A Macroeconomic Perspective on Taxing
Multinational Enterprises∗
Sebastian Dyrda

Guangbin Hong

Joseph B. Steinberg

University of Toronto

University of Chicago

University of Toronto

July 31, 2024
Abstract
We study the macroeconomic consequences of international profit shifting by multinational enterprises (MNEs) and tax reforms designed to curb this behavior. We developa theory in which MNEs shift profits by exploiting intangible capital transfer pricing
rules. We show that at the micro level, profit shifting increases MNEs’ incentives toinvest in intangible capital, increasing their output both at home and abroad. Wethen quantify the aggregate effects of the two reforms proposed by the OECD to reduce profit shifting: (i) reallocating the rights to tax MNEs’ profits to the countries
where they sell their products; and (ii) a minimum global corporate income tax. Bothreforms would reduce profit shifting substantially, but (i) would reduce global output
substantially whereas (ii) would have little macroeconomic impact. Both reforms would
increase high-tax countries’ national incomes, but would also reduce their wages andprofits.
Keywords: Multinational enterprise; transfer pricing; profit shifting; base erosion;
intangible capital; corporate tax.
JEL Codes: F23, H25, H26∗

Steinberg:
joseph.steinberg@utoronto.ca;
Hong:ghongecon@gmail.com;
Dyrda:
sebastian.dyrda@utoronto.ca. Address: University of Toronto, Max Gluskin House, 150 St. George Street,Toronto, ON M5S 3G7, Canada. Acknowledgments: We thank the editor, Costas Arkolakis, and two
anonymous referees for their guidance, and Ellen McGrattan, James Hines, Ana Maria Santacreu, V.V.
Chari, Burhan Kuruscu, Diego Restuccia, Florian Scheuer, and Aleh Tsyvinski for useful comments anddiscussions. We also thank participants of the 37th Annual Meeting of the Canadian Macro Study Group,the 2024 International Institute of Public Finance Annual Congress, the NBER Megafirms and the Economy
Meeting Spring 2023, NBER International Finance and Macroeconomics Program Meeting Spring 2023,
the 2022 NBER Summer Institute Macro Public Finance workshop, the Society for Economic Dynamics
2022 Annual Meeting, the 2022 Macro Montréal Workshop: Business Cycles and Policy, the Midwest Macro
Spring 2022 conference, and of seminars at Texas A&M University, Arizona State University, University ofBonn, University of British Columbia, Carleton University, the Federal Reserve Bank of St Louis, Universityof Pennsylvania, Oﬀice of Tax Analysis - U.S. Department of the Treasury and Queen’s University.

11

Introduction

Multinational enterprises (MNEs) shift large portions of their profits to foreign tax havens,
costing governments in their home countries hundreds of billions of dollars per year in tax
revenue. In October 2021, 136 countries signed onto a policy designed by the OECD and
G20 governments to reduce profit shifting, making it the largest international tax reform inhistory. We analyze the macroeconomic consequences of OECD/G20 reform using a newmodel of profit shifting that emphasizes transfer pricing of intangible capital. We find that
this reform would substantially reduce profit shifting and increase tax revenues in high-tax
countries, but it would also cause global output to fall substantially.
Base erosion and profit shifting (BEPS) refers to MNEs’ use of tax planning strategies to
exploit gaps and mismatches in tax rules to artificially shift profits to low- or no-tax countries
where they conduct little or no economic activity, or to erode tax bases through deductible
payments such as interest or royalties. The scale of profit shifting is striking. For example,
Tørsløv, Wier and Zucman (2022) estimate that 36 percent of worldwide multinational profits
are shifted to tax havens, while Guvenen, Mataloni, Rassier and Ruhl (2022) find that 38
percent of foreign income reported by U.S. MNEs is actually generated at home in the UnitedStates. The implications for public finances are equally striking: Clausing (2020a) estimatesthat about a third of U.S. corporate income taxes are lost to profit shifting, which is equivalent
to more than $100 billion per year. According to the OECD, profit shifting reduces global
corporate income tax revenues by as much as 10 percent per year, or $240 billion (Johansson
et al., 2017).
Addressing this issue is a top priority for policymakers in high-tax countries where manyof the biggest MNEs are based. The OECD/G20 Inclusive Framework on BEPS outlines two
major policy changes, or “pillars.”1 The first pillar is revenue-based profit allocation, which
allocates the rights to tax some of an MNE’s profits to the countries in which it operates
in proportion to these countries’ shares of the MNE’s global sales. The second is a global
minimum corporate income tax, which would require that all corporate income, regardlessof where it is booked, be effectively taxed at no lower than 15 percent. The objective of thispaper is to study how these two pillars would affect MNEs’ production decisions and quantify
the macroeconomic consequences of these effects.
MNEs can use a variety of strategies to shift profits, but the most important one centersaround intangible capital.2 U.S. Senator Carl Levin put it eloquently in a 2013 statement
this issue: “More and more, intellectual property is the dominant source of value in the1

The press statement describing these pillars can be found here.
Empirical evidence indicates that up to 80 percent of profit shifting is related to intangible capital andmanipulating transfer prices. See the Appendix A for more details.
22global economy. It is also highly mobile—unlike more tangible, physical assets, its value canbe transferred around the globe, often with just a few keystrokes…The key to offshore tax
avoidance is transferring the profit-generating potential of that valuable intellectual property
offshore so that the profits are directed not to the United States, but to an offshore tax
haven.” One of the most prominent examples is Apple. Levin states that “95 percent ofApple’s R&D... is conducted in the United States... [During] 2009 to 2012, [Apple Ireland,
a.k.a. ASI] paid... $5 billion to [Apple USA] as its share of the R&D costs. Over that sametime period, ASI received profits of $74 billion. The difference between ASI’s costs and the
profits, almost $70 billion, is how much taxable income [should] have flowed to the UnitedStates.”3 In addition to this anecdote, there is a wide variety of empirical evidence that
intangible capital plays a central role in profit shifting. Guvenen et al. (2022) show thatprofit shifting is concentrated in the most intangible-intensive industries such as electronics
manufacturing, pharmaceuticals, and information technology. Gumpert et al. (2016) andDelis et al. (2021) find similar relationships between intangible intensity and profit shiftingat the firm level. Accoto et al. (2021) and Santacreu (2023a) document flows of intellectual
property services between high-tax countries and recognized tax havens. Perhaps the mostdirect evidence comes from Dischinger and Riedel (2011), who show that MNEs transfer
ownership of intangible capital to subsidiaries in low-tax countries.
Motivated by this evidence, we develop a theory that describes how MNEs shift profits
by transferring the rights to intangible capital and how profit shifting affects MNEs’ production decisions. As in McGrattan and Prescott (2010), intangible capital is nonrival: MNEs
produce it by doing research and development at home, but use it to produce simultaneously
in all of their foreign subsidiaries around the world.4 According to transfer pricing rules,
these subsidiaries pay licensing fees to use this capital. Normally, these fees are paid to thedomestic parent corporation, but the rights to this capital can be transferred—at a cost—to
subsidiaries in a tax haven. The end result is that the income generated by MNEs’ intangible capital is taxed at a lower rate, which increases an MNE’s optimal level of intangible
investment. Because intangible capital is nonrival, this leads to higher output in all of an
MNE’s subsidiaries, both foreign and domestic. This illustrates a potential tradeoff thatprofit shifting presents to global policymakers: although it artificially redistributes MNEs’
income to foreign tax havens, it also increases the amount of worldwide income that they
actually generate. Moreover, we show that the size of this effect is increasing in the difference
3

Levin’s complete testimony can be found here.
MNEs do some R&D in their foreign aﬀiliates as well, but as Arkolakis et al. (2018) write, “most of the
R&D is still done in the multinationals’ home country. For example, according to BEA data for 2009, theparents of U.S. multinationals accounted for 85 percent of its total RD expenditure but only 70 percent of its
value-added. See also Bilir and Morales (2020), which concludes that the parent RD is a substantially more
important determinant of firm performance than aﬀiliate R&D.”
4

3

between the corporate tax rates in the MNE’s home country and the tax haven. This has
direct implications for the OECD/G20 BEPS pillars: the higher the minimum tax rate orsales-based profit reallocation share, the larger the reduction in intangible investment.
To quantify the macroeconomic effects of the OECD/G20 proposal, we embed our theory
into a multi-country, general-equilibrium framework. Each country in our quantitative modelis populated by a representative household, a government, and a measure of firms. Households spend all their income on the final good. Governments levy taxes on corporate profits tofinance lump-sum transfers. Firms are heterogeneous in productivity and make four choices:where to export; where to establish foreign aﬀiliates; intangible investment; and profit shifting. Exporting and FDI are subject to fixed costs, so only the most productive firms engage
in multinational production in equilibrium as in Helpman et al. (2004). All firms invest in
intangible capital, but its nonrival nature makes the return greater for MNEs, and so theyaccount for the lion’s share of intangible investment, consistent with the empirical evidence.5
However, firms gain access to the profit-shifting technology only if they have an aﬀiliate ina tax-haven country. Our quantitative model makes several methodological contributions in
its own right: incorporating nonrival intangible capital into a heterogeneous-firm environment; allowing individual firms to make joint decisions about multinational production andinnovation; and, of course, incorporating our theory of profit shifting.
In our calibration, we discipline the model’s parameters so that it reproduces micro- andmacroeconomic data on production, trade, multinational activity, and, most importantly,
profit shifting. We split the world into five regions. The countries identified as tax havens
make up two of these regions: the first is a productive low-tax region that includes Ireland,
Switzerland, and other countries where most of the economy is not devoted to profit shifting;while the second is a “true” tax haven that includes the Caribbean, the Channel Islands,
and other small countries whose economies rely heavily on profit shifting. The other three
regions are North America, Europe (minus countries in the low-tax region), and the rest of
the world. Firms in these three regions can shift profits to the low-tax region and/or the tax
haven—provided they have paid the cost of establishing foreign aﬀiliates there. We choose
the costs of profit shifting to match Tørsløv et al. (2022)’s estimates lost profits at the country
level. Our model also reproduces three other sets of facts about profit shifting that we donot target in our calibration: the share of low-tax countries’ corporate income taxes that arepaid by foreign MNEs; the aggregate compensation of employees hired by MNEs to engage
in profit shifting; and the MNE-level relationship between profits reported by the domestic
parent division and the tax differential between the home country and the tax haven.
5
U.S. MNEs’ parent companies account for about 75% of all R&D in the United States post 2000. See
Foley et al., eds (2021) for an extensive discussion on the importance of the MNEs.

4

We use our calibrated model to simulate the effects of the two pillars of the OECD/G20
proposal, both together and in isolation. We find that this proposal would go a long way
toward eliminating profit shifting: lost profits would fall by 74 percent in North America,
80 percent in Europe, and 88 percent in the rest of the world. However, it would alsomaterially reduce intangible investment and overall macroeconomic performance around theworld: GDP would fall by 0.09 percent in North America, 0.14 percent in Europe, 0.46 percent
in the low-tax region, and 0.18 percent in the rest of the world. Our model predicts a decline
in global GDP more than twice as large the OECD estimates (OECD, 2020), highlighting
the quantitative importance of the intangible investment channel and general–equilibrium
effects.
Further, we find that while both pillars of the OECD/G20 plan would reduce profit shifting, the first (sales-based profit reallocation) would have significantly larger macroeconomic
consequences than the second (a global minimum corporate income tax). This is because
the former affects firms that do not shift profits and even some firms that do not engage
in multinational production at all. We find that the same reduction in profit shifting could
be accomplished at a much smaller macroeconomic cost by scrapping the first pillar entirely
and slightly increasing the minimum tax rate, and we recommend that policymakers seriously
consider this alternative. We also find that although the OECD proposal would reduce output in high-tax countries, it would actually increase their gross national income. However,this aggregate increase masks a redistribution of income from the private sector to the public
sector, indicating that the recouped corporate tax revenues should be redistributed or offset
by reductions in other taxes to ensure that households in these countries benefit from thereforms.

2

Related LiteratureThis paper relates to two strands of literature on profit shifting. The first strand consists of
empirical studies that provide motivation for our study, support for our modeling choices,and targets for our calibration. Several studies in this strand document the striking scope of
profit shifting at the aggregate level. Guvenen et al. (2022) estimate that 38 percent of U.S.
MNEs’ foreign income is the result of profit shifting and should be re-attributed to domesticGDP, while Tørsløv et al. (2022) report a similar figure at the global level. Clausing (2020a)
concludes that profit shifting reduces U.S. corporate tax revenues by as much as a third.6 We
draw on these estimates to discipline our quantitative model. Other empirical studies provide
6

See Dowd et al. (2017), Clausing (2016), and OECD (2015) for extensive reviews of the empiricalliterature on profit shifting.

5

microeconomic evidence on profit shifting. Gumpert et al. (2016) and Delis et al. (2021) showthat firms with high shares of intangible capital in total assets are more likely to shift profits,
and Accoto et al. (2021) document that profit-shifting firms import intellectual property
services from recognized tax-havens. Using cross-country data on bilateral royalty paymentsfrom 1995 to 2012, Santacreu (2023b) finds that differences in taxation impact international
technology licensing. These studies provide support for our theory of profit shifting that
centers around transfer pricing of intangible capital. Last, Schwab and Todtenhaupt (2021)
find that reducing the tax rate on corporate income in one country increases R&D activities
in other countries through the MNE networks. This provides empirical evidence for the
key implication from our model that profit shifting increases the incentive for intangible
investment.
The second strand focuses on the real economic consequences of profit shifting. Many
studies in this literature are based on Hines and Rice (1994), who develop a theory in which
MNEs can reduce their effective tax rates by paying a cost to shift profits to a tax haven.
For example, Suárez Serrato (2018) use this theory to study how U.S. MNEs responded toa policy change that limited profit-shifting to Puerto Rico, and Bilicka et al. (2022) add afixed cost of profit shifting to study the extensive margin of this phenomenon.7 Our modelhas two advantages over these studies. First, we provide a micro-foundation for the role ofintangible investment by explicitly spelling out the transfer-pricing transactions that MNEs
use to engage in profit shifting.8 Second, we embed our theory into a general-equilibrium
framework, which allows us to study the macroeconomic effects of profit shifting as well as
the microeconomic effects.9 Some of our own subsequent work on this topic is also part ofthis strand. In Dyrda et al. (2024a), we use the framework developed herein to study optimal
corporate taxation in the presence of profit shifting. In Dyrda et al. (2024b), we study how
the OECD/G20 reforms would interact with other multinational-related provisions of the
U.S. tax code, particularly the ones introduced by the Tax Cuts and Jobs Act on 2017.
More broadly, this paper contributes to the literature on globalization and multinational
7

Other studies documenting real effects of profit shifting include Buettner et al. (2018), de Mooij and
Liu (2020), and Schwab and Todtenhaupt (2021).
8
In the Hines and Rice (1994) framework, the channel by which firms shift profits is left unspecified;firms can simply pay a cost to mechanically shift a portion of their profits abroad, which reduces the effective
tax rate paid on these profits. Moreover, investment increases under profit shifting because it is not tax
deductable, which means it is increasing in a firm’s effective tax rate. However, intangible investment is tax
deductable in most jurisdictions, including the United States.
9
Ferrari et al. (2023) also build a general-equilibrium model of profit shifting based on Hines and Rice
(1994). Aside from micro-founding the profit-shifting technology, our approach offers several advantages
over theirs. First, our model features endogenous selection into profit shifting, which allows it to capture
the fact that only a small number of the largest MNEs engage in this behavior and are therefore affected
directly by anti-BEPS policies. Second, our approach allows profit shifting to alter the balance of paymentsin equilibrium, generating effects like those documented in Guvenen et al. (2022) and Hebous et al. (2021).

6

activity. One strand of this literature emphasizes the role of firm heterogeneity and selection.
The seminal papers of Melitz (2003) and Chaney (2008) study selection into exporting. Helpman et al. (2004) develop a model of the “proximity-concentration tradeoff,” in which firms
can serve foreign markets by exporting, which requires a small fixed cost but larger variable
costs, or by establishing foreign aﬀiliates, which requires a large fixed cost but smaller variable
costs. More recent work incorporates additional margins like export platforms (Tintelnot,2017), endogenous product creation (Arkolakis et al., 2018), selection dynamics (Garetto etal., 2019), and offshoring (Spencer, 2021). Another strand emphasizes the role of nonrival
intangible capital in shaping the aggregate effects of foreign direct investment (FDI). McGrattan and Prescott (2009) build a neoclassical growth model in which the representative
multinational invests in intangible capital that can be used simultaneously to produce output
at home and abroad, and show that this channel substantially increases the gains to openness
to FDI. McGrattan and Waddle (2020) use a multi-country version of this model to study
the macroeconomic consequences of FDI restrictions caused by Brexit. We synthesize these
two approaches by developing a model in which heterogeneous firms choose where to export,
where to establish foreign aﬀiliates, and how much to invest in nonrival intangible capital.
On top of this new framework, we incorporate our theory of profit shifting, allowing firms toadditionally choose whether to establish aﬀiliates in a tax haven and how much intangible
capital to shift.
In terms of quantitative methodology, the most similar papers to ours are Arkolakis
et al. (2018) and Wang (2020). Arkolakis et al. (2018) studies the relationship between
innovation and multinational production. In their model, innovation is used to create newfirms which then go on to make decisions about where to establish foreign aﬀiliates. This
innovation occurs at the aggregate level (it is pinned down in equilibrium by a sort of freeentry condition) and is separate from the firm’s individual optimization problem.10 In ourmodel, each individual firm chooses its own level of intangible investment as well as whereto establish foreign aﬀiliates. Moreover, the nonrival nature of intangible capital creates
an important interaction between these two decisions: the more foreign aﬀiliates a firm
establishes, the greater the return to intangible investment. Wang (2020) extends Arkolakis
et al. (2018) to incorporate corporate taxes and profit shifting. Wang (2020)’s reduced-form
approach to modeling profit shifting affects where firms choose to establish foreign aﬀiliates,
but it does not affect the scale of these operations. Our micro-founded approach to modelingprofit shifting, which explicitly lays out the transfer pricing transactions that MNEs use to10

This is true even in the extension of their model described in their online appendix in which they allow
for innovation that improves productivity. In this version of their model, entrants can augment the expected
productivity of the firms they create, but cannot do any further productivity-enhancing innovation once thesefirms’ productivities are drawn.

7

reallocate intangible income to tax havens, affects firms’ incentives to invest in intangible
capital, and thus affects their output both at home and abroad.

3

Model of multinational production and profit shifting

In this section, we present a theory of profit shifting integrated into a general equilibrium
model with heterogeneous firms in the tradition of the international economics literature.
With our profit-shifting theory, our quantitative framework synthesizes Helpman et al. (2004)
and McGrattan and Prescott (2009). There are I “productive” regions, each populated bya representative household, a measure of heterogeneous firms, and a government. Indexedby i and j, regions differ in population, total factor productivity, trade costs, FDI costs,
and corporate income taxes. Firms in each region decide the following: where to export andwhere to establish foreign subsidiaries; how much labor to hire in the parent division andeach foreign subsidiary; and how much intangible capital to produce in the parent division.
Importantly, intangible capital is nonrival in that it can used simultaneously in all of a firm’s
divisions.
Multinational firms (firms with foreign aﬀiliates) use transfer pricing to allocate the costsof producing intangible capital across their foreign aﬀiliates in proportion to the scale at whichthese aﬀiliates use this capital. Aﬀiliates license the right to use intangible capital from thedivision that owns this capital. MNEs can shift profits by selling their intangible capital toaﬀiliates in lower-tax regions. We denote the “productive” region with the lowest corporate
income tax rate by LT . Additionally, there is an “unproductive” tax haven populated bya representative household and a government, labeled as T H, where no economic activity
occurs. MNEs based in high-tax regions can transfer their intangible capital rights to either(or both) of these regions, provided they have established subsidiaries there.
Representative households in each region choose consumption subject to budget constraint. The household receives income from labor, ownership of domestic firms, and lumpsum transfers. The government collects corporate income tax revenues and passes them tothe household. We present the details of the model in what follows.

3.1

Households

Each region i has a population Ni of identical households that supply labor inelastically andhave standard preferences over consumption, Ci , given by ui (Ci ) = log(Ci ). The representative household’s budget constraint is
P i C i = W i N i + Di + T i ,8(1)where Wi is the wage, Di is the aggregate dividend payment from firms based in region i,
and Ti is a transfer from the government.
Consumption is a constant-elasticity-of-substitution aggregate of products from different
source countries,
ρ
# ρ−1
" J Z
X
ρ−1
Ci =
qji (ω) ρ dω
,
(2)
j=1

Ωji

where qji (ω) is the quantity of variety ω from region j, Ωji is the set of goods from j available
in i, and ρ is the elasticity of substitution between varieties. The demand curve for eachvariety can be written as
1

pji (ω) = Pi Ciρ qji (ω)− ρ .
1(3)

The aggregate price index is

Pi =

j=1

3.2

1
# 1−ρ

" J Z
X

pji (ω)1−ρ dω

.

(4)

Ωji

Firms: technology

Each productive region i has a unit measure Ωi of firms that compete monopolistically as in
Melitz (2003) and Chaney (2008). Firms are heterogeneous in productivity, a, which is drawn
from a distribution Fi (a). Firms produce their products using labor and intangible capital.
Intangible capital, which we denote by z, is nonrival: it is produced in the home country
but can be used to produce abroad as well, provided that a firm pays the cost of setting
up a foreign aﬀiliate in another productive region. We index firms by their productivities
instead of their varieties to economize on notation; all firms from a given region with thesame productivity make the same decisions.
Production. A firm from region i with productivity a and intangible capital z can produce
its good in any productive region j, populated by Nj people, using the technology
yij = σij Aj a (Nj zi )ϕ ℓγj .

(5)where ℓj stands for labor hired locally in j. It also depends on the firm’s idiosyncratic
productivity as well as region j’s aggregate productivity Aj ; and the firm’s ability to deploy
its productivity and intangible capital abroad may be limited by FDI barriers, σij , as in
McGrattan and Waddle (2020). We assume that σij ∈ [0, 1] and that σii = 1.
Intangible capital. Firms hire workers in their domestic parent corporations to produce9intangible capital (R&D). We assume that firm from region i produces intangible capital
according to the following technology:z = Ai aliz

(6)

In other words, it takes 1/ (Ai a) workers in region i to produce one unit of intangible capital,i.e., the cost to produce z units of intangible capital is Wi / (Ai a). This is similar to McGrattan
and Prescott (2009), who assume that firms can transform their output one-for-one into
intangible capital. We assume that R&D expenditures are tax-deductible, which is how they
are treated under most countries’ tax codes.
Trade and foreign direct investment. Firms can sell in the domestic market freely, but
serving foreign markets is costly. There are two options for serving foreign markets: (i)Fpay a fixed cost κX
i to export domestically produced goods; and (ii) pay a fixed cost κito open a foreign aﬀiliate and produce locally. Fixed costs are denominated in units of
the home country’s labor. Each unit of goods shipped from region i to j incurs an icebergtransportation cost ξij . As in Garetto et al. (2019) and McGrattan and Waddle (2020),
we assume that exported and locally produced products are considered distinct varieties, so
firms can simultaneously export to, and produce locally for, the same foreign country.11 Let
JX ⊆ I \ {i} denote the set of foreign regions to which a firm exports, and let JF ⊆ I \ {i}denote the set of regions in which it operates a foreign aﬀiliate. The firm’s resource constraints
can then be written as follows:yii = qii +Xξij qijX ,

(7)

j∈JX

yij = qij , j ∈ JF ,(8)

where we distinguish exported goods, denoted as qijX , from goods that are produced andconsumed in the same location, qij . We refer to a multinational as a firm with JF ̸= ∅.

3.3

Firms: profit shifting

Multinationals’ foreign aﬀiliates are required to pay licensing fees to use intangible capital
according to the rules of transfer pricing. The licensing fee of a subsidiary in region j is given
11
In a version of the model where firms must choose whether to export or produce locally for each foreign
market as in Helpman et al. (2004), the results of our experiments are similar to our baseline results, but
non-MNEs’ share of value added is too large relative to the data. While we do not explicitly allow for export
platforms as in Arkolakis et al. (2018) and Wang (2020), our approach of aggregating the world into five
regions can be interpreted as allowing foreign subsidiaries in a given region to “export” to all of the countries
within that region costlessly.

10

by ϑij (z)z, where ϑij (z) ≡ γpij yij /z is the marginal revenue product of intangible capital,
which captures the “arm’s length” rule for how transactions between related parties aresupposed to be priced. The total amount of licensing fees across the conglomerate is νi (z)z ≡Pj∈JF ∪{i} ϑij (z)z. Note that this includes the licensing fee for the parent corporation’s use of
its own intangible capital, and thus captures the total value of an MNE’s intangible capital.
A multinational based in a high-tax region can shift intangible capital licensing income
to the low-tax region and/or the tax haven by transferring ownership of its intangible capital
to its aﬀiliates in these regions (provided that the fixed costs to establish these aﬀiliates havebeen paid). To make this concrete, suppose an MNE sells a fraction λLT of its intangible
capital to the former and a fraction λT H to the latter. Then, its aﬀiliate in the LT regionPcollects licensing fees of λLT j∈JF ∪{i}\{LT } ϑij (z)z, its aﬀiliate in the TH region collectsP
λT H j∈JF ∪{i} ϑij (z)z, and the domestic parent corporation collects the remaining fees, (1 −P
λLT − λT H ) j∈JF ϑij (z)z. MNEs based in the low-tax region cannot shift profits.
The sale of intangible capital from an MNE’s domestic parent in region i to its aﬀiliate
in region j ∈ {LT, T H} is priced at markdown µij < 1 below the intangible capital’s total
market value per unit, νi (z). This captures the idea that profit shifting hinges on MNEs’
ability to exploit the diﬀiculty and lack of transparency involved in valuing intangible capital,
as argued for example by Neubig and Wunsch-Vincent (2017).12 Recall the figures from U.S.
Senator Carl Levin’s testimony cited in section 1: Apple’s Irish aﬀiliate paid $5 billion for
the rights to license Apple U.S.A’s intellectual property and collected $74 billion in income.
These figures suggest that the purchase price for these licensing rights was far below the fairmarket value. It it important to emphasize that this markdown is what creates the incentive
for MNEs to shift profits in the first place. If the sale of intangible capital occurred at fairmarket value (µij = 1), then an MNE’s parent corporation would generate the same profits
regardless how much intangible capital is transferred; the amount of profits shifted from theparent to the tax haven is precisely the difference between the price paid by the tax-havenaﬀiliate to acquire the intangible capital and that capital’s fair market value. We illustrate
this formally in section 4 below.
While there is a benefit to profit shifting generated by the markdown, there is also a cost.
We denote the cost (in units of home-country labor) to sell a fraction λj of intangible capital
to country j ∈ {LT, T H} by Ci (λLT , λT H ). We assume that this function satisfies several
economically intuitive properties:
12

We have explored an alternative formulation in which MNEs can “mark up” the licensing fees above
the marginal product of intangible capital instead of marking down the price at which this capital can besold. These two setups are mathematically isomorphic, provided that the markdown and markup are chosen
appropriately. A proof of this equivalence is available upon request.

11

Assumption 1 Let λ = [λLT , λT H ] andΓ = λ ∈ [0, 1]2 : λLT + λT H ≤ 1 .

(9)

The cost function Ci : Γ → R+ has the following properties:
1. At least twice continuously differentiable.
∂Ci
2. Cij ≡ ∂λ
> 0 for j ∈ {LT, T H}.
j∂ Ci
3. Cijj ≡ ∂λ
2 > 0 for j ∈ {LT, T H}.
j
4. Ci (0) = 0. Additionally, for every sequence {λn } ⊆ Γ with λn → λ∗ and λ∗LT +λ∗T H = 1,
it holds that limn→∞ Cij (λn ) = ∞ for j ∈ {LT, T H}.
2

The first assumption is for mathematical convenience. The second assumption says thatthe cost of transferring intangible capital to each destination is increasing in the amounttransferred. The third says that the marginal cost is also increasing, i.e., each additional unitof transferred intangible capital incurs a larger and larger cost. The fourth assumption saysthat firms that do not engage in profit shifting do not incur any costs, and that transferring
the entire stock of intangible capital away from the parent location is prohibitively costly.
It is important to note that Ci (λ) captures the direct costs of profit shifting (e.g., increased
spending on lawyers, accountants, and transfer pricing consultants) but also, in a reducedform way, the increased risk of penalization by the government (see, e.g., Allingham andSandmo, 1972; Rotberg and Steinberg, 2022).

3.4

Firms: profit-maximization problem

The firm’s objective is to maximize its dividend payout. The firm chooses where to export(JX ); where to open foreign aﬀiliates (JF ); intangible investment (z); employment in eachof its divisions (ℓij ); quantity sold in each of its markets (qij , qijX ); and how much intangible
capital to transfer to the low-tax region (λLT ) and the tax haven (λT H ). We break thisproblem into two stages, working backward. In the second stage, the firm maximizes eachdivision’s gross operating profits taking {JX , JF , z, λLT , λT H } as given. In the first stage, thefirm maximizes its global after-tax profits by choosing these objects.
Stage 2: Operating profits. The domestic parent corporation’s profits are

12(πiD (a, z; JX ) =
s.t

max

X}
qii ,{qijj∈JX ,ℓiqii +Xpii (qii )qii +X)
pij (qijX )qijX − Wi ℓij∈JXξij qij = yi = Ai a(Ni z)γ ℓϕi .

(10)

j∈JX

Foreign subsidiaries’ profits are
πijF (a, z) = max pij (qij )qij − Wj ℓj , j ∈ JF .

(11)qij ,ℓj

Stage 1: Locations, intangible capital, and profit shifting.
global profits aredi (a) =max

z,JX ,JF ,λT L ,λT H ∈Γ

The firm’s after-tax

(1 − τi )πii + (1 − τLT )πi,LT 1{LT ∈JF } + (1 − τT H )πi,T H 1{λT H >0}+X(1 − τj )πij

(12)j∈JF \{LT }The first term in (12) represents the taxable profits of the parent division, πii . The second
term represents the taxable profits of the low-tax aﬀiliate, πi,LT . The third represents thetaxable profits of the tax-haven aﬀiliate, πi,T H . The fourth represents the taxable profits ofaﬀiliates in other high-tax regions, πij .13 We now discuss the components of these terms in
more detail.
13

We abstract in our model from the Global Intangible Low Tax Income (GILTI), adopted by the U.S.
government in 2017, for two reasons. First, once we take the model to the data (see next section) we treat
North America as a single region. Second, according to the scarce literature on GILTI, see Clausing (2020b)
and Garcia-Bernardo et al. (2022), it had limited impact on profit shifting of U.S. multinationals. We addressthese issues in Dyrda et al. (2024b).

13

The parent division’s taxable profits are defined as
Costs of intangible capital production and fixed costsz

πii = πiD (a, z; JX ) − Wi liz +

X

}|
{
X
κX
κFij + κiT H 1{λT H >0}
ij +

j∈JX

(13)

j∈JF
Licensing fee receipts

Proceeds from selling z
fee payments}|{ z Licensing }|
z
}|
{ zX
{
+ (µiLT λLT + µiT H λT H ) νi (z)z +(1 − λLT − λT H )ϑij (z)z − (λLT + λT H )ϑii (z)zj∈JF
Cost of transferring zz}|{− Wi Ci (λLT , λT H )νi (z)z .
The first term represents the parent’s operational profit as defined in (10). The second
term captures the cost of producing intangible capital and the fixed costs of exporting andestablishing foreign aﬀiliates, both of which use domestic labor. The third term is the revenue
from selling marked-down intangible capital to the two profit-shifting destinations. The
fourth term represents the licensing fee income associated with intangible capital retained by
the parent. The fifth term contains the associated licensing fees paid by the parent divisionon the transferred intangible capital. The sixth term shows the costs of profit shifting.
Taxable profit of a subsidiary in the low tax region is given byz
F
πiLT = πiLT(a, z) +Licensing fee receiptsX}|{
λLT ϑij (z)z − µiLT λLT νi (z)z − (1 − λLT )ϑiLT (z)z
|
{z
} |
{z
}

j∈JF ∪{i}\{LT }Cost of buying z(14)

Licensing fee payment

The first term is operating profit defined in (11). The second term represents the licensing
fees collected on the fraction of intangible capital transferred to the LT region, λLT . The
third term represents the marked-down cost of purchasing this intangible capital from theparent division. The last term represents the licensing fee the aﬀiliate in this region pays on
the fraction of intangible capital that it does not purchase, 1 − λLT .
Taxable profits of a subsidiary in the unproductive tax haven, are defined as
πiT H =X

λT H ϑij (z)z − µiT H λT H νi (z)z.
|{z}j∈JF ∪{i}
Cost of buying z
{z
}
|

(15)

Licensing fee receipts

The first term represents the licensing fees collected on the fraction of intangible capitaltransferred to the T H region, λT H . The second term represents the marked-down cost ofpurchasing this capital.

14

Finally, taxable profits of a subsidiary in another high-tax region j are
πij = πijF (a, z) − ϑij (z)z.
| {z }(16)

Licensing fee

The two terms are the operating profit defined in (11) and the licensing fees paid for the useof intangible capital, respectively.

3.5

Aggregation and accounting measures

Several national and international accounting measures are required to close the model andcompare it to the data. Here, we revert to expressing firms’ choices as functions of theirvarieties (ω) for notational brevity.
Gross domestic product. Nominal GDP is the total value of goods produced in a given
region:I Z
X
pji (ω)yji (ω) dω.
(17)
GDPi =j=1

ω∈Ωj ,i∈JF (ω)

We compute real GDP by deflating by the consumer price index Pi defined in (4).
Goods trade. Aggregate goods trade flows are given by
EXiG =XZ
j̸=i

IMiG =

XZ
j̸=i

X
pX
ij (ω) (1 + ξij ) qij (ω) dω,

(18)

X
pX
ji (ω) (1 + ξji ) qji (ω) dω.

(19)

Ωi

Ωj

Services trade. Consistent with Guvenen et al. (2022) and Accoto et al. (2021), intangible
capital licensing fees enter the national accounts as exports or imports of intellectual property

15

services.14 High-tax regions’ services trade flows are given by
EXiS =XZ
j̸=i[1 − λLT (ω) − λT H (ω)] ϑij (ω)z(ω) dω
Ωi

(20)

Z
+

[µi,LT λLT (ω) + µi,T H λT H (ω)]νi (ω)z(ω) dωXZXZS[λLT (ω) + λT H (ω)] ϑij (ω)z(ω) dω +ϑji (ω)z(ω) dω.
IMi =
Ωi

j̸=i

Ωi

j̸=i

(21)

Ωj

The low-tax region’s services trade flows are
S
EXLT
=

S
=
IMLT

XZ

ϑLT,j (ω)z(ω) dω +

j̸=LT

ΩLT

j̸=LT

Ωj

XZ

XZ

λLT (ω)Ωjj̸=LT[1 − λLT (ω)]ϑj,LT (ω)z(ω) dω +Xϑj,k (ω)z(ω) dω,

k̸=LT

XZ
j̸=LT

µj,LT λLT (ω)νj (ω)z(ω) dω.

IMTSH =

j̸=T Hj̸=T H

Ωj

X Z

(23)

Ωj

The tax haven’s services trade flows are
X ZS
λT H (ω)νj (ω)z(ω) dω,
EXT H =
Ωj(22)

µj,T H λT H (ω)νj (ω)z(ω) dω.

(24)
(25)

Net factor receipts and payments. Net factor receipts from (payments to) foreigners are
the sum total of the dividends paid by foreign subsidiaries of domestic multinationals (domestic subsidiaries of foreign multinationals):
N F Ri =N F Pi =

XZ
j̸=i

Ωi

j̸=i

Ωj

XZ

(1 − τj )πij (ω) dω,(26)(1 − τi )πji (ω) dω.

(27)

14

For simplicity, we include marked-down transfers of intangible capital ownership as services trade as
well as licensing fees. In reality, these transfers may actually enter the financial account depending on how
they are structured. However, due to the balance of payments identity this does not affect the way thesetransfers affect the overall balance of payments. Our accounting allows us to avoid defining the financial
account altogether.

16

3.6

Market clearing and equilibrium

In a general equilibrium of our model, the labor market must clear, the government’s budget
constraint must be satisfied, and the balance of payments must hold in each productive
region.
Labor market. Labor demand comes from four sources: production of intermediate goods;
production of intangible capital; fixed costs of exporting and setting up foreign aﬀiliates;
and the costs of transferring intangible capital. The labor market clearing condition can be
written as
fixed costs

goods production
z
}|
z
}|
{ zz production {}| { Z 
Z
Z
I
X
X
X

Ni =
ℓji (ω) dω +liz dω +κX+κFi + 1{λT H (ω)>0} κTi H  dω
i
j=1

Z
+
|

Ωi

Ωj

Ωi

Ωi

j∈JX (ω)

j∈JF (ω)

Ci (λLT , λT H )ν(ω)z(ω) dω .
{z
}

(28)

costs of shifting z

Note that at the macro level, profit shifting diverts labor from goods production and R&D
to wasteful administrative costs, potentially offsetting the positive macroeconomic effects
of increased R&D at the micro level, and policies that reduce profit shifting such as the
OECD/G20 proposal free up some of these wasted resources. We discuss the quantitative
importance of this channel in section 5.3 below.
Government budget constraint. We assume that revenue from corporate income taxation is rebated lump-sum to households.15 Lump-sum transfers are given by
T i = τi

I Z
X
j=1

πji (ω) dω.

(29)

Ωj

Balance of payments. The balance of payments requires that each region’s current account must be zero:
EXiG + EXiS − IMiG − IMiS + N F Ri − N F Pi = 0.

(30)

Note that several things happen to the balance of payments when a firm shifts profits awayfrom its home region. First, that region’s services trade balance worsens: the firm receives
15

With a fixed supply of labor, this assumption is without loss of generality. We have also analyzed aversion of the model with endogenous labor supply. In this model, the results are similar with lump-sumtransfera and when labor income taxes adjust to clear the government’s budget constraint.

17

fewer licensing fees from its foreign subsidiaries and makes more licensing payments. Second,
net factor receipts rise: the firm’s profits in the tax haven (or low-tax region) rise, and theseincreased profits are ultimately rebated back to the home country. These two effects offset
one another, but not completely: some of the shifted profits are taxed and therefore remainin the tax haven and/or low-tax region. Thus, the net effect is that the current accountworsens. The reduction in the services trade balance and the increase in net factor income
are consistent with the accounting of Guvenen et al. (2022). The net negative effect on
the balance of payments is consistent with the findings of Hebous et al. (2021). To regainequilibrium, that trade balance and/or net factor income balance must improve, which shows
up in our model as a real exchange rate depreciation.
Competitive equilibrium. Given a set of parameters, an equilibrium in our model is defined as a set of aggregate prices and quantities {Wi , Pi , Ci } and a set of firm decision rules{JX (ω), JF (ω), z(ω), ℓ(ω), q(ω), λLT (ω), λT H (ω)} for each productive region i ∈ I that satisfy
the household’s problem, the firm’s problem, and the market-clearing conditions.

4

Theoretical properties of the model

In this section, we study a stripped-down version of the model outlined in Section 3 to formallycharacterize the real effects of profit shifting and the economic implications of the OECD/G20
proposal. We make five simplifying assumptions. First, we confine our analysis to a partialequilibrium framework, concentrating on the firm’s profit-maximization problem laid out in
Section 3.4. Second, we assume that firms do not export and produce freely in an exogenous
set of foreign locations JF . Third, we assume perfect competition with decreasing returns
to scale instead of monopolistic competition with constant returns. Fourth, we assume that
MNEs do not internalize the impact of their intangible capital decisions on licensing fees,i.e.., they take ϑij (z) as given.16 Finally, we assume that there is a single destination for
profit shifting, specifically the tax haven (TH). These assumptions allow us to isolate the key
drivers of profit shifting and examine their impact on the allocation of intangible capital.
Under these simplifying assumption specified, the profit of the MNE becomes:di (a) = maxz, λ∈[0,1](1 − τi )πii + (1 − τT H )πi,T H +X(1 − τj )πij

(31)

j∈JF

where πii , πi,T H and πij are adjusted accordingly to reflect our simplifying assumptions.17
To economize on notation, we denote by λ the fraction of intangible capital sold to the tax
16

This assumption simplifies formulas but does not change the economic message from our analysis. We
relax this assumption in Appendix F.3.
17
The details of all derivations are provided in the Appendix F.

18

haven. We impose the following profit-shifting cost function, which satisfies properties 1–3
of in Assumption 1.
C (λ) ≡ λ + (1 − λ) log (1 − λ)
(32)

4.1

Intangible investment without profit shifting

We begin by characterizing a scenario without profit shifting in which MNEs cannot sellintangible capital to the tax haven. The profit-maximizing level of intangible investment inthis case is:1−γ! 1−ϕ−γPAaΛ
ijj∈JF ∪{i}zN S =
,
(33)
Wi
γ
1−γ

1
1−γ

1
1−γ



γ
 1−γ

ϕ

Nj1−γ . Several properties are obvious: intangible inwhere Λj ≡ ϕγ pij Aj
vestment is increasing in an MNE’s idiosyncratic productivity level a, as well as the aggregate productivity level Aj , the population Nj , and the price pij in each production locationj ∈ JF ∪ {i}, and it is decreasing in the cost of R&D labor Wi and in the wage Wj in eachproduction location.
There are two important properties worth highlighting. First, intangible investment isincreasing in the number of foreign production locations #JF due to nonrivalry, which means
that, ceteris paribus, MNEs do more intangible investment than non-MNEs, and more-global
MNEs do more than less-global ones.18 Second, it does not depend on the corporate tax ratein the home country or in any of the foreign locations because both the costs and benefits
are tax deductible in the home country due to transfer pricing, which implies that corporate
taxes are not distortionary in the absence of profit shifting.

4.2

1
Wj

Optimal profit shifting

We now bring back the profit shifting margin into (31). We first study the MNE’s choice of
how much intangible capital to shift to tax haven, λ. The profit-maximizing solution for λ is

(1 − µ) (τi − τT H )λ = 1 − exp −Wi (1 − τi )


.

(34)

The following lemma provides a formal characterization of how this solution depends on the
profit shifting technology, which is governed by the markdown µ, and the potential gain fromshifting profits, which is governed by the tax haven’s tax rate τT H .
18

Of course, all else is not equal in equilibrium. In the full quantitative model, where JF is endogenous,
higher-productivity firms choose to open more foreign aﬀiliates, and which increases the elasticity of intangible
investment to idiosyncratic productivity. This is one reason that firm heterogeneity matters for quantitative
analysis in this context.

19

Lemma 2 The share λ of intangible capital sold to the tax haven is:
1. decreasing in µ with elasticityελµ = −λ−1
λ

log(1 − λ)

µ
< 0,
1−µ

(35)

log (1 − λ)

τT H
< 0.
τi − τ T H(36)

2. decreasing in τT H with elasticityελτT H = −

λ−1
λ



The first part of this lemma says that the smaller the markdown below the competitive
price (i.e. the larger µ is), the smaller the fraction of intangible capital that is shifted tothe tax haven. In particular, if the MNE has to sell the rights to intangible capital at thecompetitive price with no markdown (i.e., µ = 1), then no profit shifting takes place at all.
The second part says that λ is decreasing in the tax haven’s tax rate, τT H . Specifically, theelasticity of λ with respect to τT H is larger when λ is closer to zero, when τT H is larger, andwhen τi is smaller.

4.3

Profit shifting and intangible investment

Having characterized the MNE’s decision about how much intangible capital to transfer tothe tax haven, we can now characterize the effect of this decision on the MNE’s intangible
investment choice.

z=z

NS

1−γ
 1−ϕ−γλ (1 − µ) (τi − τT H ) 
× 1 − Wi C (λ) +
1 − τi


|
{z
}

,

(37)

Ω(λ)

The first term in (37) is the intangible investment without profit shifting as derived in (33).
The second term, Ω(λ), represents the is the gain from profit shifting per unit of intangible
capital, where λ is endogenous and given by (34).
Proposition 1 The following hold if τT H < τi and µ < 1:
1. z > z N S , i.e., profit shifting increases intangible investment.
2. z is decreasing in τT H with an elasticity given by:εzτT H = −

1−γ
1−ϕ−γ



τT H
τi − τT H

20




1
i C(λ)
1 + 1−W
λWi C ′ (λ)

 < 0;(38)

3. z is decreasing in µ with an elasticity given by:εzµ = −

1−γ
1−ϕ−γ



µ
1−µ




1
i C(λ)
1 + 1−W
λWi C ′ (λ)

 < 0.

(39)

The first part of the proposition states that if the MNE chooses to shift profits, whichhappens when the tax haven’s tax rate is lower than the home country’s and the markdown
is positive, then intangible investment is strictly higher than it would be in the absence ofprofit shifting. The intuition is that under these conditions, the net gain from profit shifting
is positive, i.e., Ω(λ) > 1, which increases the marginal return on intangible investment. The
second and third parts characterize how changes in these conditions vary the magnitude ofthe effect described in the first part. As τT H or the markdown parameter µ increase, λ falls
as shown in Lemma 2, and so does the gain from profit shifting, Ω(λ), reducing the returnon intangible investment closer to what it would be without profit shifting.
These results highlight the central economic trade-off we uncover in this paper: profit
shifting erodes high-tax countries’ tax bases, but also boosts economic activity by increasing
MNEs’ intangible investment. This trade-off has important implications for the OECD/G20
BEPS framework. Specifically, a global minimum corporate income tax—which in this simple
environment can be interpreted as an increase the tax haven’s tax rate τT H —will reduce profit
shifting, but this reduction will come at the cost of lower intangible investment.

4.4

Effects of sales-based profit allocation

We can also use our simplified model to illustrate the impact of the first pillar of the
OECD/G20 framework, which allocates the rights to tax a portion of an MNE’s global
profits to the regions in which it operates in proportion to these regions’ shares of the MNE’s
overall sales.
Under this rule, the tax base of a subsidiary in region j is the sum of local routine profitrπj , a share (1 − θ) of local residual profit πjR , and a fraction of total global residual profit
ΠR that is based on this region’s share of the MNE’s total global sales:
Tj = πjr + (1 − θ) · πjR + θ · P

Rjk∈JF ∪{i} Rk· ΠR .

(40)

Routine profit is defined as the fraction ι of the revenues Rj in jurisdiction j: πjr = ιRj .
Residual profit is defined as the complementary fraction: πjR = πj −πjr . Global residual profit
P
is the sum of residual profits across regions: ΠR = j∈JF ∪{i} πjR . The two key parametersof the rule are: (i) the fraction of residual profits that are allocated across regions based on21

sales, θ; and (ii) the routine profitability margin, ι. Under the OECD/G20 proposal, theseare set to θ = 0.25 and ι = 0.1, but in what follows we will analyze comparative statics withrespect to their values.
The MNE’s profit-maximization problem under the sales-based profit allocation rule canbe written asXmax(πj − τj Tj ) .
(41)
z,{ℓj }j∈J

F ∪{i},λj∈JF ∪{i}

We use hats to distinguish the solutions to this modified problem from the solutions to (31).
The share of intangible capital sold to the tax haven under this rule is(1 − µ) (1 − θ) (τi − τT H )λ̂ = 1 − exp −Wi (1 − ((1 − θ) τi + θb
τ ))


(42)

.

where τb is the sales-weighted average tax rate across regions:τb ≡Xτj · Pj∈JF ∪{i}

Rjk∈JF ∪{i} Rk

(43)

.

Intangible investment is given byẑ = zNSλ (1 − θ) (1 − µ) (τi − τT H )1 − Wi C (λ) +1 − ((1 − θ) τi + θb
τ)1−γ
 1−ϕ−γ.

(44)

The following lemma and proposition illustrate how the sales-based profit allocation ruleaffects profit shifting and intangible investment.19
Lemma 3 The following hold if θ ∈ (0, 1):
1. λ̂ < λ, i.e., sales-based profit allocation reduces profit shifting.
2. λ̂ is decreasing in θ with elasticityελ̂θ = −λ̂ − 1λ̂log 1 − λ̂

1 − τ̂θ< 0.
1 − ((1 − θ)τi + θbτ) 1 − θ(45)

3. λ̂ is decreasing in τT H with an elasticity that takes the same form as (36).
Proposition 2 The following hold if θ ∈ (0, 1):
1. ẑ < z, i.e., sales-based profit allocation reduces intangible investment.
19

In Appendix F.2, we show that the profitability margin parameter ι does not affect profit shifting or
intangible investment.

22

2. ẑ is decreasing in θ with elasticityεẑθ = ελ̂θ

1−γ
1−ϕ−γ



λ̂
C(λ̂)(1 − λ̂)

!



1
i C(λ̂)1 + 1−W
Wi λ̂C ′ (λ̂)

 < 0;(46)

3. ẑ is decreasing in τT H with an elasticity that takes the same form as in (38).
In short, these results show that the sales-based profit reallocation rule has qualitatively
similar effects as a global minimum tax (which can be captured in this setting as an increasein τT H as described above), and is thus subject to the same trade-off discussed above at theend of section 4.3. Both policies reduce the marginal gain from shifting profits, which reduces
both profit shifting and intangible investment in equilibrium.
These results also show that increasing τT H has the same marginal effects under the profit
reallocation rule as without it, but this does not mean that the two OECD/G20 pillars canbe studied independently or that there would be no interaction between them. The key
elasticities with respect to the two pillars’ key parameters (ελτT H , εzτT H , ελ̂θ , and εẑθ ) are all
increasing in the current level of profit shifting, λ, which implies that the two pillars are, ina sense, substitutes. Introducing the first pillar in isolation would reduce profit shifting, andwould thereby would reduce the marginal effects from subsequently introducing the second
pillar (and vice versa). Quantifying the extent of this interaction and measuring which pillar
would have a greater “bang for the buck”—how much it would reduce profit shifting relative
to how much it affect the real economy—is one of the main goals of our quantitative analysis.

5

Calibration

We calibrate our model’s parameters so that its equilibrium under the current internationaltax regime reproduces salient facts about production, international trade, foreign direct investment, and, most importantly, profit shifting. Some of the parameters, like elasticities ofsubstitution, are assigned externally to standard values, while others, like population, canbe set directly to exact data analogues. The remaining parameters are jointly calibrated bymatching a set of target moments. These parameters influence all of the target moments tosome degree, but there is one target that provides most of the identification for each parameter. Thus, in what follows, we describe each calibrated parameter alongside its main target.
Table 1 lists target moments and calibrated parameter values for each region. Appendix B
provides details on the data sources we use to discipline the model.

23

5.1

Technological parameters

Regions. We partition the world into five regions. The countries identified as tax havens
by Tørsløv et al. (2022) are split into two regions: a low-tax productive region, LT , including Belgium, Ireland, Hong Kong, the Netherlands, Singapore, and Switzerland; and an
unproductive tax-haven region, T H, including Luxembourg, small European countries andterritories like Cyprus, Malta, and the Isle of Man, and a number of Caribbean countries.
The other three regions are North America, Europe (except for the countries in the low-tax
and tax-haven regions), and the rest of the world. Data for each region are obtained byaggregating or averaging country-level data. See Appendix B for more details.
Assigned parameters. The elasticity of substitution between varieties, ρ, is set to thestandard value of 5. Each region’s population, Ni , is set by aggregating country-level datafrom the World Bank’s World Development Indicators database. Corporate income tax rates,
τi , are set by averaging country-level estimates of effective corporate income tax rates from
Tørsløv et al. (2022).
Technology capital share (ϕ). We set the technology capital share in the production function (5) to match the share of foreign-owned firms’ income that accrues to intangible capital,
which is estimated by Cadestin et al. (2021) to be 28%. Note that domestic-owned firms havelower intangible income shares, at around 22%. Although we do not target this moment inour calibration, our model is consistent with this fact. This is because technology capital
is nonrival, which means that multinational firms have a greater incentive to invest in it
than non-MNEs. Thus, our model captures the extent to which nonrivalry creates increasing
returns at the MNE level.
Total factor productivity (Ai ). Each region’s TFP is set to match its aggregated real
GDP based on PPP-adjusted data from the World Development Indicators database.
Productivity distribution (Fi (a)). We assume that firms’ productivities are drawn from
Pareto distributions with region-specific tail parameters ηi . We calibrate these tail parameters
to match the share of aggregate employment that is accounted for by firms with fewer than
100 times the average number of employees, which is equal to 58.9% in data published by
the U.S. Census Bureau. Although this is the only moment of the firm-size distribution that
we target, our model’s Lorenz curve is very close to its empirical counterpart.
Variable trade cost (ξij ). We set the iceberg trade barriers to match aggregate bilateralimports of goods (agriculture, resource extraction, and manufacturing) relative to nominal24

GDP. Import data are from the World Input Output Database. Nominal GDP data are fromthe World Development Indicators. For both, we sum across the countries within each region.
Fixed export cost (κXi ). Each region’s fixed cost of exporting is chosen so that 22.7% offirms export, as reported by Alessandria et al. (2021).
Variable FDI cost (σij ). We calibrate the parameters that govern the eﬀiciency with which
intangible capital can be deployed abroad to match the share of each region’s gross value
added that is accounted for by foreign multinationals. These data come from the OECDAMNE database. This share is equal to 11.12% in North America, 19.82% in Europe, 28.74%
in the low-tax region, and 9.55% in the rest of the world.
Fixed FDI cost to productive regions (κFi ). The fixed costs of establishing foreign affiliates in other productive regions are set to match the average employment of multinationalfirms (i.e., firms with foreign aﬀiliates) relative to the overall average employment of all
firms. This ratio is equal to 444. The former is calculated using Compustat, while the latteris calculated using data from the U.S. Census.20
Fixed FDI cost to tax haven (κTi H ). The fixed costs of establishing aﬀiliates in the tax
haven region are set to match the average employment of firms that have aﬀiliates in at least
one country in our tax haven region. This ratio is equal to 981. It is also calculated using
Compustat.

5.2

Profit-shifting costs

We discipline the profit-shifting cost function by matching estimates from Tørsløv et al.
(2022) of the profits shifted out of high-tax regions. To compute these “lost profits” in themodel, we first define πijN S (ω) as the profits a firm would have reported in region j if it did
not shift profits, holding fixed all of its other policy functions. Then, we can define the profits
shifted out of region j by firm ω as
psij (ω) = πijN S (ω) − πij (ω).

(47)

When psijt (ω) > 0, this indicates that the firm has shifted profits away from region j.
Region-level lost profits are then given by:
P Sj =I Z
X
i=1

psij (ω) dω.

(48)

Ωi

20

Compustat contains data on public firms only. We do not have information on employment of private multinational firms. Our approach assumes that private multinationals are similar in size to public
multinationals.

25

We impose the following functional form for the profit-shifting cost function, which satisfies the properties specified in Assumption 1:
1

Ci (λLT , λT H ) = [(χi,T H C (λT H ))ϵ + (χi,LT C (λLT ))ϵ ] ϵ ,(49)

where with a slight abuse of notation, we denote C (λj ) = λj + (1 − λj ) log (1 − λj ) , j ∈{T H, LT }. The parameter χi,j , j ∈ {T H, LT } controls the marginal cost of shifting profit
from i to j. We calibrate these parameters by matching Tørsløv et al. (2022)’s estimatesof (i) total lost profits, and (ii) the share of lost profits that are shifted to countries in our
tax-haven region. As with production and trade data, we obtain region-level measures bysumming the country-level estimates reported in this paper. Total lost profits are $143bn for
North America, $216bn for Europe, and $257bn for the rest of the world. The shares of these
totals that are shifted to the tax-haven region are 66.39%, 44.50%, and 71.69%, respectively.
We set the markdown parameters µij to zero as they cannot be separately identified fromthe parameters controlling marginal costs χi,j .21
The parameter ϵ governs the cross-derivative of the profit-shifting cost function, i.e.
∂Ci2 (λT H ,λLT )∂Ci2 (λT H ,λLT ). It is easy to show that ∂λ> 0 when ϵ < 1. A positive cross-derivative∂λT H ∂λLTT H ∂λLT
implies that the marginal cost of shifting a share of z to T H increases with the share shiftedto LT , and vice versa for the marginal cost of shifting to LT . It implies that it is costly tocoordinate profit shifting endeavors to more than one destinations. On the other hand, we∂Ci2 (λT H ,λLT )have ∂λ< 0 when ϵ > 1. The negative cross-derivative happens if the headquarter
T H ∂λLTof an MNE can economize resources that are used to shift profits to both LT and T H. An
ideal empirical setting to discipline ϵ is to assess the degree to which λ shifted to one regionchanges in response to a change in corporate tax rate in another tax-haven region. However,
we have not found such an empirical estimate from the literature. In the benchmark calibration, we set ϵ = 1, but we conduct sensitivity analyses with different values of ϵ in Appendix
D.
The flexibility of the cost function renders the firm’s problem challenging to solve with alarge number of regions. Specifically, the benefit of opening a tax haven subsidiary depends
on the set of foreign subsidiaries it already establishes and the cost substitutability of shiftingz to multiple regions. Recent developments in computational methods have advanced theresolution of large combinatorial problems, as evidenced by the works of Jia (2008), Fan and
21

What matters from the MNE’s perspective at the micro level is not the price the aﬀiliate pays to acquire
intangible capital per se, but the overall effect on the MNE’s global after-tax profit relative to the cost of
shifting, which is controlled by the parameter χi,j . A lower markdown (smaller µ) and lower marginal cost(smaller χ) can both generate the same increase in λ and lost profits in equilibrium. As discussed above, thisassumption is a reasonable approximation of reality; the figures for Apple taken from Senator Carl Levin’s
testimony imply a markdown of more than 93%.

26

Yang (2020), and Arkolakis et al. (2023). Arkolakis et al. (2023) highlight that applying thesemethods necessitates the complementarities among locations to be consistently either weakly
positive or weakly negative. As we discuss in Appendix F.4, a positive cross-derivative of
the profit-shifting cost function disrupts the global complementarity property, so we opt fora brute-force approach, which is feasible with our limited number of regions. See Appendix
F.4 for a more detailed discussion.

5.3

External validation

We have calibrated the key parameters of our model—the profit-shifting costs, χi,j —tomatch macroeconomic estimates of aggregate lost profits. However, our calibrated model
also matches very closely several other facts about profit shifting that we did not target inour calibration. This indicates that it is well suited to measuring the macroeconomic effects
of profit shifting and the OECD/G20 reform.
One way to validate our calibration is to measure the share of corporate income tax
revenues in each region that are paid by local aﬀiliates of foreign MNEs. The idea is that
foreign MNEs should pay a large share of taxes in the low-tax region because the profits theyreport in this region have been artificially increased. Panel (a) of Table 2 reports the share ofcorporate income tax revenues paid by foreign MNEs in each region in our model according
to the OECD’s Corporate Tax Statistics Database (OECD, 2022a). The rest of the world has
the lowest share (16.3%), followed closely by North America (16.6%). Europe has a higher
share (41.6%), but, as one expects, the low-tax region has the highest share by a large margin(72.4%). Our model matches the data for Europe, the rest of the world, and the low-tax
region very closely, although it overshoots the data for North America. The low-tax region’sshare is the most informative moment about the suitability of our calibration, however, andwe reproduce this figure almost exactly.
Another way to validate our calibration is to measure MNEs’ spending on profit shifting
costs. Although MNEs do not report this spending in reality for obvious reasons, Tørsløv etal. (2022) argue that it can be inferred by estimating the salaries earned by transfer pricing
specialists. Using data from LinkedIn and Glassdoor, they estimate that transfer pricing
specialists employed in the private sector earned $25 billion in base salary income worldwide
in 2020. We compute the model counterpart of this figure by summing profit shifting costs,
Wi Ci (λT H , λLT ), across all firms in all regions, which yields a value of $82 billion. Bothfigures are reported in panel (b) of Table 2. Although our model’s figure is about threetimes larger than Tørsløv et al. (2022)’s estimate, the latter is likely to be biased downward
for several reasons. First, it does not include benefits, bonuses, and other components oftransfer pricing specialists’ compensation. Second, it excludes salaries earned by lawyers,27

accountants, compliance oﬀicers, executives in tax-haven aﬀiliates, and other workers thatfacilitate transfer pricing but are not classified as transfer pricing specialists. Finally, it also
excludes non-salary profit shifting costs such as transfer pricing software.22 The fact that ourmodel produces a figure of the same magnitude as Tørsløv et al. (2022)’s estimate indicatesthat our calibrated profit shifting costs are empirically reasonable.
Yet another way to validate our calibration is to analyze the determinants of profit shiftingat the firm level. One of the key objects of interest in the empirical literature on profit
shifting is the semi-elasticity of reported pre-tax profits in a MNE’s domestic parent division
to the tax differential between the home country and a foreign tax haven. Panel (c) of
Table 2 reports three estimates of this elasticity. They range from 0.8 to 1.1, which meansthat one-percentage-point increase in the tax differential is associated with a 0.8% to 1.1%
increase in profits reported at home.23 We estimate this elasticity in our model by solving forcounterfactual equilibria with different tax rates, constructing simulated datasets from theseequilibria, and running the following regression:log πik,P S (ω) = β0 + βℓ log ℓki (ω) + βz log z k (ω) − βτ τ̂ik + ϵki (ω),(50)

where k denotes the index of the counterfactual economy and τ̂ik denotes the tax differential
between an MNE’s home region and the profit-shifting destination region (either the lowtax region or the tax haven).24 The parameter of interest is βτ . We obtain an estimate ofβτ = 0.90, which lies comfortably within the narrow bounds of the empirical estimates.

6

Quantitative Results

We now use our calibrated model to conduct four experiments to analyze the macroeconomic
consequences of the policies proposed in the OECD/G20 Inclusive Framework on BEPS. First,
we focus on the first pillar of this framework, which allocates a portion of an MNE’s overall
global profit to its subsidiaries based on these subsidiaries’ revenues. Second, we focus on thesecond pillar, which imposes a global minimum corporate income tax. Third, we analyze the
combined effects of these two pillars together. In the last experiment (which is really a set ofsub-experiments), we study the combined effects of both pillars under different values for the
profit reallocation share and global minimum tax rate. In all four experiments, we restrict
22

See, for example, the specialized transfer pricing solutions offered by Thomson Reuters, Workiva, andInsight Software.
23
Appendix C provides a detailed discussion of this literature and the methodology employed in the threestudies cited in the table.
24
Appendix C.3 contains more details on how we produce the model-generated data and specify theempirical regression.

28

attention to long-run analysis, comparing the steady state under the current regime to thesteady state after the policy is implemented. Tables 3–4 and Figure 1 show the results ofthese experiments, which we will explain in detail below. Appendix D shows that our results
are robust to a wide range of alternative setups and calibrations, such as different intangible
capital shares and profit-shifting costs.

6.1

OECD pillar one: sales-based profit allocation

The first pillar of the OECD BEPS project allocates, for the purposes of taxation, a fractionof a firm’s global profits to the countries in which the firm sells its products. Following theOECD proposal, this allocation is based on these countries’ shares of the firm’s overall global
sales. Importantly, it is independent of whether the firm has a physical presence in thesecountries, which implies that non-MNE exporters are also subject to this rule.25 Recall from
Section 4.4 that under pillar one, the tax liability faced by an MNE from i in a region j is:
TijP 1 (a, z) = πijr (a, z) + (1 − θ) · πijR (a, z) + θ · Ŝij (a, z) · ΠRi (a, z),where πijr is a subsidiary’s routine profit, which is a fraction ι of its revenue; πijR is a its
residual profit, which is its revenue net of routine profit; ΠR
i is the MNE’s total worldwide
residual profit; Ŝij is a region’s share of the firm’s total global sales; and θ is the fractionof residual profits that are reallocated. Note that under this pillar, an MNE pays corporate
income taxes to each of its export destinations even if it does not produce any its goods
there. The firm’s problem under this rule can be written asdPi 1 (a) =maxz,JX ,JF ,λT L ,λT H ∈Γπii + πi,LT 1{LT ∈JF } + πi,T H 1{λT H >0}+

Xj∈JF \{LT }

πij −

X

τj TijP 1 (a, z)

(51)

,

j∈JF ∪JX ∪{i}with the profit terms defined by equations (13)-(15).
Panel (a) of Table 3 shows the effects of this pillar. It would indeed make a large dent
in international profit shifting and materially raise high-tax countries’ corporate income tax
revenues. Lost profits would fall by 27–32% in North America, Europe, and the rest of theworld, and tax revenues would increase by 1.6–2.3%. In the low-tax region, profits shifted
inward would fall by 24% and tax revenues would fall by 10.9%. At the same time, however,25

According to the current implementation timeline of pillar one, its scope will be initially limited to thelargest MNEs. However, the OECD intends to extend the coverage in future years. Our approach reflects
these long-term policy goals.

29pillar one would reduce output in all regions of the world economy. This would be driven
by a reduction in intangible investment by MNEs based in the high-tax regions, especiallyin North America. In these regions, these effects would be partially, but not entirely, offset
by an increase in non-MNEs’ intangible investment caused by a decline in labor costs. Thishighlights the importance of accounting for general-equilibrium forces and redistribution of
resources across firms. In the low-tax region, all domestic firms would increase their intangible
investment, but the decline in foreign MNEs’ output would be large enough to ultimately
drag overall output downward as well. This highlights the macroeconomic importance of
foreign MNEs’ intangible investments for profit-shifting destinations.

6.2

OECD pillar two: Global minimum corporate income tax

The second pillar is a global minimum corporate income tax. Following the OECD guidance,
we implement this policy through top-up taxes levied by the governments of MNEs’ homecountries. Specifically, if a firm based in jurisdiction i reports profits in a jurisdiction j
where the tax rate is below the global minimum tax rate τ = 15%, such profits are taxedin jurisdiction i at a rate equal to the tax differential, τ − τj . Thus under pillar two, theheadquarter of an MNE’s additional tax liability is
TiP 2 (a, z) =Xmax (τ − τj , 0) · πij (a, z).

(52)

j∈JF

The firm’s problem is thendPi 2 (a) =maxz,JX ,JF ,λT L ,λT H ∈Γ
(1 − τi )πii (a, z) + (1 − τLT )πi,LT (a, z)1{LT ∈JF } + (1 − τT H )πi,T H (a, z)1{λT H >0}+X(1 − τj )πij (a, z) − TiP 2 (a, z)

.

(53)

j∈JF \{LT }Panel (b) of Table 3 shows the effects of the second pillar. This policy would have evenlarger effects on profiy shifting than the first pillar. Lost profits in North America, Europe,and the rest of the world would fall by 62–84% and tax revenues would rise by 2.7–5.0%.
On the other hand, the macroeconomic effects would be smaller, and in some regions theywould even be positive. MNEs based in Europe and the rest of the world would reduce
intangible investment by more than under the first pillar (0.39% vs. 0.18% for Europe and0.22% vs. 0.09% for the rest of the world), whereas North American MNEs’ R&D would fallmuch less (0.29% vs. 0.80%). As with the first pillar, non-MNEs would expand as MNEs
contract, and in North America and Europe this general-equilibrium reallocation would be30

large enough to push output slightly upward. This reinforces the importance of accounting
for general-equilibrium responses and firm heterogeneity. In the low-tax region, while tax
revenues would fall further than under pillar one due to the larger drop in profit shifting, themacroeconomic response would be smaller due to the more muted effects on foreign MNEs’
intangible investment.

6.3

Both pillars combined

Separately, the two pillars of the OECD/G20 BEPS Framework would both work to reduce
profit shifting, but pillar two would be more effective in achieving this goal and would havesmaller macroeconomic consequences. What would happen if and when both pillars are
implemented together?
Panel (c) of Table 3 shows the results of this third experiment. Consistent with lemma 3
and proposition 2 and the discussion at the end of section 4.4, the effects of the full policy
framework would be larger than the effects of each pillar in isolation, but the effects would
not be additive; each pillar would have smaller marginal effects when combined with theother. The full policy framework would indeed reduce profit shifting and increase high-tax
countries’ corporate tax revenues substantially, but not much more than under pillar twoalone. Conversely, the macroeconomic effects of the combined framework would be only
slightly larger than the effects of pillar one in isolation. This reinforces our finding that pillar
one is a less eﬀicient way to reduce profit shifting than pillar two.
Figure 1 shows the effects of the combined framework under alternative values of thetwo pillars’ parameters. The x-axis in each plot is pillar one’s profit reallocation share andthe y-axis is pillar two’s global minimum tax rate. The first column of plots in the figure
shows how the effects on lost profits change and the second column shows how the effects on
output change. In both columns, darker shades of red indicate “worse” outcomes (smaller
reductions in lost profits in the first column and larger output losses in the second column).
Clearly, a global minimum tax rate is better policy than profit reallocation. Both pillars are
effective at reducing profit shifting, but profit reallocation causes much larger output losses.
A 20 percent minimum tax rate would essentially eliminate profit shifting entirely but would
not reduce output much more than the benchmark 15 percent rate. It would take a profit
reallocation share of at least 90 percent to achieve the same reduction in lost profits, but theoutput losses from this policy would be an order of magnitude greater.

6.4

Why does pillar one have larger macroeconomic consequences?

Our results show that either pillar of the OECD/G20 Framework would reduce profit shifting
substantially, but pillar one would have larger effects on output. The explanation for this31

is that pillar one affects firms that do not shift profits—and even some firms that do not
engage in multinational production at all—while pillar two only affects MNEs that actuallyshift profits. Specifically, pillar one allocates taxation rights based on where firms make theirsales, including export markets. This aspect of the rule increases effective tax rates for firms
in Europe, the low-tax region, and the rest of the world because North America, the largest,richest export market, has the highest tax rate. In Appendix D, we show that a version ofpillar one that allocates taxation rights based on production instead of sales would achieve
the same reduction in profit shifting at a lower macroeconomic cost in these regions. In thecase of North America, pillar one has larger macroeconomic effects because the home shareof revenue is larger than the home share of profits for firms based in this region, as intangible
investment expenses (as well as the fixed costs of selling abroad) are incurred at home.

6.5

Comparison with the OECD’s estimates

The OECD predicts that implementing the two pillars will increase global corporate income
tax revenue by 3.0%–5.1% and reduce global GDP by about 0.07% (OECD, 2020).26 They
arrive at these figures by combining a formulaic application of the pillars to pre-reform
corporate profits with a partial-equilibrium, reduced-form estimate of how profit shifting andtangible investment will change based on relevant elasticities from the empirical literature. In
comparison, our results indicate a 3.20% increase in global corporate income tax revenue anda 0.17% decrease in global GDP. Thus, while our estimate of the revenue effect is similar to
the OECD’s, our estimate of the macroeconomic effect is more than twice as large. The main
reason for this difference is the nonrival nature of intangible capital, which OECD (2020) do
not take into account. When an MNE’s intangible investment declines, its output falls bothat home and abroad. Our results show that this channel is particularly important for low-tax
countries, where foreign MNEs account for a large fraction of economic activity.

6.6

Effects on components of national income

We have focused our analysis thus far on the effects of the OECD/G20 BEPS Framework
on profit shifting and aggregate economic activity. Here, we ask how this framework would
affect different components of national income to dig deeper into how it might affect different
groups of economic agents.27 Table 4 shows how each of our three main experiments would
affect labor compensation, dividends, and overall tax revenue.
26

Note that the OECD’s headline figure for the global tax revenue effect of the policy, reported in Table
1.1 of OECD (2020), is 2.3%-4.0%. However, this number is calculated using a 12.5% minimum tax rate in
Pillar. Panel B of Table 3.15 reports results for a minimum tax rate of 15%.
27
In our model, we assume that dividends and tax revenues are rebated to consumers. Since we do not
explicitly model heterogeneity across households in terms of income, taxation, or firm ownership, we hesitate
to draw strong conclusions from our results about welfare implications.

32

There are several important differences relative to the macroeconomic results. First, labor
income falls in all regions in each of the three experiments, even under pillar two which raises
GDP slightly in North America and Europe. Thus, these policies could make consumers
worse off even if they do not materially shrink the economy. Second, while pillar one haslarger macroeconomic effects, pillar two actually has larger effects on dividends in high-tax
countries (note that this result is closely related to the fact that pillar two generates more
corporate income tax revenue). Third, the increase in high-tax regions’ tax revenue would belarger than the decreases in their labor income and dividends, which implies that while theseregions’ output would generally fall, their gross national income (which is the sum of labor
income, dividends, and tax revenue) would actually rise. Fourth, the effects of these policies
on labor income and dividends in the low-tax region would be much smaller than the effects
on output; in fact, dividends of firms based in this region would rise. Thus, while thesepolicies would significantly hurt public finances in profit-shifting destinations, the private
sector in these countries may be relatively insulated.
Overall, this portion of the analysis paints a more subtle picture of the framework’s
consequences. On the one hand, it highlights that multinational production can lead todifferences in the effects on gross national income versus gross domestic product, which
implies that GDP may not tell the whole story about whether these policies are desirable
to implement. At the same time, it indicates that any potential welfare gains in high-tax
countries from reducing profit shifting are only likely to be realized if the increased tax
revenues find their way into consumers’ pockets.

7

Conclusion

We have developed a model of multinational profit shifting to study the macroeconomic
implications of this phenomenon. In our model, MNEs invest in nonrival intangible capitalwhich they can use simultaneously in all of their divisions around the world. MNEs charge
their foreign aﬀiliates licensing fees to use intangible capital according to transfer pricing
rules, and they can shift profits by transferring the rights to this capital to aﬀiliates in
low-tax jurisdictions.
We make two substantive contributions in addition to our methodological contribution.
First, we prove that profit shifting presents a trade-off at the firm level between economic
performance and tax revenues. On the one hand, profit shifting erodes the corporate income
tax base in an MNE’s home country. On the other hand, it incentivizes MNEs to do moreintangible investment, which boosts output at home as well as abroad. Second, we calibrate
our model to match empirical facts about profit shifting under the current international tax
regime and use it to quantify the aggregate impact of the OECD’s plan to eliminate profit
33

shifting. This plan features two pillars: taxing MNEs in the countries in which they sell theirproducts rather than the countries in which they book their profits; and a global minimum
corporate income tax rate. We find that this reform would indeed largely eliminate profit
shifting and boost tax revenues in high-tax jurisdictions, but it would also reduce capital
investment and shrink the global economy. However, while both pillars would contributeto the decline in profit shifting, the adverse macroeconomic consequences would be driven
entirely by the first pillar; the second pillar would have little macroeconomic effect on its
own. Thus, we encourage policymakers to abandon the former and focus their attention on
the latter.
To put our quantitative results in context, it is helpful to compare them to the effects
of other major international policy changes that have been analyzed elsewhere in the literature. Caliendo and Parro (2014) estimate that the North American Free Trade Agreement
increased welfare by 0.08% in the United States and reduced it by 0.06% in Canada, while
di Giovanni et al. (2014) find that the average country gained 0.13% from liberalizing tradewith China. Caliendo et al. (2021) find that the 2004 EU enlargement, which liberalizedinternational labor markets as well as trade, increased welfare in the original EU member
states by 0.04%. Despite the small number of firms involved in profit-shifting—far fewer
firms engage in multinational production than trade, and only a small fraction of the former
shift profits—we find that the macroeconomic effects of the OECD/G20 BEPS framework
would be even larger than these examples.

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38

Table 1: Calibration
Statistic or parameter value(a) Assigned parameters and target moments
Population (NA = 100)
Real GDP (NA = 100)
Corporate tax rate (%)
Labor tax rate (%)
Foreign MNEs’ VA share (%)
Total lost profits ($B)
Lost profits to TH (%)
Imports from… (% GDP)
North America
EuropeLow tax
Row(b) Calibrated parameter values
TFP (Ai )Prod. dispersion (ηi )Fixed export cost (κXi )Variable FDI cost (σi )Fixed FDI cost (κFi )Cost of shifting profits to LT (ψiLT )Cost of shifting profits to TH (ψiT H )Fixed FDI cost to TH (κTi H )Variable export cost (ξij ) from …
North America
EuropeLow tax
RoW

North
America

EuropeLow-tax

RoW

Tax haven

100
100
22.5
22.4
11.12
143
66.4

92
80.78
17.3
22.4
19.82
216
44.5

11
14.57
11.4
22.4
28.73
–
–

1,323
297.10
17.4
22.4
9.55
257
71.1

–
–
3.3
–
–
–
–

–
1.70
0.35
6.15

1.28
–
2.98
7.96

1.77
12.39
–
6.78

1.74
3.78
0.59
–

–
–
–
–

1.00
4.28
1.7e-3
0.47
1.80
3.40
2.25
0.09

0.89
4.31
3.5e-3
0.56
1.59
0.38
1.25
0.06

1.58
4.83
1.0e-3
0.52
0.46
–
–
–

0.20
4.12
1.4e-2
0.53
8.75
2.35
1.76
0.59

–
–
–
–
–
–
–
–

–
1.89
2.04
2.26

3.21
–
1.59
2.59

3.41
1.69
–
3.01

2.07
1.33
1.56
–

–
–
–
–

Notes: Population and real GDP from World Bank WDI. Corporate tax rate from Tørsløv et al. (2022). Foreign MNEs’
VA share from OECD AMNE database. Fractions of firms with foreign aﬀiliates from Compustat. Lost profits from
Tørsløv et al. (2022). Imports/GDP from WIOD. Dashes (–) represent “not applicable.”39

Table 2: Validation(a) Share of corporate taxes paid by foreign MNEs (%)
North
SourceEurope Low tax
RoWAmericaOECD (2022a)
Model

16.65
24.44

41.58
40.13

72.40
73.62

16.32
18.35

(b) Global profit-shifting costs ($bn)
SourceEstimate

Tørsløv et al. (2022)
Model

25
82

(c) Firm-level semi-elasticity of profit shifting
SourceEstimate

Johansson et al. (2017)
Heckemeyer and Overesch (2017)
Beer et al. (2020)
Model

1.11
0.79
0.98
0.90

Notes: Panel (a): Data source is OECD Corporate Tax Statistics
Database (OECD, 2022a). Shares are first calculated at the country
level, and then aggregated to the region level by averaging, weighting
by total corporate tax revenues. Panel (b): Model value calculated bysumming C(λ) across all firms, dividing by world GDP in the model, andmultiplying by 2020 world GDP in the data from the World Bank ($84.91
tn). Panel (c): See Appendix C.2 for empirical estimates and Appendix
C.3 for model estimate.

40

Table 3: Macroeconomic effects of profit shifting and OECD BEPS pillars
Value added (% chg.)
Lost profits(benchmark = 1)

Tech. capital (% chg.)

Corp. tax
rev. (% chg.)

Total

Non
MNEs

Domestic
MNEs

Foreign
MNEs

Total

Non
MNEs

Domestic
MNEs(a) Pillar 1: Profit reallocation
North America
0.68
Europe0.73
Low tax
0.76
Rest of world
0.70

2.27
2.15
-10.92
1.55

-0.09
-0.15
-0.37
-0.17

0.04
-0.11
-0.39
-0.15

-0.27
-0.19
0.15
-0.18

0.02
-0.18
-0.75
-0.21

-0.70
-0.15
1.06
-0.08

0.19
0.09
0.08
0.04

-0.80
-0.18
1.21
-0.09

(b) Pillar 2: Global minimum tax rate
North America
0.38
Europe
0.27
Low tax
0.49
Rest of world
0.16

3.27
4.95
-9.80
2.65

0.01
0.02
-0.16
-0.04

0.07
0.09
0.01
0.00

-0.05
-0.07
0.03
-0.08

-0.03
0.03
-0.59
-0.06

-0.25
-0.33
0.18
-0.19

0.16
0.16
0.17
0.07

-0.29
-0.39
0.19
-0.22

(c) Pillars 1 & 2 together
North America
0.26
Europe
0.20
Low tax
0.37
Rest of world
0.12

4.30
5.27
-16.52
3.25

-0.09
-0.14
-0.46
-0.18

0.07
-0.06
-0.34
-0.14

-0.29
-0.22
0.20
-0.21

0.01
-0.16
-1.21
-0.23

-0.81
-0.31
1.18
-0.17

0.26
0.16
0.23
0.07

-0.92
-0.36
1.33
-0.20

RegionNotes: Lost profits are measured relative to the benchmark. Note that for the low-tax region, lost profits are negative inboth the benchmark equilibrium and in the policy counterfactuals, i.e., profits are shifted inward to the low-tax region.
However, the magnitude of these lost profits are smaller in the counterfactuals. For example, in panel (b), the amount of
profits shifted into the low-tax region under pillar 2 is about half of the amount in the benchmark.

Table 4: Effects of profit shifting and OECD BEPS pillars on components of national income
Dividends

Tax revenue

Labor income+Dividends

Labor income+Tax revenue

All three

0.02
-0.06
-0.20
-0.04

2.27
2.19
-10.81
1.57

-0.02
-0.02
-0.06
-0.01

0.08
0.07
-0.37
0.06

0.07
0.05
-0.34
0.04

(b) Pillar 2: Global minimum tax rate
North America
-0.02
-0.09
Europe-0.01-0.09
Low tax-0.05
0.10
Rest of world
-0.01
-0.13

3.27
4.94
-9.78
2.64

-0.03
-0.02
-0.03
-0.03

0.14
0.17
-0.35
0.09

0.10
0.13
-0.28
0.06

(c) Pillars 1 & 2 together
North America-0.04
Europe-0.02
Low tax-0.07
Rest of world
-0.01

4.30
5.30
-16.42
3.27

-0.04
-0.03
-0.08
-0.04

0.17
0.18
-0.58
0.12

0.14
0.14
-0.51
0.07

RegionLabor income(a) Pillar 1: Profit reallocation
North America-0.03
Europe-0.01
Low tax-0.03
Rest of world
-0.00

-0.03
-0.11
-0.12
-0.17

Notes: Table reports percent changes in outcomes adjusted for purchasing power parity.

41

Figure 1: Varying the sizes of the pillars

North America

0 2 4 6 8 10 12 14 16 18 20

Europe0 2 4 6 8 10 12 14 16 18 20

Low tax

1.0

0 2 4 6 8 10 12 14 16 18 20

Rest of world

1.0

1.0

0 2 4 6 8 10 12 14 16 18 20

Lost profits (benchmark=1)

1.0

Real GDP (% drop.)

0.5
0.4

0.8

0.3
0.6

0.2

0.4

0.1
0.0

0.2

−0.1

0.0

−0.2
0.5
0.4

0.8

0.3
0.6

0.2

0.4

0.1
0.0

0.2

−0.1

0.0

−0.2
1.0
0.8

0.8

0.6

0.6

0.4
0.4

0.2

0.2

0.0

0.0

−0.2
0.5
0.4

0.8

0.3
0.6

0.2

0.4

0.1
0.0

0.2

−0.1

0.0
0

10

20

30

40

50

60

70

80

90

0

10

20

30

40

50

60

70

80

90

−0.2

Notes: Each column reports effects on one variable for each region. First column: Lost profits (reported relative to thebenchmark equilibrium). Second column: real GDP (reported as a percent change from the benchmark equilibrium).
X-axis in each plot represents the reallocation share for Pillar 1. Y-axis in each plot represents the global minimum
corporate income tax rate for Pillar 2.

42

Appendix (For Online Publication)
A

Institutional BackgroundIn this section we provide a brief overview of the current international tax regime and describe the mainfeatures of the two-pillar reform proposed by the OECD. We aim here to deliver an executive summary, rather
than an exhaustive discussion, of these immensely complex issues.28 Understanding the main componentsof the international tax architecture is crucial since they largely dictate the setup of our theory and impose
restrictions on what any reform proposal can achieve.

A.1

The Current International Tax Regime

Existing international law entitles a country to tax persons, either natural or legal, with which it has suﬀicientties. In practice, taxing rights are a product of multiple national laws and international treaties that often
contradict one another. The following are the most important characteristics of the current regime.
Legal separation of entities. The current regime treats subsidiaries within one MNE as separate legal
entities. Thus, any transaction between parts of an MNE in different tax jurisdictions, such as for example
an asset purchase, has real tax consequences. This characteristic coupled with heterogeneity of the tax
systems across jurisdictions and manipulation of transfer prices gives rise to profit-shifting opportunities.
Allocation of taxing rights. There are at least four possible locations where a multinational company
might in principle be taxed: the location of its shareholders, parent companies, aﬀiliates, or customers.
According to the current regime MNEs are taxed primarily in the third location (aﬀiliates’ location), butsometimes also in the second. This is achieved by a combination of legal rules allowing the countries concerned
to tax on to a source or residence basis.29
Transfer prices. Within-MNE transactions occur at transfer prices, which are disciplined by the so-called
arm’s length principle (ALP). The basic idea behind the ALP is that within-MNE prices should reflect themarket prices that would have been charged by two independent parties of transactions. There are fivecore methods to achieve the ALP standard: the comparable uncontrolled price (CUP), resale price minus,
cost plus, profit split, and transactional net margin methods. The practical implementation of this principle
is challenging and requires complex guidelines published regularly by the OECD which member countries
should obey—see OECD (2022b) for the latest guide.
Treatment of intangibles. The method preferred by the OECD to implement ALP is CUP, which simply
employs the price charged on comparable transactions between independent parties. CUP however is hard to
implement in case of trading intangibles, since most of the time a comparable transaction is non-existent. In
such cases the preferred method is the profit split method, which essentially inspects the relative financial orother contributions made by the two companies entering into a transaction. A profit split is then determined28

Our summary is largely based on Devereux et al. (2021), OECD (2015), OECD (2017), and OECD
(2022b).
29
From a legal perspective, a country taxes on a residence basis when it taxes companies that are resident
in that country for tax purposes on income arising in that or in another country. A country taxes on a source
basis when it taxes companies that are not resident in that country for tax purposes on income deemed toarise in that country. For a thorough discussion of these concepts see Devereux et al. (2021).

43

based on these contributions. OECD (2014) provides extensive guidelines on pricing transactions involving
intangibles.

A.2

Tax Avoidance and Profit Shifting Channels

Tax avoidance and profit shifting is conducted by MNEs using variety of channels. In what follows we briefly
discuss the most important ones.30
1. Transfer Pricing Manipulations. The global allocation of tax base between source and residence
countries is impacted by the valuation of intracompany transactions within an MNE. The arm’s lengthprinciple, which requires that internal prices between related parties be similar to prices that would
exist between independent parties, is used by most countries. However, this principle can be subject
to significant subjective interpretation and may not have a ”correct” arm’s length price if there are nocomparable third-party transactions. MNEs can manipulate transfer pricing by charging lower prices
for exports from high-tax to low-tax countries or higher prices for inputs from low-tax countries, thus
reducing their global tax liability.
2. Strategic Location of IP. The global tax of an MNE can also be reduced through the strategic locationof IPs. A company may carry out R&D in one country and then transfer ownership of the resulting
patent to a subsidiary in a low-tax jurisdiction, where the income generated from it will be taxed ata lower rate. Determining the arm’s length price for intangible transactions within a company can be
diﬀicult, as there are often no comparable transactions between unrelated parties. This creates room
for transfer pricing manipulation for tax purposes.
3. International Debt Shifting. Intracompany loans can also serve as a tool for reducing the tax bill of
an MNE. The variation in corporate tax rates across countries creates the possibility of lending from
low-tax countries to high-tax aﬀiliates or borrowing from external sources in high-tax countries. The
deductibility of interest payments on debt from taxable income results in a reduced tax bill for thegroup, without affecting its overall debt exposure and hence, bankruptcy risk.
4. Tax Treaty Shopping. Considerable variation in the withholding taxes (WHT) in more than 3000
bilateral double tax treaties creates opportunities of treaty shopping. This enables MNCs to linkdifferent treaties and divert cross-border payments through the country with the lowest WHT rate.
5. Tax Treaty Shopping. The presence of the withholding taxes (WHT) disparities in 3000-plus bilateral
double tax agreements produces prospects for treaty shopping. This gives MNEs the capability to
tie together varied pacts and divert cross-border payments through the nation with the least possible
WHT rate.

A.2.1

The importance of intangible capital and strategic IP location.

In an influential paper Grubert (2003) examines the links between intangible income, income shifting, intercompany transactions, and location choices by utilizing data from U.S. parent corporations and their
manufacturing subsidiaries. He finds that income from R&D-based intangible assets makes up roughly halfof the income that is shifted from high-tax to low-tax jurisdictions. Heckemeyer and Overesch (2017) distinguish between the tax response through financial planning, such as inter-company debt financing, andthe response through transfer pricing and licensing. They specifically compare the tax sensitivity of pre-tax
30

This discussion is largely based on Johansson et al. (2017) and Beer et al. (2020).

44

profits, which encompasses shifting through various means, with the tax sensitivity of earnings before interest and taxes (EBIT), which only captures non-financial shifting mechanisms. The results of their stylized
calculations indicate that transfer pricing and licensing, not inter-company debt financing, is the principal
channel for profit shifting. The overall semi-elasticity of pre-tax profits is estimated to be 0.786, and thenon-financial component of this response accounts for 82% of the total response. In their headline analysis
OECD (Johansson et al., 2017) concludes that a comprehensive analysis of the allocation of third-party debt,
among MNEs presents evidence of debt manipulation, accounting for 20% of profit shifting. Thus the rest,
the vast majority, is accounted for by mispricing and strategic location of intangible capital. Moreover OECDfinds that tax sensitivity of profit is almost twice as high among patenting MNEs than other MNEs (see Table
A5.4 in their study). Beer, de Mooij and Liu (2020) extend the meta analysis conducted by Heckemeyer andOveresch (2017) by almost doubling the sample size of primary estimates. They conclude that debt-shifting
channel plays, on average, a minor role.

A.3

OECD Base Erosion and Profit Shifting Project

In what follows we briefly summarize the key provisions of reform proposed by OECD/G20 Inclusive Framework on BEPS, as they were at the time of the writing of this paper.31

A.3.1

Pillar 1: Profit allocation and nexus

The general principle behind Pillar 1 is to allocate taxing rights more closely where the customers and usersof the in-scope MNEs are located. The key elements of Pillar 1 are as follows.
Scope. The new profit allocation rule will apply to groups with greater than e20 billion in worldwide
revenues and a profitability before tax margin of at least 10 percent. There are some exclusions for extractive
industries and regulated financial services.
Nexus. The allocation key is based on the revenue that is sourced to each jurisdiction. It will be sourced
to the end-market jurisdictions, where goods or services are used or consumed, permitting allocation to amarket jurisdiction from which the in-scope MNE derives at least e1 million in revenues.
Quantum. For in-scope MNEs, 25% of residual profit (i.e. profit in excess of 10% of revenue) will beallocated to market jurisdictions with nexus using a revenue-based allocation key.
Elimination of double taxation. Profit allocated to a market jurisdiction will be dispensed from double
taxation through direct exemption of credit method.
Unilateral Measures. The agreement requires all parties to remove all digital services taxes and otherrelevant, similar measures with respect to all companies and to commit not to introduce such measures in
the future.

A.3.2

Pillar 2: Global minimum taxation

The second pillar consists of two sets of rules granting jurisdictions additional taxing rights: (i) interlocking
domestic rules termed Global anti-Base Erosion (GloBE) rules, and (ii) a treaty-based Subject to Tax Rule
(STTR). Their key features are as follows.
31

The details of both pillars as well as the exact implementation plan are very much a work in progressat the time of writing this paper. Since November 2021 the OECD has been organizing a series of public
consultation meetings in order to work out technical details and parameters of the reform.

45

Scope. GloBe rules apply to multinational enterprise groups with a total consolidated group revenue above€750 million in at least two of the four preceding years.
Minimum tax rate. GloBE rules apply a system of top-up taxes that brings the total amount of taxes
paid on an MNE’s profit in a jurisdiction up to the minimum rate of 15%.
Exclusions. GloBe rules will also provide for an exclusion for those jurisdictions where the MNE hasrevenues of less than EUR 10 million and profits of less than EUR 1 million.
Subject to Tax Rule (STTR). This complements the GloBE rules by targeting intra-MNE payments
exploiting certain provisions of the treaty to shift profits from source countries to payee jurisdictions where
those payments are subject to no or low rates of nominal taxation. In such cases, it reallocates taxing rights
to source jurisdictions. It applies to such payments as covered payments—interest, royalties, brokerage,
marketing, procurement, agency or other intermediary services, and so on. The minimum rate for the STTR
will be 9 percent.

B

Data sources

Region definitions. We take the list of tax havens from Tørsløv et al. (2022). The complete list of countries
in the tax-haven region is: Andorra, Anguilla, Antigua, Aruba, the Bahamas, Bahrain, Barbados, Belize,
Bermuda, British Virgin Islands, Cayman Islands, Curacao, Cyprus, Gibraltar, Grenada, Guernsey, theIsle of Man, Jersey, Lebanon, Liechtenstein, Luxembourg, Malta, Marshall Islands, Mauritius, Monaco, theNetherlands Antilles, Panama, Puerto Rico, Samoa, Seychelles, Sint Maartin, St. Kitts & Nevis, St. Vincent& the Grenadines, St. Lucia, the Turks & Caicos, and Vanuatu.
World Development Indicators. Data on population and output come from the World Bank’s World
Development Indicators database. The specific series that we use are total population (SP.POP.TOTL),
GDP in current US dollars (NY.GDP.MKTP.CD), and GDP at purchasing power parity in constant 2011
international dollars (NY.GDP.MKTP.PP.KD). For each of these variables, when constructing regional aggregates, we sum across countries within a region following McGrattan and Waddle (2020), and then averageover the period 2014–2017.
World Input-Output Database. International goods trade data are taken from the World Input-Output
Database (Timmer et al., 2015). For each bilateral import relationship, we sum all intermediate inputs andfinal uses of goods (industries 1–23, which represent agriculture, resource extraction, and manufacturing)from countries in the source region by countries in the destination region. We use data from 2014, the mostrecent year available.
OECD AMNE Database. This is a new dataset provided by the OECD which distinguishes between three
types of firms: foreign aﬀiliates (firms with at least 50% foreign ownership), domestic MNEs (domestic firms
with foreign aﬀiliates), and domestic firms not involved in international investment. It includes a full matrixof the output of foreign aﬀiliates in 59 countries plus the rest of the world (in the host country, industry,
parent country dimension), as well as matrices for value-added and for exports and imports of intermediate
inputs (host country and industry). A second set of matrices in the database provides information on output,
value-added, and exports and imports of intermediate inputs of domestic MNEs and non-MNE domestic firms(from 2008 onwards). In addition, split Inter-Country Input-Output tables are provided distinguishing for all
countries the transactions of domestic-owned and foreign-owned firms. These tables can be used to analyze

46multinational production in value-added terms. We exploit them to discipline our model and make sure it
replicates the share of each region’s gross value added that is accounted for by foreign multinationals. We
first map the set of 59 countries from the AMNE dataset to our five regions and then compute the averagevalue-added shares for three types of firms (foreign aﬀiliates, domestic MNES, and domestic non-MNEs) ineach region over the time period 2008–2016. The data can be accessed at OECD AMNE Database.
Compustat. Data on sales, employment, and country of origin of parent companies come from the Compustat North America Fundamentals Annual database. This database contains data of North Americancompanies parsed from SEC filings. Data on subsidiaries come from the Wharton Research and Data Services (WRDS) Subsidiary Data. These data also come from SEC filing, particularly Exhibit 21, in whichfirms filing with the SEC must list the names of all existing Significant Subsidiaries. For a detailed, legal
definition of Significant Subsidiaries, see here. Roughly, if the parent company controls at least 10% of
the subsidiary, it is considered Significant. The WRDS data are available from 1995 to 2019, and containidentifying information for the parent company, as well as the name and country of residence of all Significant Subsidiaries. These two datasets were linked using a common identifier of the parent company, thegvkey. Mean and median sales and employment statistics were computed for the years 2010-2019. The unitof observation was parent company-year.
U.S. Census Data. To discipline the firm size distribution we exploit data from the Statistics of U.S.
Businesses (SUSB). SUSB is an annual series that provides national and subnational data on the distributionof economic data by establishment industry and enterprise size. SUSB covers most of the country’s economic
activity. The series excludes data on nonemployer businesses, private households, railroads, agricultural
production, and most government entities. We construct a Lorenz employment curve for the U.S. at thefirm level using two Excel spreadsheets available at the Census website. We combine the table with detailed
employment sizes with the table with larger employment sizes (20,000+ employees), both from 2019 SUSB.
This allows us to account for a long right tail of the firm size distribution in our model, which is crucial giventhat average MNE is three orders of magnitude larger than the average firm in the U.S. economy. Both Excel
files can be downloaded from the SUSB website.
OECD Corporate Tax Statistics Database. To compute the share of corporate income tax revenue ineach region that is paid by local aﬀiliates of foreign MNEs, we use data from the OECD Corporate Tax
Statistics Database (OECD, 2022a). First, for each country in the database, we compute two numbers from
Table 1: (i) corporate income taxes paid by domestic MNEs’ aﬀiliates; and (ii) corporate income taxes paidby foreign MNEs’ aﬀiliates. Second, we compute (i) as a share of (ii). Third, for each region in our model,
we compute the average of these shares across the countries in that region, weighting by (i) + (ii). The data
can be accessed here.
Tørsløv et al. (2022). Two kinds of data are taken from this paper: lost profits and effective corporate
income tax rates. Total lost profits are from sheet Table3 of the Main Data Excel file. We first sum across all
countries within the North America and Europe regions, and then set the rest of the world’s lost profits by
subtracting the North America and Europe totals from the overall world total. The share of lost profits thatare shifted to the tax haven region is constructed in the same way using sheet TableC2 in the Replication
Guide Tables Excel file. The effective corporate income tax rates come from sheet DataF2 in the Main Tables
Excel file. Here, we take the average across countries within each region. Both Excel files can be downloaded
from https://missingprofits.world/.

47

C

Firm-level profit shifting estimates

In this section we briefly discuss the empirical literature on profit shifting, which aims to estimate the elasticityof reported profits with respect to the tax rate differentials across jurisdictions. We begin with an overview ofthe empirical strategy adopted in this line of research, then move to the discussion of the headline, consensus
estimates emerging from the literature. Finally we link our structural modelling approach to the empiricalstrategy.

C.1

Empirical strategy

Most of the empirical literature on elasticity of the profit shifting margin follows the concept presented by
Grubert and Mutti (1991) and Hines and Rice (1994) that the reported pre-tax profit of a multinationalTS
entity, ΠRi , is a sum of the “true” profit, Πi , and the profit shifted for tax reasons, ΠiTSΠRi = Π i + Πi .

(C.1)

This shifted profit would be positive in low-tax countries and negative in high-tax countries. The idea hereis that the actual profitability of multinational enterprises with similar characteristics (e.g. size, industry,
country etc.) is similar. However, the opportunities to shift profits differ since they depend on such characteristics as locations of the other subsidiaries and statutory tax rates in these locations. Thus, the entities
linked to low-tax jurisdictions are more likely to shift profits and the entities linked to high-tax jurisdictions
are more likely to receive profits. The fundamental challenge for estimating the elasticity of profit shifting
margin is that neither “true” profits nor shifted ones are directly observable in the firm-level data. To tackle
this problem the literature usually assumes that “true” profits are equal to output minus the wage bill, withthe wage being equal to marginal product of labor (see for example Huizinga and Laeven (2008)). As for theshifted profits, the literature typically specifies some stylized framework that allows linking shifted profits to
tax differentials between jurisdiction j and other operating jurisdictions. This strategy leads to the following
generic equation to identify shifting profits:R
πi,j,t= βXi,j,t − γCi,j,t + δt + ε

(C.2)

R
where πi,j,t= ln ΠR
i,j,t are log reported profits of a multinational i located in jurisdiction j at time t, Xi,j,t isa vector of determinants of true profitability, which includes capital and labor inputs among others. It may
also include a number of macroeconomic variables, such as GDP growth, exchange rate, or inflation. Ci,j,t is
a composite variable that summarizes the tax differentials between jurisdiction j and other jurisdictions inwhich the MNE located in jurisdiction i has subsidiaries. The specific formula for Ci,j,t differs across papers
but in all of them it reflects the tax incentives to shift profits away from or into jurisdiction j. Finally δtdenotes time fixed-effect and ε denotes the residual term. The coeﬀicient of interest is then γ which reflects
the extent to which the multinational shifts profits into or out of aﬀiliate i. It is important to note that thisestimate represents a marginal effect – i.e. the change in reported profits associated with a small change intax rates, holding all else constant. We can interpret γ in equation (C.2) as the semi-elasticity of observed
profits πiO with respect to the composite tax variable Ci,j,t . The semi-elasticity indicates the percentagechange of reported profit in response to a one percentage point change in the tax differential vis-a-vis otherinternational locations, reflecting the incentive to shift profits abroad.

48

C.2

Empirical estimates

A number of papers estimate different versions of equation (C.2) for a variety of datasets and time periods.
A thorough and detailed review of this literature is beyond the scope of this paper.32 Instead, we focus hereon the two most recent survey papers, which conduct meta analyses of existing estimates, and on the main
OECD estimate, all of which report the headline semi-elasticity number.
Johansson et al. (2017) provide the main estimate of the magnitude of the profit shifting used by theOECD. They conduct a comprehensive study using firm-level data from the ORBIS database to assessinternational tax planning by multinational enterprises (MNEs). Their results are based on an impressively
large sample of firms (1.2 million observations of MNE accounts) in 46 OECD and G20 countries and asophisticated procedure to identify MNE groups. Their headline estimate of the semi-elasticity of the profit
shifting margin with respect to the tax differential is 1.11 (see Table 1, column 1 and footnote 31 in theirpaper). Hence, reported profits decrease by about 1.1% if the international tax rate differential increases by
one percentage point. The estimated elasticities combined with a number of assumptions are then used toestimate the effect of international tax planning on corporate tax revenues: the estimated net tax revenue
loss ranges from 4% to 10% of global corporate tax revenues.
Heckemeyer and Overesch (2017) construct a meta-database containing 203 primary estimates sampledfrom 27 empirical studies identified by means of article search engines. All of the included studies estimate
the empirical relationship between reported parent and subsidiary profitability and the tax incentive to shiftprofits abroad. Therefore, this meta-analysis reviews the literature, providing indirect evidence for profit
shifting without specifying directly the shifting methods. They find a tax semi-elasticity of pre-tax profit
of about 0.79, in absolute terms. They conclude that across all specifications the predicted semi-elasticities
turn out to be statistically significant and rather robust in magnitude. They also provide a 95% confidence
interval in addition to the point estimate and conclude that conditional on a hypothetical state-of-the-art
study design, the set of semi-elasticities that should not be rejected at the 5% significance level ranges from0.546 to 1.026.
Beer, de Mooij and Liu (2020) extend the analysis conducted by Heckemeyer and Overesch (2017) andinclude 11 additional studies and 199 additional primary estimates. They also reduce specification bias, andadopt an enhanced estimation method that corrects for within-study correlation of primary estimates. Theirresults indicate that a semielasticity of reported pretax profits with respect to international tax differentials
equal to 0.98 is a good reflection of the literature. This means that a one-percentage-point larger tax rate
differential reduces reported pretax profits of an aﬀiliate by 1%.

C.3

Model counterpart of semi-elasticity

We now describe how we estimate the model counterpart of the semi-elasticity summarized above. We view
this as a validation exercise of the cost function C(λ) upon which the extent of profit shifting in the presence oftax differentials between jurisdictions heavily depends. Since our parsimonious model of only four productive
regions does not provide suﬀicient variation in cross-jurisdiction differences in corporate tax rates (regressor
Ci,j,t in equation (C.2)), we conduct a simulation exercise as follows.
We simulate 200 counterfactual economies, raising the corporate tax rate of the LT region incrementallyfor the first 100 economies and the rate of the T H region for the latter 100. We set the highest counterfactual
corporate tax rate to 11.9%, which is the corporate tax rate of LT . In each of these counterfactual economies,32

See Dharmapala (2014), Heckemeyer and Overesch (2017), Johansson et al. (2017) and Beer et al. (2020)
for extensive reviews of this line of research.

49

we hold fixed the set of firms’ FDI and exporting destinations, JF and JX , as well as the final good price andwage rate of each region, Pi and Wi . We allow firms to solve for their optimal choices of labor ℓ, intangible
capital z and shifting shares λLT and λT H . In other words, the firms’ problem is re-solved in a partial
equilibrium setting, which allows us to isolate the relationship of reported profits in home divisions to tax
rate differentials relative to the profit-shifting destination.
Denote k as the index of a counterfactual economy. We follow the empirical specification of equation(C.2) and run the regression using the model-simulated dataset:log πik,P S (ω) = β0 + βℓ log ℓki (ω) + βz log z k (ω) − βτ τ̂ik + ϵki (ω)

(C.3)

k
where we denote by τik the counterfactual tax differential defined as τ̂ik = τi −τLTfor k ≤ 100 and τ̂ik = τi −τTk H
otherwise. For each experiment k, we include in the regression only home divisions of firms doing FDI in theregion for which we change the corporate tax rate. We only include home divisions of profit-shifting MNEs
because we do not model profit shifting originating from a foreign subsidiary. Nonetheless, such regression
informs us of how reported profit responds to changes in profit-shifting relevant tax differentials, which is
captured by the coeﬀicient of interest βτ . We report the coeﬀicient estimate of βτ in Table 2.

D Sensitivity Analysis
Our quantitative results are robust to a variety of alternative assumptions and calibrations. Here, we describe
the results of three sensitivity analyses that illustrate the impact of some of the most important elements ofour model and policy experiments. Tables D.1–D.2 show the results of these sensitivity analyses.
Alternative profit reallocation rules. The first pillar of the OECD’s BEPS project reallocates the rights
to tax a portion of a firm’s global profits to the regions in which it operates in accordance with these regions’shares of the firm’s global sales. Importantly, some of these rights are allocated to a firm’s export markets,
even if the firm does not operate foreign aﬀiliates in these markets. This aspect of the rule increases effective
tax rates for firms based in Europe, the low-tax region, and the rest of the world because North America,
which is a large, rich export market, has the highest corporate income tax rate. This reduces these firms’
incentives to invest in intangible capital, even if they do not shift profits at all. This partly explains why Pillar
1 has larger macroeoconomic consequences than Pillar 2, despite having smaller effects on profit shifting. To
explore the importance of this aspect of Pillar 1, we have analyzed the effects of alternative versions in which
profit taxation rights are allocated for MNEs only, or are based on output shares instead of sales shares. Panel(a) of Table D.1 shows the effects of a profit allocation rule that applies only to MNEs, as opposed to firmsthat export but do not operate foreign aﬀiliates. The effects on profit shifting are the same as the OECD’s
version but the macroeconomic consequences are smaller, especially outside of North America. Panel (b) of
Table D.1 shows what happens when profit-taxation rights are allocated based on output rather than sales.
Under this version of the pillar, export destinations do not receive any taxation rights at all. The results
are almost identical to panel (a). These results indicate that allocating taxation rights based on export sales
should be avoided.
Intangible share. We have set the share of intangible capital in production, ϕ, to match the share of incomethat accrues to intangible capital in MNEs’ foreign aﬀiliates. This approach ensures that our model captures
the extent to which nonrivalry governs MNEs’ incentives to invest in intangible capital. This share is the
key determinant of the potential scope for profit shifting; a greater intangible share means more licensing

50fee income that can be transferred to the low-tax region and/or the tax haven. Of course, it is also the key
determinant of the macroeconomic impact of policies that affect incentives to invest in intangible capital,
including the policies designed to reduce profit shifting that we study. Panels (c) and (d) of Table D.1
show the results of our experiments under alternative calibrations with different intangible shares. In each,
we recalibrate all model parameters except for those that govern profit shifting. This allows us to explore
how the intangible share affects profit shifting under the current international tax system as well as theeffects of changes to this system. The results of these analyses show that a lower intangible share reduces
macroeconomic effects of transfer pricing and profit shifting, reduces the amount of profit shifting under thecurrent tax code, and reduces the macroeconomic consequences of the OECD BEPS pillars; the reverse istrue for a higher intangible share. However, the extent to which the BEPS pillars reduce profit shifting isabout the same as in the baseline model. For example, with a lower intangible share, lost profits in North
America fall by 1 - 0.27/0.41 = 34% under Pillar 1, which is similar to the decline of 32% reported in Table
3.
Endogenous labor supply. In our baseline model we assume that labor supply is fixed, which means thatthe only way for the labor market to clear is for wages to adjust. Here we explore how allowing households
to endogenously choose labor supply changes the results. Panel (e) of Table D.1 shows the results whenpreferences are assumed to be log-separable in consumption and leisure as in McGrattan and Waddle (2020),
and panel (f) shows results in a model with GHH preferences where there is no wealth effect on labor supply.
The main difference between these models and the baseline is that the effects on GDP are larger, which isdriven by the fact that households reduce labor supply for two reasons: (i) wages fall due to reduced labordemand from MNEs; and (ii) in the case of log-separable preferences, lump-sum transfers rise due to theincrease in tax revenue. Now, output falls in all regions in all three experiments. One interesting result
aspect of the results is that the macro effects of profit shifting and pillar 2 are much smaller for the low-tax
region in the model with log-separable preferences. This highlights that profit shifting may cause a kind of
Dutch disease, whereby low-tax regions’ labor supply is depressed by the increase in income from foreign
MNEs. This is kind of funny, since the Netherlands is in our low-tax region).
Variable profit-shifting costs. We have set the costs of profit shifting, χi,LT and χi,T H , to match estimates in the literature about the amount of profit shifting and the extent to which profits are shifted to
low-tax “productive” regions versus “unproductive” tax havens. These estimates are inferred from information about the profitability and labor shares of MNEs’ foreign aﬀiliates in these regions—it is impossible
to measure lost profits directly without access to detailed information about intra-MNE transactions—so
there is some uncertainty about how much profit shifting truly occurs. To determine the sensitivity of ourresults to these key parameters, we have conducted our experiments in alternative calibrations within whichthese parameters are set to higher or lower values. Panel (g) of Table D.2 shows the results when χi,LTand χi,T H are halved, while panel (h) shows the results when they are doubled. With lower profit-shifting
costs, there is more profit shifting under the current tax system and the OECD BEPS pillars have larger
macroeconomic effects; the reverse holds with higher costs. As in the previous exercise, the BEPS pillars
reduce profit shifting by about the same amount as in the baseline. For example, with lower shifting costs,
lost profits in North America fall by 1 - 1.43/2.02 = 29% under Pillar 1, which is again quite similar to theresult of the benchmark model.
Separability of profit shifting costs across destinations. In the benchmark model, we set ϵ = 1 withthe lack of a relevant empirical moment to discipline this cost parameter. This implies that profit-shifting∂Ci2 (λT H ,λLT )cost function is additively separable in the two components, that is ∂λ= 0 and Ci (λLT , λT H ) =T H ∂λLT51

Ci (0, λT H ) + Ci (λLT , 0). To gauge how the substitution parameter ϵ affects our results, we perform two
sensitivity tests where we set ϵ = 0.75 and ϵ = 1.25. All other model parameters are re-calibrated. The results
are shown in Panels (g) and (h) of Table D.2. The effects of Pillar 1 are quite similar to the benchmark
model. For Pillar 2, however, there is greater reductions of lost profits in the case with positive crossderivatives (Panel (g)) than with the negative cross-derivatives (Panel (h)). The results of the two pillars
together are thus also different. As expected, the effects in the benchmark model is in between of these twopanels. This is because, with a positive cross-derivative cost function, the return of shifting to both LT and
T H is smaller. In response to Pillar 2, more firms that used to operate in both LT and T H will exit from oneof them when there is a positive cross-derivative than a negative cross-derivative. This generates a greater
reduction in lost profits in Panel (g). This differential impact is absent with Pillar 1. This is because Pillar
1 increases the effective tax rate of T H more than LT . With a positive cross-derivative, fewer firms shift toboth T H and LT . However, the firms which still shift to both will have greater relatively λLT than in the
LT ,λT H )decreases by more. These two effects happen to cancel
case with a negative cross-derivative, as ∂Ci (λ∂λLTout. The policy effects on GDP across the world is insensitive to choosing different values of ϵ.
Exogenously restricting some firms from profit shifting. In the benchmark model, we assume that
all firms have access to the profit shifting technology. In reality, profit shifting is concentrated in certain
sectors, suggesting that not all sectors have the same kind of profit shifting opportunities. Barrios andd’Andria (2019) document significant sectoral differences in profit shifting which cannot be fully attributed
to heterogeneity in intangible intensity. One naive way to assess the importance of this assumption is
to assume that only 50% of firms in the model are allowed to shift profits, while continuing to use thebaseline parameterization. Panel (k) of Table D.2 shows the results of this experiment. The macroeconomic
consequences of profit shifting and the two OECD pillars are smaller than in the baseline model, but theaggregate amount of profit shifting in this model is too low (about 50% of the observed values). This should
not be surprising, since the costs of profit shifting have not changed but only half of the firms in the model
can shift profits. This suggests that a more appropriate way to assess the importance of this assumption is torecalibrate the profit shifting costs so that even though fewer firms can shift profits, the model still matches
the aggregate amount of profit shifting observed in the data. Panel (l) of Table D.2 shows the results of thisversion of the experiment. The aggregate results are extremely similar to the baseline results in all respects,
but of course the profit shifting costs must be lower and the amount of profit shifting per firm (conditionalon engaging in this activity) must be higher to rationalize the aggregate amount of profit shifting.

52

Table D.1: Sensitivity analysis
Lost profits (benchmark = 1)

GDP (% chg.)

North
America

EuropeLow tax

Rest of
World

North
America

EuropeLow tax

Rest of
World

1.00
0.68
0.38
0.26

1.00
0.73
0.27
0.20

1.00
0.76
0.49
0.37

1.00
0.70
0.16
0.12

0.01
-0.09
0.01
-0.09

0.02
-0.15
0.02
-0.14

0.29
-0.37
-0.16
-0.46

0.08
-0.17
-0.04
-0.18

(a) Profit reallocation rule applies to MNEs only
Pillar 1
0.69
0.73
0.76
Pillars 1 & 2 together
0.26
0.20
0.37

0.70
0.12

-0.07
-0.06

-0.09
-0.08

-0.23
-0.33

-0.12
-0.14

(b) Production-based profit reallocation rule
Pillar 1
0.69
0.73
Pillars 1 & 2 together
0.27
0.20

0.76
0.37

0.70
0.12

-0.07
-0.07

-0.08
-0.07

-0.22
-0.31

-0.11
-0.13

(c) Low intangible share
Effects of profit shifting
Pillar 1
Pillar 2
Pillars 1 & 2 together

0.41
0.27
0.15
0.11

0.39
0.28
0.10
0.08

0.40
0.31
0.20
0.15

0.39
0.27
0.06
0.04

-0.01
-0.06
0.01
-0.05

-0.01
-0.12
0.02
-0.11

0.10
-0.27
-0.06
-0.31

0.02
-0.12
-0.01
-0.13

(d) High intangible share
Effects of profit shifting
Pillar 1
Pillar 2
Pillars 1 & 2 together

1.76
1.21
0.67
0.47

1.81
1.32
0.49
0.36

1.75
1.34
0.87
0.65

1.84
1.31
0.30
0.21

0.05
-0.13
-0.01
-0.13

0.07
-0.19
0.00
-0.19

0.56
-0.50
-0.30
-0.67

0.17
-0.23
-0.09
-0.27

(e) Endogenous labor supply (log-separable preferences)
Effects of profit shifting
1.00
1.00
1.00
Pillar 1
0.68
0.73
0.76
Pillar 2
0.38
0.27
0.49
Pillars 1 & 2 together
0.26
0.20
0.37

1.00
0.70
0.16
0.12

0.09
-0.15
-0.06
-0.18

0.12
-0.19
-0.06
-0.22

0.02
-0.19
-0.02
-0.21

0.11
-0.19
-0.07
-0.22

(f) Endogenous labor supply (GHH preferences)
Effects of profit shifting
1.00
1.00
Pillar 1
0.68
0.73
Pillar 2
0.38
0.27
Pillars 1 & 2 together
0.26
0.20

1.00
0.70
0.16
0.12

0.03
-0.12
-0.01
-0.12

0.03
-0.16
0.00
-0.16

0.36
-0.39
-0.20
-0.52

0.09
-0.17
-0.05
-0.20

ExperimentBaseline model
Effects of profit shifting
Pillar 1
Pillar 2
Pillars 1 & 2 together

1.00
0.76
0.49
0.37

Notes: Panel (a): profit-reallocation rule for pillar 1 applies only to MNEs (not firms that export but do not operate
foreign aﬀiliates). Panel (b): rule is based on value added rather than sales; profits are not reallocated to export
destinations. Panels (c) and (d): intangible share is changed and all parameters except for profit-shifting costs arerecalibrated. Panel (e): households have GHH preferences (no income effects on labor supply). Panel (f): labor
supply is fixed. Lost profits measured relative to benchmark equilibrium in baseline calibration. Baseline results
shown at top of table for ease of comparison.

53

Table D.2: Sensitivity analysis, continued
Lost profits (benchmark = 1)

GDP (% chg.)

North
America

EuropeLow tax

Rest of
World

North
America

EuropeLow tax

Rest of
World

1.00
0.68
0.38
0.26

1.00
0.73
0.27
0.20

1.00
0.76
0.49
0.37

1.00
0.70
0.16
0.12

0.01
-0.09
0.01
-0.09

0.02
-0.15
0.02
-0.14

0.29
-0.37
-0.16
-0.46

0.08
-0.17
-0.04
-0.18

(g) Low variable profit-shifting costs
Effects of profit shifting
2.02
Pillar 1
1.43
Pillar 2
0.80
Pillars 1 & 2 together
0.56

1.95
1.44
0.54
0.40

1.90
1.46
0.96
0.73

2.04
1.46
0.35
0.25

-0.00
-0.09
0.02
-0.07

0.03
-0.16
0.03
-0.14

0.56
-0.48
-0.29
-0.65

0.14
-0.20
-0.07
-0.23

(h) High variable profit-shifting costs
Effects of profit shifting
0.48
Pillar 1
0.32
Pillar 2
0.18
Pillars 1 & 2 together
0.12

0.50
0.36
0.13
0.10

0.51
0.39
0.25
0.19

0.48
0.33
0.08
0.05

0.01
-0.09
0.00
-0.09

0.01
-0.15
0.01
-0.14

0.15
-0.31
-0.08
-0.36

0.04
-0.15
-0.02
-0.16

(i) Positive cross-destination effects on marginal profit shifting costs
Effects of profit shifting
1.00
1.00
1.00
1.00
Pillar 1
0.69
0.73
0.76
0.71
Pillar 2
0.38
0.25
0.40
0.15
Pillars 1 & 2 together
0.26
0.18
0.30
0.10

0.01
-0.09
0.01
-0.09

0.03
-0.15
0.01
-0.14

0.36
-0.37
-0.18
-0.47

0.09
-0.17
-0.04
-0.18

(j) Negative cross-destination effects on marginal profit-shifting costs
Effects of profit shifting
1.00
1.00
1.00
1.00
Pillar 1
0.67
0.72
0.78
0.70
Pillar 2
0.41
0.33
0.78
0.23
Pillars 1 & 2 together
0.29
0.25
0.60
0.17

0.01
-0.09
0.01
-0.09

0.02
-0.15
0.02
-0.13

0.28
-0.36
-0.09
-0.42

0.08
-0.17
-0.04
-0.18

(k) Some firms exogenously restricted from profit shifting, baseline profit shifting costs
Effects of profit shifting
0.50
0.50
0.50
0.50
0.00
0.00
Pillar 1
0.34
0.36
0.38
0.35
-0.08
-0.13
Pillar 2
0.19
0.13
0.25
0.08
0.01
0.02
Pillars 1 & 2 together
0.13
0.10
0.19
0.06
-0.08
-0.13

0.15
-0.29
-0.08
-0.35

0.04
-0.13
-0.01
-0.15

(l) Some firms exogenously restricted from profit shifting, recalibrated profit shifting costs
Effects of profit shifting
1.00
1.00
0.99
1.00
-0.00
0.02
Pillar 1
0.69
0.74
0.77
0.71
-0.09
-0.14
Pillar 2
0.39
0.28
0.50
0.17
0.01
0.02
Pillars 1 & 2 together
0.27
0.21
0.38
0.12
-0.08
-0.13

0.36
-0.37
-0.16
-0.46

0.08
-0.16
-0.04
-0.18

ExperimentBaseline model
Effects of profit shifting
Pillar 1
Pillar 2
Pillars 1 & 2 together

Notes: Panel (g): parameters that govern marginal cost of profit shifting, ψij , are halved. Panel (h): ψij aredoubled. Panel (i): ϵi = 0.75. Panel (j): ϵi = 1.25. Panel (k): 50% of firms exogenously restricted from profit shifting, using values for profit-shifting cost parameters from baseline calibration. Panel (l): 50% of firms exogenously
restricted from profit shifting, using recalibrated profit-shifting cost parameters. Lost profits measured relative tobenchmark equilibrium in baseline calibration. Baseline results shown at top of table for ease of comparison.

54

E

Quantitative Model Derivations

E.1

Firm’s problem

E.1.1

Scale choice: the parent division

We start from the parent division of a firm ω ∈ Ωi ’s scale choice here. A parent division that produces for thedomestic market and exports to a set of JX regions chooses its scale and how to allocate its output across its
markets. Note that this problem nests the problem for firms only producing for the domestic markets when
JX = ∅. The parent division’s problem can then be written as
πiD (a, z; JX ) =
s.t



max
qii ,(qij )j∈JX ,ℓ

qii +

X



pii (qii )qii +XX X
pij (qij)qij − Wi ℓ

j∈JX





,

X
ξij qij= yi = Ai a(Ni z)γ ℓϕ .

j∈JXThe first-order conditions are[qij ]
[ℓ]

1
−1
ρ−1
Pj Qjρ qij ρ = λξij ,ρ

Wi = λϕAi a(Ni z)γ ℓϕ−1 ,where ξii = 1. Rearrange to get
1−1
τij Wiρ−1
Pj Qjρ qij ρ =.
ρ
ϕAi a(Ni z)γ ℓϕ−1

The solution isqij =ϕ(ρ − 1)
ρ

ρ

ρ 
ρ
1
1

ρ 
ρ
Pj Qjρ
Pj Qjρ Ai a(Ni z)γ ℓϕ−1
Ai a(Ni z)γ ℓϕ−1
 =
 ϕ(ρ − 1).
ξij Wiξijρ
WiPlugging this back into the resource constraint, can solve for labor as1 ϕ+ρ−ρϕ

ρ



X
ϕ(ρ
−
1)
ℓ = Piρ Qi +.
Pjρ τj1−ρ Qj 
Wi−ρ (Ai a)ρ−1 (Ni z)γ(ρ−1)


ρ

(E.1)

j∈JX

We can use the equations above to compute qij , pij , and πiD (a, z; JX ). It is convenient to express domestic55

parent revenues as
pii qii +

X

ρ−1

1

pij qij = Pi Qiρ qii ρ +

j∈JX

X

1

ρ−1

Pj Qjρ qijρ

j∈JX


ρ−1
ρ

1
ρ

= Pi Qi Q̄ii

+

X


1
ρ

ρ−1
ρ

Pj Qj Q̄ij 

j∈JX
ϕ

 ρ−1


ρ

 ρ ϕ+ρ−ρϕ
X
ϕ(ρ
−
1)
Pjρ τj1−ρ Qj × Piρ Qi +
W −ρ


ρ

(E.2)

j∈JX

× (Ai a)ρ−1ϕ+ρ−ϕρ

γ(ρ−1)

γ(ρ−1)

Niϕ+ρ−ϕρ z ϕ+ρ−ϕργ(ρ−1)= R̄ii z ϕ+ρ−ϕρ .
Similarly, domestic parent costs can be expressed as1 ϕ+ρ−ρϕ


ρ


X
ϕ(ρ − 1)
Wi ℓ + Wi z/(Ai a) = Wi Piρ Qi +Pjρ τj1−ρ Qj 
W −ρ (Ai a)ρ−1 (Ni z)γ(ρ−1)+ Wi z/(Ai a)


ρ

j∈JX

= C̄ii z

E.1.2

γ(ρ−1)
ϕ+ρ−ρϕ(E.3)+ Wi z/(Ai a).

Scale choice: foreign subsidiaries

Foreign subsidiaries are similar to domestic-only firms. They just choose scale to maximize profits fromselling to the host market given the demand curve and production technology. The only difference is thepresence of the FDI barrier σij . The foreign subsidiary’s problem isF
πij(a, z) = max pij (q)q − Wi ℓ
q,ℓ

1

ρ−1

= max Pj Qjρ (σij Aj a) ρ (Nj z)

γ ρ−1
ρ

ℓ

ρ−1

ℓϕ ρ − Wj ℓ.

The optimal ℓ, which yields all the other quantities immediately, isℓ=ϕ(ρ − 1)ρρρ

(Pj /Wj ) Qj (σij Aj a)

ρ−1(Nj z)1γ(ρ−1)1 ϕ+ρ−ϕρ

.

(E.4)

−1

We can use this to compute qij = yij = σij Aj a(Nj z)γ ℓϕ , pij = Pj Qjρ qij ρ , and πjF (a, z). It is convenient toexpress foreign aﬀiliate revenues as1

ρ−1

pij qij = Pj Qjρ qijρ ϕ(ρ−1)γ(ρ−1)ϕ1
ρ−1γ(ρ−1)ϕ(ρ − 1) ϕ+ρ−ϕρ ρ−1ρ(Pj /Wj )= Pj Q j
Qj ρ ϕ+ρ−ϕρ (Aj σij a) ϕ+ρ−ϕρ Njϕ+ρ−ϕρ z ϕ+ρ−ϕρργ(ρ−1)= R̄ij z ϕ+ρ−ϕρ ,

56

(E.5)

and express foreign aﬀiliate costs as
Wj ℓ = Wj

ϕ(ρ − 1)ρρρ

(Pj /Wj ) Qj (Aj σij a)

ρ−1(Nj z)

γ(ρ−1)1 ϕ+ρ−ϕρ(E.6)γ(ρ−1)(E.7)= C̄ij z ϕ+ρ−ϕρ .

E.1.3

Technology and Profit Shfiting Choice

Here, we solve the optimal nonrival technology allocation z and profit shifting shares λT H and λLT in theenvironment with transfer pricing and profit shifting, taking JX and JF as given. Letting Πi (a; JX , JF )be the maximized dividend for a firm in region i, given productivity a and the sets of exporting and FDI
destinations JX and JF , we have(Πi (a; JX , JF ) =maxz,λLT ,λT H(1 − τi )
πiD (a, z; JX )+− (λLT + λT H )ϑii (z) + (1 − λLT − λT H )X

ϑij (z)

j∈JF

 
Wi
−
− Wi Ci (λT H , λLT ) νi (z) + (µiT H λT H + µiLT λLT )νi (z) z
Ai a


 
X
F
+(1 − τLT ) πi,LT (a, z) + λLT
ϑij (z) − (1 − λLT )ϑiLT (z) − µiLT λLT νi (z) z+(1 − τT H )

λT H

X

j∈JF ∪{i}\{LT } ϑij (z) − µiT H λT H νi (z) zj∈JF ∪{i}

+

X

)
 F

(1 − τj ) πij (a, z) − ϑij (z)z .

j∈JF \{LT }Here, we solve the full problem where the firm operates in both LT and T H. The optimal choices of z andλ could be derived similarly for firms only operate in fewer than two profit-shifting destinations. Substituting
in the optimal scale choices specified in equation (E.1) and (E.4) and letting λ = λT H + λLT , we can write57Πi (a; JX , JF ) as
maxz,λT H ,λLT

(1 − τi )  1 − λγ(ρ − 1)
ϕ + ρ − ϕρ(R̄ii − C̄ii ) + (1 − λ)j∈JF−(1 − τi ) (Wi Ci (λT H , λLT ) − (µiT H λT H + µiLT λLT ))"
+(1 − τLT )
1 − (1 − λLT )

λLT


X
j∈JF ∪{i}\{LT }X  γ(ρ − 1) γ(ρ − 1)
ϕ + ρ − ϕρXj∈JF ∪{i}γ(ρ − 1)
ϕ + ρ − ϕρ

ϕ + ρ − ϕρ(R̄ij − C̄ij )

γ(ρ − 1)
ϕ + ρ − ϕρ(R̄ij − C̄ij )

(R̄i,LT − C̄i,LT )+
(R̄ij − C̄ij ) − µiLT λLT

Xj∈JF ∪{i}γ(ρ − 1)
ϕ + ρ − ϕρ#(R̄ij − C̄ij )



γ(ρ
−
1)
+(1 − τT H ) (1 − µiT H )λT H(R̄ij − C̄ij )
ϕ + ρ − ϕρj∈JF ∪{i}



X

γ(ρ−1)γ(ρ − 1)+(1 − τj ) 1 −R̄ij − C̄ijz ϕ+ρ−ϕρ − (1 − τi )Wi z/(Ai a).
ϕ + ρ − ϕρXj∈JF \{LT }And further simplifyingmaxz,λT H ,λLTγ(ρ − 1)(1 − τj )(R̄ij − C̄ij ) −(τi − τj )(R̄ij − C̄ij )ϕ + ρ − ϕρj∈JF ∪{i}j∈JF ∪{i}X  γ(ρ − 1) (R̄ij − C̄ij )+ (1 − µiLT )(τi − τLT )λLTϕ + ρ − ϕρj∈JF ∪{i}X  γ(ρ − 1) 
+ (1 − µiT H )(τi − τT H )λT H(R̄ij − C̄ij )ϕ + ρ − ϕρj∈JF ∪{i}X  γ(ρ − 1) γ(ρ−1)(R̄ij − C̄ij ) z ϕ+ρ−ϕρ − (1 − τi )Wi z/(Ai a).
− (1 − τi )Wi Ci (λT H , λLT )ϕ + ρ − ϕρX

Xj∈JF ∪{i}With the functional form assumption of C specified by equation (49), the optimal λ values can be solved
independent of z from the following two first-order conditions:
ϵ 1 −1ϵ(1 − τi ) Wi [(χi,T H C (λT H )) + (χi,LT C (λLT )) ] ϵϵ· χϵi,T H C (λT H )ϵ 1 −1(1 − τi ) Wi [(χi,T H C (λT H )) + (χi,LT C (λLT )) ] ϵ· C (λT H ) = (1 − µiT H ) (τi − τT H )ϵ−1· C (λLT ) = (1 − µiLT ) (τi − τLT ) .

· χϵi,LT C (λLT )

58

′

ϵ−1

′

The FOC for z isγ(ρ−1)γ(ρ − 1)
−1ϕ+ρ−ϕρ
z(1 − τi )Wi /(Ai a) =ϕ + ρ − ϕρX

(1 − τj )(R̄ij − C̄ij )j∈JF ∪{i}X−(τi − τj )j∈JF ∪{i}γ(ρ − 1)
ϕ + ρ − ϕρ(R̄ij − C̄ij )γ(ρ − 1)+(1 − µiLT )(τi − τLT )λLT(R̄ij − C̄ij )ϕ + ρ − ϕρj∈JF ∪{i}X  γ(ρ − 1) +(1 − µiT H )(τi − τT H )λT H(R̄ij − C̄ij )ϕ + ρ − ϕρj∈JF ∪{i}X  γ(ρ − 1) (R̄ij − C̄ij ) .
−(1 − τi )Wi Ci (λT H , λLT )ϕ + ρ − ϕρXj∈JF ∪{i}

We can solve the optimal z as:z=

ϕ + ρ − ϕργ(ρ − 1)

(1 − τi ) Wi /(Ai a)
DEN OM P S

ϕ+ρ−ϕρ
 γρ+ϕρ−γ−ϕ−ρ

,

(E.8)

where DEN OM P S is the sum of terms inside the big brackets above.

E.1.4

Market choice

Given Πi (a; JX , JF ), ∀JX , JF , firms decide where to export and where to operate foreign subsidiaries, according to the following problemdi (a) = max

JX ,JF Πi (a; JX , JF ) − Wi 

X

κjX −

j∈JX

X
j∈JF



κjF − κiT H 1(λT H > 0) .


(E.9)

where d denotes the optimal firm dividend. This is a combinatorial discrete choice problem as a firm’s
exporting and FDI choices are interdependent across regions. This problem is hard to solve since the numberof potential decision sets grows exponentially in the number of regions. We limit the number of regions in
the quantitative model to ease the computational burden. See Appendix F.4 for more discussions on the
combinatorial problem.

E.2

Firm’s problem under sales-based profit allocation

Under sales-based profit allocation, the scale and market choices can be solved in the same way as in Appendix
E.1. The only difference of the firm’s problem is the technology and profit shifting choices. As before, wesolve for the full problem where λLT > 0 and λT H > 0. It’s easier to state the firm’s problem as:dˆi (a; JX , JF ) =



max

z,JX ,JF ,λT L ,λT H Π̂i (a; JX , JF ) − Wi 

X

j∈JX

59

κjX −

X
j∈JF



κjF − κiT H 1(λT H > 0) .
Each firm, taking JX and JF as given, chooses z and λ to maximize(Π̂i (a; JX , JF ) =X

maxz,λT H ,λLT

πij (a, z) − τj TijP 1

)(E.10),

j∈{i}∪JX ∪JF

where
(
Π̂i (a; JX , JF ) =πiD (a, z; JX ) +maxz,λLT ,λT H−(λLT + λT H )ϑii (z) + (1 − λLT − λT H )X

ϑij (z)

j∈JF



Wi
− Wi Ci (λT H , λLT ) νi (z) + (µiLT λLT + µiT H λT H )νi (z) z − τi Ti
−
Ai a




X
F
+ πi,LT (a, z) + λLT
ϑij (z) − (1 − λLT )ϑiLT (z) − µiLT λLT νi (z) z − τLT TLT
+j∈JF ∪{i}\{LT }ϑij (z) − µiT H λT H νi (z) z − τT H TT H

X

λT H

j∈JF ∪{i}

X

+

 F

πij (a, z) − ϑij (z)z − τj Tj +X−τj TijP 1).

j∈JX \JFj∈JF \{LT }The term TijP 1 is the tax base in region j, which consists of local firms’ routine profit, a proportion of
local firms’ residual profits and reallocated residual profits to this region:
Rj
TijP 1 = πjr + (1 − θ) · πjR + θ · P
· ΠR
i
R
k k
Rj
·
= ιRj + (1 − θ) · (πj − ιRj ) + θ · P
k Rk
Rj= (1 − θ) · πj + θ · P
·
k Rk

X

X

(πk − ιRk )k∈{i}∪JX ∪JFπk .

k∈{i}∪JX ∪JF

Profit πj is the profit earned in region j and it is zero if the firm does not operate in the region. Revenue
earned in region j, denoted as Rj , include sales of both goods produced locally (by parent division or FDI)
and goods exported to the region. Formally:
Ri = pii (qii ) qii ,R j = pF
/ JX ,ij (qij ) qij , j ∈ JF , j ∈ XXX
Rj = pij qij qij , j ∈ JX , j ∈/ JF , X
F
X
X
Rj = pij (qij ) qij + pij qij qij , j ∈ JX ∩ JF ,Rj = 0,j∈/ {i} ∪ JF ∪ JX .

We can rewrite firm’s problem as:(Π̂i (a; JX , JF ) =maxz,λT H ,λLTXj∈{i}∪JX ∪JF

X
Rj(1 − τj (1 − θ)) πj (a, z; JX ) − τj θ · P·
πk (a, z; JX )
j Rj
k

60

!)
.

Further, substituting in πi and denoting λ = λT H + λLT , we getmaxz,λT H ,λLT

(1 − (1 − θ)τi )  1 − λγ(ρ − 1)
ϕ + ρ − ϕρ(R̄ii − C̄ii ) + (1 − λ)j∈JF−(1 − (1 − θ)τi ) (Wi Ci (λT H , λLT ) − (µiLT λLT + µiT H λT H ))"X  γ(ρ − 1) 
ϕ + ρ − ϕρXj∈JF ∪{i}(R̄ij − C̄ij )

γ(ρ − 1)
ϕ + ρ − ϕρ(R̄ij − C̄ij )

γ(ρ − 1)(R̄i,LT − C̄i,LT )+ϕ + ρ − ϕρ#XX  γ(ρ − 1) γ(ρ − 1)λLT
(R̄ij − C̄ij ) − µiLT λLT(R̄ij − C̄ij )ϕ + ρ − ϕρ
ϕ + ρ − ϕρj∈JF ∪ij∈JF ∪{i}\{LT }X  γ(ρ − 1) +(1 − (1 − θ)τT H ) (1 − µiT H )λT H(R̄ij − C̄ij )
ϕ
+
ρ
−
ϕρ
j



X

γ(ρ−1)γ(ρ − 1)+(1 − τj ) 1 −R̄ij − C̄ijz ϕ+ρ−ϕρ − (1 − (1 − θ)τi )Wi z/(Ai a)
ϕ + ρ − ϕρ+(1 − (1 − θ)τLT )j∈JF \{LT }X−j∈{i}∪JX ∪JF







1 − (1 − λLT )XRjτj θ · P·
πk (a, z; JX ).
j RjkHere we define R̃ij as the revenue shifter in region j for firms from region i, depending on region j isserved. These terms are defined analogously of R̄ij in equations (E.2) and (E.5):
ρ−1
ρ

1
ρ

R̃ii = Pi Qi Q̄ii

ϕ

 ρ−1

ρ ϕ+ρ−ρϕργ(ρ−1)Xρ−1ϕ(ρ − 1)Piρ Qi +Wi−ρ(Ai ) ϕ+ρ−ϕρ Niϕ+ρ−ϕρ ,Pjρ τj1−ρ Qj 


ρ

j∈JX

ϕ
 ρ−1


ρ ϕ+ρ−ρϕργ(ρ−1)
ρ−1 
1
X
ρ−1
ϕ(ρ − 1)Piρ Qi +R̃ij = Pj Qjρ Q̄ijρ
Wi−ρ
Pjρ τj1−ρ Qj (Ai ) ϕ+ρ−ϕρ Niϕ+ρ−ϕρ ,ρj ∈ JX , j ∈/ JF ,

j∈JX



1
ρ

R̃ij = Pj Qjϕ(ρ − 1)
(Pj /Wj )ρϕ(ρ−1)
 ϕ+ρ−ϕρ

ρ−1

ϕ

ρ−1

γ(ρ−1)

Qj ρ ϕ+ρ−ϕρ (Aj σij ) ϕ+ρ−ϕρ Njϕ+ρ−ϕρ ,j ∈ JF , j ∈/ JX , ϕ(ρ−1)γ(ρ−1)ϕ1
ρ−1
ϕ(ρ − 1) ϕ+ρ−ϕρ ρ−1R̃ij = Pj Qjρ (Pj /Wj )Qj ρ ϕ+ρ−ϕρ (Aj σij ) ϕ+ρ−ϕρ Njϕ+ρ−ϕρ
ρ
ϕ

 ρ−1

ρ

 ρ ϕ+ρ−ρϕγ(ρ−1)
ρ−1 
1
X
ρ−1
ϕ(ρ
−
1)
Piρ Qi ++ Pj Qjρ Q̄ijρWi−ρ(Ai ) ϕ+ρ−ϕρ Niϕ+ρ−ϕρ ,Pjρ τj1−ρ Qj ρj ∈ JX ∩ JF ,j∈JXR̃ij = 0,j∈/ {i} ∪ JF ∪ JX .
R

R̃

j

j

With these definitions, it’s straightforward to show that the revenue share ∑ jRj = ∑ ijR̃ . We can61

ijfurther simplify the problem to


(
max

z,λT H ,λLT

(1 − (1 − θ)τi )  1 − λγ(ρ − 1)
ϕ + ρ − ϕρ(R̄ii − C̄ii ) + (1 − λ)j∈JF−(1 − (1 − θ)τi ) (Wi Ci (λT H , λLT ) − (µiLT λLT + µiT H λT H ))"X  γ(ρ − 1) 
ϕ + ρ − ϕρXj∈JF ∪{i}(R̄ij − C̄ij )

γ(ρ − 1)
ϕ + ρ − ϕρ(R̄ij − C̄ij )

γ(ρ − 1)(R̄i,LT − C̄i,LT )+ϕ + ρ − ϕρ#XX  γ(ρ − 1) γ(ρ − 1)λLT
(R̄ij − C̄ij ) − µiLT λLT(R̄ij − C̄ij )ϕ + ρ − ϕρ
ϕ + ρ − ϕρj∈JF ∪{i}\{LT }j∈JF ∪{i}X  γ(ρ − 1) +(1 − (1 − θ)τT H ) (1 − µiT H )λT H(R̄ij − C̄ij )
ϕ
+
ρ
−
ϕρ
j


)
X

γ(ρ−1)γ(ρ − 1)+(1 − τj ) 1 −R̄ij − C̄ijz ϕ+ρ−ϕρ − (1 − (1 − θ)τi )Wi z/(Ai a)
ϕ + ρ − ϕρj∈JF \{LT }XX γ(ρ−1)R̃ij−
τj θ · P·R̄ik − C̄ik z ϕ+ρ−ϕρ − Wi z/(Ai a)−j R̃ijkj∈{i}∪JX ∪JFX  γ(ρ − 1) γ(ρ−1)(R̄ij − C̄ij )z ϕ+ρ−ϕρ .
Wi Ci (λT H , λLT ) ·ϕ + ρ − ϕρj+(1 − (1 − θ)τLT )







1 − (1 − λLT )As before, the shift shares λT H and λLT can be solved from the first-order conditions:
ϵ 1 −1ϵ[(χi,T H C (λT H )) + (χi,LT C (λLT )) ] ϵ· χϵi,T H C (λT H )ϵ−1′· C (λT H ) =1 (1 − µiT H )(1 − θ) (τi − τT H )Wi 1 − (1 − θ)τi − θ P τk · ∑R̃ikkϵϵ[(χi,T H C (λT H )) + (χi,LT C (λLT )) ]1
ϵ −1

j R̃ij1 (1 − µiLT )(1 − θ) (τi − τLT )ϵ−1· χϵi,LT C (λLT )· C (λLT ) =Wi 1 − (1 − θ)τi − θ P τk · ∑R̃ik′k

The optimal z is given byϕ+ρ−ϕρ γρ+ϕρ−γ−ϕ−ρPR̃ ϕ + ρ − ϕρ 
1 − (1 − θ)τi − θ j τj ∑ ijR̃Wi /(Ai a) 
ik
k


z=
,
 γ(ρ − 1)
DEN OM P 1

62

j R̃ijwhere DEN OM P 1 is defined as(
X(1 − (1 − θ)τj )(R̄ij − C̄ij ) −γ(ρ − 1)(1 − θ)(τi − τj )(R̄ij − C̄ij )ϕ + ρ − ϕρj∈JF ∪{i}j∈JF ∪{i}X  γ(ρ − 1) 
+ (1 − θ) [(1 − µiLT )(τi − τLT )λLT + (1 − µiT H )(τi − τT H )λT H ](R̄ij − C̄ij )ϕ + ρ − ϕρj∈JF ∪{i}X  γ(ρ − 1) 
− (1 − (1 − θ)τi )Wi Ci (λT H , λLT ) ·(R̄ij − C̄ij )ϕ + ρ − ϕρX−j∈{i}∪JX ∪JF

F

R̃ij
·
τj θ · Pk R̃ikX

j∈JF ∪{i}

X

R̄ik − C̄ik − Wi Ci (λT H , λLT )k∈JF ∪{i}

X
j∈JF ∪{i}γ(ρ − 1)
ϕ + ρ − ϕρ)(R̄ij − C̄ij )Proofs of Theoretical Results

This Appendix contains the proofs of the lemmas and propositions from the main body of the paper.

F.1 Optimal Profit-Shifting and Effect on Intangible Investment
Proof of Lemma 2. Let νi ≡P

j∈JF ∪{i} ϑij . The MNE’s profit maximization problem can be written as
max(1 − τi ) pii Ai a (Ni zi ) liγ − Wiϕz,λ,{lj }Ij=1



z
Ai a




+ z µλνi +X(1 − λ) ϑij − λϑii − Wi Ci (λ) νi j∈JF+ (1 − τT H ) z (λνi − µλνi )


X
ϕ
+
(1 − τj ) pij Aj (Nj z) ljγ − Wj lj − ϑij z

(F.1)

j∈JF

where we subsumed the subscripts of µ and λ. The FOCs are then:ϕli : 0 = γpii Ai (Ni z) liγ−1 − Wi
z:0=

X



(1 − τj ) ϕNj pij Aj (Nj z)

j̸=T H+ (1 − τT H ) (λνi − µλνi ) −
λ : 0 = (1 − τi ) z µνi −ϕ−1 γ
lj + (1 − τi ) µλνi +X(1 − λ) ϑij − λϑii − Wi Ci (λ) νi  +j∈JF(1 − τj ) ϑij

j∈JF

X

X

(F.2)


(F.3)


ϑij − ϑii − Wi Ci′ (λ) νi j∈JF

+ (1 − τT H ) z (νi − µνi ) .
From the FOC wrt to λ, we can get
C ′ (λ) =(1 − µ) (τi − τT H )Wi (1 − τi )

63

(F.4)

.

and under our assumption of the profit-shifting cost function by equation (32), this can be written as(1 − µ) (τi − τT H )λ = 1 − exp −Wi (1 − τi )

.

Now towards proving the lemma, we have



∂λ
(1 − µ) (τi − τT H )τi − τT H= − exp −<0∂µWi (1 − τi )Wi (1 − τi )



∂λ
(1 − µ) (τi − τT H )1−µ= − exp −<0∂τT H
Wi (1 − τi )Wi (1 − τi )and therefore the elasticities are(1 − µ) (τi − τT H ) = − exp −(1−µ)(τ−τ)
iTH∂µ 1 − exp −Wi (1 − τi )Wi (1−τi )


µ
λ−1
log(1 − λ)
<0
=−
λ
1−µ

∂λ
ελµ =

µ



τi − τT H
Wi (1 − τi )

1 − expµi −τT H )− (1−µ)(τWi (1−τi )






∂λ
τ∗
(1 − µ) (τi − τT H )
1−µ
τ
 i
 TH
 = − exp −∂τT H 1 − exp − (1−µ)(τi −τT H )Wi (1 − τi )Wi (1 − τi ) 1 − exp − (1−µ)(τi −τT H )Wi (1−τi )Wi (1−τi )


λ−1
τT H
=−
log(1 − λ)<0λτ i − τT H

ελτT H =which proves 1. and 2.
Proof of Proposition 1. To prove this proposition, we start by deriving optimal z N S of the MNE in the
no-shifting case, and optimal z in the profit-shifting case. Inspecting the FOC for z, equation (F.3), we canget in the no-shifting case (λ = 0):


X

0=

(1 − τj ) Λj z

ϕ+γ−1
1−γ

− (1 − τi ) j∈JF ∪{i}

Wi
+
Ai a

X


ϑij  −j∈JF

X

(1 − τj ) ϑij .

j∈JF

Note we have


ϕ−1 γ
ϑij (z) = ϕpij Nj Aj (Nj z)
lj

γ 
! 1−γ
ϕ
γp
A
(N
z)
ij
j
j
ϕ−1

= ϕpij Nj Aj (Nj z)
Wj
= ϕγ
γ

1

γ
1−γ

1
1−γ

X
j∈JF ∪{i}

pij Aj1where we define Λj ≡ ϕγ 1−γ pij1−γ Aj1−γ
0=

1
1−γ



ϕ+γ−1

1
Wj

γ
 1−γ

1
Wj

γ
 1−γ

ϕ

ϕ+γ−1

ϕ+γ−1

Nj1−γ (z) 1−γ = Λj (z) 1−γ ,ϕ

Nj1−γ . Then, we can rewrite the FOC as(1 − τj ) Λj z 1−γ − (1 − τi )

Wi
+
Ai a

64

X
j∈JF ∪{i}ϕ+γ−1

Λj z 1−γ ((1 − τi ) − (1 − τj )) .

We can solve for the optimal z as

z

NS

=

Ai a

P

j∈JF ∪{i} Λj1−γ! 1−ϕ−γWi.

Now turn into the profit-shifting case, the FOC of z can be rewritten as
X

0=

ϕ+γ−1

(1 − τj ) Λj z 1−γ − (1 − τi )j∈JF ∪{i}XWi+ λνi (1 − µ) (τi − τT H ) +ϑij (τj − τi ) − (1 − τi ) Wi Ci (λ) νi .
Ai a
j∈JF

Following the same steps as before, we can obtain,

z=

Ai a

P

1−γ

  1−ϕ−γλ(1−µ)(τi −τT H )
Λ
1
−
W
C
(λ)
+
i i
j∈JF ∪{i} j(1−τi )
,Wi

hence we have


z=z

NS

λ (1 − µ) (τi − τT H )1 − Wi Ci (λ) +(1 − τi )1−γ
 1−ϕ−γ.

Now, to show 1, that is z > z N S , we would need to prove that
1 − Wi Ci (λ) +which can be rewritten as
C (λ) <λ (1 − µ) (τi − τT H )>1(1 − τi )λ (1 − µ) (τi − τT H ).
Wi (1 − τi )(F.5)

We have already shown that
C ′ (λ) =(1 − µ) (τi − τT H ).
Wi (1 − τi )Thus, to prove (F.5), it suﬀices to show that
C (λ) < λC ′ (λ) .
Let G (λ) = C (λ) − λC ′ (λ), we know that G (0) = 0, andG′ (λ) = C ′ (λ) − C ′ (λ) − λC ′′ (λ) = −λC ′′ (λ) < 0, ∀λ ∈ (0, 1]
hence
G (λ) = C (λ) − λC ′ (λ) < 0, ∀λ ∈ (0, 1].
andC (λ) < λC ′ (λ) =λ (1 − µ) (τi − τT H )Wi (1 − τi )which proves (F.5) and hence establishes z > z N S . To show 2. and 3. we can derive the elasticity with65

respect to the tax rate asεzτT H =∂z τT H
∂τT H z



−1 
1−γ
λ (1 − µ) (τi − τT H )τT H (1 − µ)=1 − Wi Ci (λ) +−λ1−ϕ−γ(1 − τi )1 − τi


1−γ
τT H
1


=−
1−Wi Ci (λ)
1 − ϕ − γ τi − τ T H
1+′
λWi C (λ)

Now note that for this to be negative we have to show that1
i Ci (λ)
1 + 1−W
λWi C ′ (λ)

 >0

1 − Wi Ci (λ)> −1
λWi C ′ (λ)
Wi Ci (λ) − 1<1
λWi C ′ (λ)
what we have shown already is
C (λ) < λC ′ (λ)

implying

Wi Ci (λ) − 1
λWi C ′ (λ) − 1
1
<
=1−
<1
′
λWi C (λ)λWi C ′ (λ)λWi C ′ (λ)

where the last inequality comes from the fact that



1
= −∞
λ→0
λWi C ′ (λ)
1
lim 1 −
=1λ→1
λWi C ′ (λ)
lim

1−

1
and the fact that the function 1 − λWi (log(1−λ))is strictly increasing for λ ∈ [0, 1). This proves 2. Now toprove 3., we can derive the elasticity with respect to µ as

εzµ =

∂z µ
∂µ z


−1 

1−γ
λ (1 − µ) (τi − τT H )µ (τi − τT H )1 − Wi Ci (λ) +−λ1−ϕ−γ(1 − τi )1 − τi


1−γ
µ
1

.
=−
1−ϕ−γ 1−µ
1 + 1−Wi C′i (λ)=λWi C (λ)

By the same argument as above we conclude that εzτT H < 0.

66

F.2 Effects of Sales-Based Profit Allocation (OECD/G20 Pillar 1)
We first establish the following lemma characterizing how λ̂ depends on the parameters of the profit allocation
rule and how it differs from the share λ that is transferred under the existing tax regime.
Proof of Lemma 3. We start with the tax liability faced by a subsidiary in region j under pillar 1,
Rj· ΠR
Tj = πjr + (1 − θ) · πjR + θ · P
k Rk
Rj= ιRj + (1 − θ) · (πj − ιRj ) + θ · P
·
k Rk
Rj
= (1 − θ) · πj + θ · P
·
k Rk

X

X

(πk − ιRk )k∈{i}∪JFπk .

k∈{i}∪JF

We can see that the profitability margin parameter ι does not affect into Tj , so it will not affect any
firm decision under pillar 2. Plugging the tax liabilities in to the profit maximization problem of the MNE
specified by equation (51), we have


Wi z
ϕ
(1 − τi (1 − θ)) pii Ai (Ni z) ℓγi − Wi ℓi −Ai az,λ,{ℓi }Ii=1
XX+ z µλϑk (z) − λϑii (z) + (1 − λ)ϑk (z) − Wi C(λ)
maxk∈JF ∪{i}k∈JF"+ (1 − τT H (1 − θ)) z λ+Xϑk (z) − µλ

k∈JF

!
ϑk (z)

k∈JF ∪{i}#ϑk (z)

k∈JF

 


ϕ
(1 − τk (1 − θ)) pik Ak (Nk z) ℓγk − wk ℓk − ϑk (z) z

X
k∈JF

−θ

X

X

X
j∈JF ∪{i}τj · Ppij yijk∈JF ∪{i} pik yik



X

·



ϕ



pik Ak (Nk z) ℓγk − wk ℓkk∈JF ∪{i}

Wi z− Wi C(λ)−
Ai aXk∈JF ∪{i}

We can derive the following from the FOC with respect to λ:(1 − µ) (1 − θ) (τi − τT H )λ̂ = 1 − exp −Wi (1 − ((1 − θ) τi + θb
τ ))

(F.6)

where
τb =

X

τj · Pj∈JF ∪{i}=Xτj · Pj∈JF ∪{i}

Rjk∈JF ∪{i} Rk

pij qijk∈JF ∪{i} pik qik

Towards proving 1., with equation (34) we have that the following sequence of inequalities holds for any

67ϑk (z) .

0 < θ < 1:

(1 − µ) (1 − θ) (τi − τT H )(1 − µ) (τi − τT H )> 1 − exp −1 − exp −Wi (1 − τi )Wi (1 − ((1 − θ) τi + θb
τ ))
1
1−θ
>
1 − τi1 − (1 − θ) τi − θbτX
pij yij< 1.
τj · Pk∈JF ∪{i} pik yikj

The last inequality holds, since τk < 1 ∀k and all sales shares are by construction less than one. This
proves that λ̂ < λ. Now, towards showing 2, inspect how θ affects λ̂∂ λ̂(1 − µ)(1 − θ) (τi − τT H )1 − τ̂
= − exp −· (1 − µ) (τi − τT H )2 <0∂θWi (1 − ((1 − θ)τi + θb
τ ))[(1 − ((1 − θ)τi + θb
τ ))]and the elasticity is given by(1 − µ)(1 − θ) (τi − τT H )1 − τ̂
θελ̂θ = − exp −· (1 − µ) (τi − τT H )2
Wi (1 − ((1 − θ)τi + θb
τ ))[(1 − ((1 − θ)τi + θbτ ))] λ̂θ
λ̂ − 11 − τ̂
< 0,=−· log 1 − λ̂ ·1 − ((1 − θ)τi + θbτ) 1 − θλ̂where we used the FOC of the profit function with respect to λ̂. Hence, we have established 2. Now, inspecthow τT H affects λ̂ to prove 3. First, compute the relevant partial derivative∂ λ̂(1 − µ)(1 − θ)
(1 − µ)(1 − θ) (τi − τT H )·< 0,= − exp −∂τT H
Wi (1 − ((1 − θ)τi + θb
τ ))Wi (1 − ((1 − θ)τi + θb
τ ))and hence the elasticity(1 − µ)(1 − θ) (τi − τT H )1
τT H(1 − µ)(1 − θ) (τi − τT H )·−Wi (1 − ((1 − θ)τi + θb
τ ))Wi (1 − ((1 − θ)τi + θbτ )) τi − τT H λ̂ τλ̂ − 1TH· log 1 − λ̂< 0.
=−τi − τT Hλ̂ελ̂τT H = − exp

Proof of Proposition 2. Following the same procedure as in the first part of the proof for Proposition 1,
we can first show thatẑ = zNS1−γ  λ (1 − θ) (1 − µ) (τ − τ )  1−ϕ−γiTH
1 − Wi C λ̂ +.
1 − ((1 − θ) τi + θbτ)With the optimal allocation of intangible capital, the proof for 1. relies on the following sequence of iff

68inequalities:ẑ < z (1 − µ) (τi − τT H )(1 − τi ) (1 − θ)λ (1 − µ) (τi − τT H )1 − Wi C λ̂ + λ̂
< 1 − Wi C (λ) +1 − τi1 − ((1 − θ) τi + θbτ)
1 − τi(1 − µ) (1 − θ) (τi − τT H )(1 − µ) (τi − τT H )λ− λ̂> C (λ) − C λ̂ ,Wi (1 − τi )Wi (1 − ((1 − θ) τi + θb
τ ))To simplify notation, let’s denote:(1 − µ) (1 − θ) (τi − τT H ),Wi (1 − ((1 − θ) τi + θb
τ ))(1 − µ) (τi − τT H ).
A=
Wi (1 − τi )Â =Plugging equations (42) and equation (32) to the inequality we want to show, we have








1 − exp (−A) + exp (−A) (−A) − 1 + exp −Â − exp −Â −Â < (1 − exp (−A)) A − 1 − exp −Â Â

Â + exp −Â < A + exp (−A) .
We have shown that 0 < Â < A, ∀θ > 0, thus proving the inequality above amounts to proving thatfunction f (x) = x + exp (−x) is monotonically increasing when x > 0. Taking its derivative we get:f ′ (x) = 1 − exp (−x) > 0, x > 0.
To prove 2., we start with the partial derivative with respect to θ:


1−γ
1−ϕ−γ



!−1 (


 
∂ λ̂ (1 − θ) (1 − µ) (τi − τT H )− Wi C ′ λ̂ +∂θ1 − ((1 − θ) τi + θbτ))−λ̂ (1 − µ) (τi − τT H ) (1 − ((1 − θ) τi + θbτ )) − (τi − τ̂ ) (1 − θ) λ̂ (1 − µ) (τi − τT H ),2[(1 − ((1 − θ) τi + θb
τ ))]

∂ ẑ
=
∂θ

ẑ

  (1 − θ) λ̂ (1 − µ) (τ − τ )iTH
1 − Wi C λ̂ +1 − ((1 − θ) τi + θbτ)·and notice that the FOC w.r.t. λ̂ is given by  (1 − θ) (1 − µ) (τ − τ )i
THWi C ′ λ̂ =.
(1 − ((1 − θ) τi + θb
τ ))Also, we can show that−λ̂ (1 − µ) (τi − τT H ) (1 − τ̂i (θ)) − (τi − τ̂ ) (1 − θ) λ̂ (1 − µ) (τi − τT H )[(1 − ((1 − θ) τi + θbτ ))]=λ̂ (1 − µ) (τi − τT H ) (τ̂ − 1)[(1 − ((1 − θ) τi + θbτ ))]Thus we have established that

2

< 0.

∂ ẑ
< 0.
∂θ

69

2

And the elasticity is  (1 − θ) λ̂ (1 − µ) (τ − τ )iTHẑ 1 − Wi C λ̂ +1 − ((1 − θ) τi + θb
τ)

!


1
−
γ
λ̂
1

 < 0.
= ελ̂θ
1−ϕ−γC(λ̂)(1 − λ̂)
1 + 1−Wi C(λ̂)εẑθ =

1−γ
1−ϕ−γ

!−1 "

#
λ̂ (1 − µ) (τi − τT H ) (τ̂ − 1) θ2zb
[1 − ((1 − θ) τi + θb
τ )]Wi λ̂C ′ (λ̂)

Now, to show 3. consider the partial derivative of ẑ with respect to τT H ,!
  (1 − θ) λ̂ (1 − µ) (τ − τ ) −1
1−γiTHẑ 1 − Wi C λ̂ +·1−ϕ−γ[1 − ((1 − θ) τi + θb
τ )]
#

 
(1 − µ) (τi − τT H ) (1 − θ)
(1
−
θ)
λ̂
(1
−
µ)
∂ λ̂
− Wi C ′ λ̂
−
.
∂τT H
1 − ((1 − θ) τi + θbτ)
1 − ((1 − θ) τi + θb
τ)

∂ ẑ
=
∂τT H
"



Plugging in the optimality condition of λ̂, the elasticity becomesεẑτT H =−τT Hτi − τT H



1−γ
1−ϕ−γ




1
1−Wi C (λ̂)
1 + W λ̂C ′ λ̂
( )
i

.

F.3 Analytical Results when MNEs Take ϑ′ik (z) into AccountHere, we assume that MNEs internalize the effect of changing z on the licensing fee ϑik (z) and solve for
optimal z under different scenarios. We then prove Proposition 2 under this assumption.33 As before, westart from the optimal z.
Proof of Proposition 2 under alternative assumption. We can first derive the allocations of intangible
capital are as follows if firms internalize the effect of changing z on the licensing fee ϑk (z) when deciding
intangible capital z̃:Pz̃ N S =z̃ =1−γ! 1−ϕ−γ(1 − τ̂i (θ)) Wi /(Ai a)
 P
ϕ
− 1−γ
C λ̂
k Λk

(F.7)

,

Wi /(Ai a)
P

+

ϕ P
k (1 − τ̂k (θ)) Λk − 1−γ
k (1 − θ) (τi − τk ) ΛkP
ϕ Pϕk (1 − τ̂k (θ)) Λk − 1−γ
k (1 − θ) (τi − τk ) Λk + λ̂ 1−γ (1 − θ) (τi − τT H ) (1 − µ)
k Λk

1−γ
! 1−ϕ−γ(1 − τ̂i (θ)) Wi /(Ai a)(F.8)

where with a slight abuse of notation, we denote in this sectionτ̂i (θ) = (1 − θ) τj + θXτj · Pj∈JF ∪{i}
33

Proposition 1 can be proved similarly by setting θ = ι = 0.

70

pij qijk∈JF ∪{i} pik qik.

We start from proving 1 from deriving a set of iff inequalities:
"
#
P

 P
  λ̂ (1 − θ) (τ − τ ) (1 − µ)ϕ + γ − 1 k (1 − θ) (τi − τk ) Λk
ϕ+γ−1
i
TH
k Λk
−
− 1+
Wi C λ̂ −Wi /(Ai a)
1−γ(1 − τ̂i (θ)) Wi /(Ai a)
1−γ
Wi /(Ai a)(1 − τ̂i (θ))
P
P

 P


ϕ+γ−1
ϕ+γ−1
λ (τi − τT H ) (1 − µ)k Λkk (τi − τk ) Λk
k Λk
<
−
− 1+
Wi C (λ) −Wi /(Ai a)
1 − γ (1 − τi ) Wi /(Ai a)
1−γ
Wi /(Ai a)(1 − τi )
P
P


(τ
−
τ
)
Λ
Λ
(τ
−
)
(1
µ)
1−ϕ−γ
ϕ
λ
τ
−
i
k
k
i
TH
k
k k
+
Wi C (λ) −−1 − γ (1 − τi ) Wi /(Ai a) 1 − γ Wi /(Ai a)(1 − τi )"#PP  λ̂ (1 − θ) (τ − τ ) (1 − µ)
1 − ϕ − γ k (1 − θ) (τi − τk ) Λk
ϕ
i
TH
k Λk
<−
+
Wi C λ̂ −.
1−γ(1 − τ̂i (θ)) Wi /(Ai a)
1 − γ Wi /(Ai a)(1 − τ̂i (θ))
P

k Λk

 
i −τT H )(1−µ)
T H )(1−µ)
We have proven before that Wi C (λ) − λ(τi −τ
<WC
λ̂ − λ̂(1−θ)(τ. It suﬀices toi(1−τi )(1−τ̂i (θ))
prove that−PP
1 − ϕ − γ k (1 − θ) (τi − τk ) Λk
1−ϕ−γk (τi − τk ) Λk<−,
1 − γ (1 − τi ) Wi /(Ai a)
1−γ(1 − τ̂i (θ)) Wi /(Ai a)

which simplifies to 1 >

P

k τk

ϕ Ai a1−γdz̃=(z̃) 1−γ
dθ
1−ϕ−γ
Wi

∑Λk . Thus, we have proven 1. We now prove 2:i Λi!
∑Λk − 1Λii
2
(1 − τ̂i (θ))

P

k τk

1−ϕ−γ Xϕλ (τi − τT H ) (1 − µ) +(τi − τk ) Λk
1−γ
1−γ

!
.

k

We have shown that
X
k

Λk
τk P
− 1 < 0.
i ΛiThe other terms are all positive, thus we have proven 2. Now to prove 3 we can show that(P
  ∂ λ̂ X
ϕ
ϕ
k Λk
·
Wi C ′ λ̂
Λk +
1−γ
∂τT H
1 − γ (1 − τ̂i (θ))2
k
!
#


X
∂ λ̂
ΛT H
(1 − µ) (τi − τT H ) (1 − θ)Λk − (1 − θ) λ̂ (1 − µ) (1 − τ̂i (θ)) + θ P(1 − θ) λ̂ (1 − µ) (τi − τT H )
∂τT H
k Λk
k
)
1−ϕ−γ
1 − τi(1 − θ) ΛT H
−
2 .
1−γ
(1 − τ̂i (θ))

∂ z̃
=
∂τT H
"



1−γ
1−ϕ−γ



(z̃)

ϕ
1−γ

Ai a
Wi

−

We have shown in previous proof that the sum of first two terms in the big bracket is negative. It is
obvious that the last term is also negative. Hence we have proven 3, that is ∂τ∂Tz̃H < 0.

F.4 Discussions on the Combinatorial Choice Problem
Arkolakis et al. (2023) (hereinafter AES) develop a computational method, namely a squeezing procedure, tosolve combinatorial problems of location decisions for MNEs. As discussed in Theorem 1 of AES, applying
the squeezing procedure requires the return function to obey the single crossing in differences in choices(SCD-C) property, from either above or below. In what follows, we discuss whether the squeezing procedure
is suitable for our model.

71In our model, we assume that each foreign subsidiary produces a different variety than the headquarter,
so the location choice problem in productive locations satisfies positive complementarities. However, In
our model, the role of T H and LT as profit-shifting destinations may break this complementarity, if it ismarginally more costly to shift profits to multiple regions. We proceed with the following two arguments,
focusing on how the decisions of intangible investment and profit shifting affects solving the combinatorial
problem of JF :1. Fixing intangible capital z, the profit function of the firm does not satisfy SCD-C if the profit shifting
2
C(λT H ,λLT )> 0.
cost function C (λT H , λLT ) has positive cross-derivatives, that is ∂ ∂λT H ∂λLT
2. The interdependence of intangible capital z and the set of foreign subsidiary locations JF makes thefirm’s problem hard to solve with many countries.

F.4.1 Cross-derivative of profit-shifting cost
In this section, we discuss how the cross-derivative of the profit-shifting function affects the SCD-C propertyof the profit function. To isolate the issue of choosing JF , we hereby assume that the intangible capital z
and the set of exporting destinations JX for each firm are fixed. We start by defining the marginal value
from adding a subsidiary location, as in Definition 1 of AES.
Definition 1 Marginal value from adding location l is defined asDl Πi (a; JF ) ≡ Πi (a; JF ∪ {l}) − Πi (a; JF \{l})where Πi (a; JF ) is the optimal after-tax dividend of a country i firm with productivity a and FDI destinations
JF .
In line with Definition 4 in AES we define the SCD-C properties as follows.
Definition 2 The return function obeys SCD-C from above if for all l ∈ I and sets of locations JF1 ⊂ JF2 ⊆ I,
Dl Πi a; JF2 ≥ 0 ⇒ Dl Πi a; JF1 ≥ 0,
Analogously, the return function obeys SCD-C from below if for all l ∈ I and sets of locations JF1 ⊂ JF2 ⊆ I,
Dl Πi a; JF1 ≥ 0 ⇒ Dl Πi a; JF2 ≥ 0.
We first show that the profit function, Πi (a; JF ), does not satisfy SCD-C from above.
Lemma 4 (SCD-C from above) The profit function does not satisfy SCD-C from above.
Proof. Suppose a firm HQed in N A maximizes its profit by setting up subsidiaries in EU , RW and T H.
Let JF1 = ∅ and JF2 = {EU, RW }. It is straightforward to show that the profit function does not satisfy
SCD-C from above that requires

DT H Πi a; JF2 ≥ 072

which can be written asX(τN A − τT H ) λT HX

ϑij (z)z − (1 − τN A ) WN A CN A (λT H , 0)

2 ∪{N A}j∈JF

X

ϑij (z)z ≥ κN A,T H,F

2 ∪{N A}j∈JF

ϑij (z)z · [(τN A − τT H ) λT H − (1 − τN A ) WN A CN A (λT H , 0)] ≥ κN A,T H,F .

2 ∪{N A}j∈JF
We now show it does not imply that for JF1 = ∅, we have DT H JF1 ; a ≥ 0. To satisfy this inequality, weneedX(τN A − τT H ) λT HXXϑij (z)z − (1 − τN A ) WN A CN A (λT H , 0)j∈{N A}ϑij (z)z ≥ κN A,T H,Fj∈{N A}ϑij (z)z · [(τN A − τT H ) λT H − (1 − τN A ) WN A CN A (λT H , 0)] ≥ κN A,T H,F ,j∈{N A}

which is not necessarily true sincePj∈{N A} ϑij (z)z <P

2 ∪{N A} ϑij (z)z.
j∈JFThe relevant case for us is when the MNE’s problem satisfies SCD-C from below. It is straightforward
to show that this property is satisfied for productive regions, excluding LT . That is for JF1 ⊂ JF2 ⊆ IDl Πi a; JF1 ≥ 0 ⇒ Dl Πi a; JF2 ≥ 0
where l ∈ {N A, EU, RW }. This is because Dl Πi (a; JF ) = (1 − τl ) πilF (a, z) − ϑil (z)z does not vary by JF
conditional on z. Hence, Dl Πi a; JF1 = Dl Πi a; JF2 , ∀JF1 , JF2 . Now, we want to discuss whether the SCD-C
from below property is satisfied for the profit shifting destinations, {LT, T H}. In other words, we want toinvestigate whether for l ∈ {LT, T H} and JF1 ⊂ JF2 ⊆ I, Dl Πi a; JF1 ≥ 0 implies Dl Πi a; JF2 ≥ 0.
Ci (λT H ,λLT )Lemma 5 If the profit-shifting cost function satisfies Assumption 1 and ∂ ∂λ
> 0, then the profit
T H ∂λLTfunction does not satisfy SCD-C from below for the profit-shifting destinations. That is, for l ∈ {LT, T H}

and JF1 ⊂ JF2 ⊆ I, Dl Πi a; JF1 ≥ 0 ⇏ Dl Πi a; JF2 ≥ 0.
2

Proof. Suppose JF1 ∩ {LT, T H} = ∅, JF2 ∩ {LT, T H} = {m} ̸= ∅, l ∈/ JF2 , and l ∈ {LT, T H}, then
Dl Πi a; JF1 ≥ 0 impliesDl Πi a; JF1 =X
ϑij (z)z · (1 − µil ) (τi − τl ) λ0l − (1 − τi ) Wi Ci,l λ0l ≥ κi,l,F(F.9)

1 ∪{i}
j∈JF

where λ0l represents the optimal profit shifting share when the MNE operates in JF1 ∪{i}∪{l}, and Ci,l (λl ) :=Ci (λl , λ−l = 0). Then, Dl Πi a; JF2 ≥ 0 requiresX
Dl Πi a; JF2 =



 


ϑij (z)z · (1 − µiT H ) (τN A − τT H ) λ1T H + (τN A − τLT ) λ1LT − (1 − τi ) Wi Ci λ1T H , λ1LT2 ∪{i}
j∈JF

−

X



ϑij (z)z · (τi − τm ) λ0m − (1 − τi ) Wi Ci,m λ0m ≥ κi,l,F(F.10)

2 ∪{i}
j∈JF

where λ1l represents the optimal profit shifting share to l when the MNE operates in JF1 ∪ {i} ∪ {LT, T H}.

73

The profit function thus does not necessarily satisfy SCD-C from below ifDl Πi a; JF2 < Dl Πi a; JF1
For simplicity, we assumeXX

ϑij (z)z =2 ∪{i}
j∈JF(F.11)

ϑij (z)z

1 ∪{i}
j∈JF

which is true when l = T H or when l = LT and LLT → 0. The inequality can then be written as(1 − µiT H )


i 


− (1 − τi ) Wi Ci λ1T H , λ1LT <τN A − τT H λ1T H + (τN A − τLT ) λ1LT

 

0
(1 − µim ) (τi − τm ) λm
− (1 − τi ) Wi Ci,m λ0m + (1 − µil ) (τi − τl ) λ0l − (1 − τi ) Wi Ci,l λ0l ,

h

and


 

(1 − µiT H ) (τi − τT H ) λ1T H − (1 − τi ) Wi Ci λ1T H , 0 + (1 − µiLT ) (τi − τLT ) λ1LT − (1 − τi ) Wi Ci λ1LT , 0 <

 

(1 − µiT H ) (τi − τT H ) λ0T H − (1 − τi ) Wi Ci λ0T H , 0 + (1 − µiLT ) (τi − τLT ) λ0LT − (1 − τi ) Wi Ci 0, λ0LT .
One can show that Dl Πi a; JF2 < Dl Πi a; JF1 if the following two conditions are both satisfied:
1. λ1l < λ0l , l ∈ {T H, LT },2. fl (λ) = (τi − τl ) λ − (1 − τi ) Wi Ci,l (λ) increases in λ ∈ [0, λ0l ].

C(λT H ,λLT )We can show that both two conditions are met if ∂ ∂λ
> 0. For 1, we know from the FOC of theT H ∂λLTfirm’s problem that2

∂Ci λT H , λ1LT
∂λT H


=

1 (1 − µiT H )(τi − τT H )Wi
1 − τiand∂Ci (λT H , 0)
1 (1 − µiT H )(τi − τT H )
=
∂λT H
Wi
1 − τi
Then to show λ1T H < λ0T H � it suﬀices to show that
∂Ci λT H , λ1LT
∂λT H
which is true when>∂Ci (λT H , 0)
> 0, ∀ λ1LT > 0∂λT H∂ 2 Ci (λT H , λLT )> 0, ∀λT H , λLT > 0.
∂λT H ∂λLT

Ci (λT H ,λLT )We can show in the same way that λ1LT < λ0LT , when ∂ ∂λ
> 0. For 2, we need to show thatT H ∂λLT2′

fl (λ) = (τi − τl ) − (1 − τi ) Wi

∂Ci,l (λ)≥ 0, λ ≤ λ0l .
∂λFrom the FOC of the firm’s problem, we know that
(τi − τl ) − (1 − τi ) Wi

∂Ci,l (λ)
= 0.
∂λ
λ=λ0
l

74

By Assumption 1,′∂ 2 Ci,l (λ)> 0. Therefore, we have fl (λ) ≥ 0,∂λ2

λ ≤ λ0l .

F.4.2 Interdependence of intangible capital and subsidiary locations
One key result of the model is that the optimal choice of intangible capital is a function of the set of foreignsubsidiaries. Suppose the profit function satisfies SCD-C from below. Then we can utilize the squeezing
procedure to solve for the optimal JF with a fixed amount of z, and obtain the corresponding firm profit.
However, in order to fully solve the firm’s problem, we would need to solve for location choice problem fordifferent amounts of z and compute the largest profit. Therefore, the interdependence between intangible
capital z and the subsidiary locations JF makes the firm’s problem hard to solve, even when the profit
function satisfies SCD-C. We instead assume a small number of locations, compute the optimal z for different
combinations of JF , and compare the associated profits.

75