Tax and Public Finance, 4(3):277–290.
Shen, Y. (2018). Corporate income taxation and multinational production. mimeo. Hanyang
University.
Slemrod, J. and Wilson, J. D. (2009). Tax competition with parasitic tax havens. Journalof Public Economics, 93(11-12):1261–1270.
Stöwhase, S. (2005). Asymmetric capital tax competition with profit shifting. Journal of
Economics, 85(2):175–196.
Stöwhase, S. (2013). How profit shifting may increase the tax burden of multinationals:
A simple model with discrete investment choices. Journal of Public Economic Theory,15(2):185–207.
Swenson, D. L. (2001). Tax reforms and evidence of transfer pricing. National Tax Journal,
54(1):7–25.
Tørsløv, T. R., Wier, L. S., and Zucman, G. (2018). The missing profits of nations. mimeo.
Wang, Z. (2020). Multinational production and corporate taxes: A quantitative assessment.
Journal of International Economics, 126:103353.
Wilson, J. D. (1991). Tax competition with interregional differences in factor endowments.
Regional Science and Urban Economics, 21(3):423–451.
Yao, J. T. (2013). The arm’s length principle, transfer pricing, and location choices. Journalof Economics and Business, 65:1–13.
Zhao, L. (2000). Decentralization and transfer pricing under oligopoly. Southern Economic
Journal, 67(2):414–426.
Ziss, S. (2007). Hierarchies, intra-firm competition and mergers. International Journal ofIndustrial Organization, 25(2):237–260.
Zucman, G. (2014). Taxing across borders: Tracking personal wealth and corporate profits.
Journal of Economic Perspectives, 28(4):121–48.

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