Is Environmental Tax Harmonization Desirable in
Global Value Chains?∗
Haitao Cheng†

Hayato Kato‡

Ayako Obashi§

May 9, 2020

Abstract
The spatial unbundling of parts production and assembly currently characterizes
globalization, leading to the worldwide dispersion of pollution. We consider socially optimal (cooperative) environmental taxes in a two-country model of global value chainsin which the location of both parts and assembly can differ. When unbundling costs
are so high that parts and assembly must colocate in the pre-globalized world, pollution is spatially concentrated, and harmonizing environmental taxes maximizes global
welfare. In contrast, with low unbundling costs triggering the dispersion of parts andthus pollution throughout the world as today, harmonization fails to maximize global
welfare. Similar results hold when the two countries non-cooperatively choose theirenvironmental taxes.

Keywords: Environmental policy; Fragmentation; Emission tax competition; International
coordination; Trade in parts and components
JEL classification: F18; F23; Q56; Q58.
∗

We wish to thank the anonymous referee and the editor Till Requate for their valuable suggestions.
Our thanks also to seminar and conference participants at the Joint Seminar of the JSIE Chubu and Kansai(Nanzan U), Keio U., the Annual Meeting of the JSIE (Kwansei Gakuin U) and the IIPF 2019 (U. of Glasgow)
for their helpful comments. Financial supports from the JSPS (JP16J01228; JP19K13693) and the Hasegawa
International Scholarship Foundation are gratefully acknowledged.
†
Graduate School of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo, 186-8601, Japan.
E-mail address: ed185013@g.hit-u.ac.jp‡
Corresponding author. Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka,
Osaka, 560-0043, Japan. E-mail address: hayato.kato@econ.osaka-u.ac.jp§
School of International Politics, Economics and Communication, Aoyama Gakuin University, 4-4-25
Shibuya, Shibuya-ku, Tokyo, 150-8366, Japan. E-mail address: obashi@sipeb.aoyama.ac.jp

1

Introduction

Globalization since the late twentieth century features not just declining barriers to trade andfactor mobility, but also the lowering of costs for coordinating activities within organizations.
This spatial separation of production stages, which Baldwin (2016) refers to as the second
unbundling, has significant implications for the environment as well as trade.1 This is because
it may promote the relocation of polluting industries to countries with lax environmental
standards, an issue known as the pollution haven hypothesis (Markusen et al., 1995; Levinson
and Taylor, 2008).
One measure taken to act against the harmful impact of unbundling production processes could be the a harmonization of environmental standards among countries (Sternerand Köhlin, 2003). Equalizing regulations among countries does not distort the location
decisions of firms and may mitigate the divergence of environmental quality. However, harmonization may be too naive a policy to address individual environmental impacts given
country heterogeneity.
We aim to evaluate the effectiveness of environmental tax harmonization using a twocountry model of global value chains à la Baldwin and Venables (2013), where firms produce
a final good through assembling the chain of many parts. Specifically, we characterize the socially optimal environmental taxes (or cooperative equilibrium) that maximize global welfare
and compare them with harmonized taxes. In the pre-globalized world where all production
processes colocate, i.e., before the second unbundling, environmental taxes do nothing to improve the global environment. Setting an equal tax between countries maximizes the global
welfare by not distorting efficient locations. However, in the globalized world where assemblyand parts can be spatially unbundled, i.e., after the second unbundling, environmental taxes
can reduce global environmental damage by avoiding the concentration of polluting processes. The simple harmonization is almost never desirable and a more careful coordinationis necessary.
This result is about whether socially optimal and harmonized taxes coincide. One interested in the need for policy coordination (not just simple harmonization) may also question
whether socially optimal taxes coincide with noncooperative taxes. We show that this is more
likely to hold before the second unbundling than in the globalized world. This is because
prior to the second unbundling, there is little scope for governments to manipulate the location of parts through environmental taxes. Each government then lacks a strong incentive
1

The first unbundling refers to the spatial separation of consumption and production owing to the development of the steam engine in the Industrial Revolution.

1

to set specific tax rates so that it realizes the socially optimal taxes in the noncooperativeequilibria. As a result, the equilibrium tax rates chosen by each country do not differ muchfrom the socially optimal tax rates. The second unbundling, however, makes the location ofparts more sensitive to environmental taxes and thus tax competition leads to equilibriumtax rates different to the socially optimal tax rates.
We can relate these findings to the experience of countries in the European Union (EU).
From the 1970s onward, the EU sought to harmonize environmental policies among its member states. Holzinger et al. (2008) confirm that some 40 environmental measures converged
across 24 advanced economies, including the EU 15, between 1970 and 2000. In addition,
Arbolino et al. (2018) analyze the diffusion process of environmental policies and find that
achievements of the environmental policy objectives of one country converged to the corresponding performance of the other country within the EU 15 from 2000 to 2014. These studies
suggest that harmonization was dominant between member states with similar characteristics(EU 15) and/or in periods covering years prior to the second unbundling (1970-1990).2
However, it would be difficult to achieve a common goal through harmonized policies
if there are significant disparities in social and economic status among countries. In thisregard, Andonova and VanDeveer (2012) examine environmental policies in the CEE in theprocess of EU accession and show that considerable divergence in environmental practices andinstitutions persists.3 Furthermore, as international fragmentation of production or offshoring
expands, less developed nations would be reluctant to raise environmental standards to thelevel of stringency level closer to those of the advanced economies because in a world ofliberalized trade and investment they fear losing the interest of foreign investors. Althoughenvironmental policy is not a sole determinant of comparative advantage, it does matter at
the margin, particularly for countries whose competitiveness depends on producing at low
cost production, as in our theoretical framework (World Bank, 2020, Ch.5).
2

According to Baldwin (2016), the second unbundling accelerated from around 1990 (p.5).
To overcome the difficulty of harmonizing environmental policies across member countries, theEU has set out plans in 2020 for monetary and technical support to make up for costs of green
investment, which are known as the Just Transition Mechanism and the Sustainable Europe Investment Plan (Launching the Just Transition Mechanism - for a green transition based on solidarity and fairness,15 January 2020, European Commission: https://ec.europa.eu/info/news/
launching-just-transition-mechanism-green-transition-based-solidarity-and-fairness-2020-jan-15_
en, accessed on 9 May 2020). For the EU to become the first climate-free bloc in the world by 2050, theJust Transition Mechanism aims at providing “tailored financial and practical support to help workers andgenerate the necessary investments in regions most affected by the transition.” The direction of the EUmight be in line with our policy prescription.
3

2

1.1

Related studies

Some studies have investigated the environmental impact of mobile firms, but the production
structure in their models is generally too simple to cover fragmentation (Pflüger, 2001; Zeng
and Zhao, 2009; Ishikawa and Okubo, 2017; Forslid et al., 2017; Ikefuji et al., 2016; Voßwinkel
and Birg, 2018).4 Pflüger (2001), for example, examines the effect of pollution taxes on
the international relocation of monopolistically competitive firms. By extending Pfluger’s
model to incorporate transboundary pollution, Ishikawa and Okubo (2017) reveal that tradeliberalization may increase global pollution through firm relocation from a country withstringent regulation to a country with lax regulation. Voßwinkel and Birg (2018) examine
non/cooperative environmental policies in an oligopolistic competition setting with a specificfocus on the quality of difference of goods. In contrast to these studies where the verticallinkages between sectors are ignored, we consider a so-called spider structure, comprisingmultiple limbs (parts) coming together to make up a body (assembly).
The studies closest to ours are Hamilton and Requate (2004); and Wan et al. (2018), which
examine unilaterally optimal taxes and Nash equilibrium taxes in two-country models withvertically linked sectors.5 Both these studies assume that upstream firms produce polluting
inputs and are taxed/subsidized by their local government, as do we. However, unlike thecurrent paper, they also consider international trade in only final goods, which corresponds
to the pre-globalized situation in our analysis. To describe the global value chains in thepresent world, we allow for trade in both inputs and assembly relocation.
Using Baldwin and Venables (2013)’s framework, Obashi (2019) characterizes optimal
combinations of trade instruments and finds that policy prescriptions proposed by traditional
trade models are not sufficient to achieve the social optimum. Although environmental issues
were outside the scope of Obashi (2019), her study and ours should be seen as complements asboth emphasize that the evolution of global value chains significantly changes policy design.
The reminder of the paper is structured as follows. Section 2 presents the model andanalyzes the location patterns of parts given assembly location and environmental taxes.
Section 3 allows for endogenous assembly location and examine socially optimal taxes in the
pre-globalized world and Section 4 does this for the globalized world. Section 5 confirms that
our main result holds in different settings. The final section discusses implications for the4

Using an evolutionary game approach, Dijkstra and De Vries (2006) conclude that environmental taxation
may induce polluting firms to stay away from consumers. However, in contrast to our analysis, their focus ison the spatial unbundling of consumption and production, not the spatial unbundling of production itself.
5
See also Wan and Wen (2017). Some studies consider a wider variety of policy tools, including bordertax adjustments as well as emission taxes, although they do not allow for vertical linkages (Lai and Hu, 2008;
Yomogida and Tarui, 2013; Keen and Kotsogiannis, 2014; Sanctuary, 2018; Ogawa and Yanase, 2019).

3

real world.

2

The model

Consider a world with two countries, N and S. The two countries have equal population
with unit mass. Each individual inelastically supplies one unit of labor. There are three
types of goods: a final good, a range of parts (intermediate inputs), and a numéraire good.
The numéraire good is produced using labor and is costlessly traded, which equalizes its
international price. With choice of units, the wage rates in both countries are equal to unity.
Each part can be produced using labor in both countries and can be internationally traded.
Parts production generates local pollution and is thus taxed by the domestic government. A
single final good producer (assembler) locates in N or S and assembles the range of parts
into one unit of the good. As in Baldwin and Venables (2013), the two countries differ in
two ways: (i) only N consumes the final good and (ii) the average cost of producing parts islower in S than in N .
To describe the second unbundling, we distinguish between two types of frictions. If
the assembler is located in S, it must pay trade costs to export the final good to N . If
the locations of parts and assembly differ, the assembler must pay additional unbundlingcosts to import parts from abroad. Unbundling costs include communication costs between
headquarters and foreign suppliers as well as physical transportation costs.6

2.1

Preferences

The utility of the representative consumer in i ∈ {N, S} is
Ui = ue1i + Xi − D(ei ),6(1)

As discussed shortly, we assume that both trade costs and unbundling/communication costs increase
proportionally to quantity. There is no general agreement about how to model communication costs (Gokan
et al., 2019). Whether communication costs affect the fixed or variable costs of trade depends on the roleof communications in transactions. The increased use of the Internet (e.g., Freund and Weinhold, 2004),
for example, facilitates the search for trading partners and thus solely affects the fixed costs. However,in the manufacturing activities, the downstream and upstream production processes need to interact tocoordinate the specification of a customized product and the timing of delivery, which would primarily affectvariable costs. Considering these interactions between headquarters and distant plants, some studies model
communication costs as an iceberg cost proportional to the firm’s output (Duranton and Puga, 2005; Fujita
and Thisse, 2006. Indeed, Fink et al. (2005) find that communication costs exert a significant impact on thevariable costs of trade, thereby affecting trade patterns, especially for differentiated goods. We follow thelatter modeling strategy for communication costs.

4

where Xi is the consumption of the numéraire good, and ei is the pollution level. 1i takes
one if i = N and zero if i = S. The consumer in N obtains ue from consuming one unit of
the final good. The disutility from pollution is expressed as D(ei ) = γe2i /2 with γ > 0. The
budget constraint is
p1i + Xi = 1 + ti ei + X,

(2)

where p is the final good’s price and ti is the environmental tax by i per unit of pollution.
The income consists of wage (wi = 1), the redistribution of tax revenues (ti ei ), and theinitial endowment of the numéraire (X). X ensures positive consumption of the numéraire.
Substituting (2) into (1) yields the indirect utility Vi .

2.2

Sourcing decision

The assembler first chooses where to locate and then from which country to source parts.
Here, we consider the sourcing decision of the assembler given its location.
Letting z be the index of parts from the set Z = [b, b], the unit cost of any part z ∈ Z is
unity if it is produced in N . If a part z ∈ Z is produced in S, on the other, its unit cost isb(z) = z with 0 < b < 1 < b. Thus N has a comparative advantage in parts b ∈ [1, b], while S
has it in parts b ∈ [b, 1). S has an average cost advantage over N , i.e., β ≡ 1 − (b + b)/2 > 0.7
Producing one unit of each part generates one unit of local pollution.
The assembler produces one unit of the final good by assembling one unit of each part.
When parts cross the border, additional unbundling costs θ arise. The sourcing decision is
on a parts basis by comparing the international cost difference. Supposing the assembler isin N , a part z is sourced there if
1 + tN < b(z) + θ + tS ,| {z }|{z}

Cost in N

Cost in S→ b(z) > bN ≡ min[max{b, 1 − θ + ∆t}, b],
where ∆t ≡ tN − tS .
The inequality is likely to hold if S’s cost is high (high b(z)), N ’s tax compared with S’s islow (low ∆t), and unbundling costs are high (high θ).
71
The average cost of parts in S is b−b

Rb
b

2

2

1
1
b̃db̃ = b−b· b −b= b+b
2
2 , while that in N is b−b

5

Rb
b

1db̃ = 1.

Supposing the assembler is in S, a part z is produced there if
1 + θ + tN > b(z) + tS ,| {z } | {z }Cost in N

Cost in S→ b(z) < bS ≡ max[min{b, 1 + θ + ∆t}, b],which can be interpreted analogously.
When unbundling costs are sufficiently high, the two unbundling thresholds degenerate,i.e., bN = b and bS = b, and all parts colocate with assembly. Specifically, supposing θ > θ ≡max{1 − b + ∆t, b − 1 − ∆t}, Fig. 1 draws such a region (N S in the figure) given assembly
location and taxes.8 The co-location motive of the assembler to save unbundling costs is sostrong that neither comparative advantage nor environmental taxes matter. The parts andassembly are spatially bundled in the pre-globalization world.
When unbundling costs are sufficiently low, the two unbundling thresholds do not degenerate. The location of some parts is dictated by comparative advantage and taxes, not by
the colocation motive. Supposing θ < θ ≡ min{1 − b + ∆t, b − 1 − ∆t}, Fig. 2 depicts thesourcing pattern.9 Unlike Fig. 1, there are two other regions in Fig. 2, N and S. Parts in N ,for example, are those in which N has a very strong comparative advantage, and are always
produced in N . As low unbundling costs also make the assembler aware of taxes, the tax
difference now matters for its sourcing decision. The spatial unbundling captures the current
globalization. In what follows, we separately present the analysis of the two cases.
The key mechanism here is that stringent environmental regulations would relocate thedirtiest parts of the production process to countries with less strict policies, which Cherniwchan et al. (2017) refer to as the pollution offshoring hypothesis. If this hypothesis holds,
domestic firms become cleaner. This is not because they have reduced the emission intensityof their own activities, but because they have shifted the dirtiest parts of their production
out of the country. There are some empirical evidences to support the pollution offshoring
hypothesis. For example, Cherniwchan (2017) found that the emission intensities of the US
manufacturing plants fell in part due to changes in their access to dirtier intermediate inputs
in Mexico following trade liberalization through the North American Free Trade Agreement(NAFTA).10
8

Note that bN = b holds if b > 1 − θ + ∆t; bS = b holds if b < 1 + θ + ∆t. These conditions lead toθ > max{1 − b + ∆t, b − 1 − ∆t}, which is equivalent to ∆t ∈ (b − θ − 1, b + θ − 1).
9This condition is equivalent to ∆t ∈ (b + θ − 1, b − θ − 1).
10
The empirical literature is yet to reach a consensus. For instance, Shapiro and Walker (2018) found thatfragmenting production or offshoring was unlikely to account for a large share of the reductions in emissions

6Fig. 1. Sourcing pattern under high unbundling costs.

Fig. 2. Sourcing pattern under low unbundling costs.

3

High unbundling costs: colocation of parts and assembly

We consider here the case where unbundling costs are high: θ > θ so that parts and assembly
are spatially bundled. We first characterize the assembly location for the given taxes andthen derive the socially optimal taxes.
intensities in US manufacturing production.

7

3.1

Assembly location

Let Ci be the total costs of producing one unit of the final good, given assembly in i ∈ {N, S}.
Noting bN = b, we have
Z bN
CN =
b

|

Z b
(eb + θ + tS )deb +(1 + tN )deb
bN
{z
}
{z
} |

Parts from S

Parts from N= (b − b)(1 + tN ).

(3)

Similarly, noting bS = b, we have
Z bS

Z b
e
e
(b + tS )db +(1 + θ + tN )deb
CS = τ +
b
b
{z
}
|
{z
} | S
Parts from N
Parts from Sb+b+ tS ,= τ + (b − b)2(4)where trade costs τ enter since the good crosses the border. All parts are sourced locally andthus θ does not appear here.
The assembler chooses the location that yields the lower Ci . Assembly takes place in N
if∆C ≡ CN − CS = −τ + (b − b) (β + ∆t) ≤ 0,
→ τ ≥ τ ∗ ≡ (b − b) (β + ∆t) ,(5)

where β ≡ 1 − (b + b)/2,
High trade costs ensure the assembler prefers the proximity to consumers. As seen from theswitching point τ ∗ , below which assembly takes place in S, the assembler is more likely tolocate in N as N ’s tax becomes lower (lower ∆t) and/or N ’s parts are more costly (higherβ). This tendency is magnified by the total number of parts: b − b.

3.2

Social optimum

Environmental taxes potentially affect pollution arising from dirty parts production via twochannels. First, as discussed in Section 2.2, a tax increase in one country makes its pro-8

duction cost of parts higher, inducing the assembler to change the sourcing pattern. The
assembler sources more parts from the other country than before, where more pollution andenvironmental damage occur. Second, as discussed in Section 3.1, taxes affect the assembler’s
location choice through changes in the switching point, τ ∗ , and may lead to a discontinuous
jump in pollution. If an increase in tN makes τ ∗ higher than the exogenously given trade
costs, τ , the assembler moves from S to N and brings N a discontinuous increase in pollution
due to the colocation motive of parts and assembly.
Under high unbundling costs, however, the first channel, i.e., the assembler’s sourcing
decision, is ineffective. The colocation motive is so strong that the unbundling thresholds
degenerate (bN = b; bS = b), implying that environmental taxes affect pollution only throughthe second channel, i.e., the assembler’s location decision.
The social/global welfare W is the sum of each country’s indirect utility Vi . Using (1) to(4), we have2
W |A=N = P
i=N,S Vi |A=N = u − (b − b) − (γ/2)(b − b)
W =
P
W |
2
A=S =
i=N,S Vi |A=S = u − τ − (1/2)(b − b)(b + b) − (γ/2)(b − b)if τ ≥ τ ∗,if τ < τ ∗where u ≡ u
e + 2(1 + X),
and where the subscript A = i ∈ {N, S} indicates the assembler’s location. Since all partsco-locate with assembly, the pollution level in i is ei = b − b if the assembler is in i and it isei = 0 otherwise. We do not examine each component of the social welfare here, but details
about the final good’s price and the environmental damage are in Appendix A1.
Surprisingly, taxes do not enter in W . Since the unbundling thresholds degenerate, theenvironmental damage does not depend on taxes: D(ei ) = (γ/2)(b − b)2 . Higher taxes
improve welfare by raising tax revenues, while they reduce welfare by raising the final good’s
price. These two counteracting effects offset each other.11 Taxes thus affect parts location
only through changes in assembly location.The social planner cannot manipulate τ ∗ directly,
but can do so indirectly by changing taxes.
Noting that τ ∗ depends on the tax difference, not individual levels, the planner chooses
11

For example, if assembly takes place in N , the sum of the consumer surplus and tax revenues in theworld is(eu − CN ) + tN (b − b) = ue − (b − b)(1 + tN ) + tN (b − b)=ue − (b − b),which is independent of taxes. The same argument holds if assembly takes place in S. See Appendix A1 forthe exact welfare expressions.

9∆t to attain max{W |A=N , W |A=S } by (indirectly) manipulating the switching point τ ∗ . The
optimal tax difference for any trade costs turns out to be ∆t = 0, as Fig. 3 illustrates.12
That is, the planner should not intervene in the assembler’s location choice. If the locationof assembly were manipulated, comparative advantage would be distorted and thus the total
cost would not be minimized. In addition, assembly location affects local environmental
damage, but does not affect global environmental damage, since the assembler sources allparts locally. The planner is thus unable to reduce the global damage by changing assembly
location. The planner fully respects the cost-minimization location choice of the assembler
by setting the tax difference to zero. The socially optimal switching point then becomesτb∗ ≡ τ ∗ |∆t=0 = β(b − b).

Fig. 3. Socially optimal tax harmonization (dashed line) and assembly location under highunbundling costs.

Proposition 1.

Under high unbundling costs, environmental tax harmonization, i.e.,tN = tS , always maximizes social welfare for any level of trade costs.

4

Low unbundling costs: separation of parts and assembly

We turn to the case where unbundling costs are low: θ < θ. Low unbundling costs allow
parts and assembly to locate in different countries, capturing the second unbundling.
12

All proofs of the propositions are in Appendix A2. Given τ , there may be other optimal tax differences
than ∆t = 0 (see Fig. A2). But only ∆t = 0 maximizes social welfare for any τ .

10

4.1

Assembly location

As Fig. 2 suggests, the two unbundling thresholds are within the interval of [b, b]. The total
cost of the final good in each location is respectivelyb + bN
CN = θ + tS +(bN − b) + (1 + tN )(b − bN ),
|
{z
}
2
|
{z
}
Parts from N
Parts from Sb + bS
CS = τ + tS +(bS − b) + (1 + θ + tN )(b − bS ),
|
{z
}
2
|
{z
}
Parts from N

(6)

(7)

Parts from S

where bN = 1 − θ + ∆t and bS = 1 + θ + ∆t. Assembly takes place in N if

b+b
∆C ≡ CN − CS = −τ + 2θ 1 −+ ∆t ≤ 0,2→ τ ≥ τ ∗∗ ≡ 2θ (β + ∆t) .
Unlike τ ∗ defined in (5), τ ∗∗ depends on θ. Lower unbundling costs make the colocation ofparts and assembly less important, whereas they make the proximity to the consumer in N
more important. A lower θ decreases τ ∗∗ , making the assembler more likely to locate in N .

4.2

Social optimum

In contrast to the case of high unbundling costs, environmental taxes affect pollution throughboth the assembler’s sourcing and location decisions. A tax increase in one country leads
to the offshoring of dirty parts production and may reduce pollution there without losing
out the assembler. In the globalized world, taxes are more effective in reducing pollution
than in the pre-globalized world. We thus expect that there is a need for more careful tax
coordination than with just simple harmonization.

11

With low unbundling costs, we use (1), (2), (6), and (7) to express the social welfare asW |A=S = P
if τ < τ ∗∗i=N,S Vi |A=S
W =
,
P
W |
∗∗
if τ ≥ τ
A=N =i=N,S Vi |A=N1γ
W |A=S = u − τ + (b + bS )(bS − b) + (1 + θ)(b − bS ) − [(b − bS )2 + (bS − b)2 ],
2
2



γ
b + bNW |A=N = u − θ +(bN − b) + (b − bN ) − [(b − bN )2 + (bN − b)2 ].
2
2
Unlike the case of high unbundling costs, the tax difference ∆t affects not just the switching
point τ ∗∗ but the unbundling thresholds bi . The planner chooses ∆t to maximize W by(indirectly) manipulating bi as well as τ ∗∗ . Although we do not look at each component ofwelfare here, one can find the details about the final good’s price and the environmental
damage in Appendix A1.
Formally, we can the socially optimal tax difference as follows and is illustrated in Fig.
4:13
2γ(β + θ)


∆t|
≡
−
if τ < τ a
A=S2γ + 1




∆b
t+ε
if τ a ≤ τ < τb∗∗
∆t =
,
τ


−β
if τb∗∗ ≤ τ < τ b
∆b
t≡


2θ


2γ(θ − β)∆t|A=N ≡if τ ≥ τ b
2γ + 12θ(β − 2γθ)2βθ2θ(2γθ + β)where τ a ≡, τb∗∗ ≡, τb ≡,
2γ + 12γ + 12γ + 1and ε > 0 is a sufficiently small constant.14 τb∗∗ is the socially optimal switching point.
The socially optimal tax difference would be zero if there were no environmental damage
γ = 0. The planner intervenes solely for reducing the global environmental damage. Since theglobal damage becomes more severe as pollution is more spatially concentrated, the planner
aims to diversify the location of parts. The optimal tax difference is thus set to make the
distribution of parts production more equal.15
As trade costs τ fall, more parts are shifted from N to S because (i) S’s cost advantage
13

For τ a to be positive, the sensitivity of environmental damage is assumed not to be too large: γ < γ ≡β/(b − b).
14
In Fig. 4, we ignore ε. ∆t|A=N can be negative if θ is low enough.
15
It can be checked that the socially optimal unbundling threshold bi is closer to the middle point of therange (b + b)/2 than the unbundling threshold under no taxes.

12begins to matter and (ii) the assembler moves from N to S. To avoid the concentration ofpollution, N ’s tax compared with S’s is set higher than before and thus the optimal tax
difference decreases with τ . The simple harmonization is no longer desirable except for a
special case at which the optimal tax difference coincides with zero.

Fig. 4. Socially optimal tax difference (dashed line) and assembly location under low
unbundling costs.

Proposition 2.

Under low unbundling costs, environmental tax harmonization nevermaximizes social welfare except for a specific level of trade costs.

5

Extensions

5.1

Environmental damage function

We assumed a convex form of the environmental damage function, i.e., D(ei ) = γe2i /2, which
is fairly common in the literature (e.g., Ulph, 1996; Copeland and Taylor, 2005, Ch. 2). Our
main results, Propositions 1 and 2, do not depend on the specific form of damage function,
as we argue below.
Under high unbundling costs, where all parts production colocates with assembly, pollution occurs only in the country with assembly. The levels of pollution and environmental
damage are then independent of taxes. Therefore, the social planner does not care about the13

function form of D(·). Regardless of whether it is convex or concave, the harmonized tax
rates are also socially optimal ones.
Under low unbundling costs, the tax difference does affect which parts are produced inwhich country, even when it does not change assembly location. In this case, the harmonizedtax rates can generally never be the socially optimal ones no matter what the function formof D(·) may be. For illustration, consider a situation where θ is close to zero and γ is so highthat the planner cares solely about the environmental damage. The sum of the environmental
damage in each country is given by (γ/2)[D(eN ) + D(eS )] = (γ/2)[D(b − b) + D(b − b)], whereb ' 1+∆t is the unbundling threshold below (above) which parts are produced in S (N ). The
planner attempts to minimize this by altering the unbundling threshold b through changes
in the tax difference ∆t ≡ tN − tS .
If D(·) is convex, as assumed in the main analysis, the global damage is minimized
when b is at the middle point: (b + b)/2.16 The socially optimal tax difference must satisfyb = 1 + ∆t = (b + b)/2, or ∆t = β ≡ 1 − (b + b)/2 > 0. The harmonized tax rates would leadto too much pollution in S.
If D(·) is concave, the global damage is minimized when b is at either of the endpoints: bor b.17 The socially optimal tax difference must be either ∆t = 1 − b > 0 or ∆t = 1 − b < 0
to induce all parts production to take place in one country. Tax harmonization that allows
for the diversification of parts production is then poor policy.

5.2

Nash equilibrium vs. social optimum

The focus of this paper is on whether the harmonization policy maximizes social welfare.
We could also ask whether decentralized policies chosen by noncooperative governments, i.e.,
Nash equilibrium policies, lead to the socially optimal outcome. Here, we here intuitively
argue that the Nash equilibrium tax difference is more likely to differ from the socially
optimal one under low unbundling costs than under high unbundling costs. Our main finding
carries over: globalization calls for more careful international coordination than a simple
harmonization rule. The full characterization of Nash equilibria is relegated to AppendicesA3 and A4.
The FOC for the minimization problem is −D0 (b − b) + D0 (b − b) = 0, noting that the SOC is satisfied
because of the convexity of D(·): D00 (b − b) + D00 (b − b) > 0. From the FOC, we have D0 (b − b) = D0 (b − b),or b = (b + b)/2.
17This result comes from the fact that the SOC for the minimization problem is not satisfied: D00 (b − b) +00
D (b − b) < 0.
16

14

5.2.1High unbundling costs

We consider the governments’ incentive to deviate from the harmonized tax rates: tN =tS , which maximizes social welfare (see Proposition 1). Since the unbundling thresholds
degenerate under high unbundling costs, i.e., bN = b; bS = b, the levels of pollution andenvironmental damage are independent of taxes. The governments can then do little toreduce local pollution and thus do not tend to prefer specific tax rates.
If trade costs are sufficiently high such that τ ≥ τb∗ , assembly takes place in N (see Section
3). In this case, government S does not wish to challenge government N over assembly by
reducing tS because attracting assembly by the reduced tS would not bring with it much tax
revenue. As there are neither assembly nor tax revenues in S, government S does not have any
incentive to raise tS , either. Government N is also unwilling to change tN because tN does notenter its objective function.18 The harmonized tax rates are then indeed Nash-equilibriumones.
If τ < τb∗ , where assembly takes place in S, government S has an incentive to set tS
higher than tN because by doing so S can increase tax revenues while not inducing assembly
relocation. The Nash equilibrium tax difference can never be zero.
In sum, if τ ≥ τb∗ , the harmonized tax rates are the Nash equilibrium ones as well as thesocially optimal ones.
5.2.2

Low unbundling costs

Under low unbundling costs, the unbundling thresholds do not degenerate, i.e., bN = 1 −θ + ∆t; bS = 1 + θ + ∆t. The country without assembly also suffer environmental damage
from dirty input production, implying that both governments, regardless of hosting assembly,
can affect the level of pollution through taxes. They want to choose a specific tax rate thatmaximizes their national welfare, which is in stark contrast to the case of high unbundlingcosts.
A tax increase by government i ∈ {N, S} causes the relocation of parts and thus pollution
to j 6= i. Government j then wishes to increase its tax rate as well to prevent environmental
damage. That is, the two countries’ tax rates are strategic complements: both governments
wish to change their tax rates in the same direction.19 Therefore, irrespective of the level
18

An increase in tN has a positive effect on tax revenues and a negative effect on the consumer surplus,
which cancel each other. Therefore, tN does not matter for government N ’s welfare.
19
The strategic complementarity leads to a race to the top, in which each country’s tax rate at the Nashequilibrium is higher than their rate at the social optimal. The argument here assumes that the governmentsemphasize environmental damage, i.e., a high γ. If instead γ is low and thus the governments emphasize tax

15

of trade costs, the Nash equilibrium tax difference is in general different from the socially
optimal one in such a way that the former is smaller than the latter.

6

Conclusion

Desirable environmental policies may drastically change before and after the current globalization characterized by the spatial unbundling of production processes. In the pre-globalized
world, environmental tax harmonization avoids distorting efficient location choices and maximizes global welfare, despite heterogeneity between countries. In the globalized world, however, it leads to the excessive spatial concentration of pollution and (almost) never maximizes
global welfare. The second unbundling may then call for careful international coordination
beyond simple harmonization. These theoretical findings have implications for the experiences of earlier member states of the European Union (EU) prior to 2004, i.e., the EU 15,
and the newer member states among the Central and Eastern European (CEE) countries
since 2004.
We highlight two important issues that have not been addressed in the current paper.
First, it would be worthwhile investigating how we should coordinate environmental andtrade polices such as import tariffs (Lai and Hu, 2008; Yomogida and Tarui, 2013; Keenand Kotsogiannis, 2014; Sanctuary, 2018; Ogawa and Yanase, 2019). In the age of thesecond unbundling, the location of parts is sensitive to the international cost differences
generated by both policy measures. Key questions would be as follows. Which measureis effective for the global environment? Are tariffs necessary as border tax adjustments
given different emission taxes at home and abroad? Second, it would also be interesting toconsider pollution emitted during the transportation of goods, considering its importanceamong all sources of pollution (Abe et al., 2014; Ishikawa and Tarui, 2018).20 Transportation
pollution is particularly relevant in snake-style production, in which parts move sequentiallyfrom upstream to downstream with value added at each stage. The snake-style production
tends to generate more pollution than the spider-style production we consider in this paper,
because parts produced in one country can be shipped multiple times before they reach thefinal stage. Incorporating these aspects into our model would lead to greater externalities
revenues, the complementarity results in a race to the bottom.
20
For example, greenhouse gas (GHG) emissions from transportation account for 28.9 percent of total US
GHG emissions in 2017, making it the largest contributor to US GHG emissions. Source: U.S. Environmental
Protection Agency (https://www.epa.gov/ghgemissions/sources-greenhouse-gas-emissions, accessedon March 23, 2020).

16and thus larger deviations between harmonized and socially optimal taxes. We leave theseissues for future research.

17

Appendix to “Is Environmental Tax Harmonization
Desirable in Global Value Chains?”
Cheng Haitao

A1

Hayato Kato

Ayako Obashi

Final good’s price and environmental damage

High-unbundling-cost case.
price asFrom the discussion in Section 3.1, we obtain the final good’s(
CN = (b − b)(1 + tN )if τ ≥ τ ∗
p = min {CN , CS } =,CS = τ + (b − b) (b + b)/2 + tS if τ < τ ∗which is shown in Fig. A1. We note that assembly takes place in A = N (A = S) if τ ≥ τ ∗(τ < τ ∗ ).

Fig. A1. Final good’s price under high unbundling costs.

The environmental damage in each country is((γ/2)(b − b)2 if τ ≥ τ ∗D(eN ) =,0
if τ < τ ∗(0if τ ≥ τ ∗D(eS ) =.
(γ/2)(b − b)2 if τ < τ ∗The sum of the two equals
D(eN ) + D(eS ) = (γ/2)(b − b)218

for any τ .

These are illustrated in Fig. A2.

Fig. A2. Environmental damage under high unbundling costs.

Low-unbundling-cost case.
From the discussion in Section 4.1, we obtain the final good’s
price as
b + bN
CN = θ + t S +if τ ≥ τ ∗∗(bN − b) + (1 + tN )(b − bN )


|
{z
}
2


|
{z
}

Parts from N
Parts fromSp = min {CN , CS } =,b + bS∗∗CS = τ + t S +(bS − b) + (1 + θ + tN )(b − bS ) if τ < τ


|
{z
}

2


|
{z
}
Parts from N
Parts from S

which is shown in Fig. A3. We note that assembly takes place in A = N (A = S) if τ ≥ τ ∗∗(τ < τ ∗∗ ).

Fig, A3. Final good’s price under low unbundling costs.

19

The environmental damage in each country is(
D(eN ) A=N = (γ/2)(b − bN )2 if τ ≥ τ ∗∗D(eN ) =,D(eN ) A=S = (γ/2)(b − bS )2 if τ < τ ∗∗(D(eS ) A=N = (γ/2)(bN − b)2 if τ ≥ τ ∗∗.
D(eS ) =D(eS ) A=S = (γ/2)(bS − b)2 if τ < τ ∗∗The global damage is then([D(eN ) + D(eS )] A=N = (γ/2) (b − bN )2 + (bN − b)2 if τ ≥ τ ∗∗
D(eN ) + D(eS ) =.
if τ < τ ∗∗[D(eN ) + D(eS )] A=S = (γ/2) (b − bS )2 + (bS − b)2
We note the following:
D(eN )|A=N > D(eN )|A=S ,D(eS )|A=N < D(eS )|A=S ,D(eN )|A=S − D(eS )|A=S = −γ(b − b)(β + ∆t + θ) < 0,
D(eS )|A=N − D(eN )|A=S = γ(bN − b + b − bS )(β + ∆t) > 0,D(eS )|A=S − D(eN )|A=N = γ(bS − b + b − bN )(β + ∆t) > 0,[D(eN ) + D(eS )] A=S − [D(eN ) + D(eS )] A=N = γ(bS − bN )(bN + bS − b − b)
= 4γθ(β + ∆t) > 0.
Although the inequalities above unambiguously hold, we still need to check the relationshipbetween the two countries’ pollution levels when the assembly is in N :D(eN )|A=N − D(eS )|A=N = −γ(b − b)(β + ∆t − θ).
Country N ’s pollution level tends to be lower when country S’s average cost advantage islarger (higher β); the tax difference is larger (high ∆t); and the unbundling costs are lower(lower θ). Depending on the sign of β + ∆t − θ, the environmental damage is illustrated in
Figs A4 and A5.

20

Fig. A4. Environmental damage under low unbundling costs if β + ∆t − θ < 0.

Fig. A5. Environmental damage under low unbundling costs if β + ∆t − θ > 0.

A2

Proofs of propositions

A2.1

Proof of Proposition 1

From (1), (2), (3), and (4), the indirect utility of the representative agent in each country isgiven by(if τ < τ ∗VN |A=S = ue − CS + 1 + X,
VN =VN |A=N = u
e − CN + tN (b − b) − (γ/2)(b − b)2 + 1 + X if τ ≥ τ ∗(VS |A=S = tS (b − b) − (γ/2)(b − b)2 + 1 + X if τ < τ ∗VS =,VS |A=N = 1 + X
if τ ≥ τ ∗where CS = τ + (b − b)/[(b + b)/2 + tS ]; CN = (b − b)(1 + tN ); τ ∗ ≡ (b − b)(β + ∆t);β ≡ 1 − (b + b)/2. The social welfare is defined by the sum of each country’s indirect utility:(
W |A=S = VN |A=S + VS |A=S = u − τ − (1/2)(b − b)(b + b) − (γ/2)(b − b)2 if τ < τ ∗W =,W |A=N = VN |A=N + VS |A=N = u − (b − b) − (γ/2)(b − b)2
if τ ≥ τ ∗where u ≡ u
e + 2(1 + X),
as given in the main text.
Taxes do not enter the expressions of social welfare and only affect the location decisionof the assembler. The social planner thus chooses the assembly location through taxes thatgives the higher social welfare. A simple comparison of welfare between the two locations

21

reveals(
W |A=S = u − τ − (b − b)(b + b)/2 − (γ/2)(b − b)2
max{W |A=N , W |A=S } =W |A=N = u − (b − b) − (γ/2)(b − b)2

if τ < τb∗,if τ ≥ τb∗

where W |A=N = W |A=S holds at τb∗ ≡ β(b − b).
To see the results intuitively, it is helpful to illustrate the assembly location pattern inthe (τ, ∆) plane, as Fig. A6 shows. The upward-sloping line is the cost-indifference one:τ = τ ∗ , or equivalently, ∆t = τ /(b − b) − β, which represents N ’s maximum tax rate thatkeeps assembly there. The social planner should set taxes so that the assembly locates in N
if τ ≥ τb∗ and it locates in S otherwise. The optimal tax difference is thus(
> τ /(b − b) − β if τ < τb∗,∆t≤ τ /(b − b) − β if τ ≥ τb∗which is represented by the shaded area in Fig. A7. As is clear from Fig. A7, only the tax
harmonization ∆t = 0 (dashed line) maximizes the social welfare for any level of trade costs.

Fig. A6. Location of assembly under high unbundling costs.

Fig. A7. Socially optimal tax difference (shaded area) and assembly location under highunbundling costs.
22

A2.2

Proof of Proposition 2

We first derive the unconstrained socially optimal taxes given the location of assembly. With
low unbundling costs, the indirect utility of the representative agent in each country is givenby(if τ < τ ∗∗VN |A=S = ue − CS + tN (b − bS ) − (γ/2)(b − bS )2 + 1 + X,
VN =VN |A=N = u
e − CN + tN (b − bN ) − (γ/2)(b − bN )2 + 1 + X if τ ≥ τ ∗∗(VS |A=S = tS (bS − b) − (γ/2)(bS − b)2 + 1 + X
if τ < τ ∗∗VS =,VS |A=N = tS (bN − b) − (γ/2)(bN − b)2 + 1 + X if τ ≥ τ ∗∗where Ci is defined in (6) and (7); and τ ∗∗ ≡ 2θ(β + ∆t); bN = 1 − θ + ∆t; bS = 1 + θ + ∆t.
The social welfare is defined by the sum of the two country’s indirect utility:(P
W |A=S = i=N,S Vi |A=S if τ < τ ∗∗,W =P
W |A=N = i=N,S Vi |A=N if τ ≥ τ ∗∗1
W |A=S = u − τ + (b + bS )(bS − b) + (1 + θ)(b − bS ) − (γ/2)[(b − bS )2 + (bS − b)2 ],2b + bNW |A=N = u − θ +(bN − b) + (b − bN ) − (γ/2)[(b − bN )2 + (bN − b)2 ],2
as given in the text.
For the social welfare level at each assembly location, the first-order conditions givedW |A=SdW |A=S
=−
= 0,
dtN
dtS
2γ
→ (tN − tS )|A=S = −(θ + β) ≡ ∆t|A=S ,2γ + 1dW |A=NdW |A=N
=−
= 0,
dtN
dtS
2γ
→ (tN − tS )|A=N =(θ − β) ≡ ∆t|A=N .
2γ + 1Since dW |A=i /dtN and (−dW |A=i /dtS ) are collinear, what matters for the social welfare
maximization is the tax difference and not the absolute levels of taxes.
We then allow for endogenous assembly location and see how it affects the optimal taxes.
As in Appendix A2.1, it is helpful to consider in the (τ, ∆t) plane. The upward-sloping line in
Fig. A8 is the cost-indifference line: τ = τ ∗∗ , or equivalently, ∆t = τ /(2θ) − β ≡ ∆bt. Putting
the unconstrained maximizers derived before into the plane, we can obtain Fig. A9 andidentify that there are three cases to be considered. Letting τ a (or τ b ) be the intersectionof the cost-indifference line and ∆t|A=S (or ∆t|A=N ), the three cases are characterized asfollows.
23

Case (i) τ < τ a .
The social optimum will be either the constrained maximum
with assembly in N , W |A=N, ∆t=∆bt , or the unconstrained maximum with assembly in S,
W |A=S, ∆t=∆t|A=S .
Case (ii) τ a ≤ τ < τ b .
The social optimum will be either the constrained maximum with assembly in N , W |A=N, ∆t=∆bt , or the constrained maximum with assembly in S,
W |A=S, ∆t=∆bt+ε .
Case (iii) τ ≥ τ b .
The social optimum will be either the unconstrained maximum
with assembly in N , W |A=N, ∆t=∆t|A=N , or the constrained maximum with assembly in S,
W |A=S, ∆t=∆bt+ε .

Fig. A8. Location of assembly under low unbundling costs.

Fig. A9. Unconstrained optimal tax differences under low unbundling costs.

For the latter reference, it is informative here to compare the constrained maxima between
the two locations.
W |A=N, ∆t=∆bt − W |A=S, ∆t=∆bt+ε = τ + β(bN − bS ) + 2[θ + γ(bN − bS )][1 − (bN + bS )/2 − β]= τ (2γ + 1) − 2βθ,24

noting that ε is sufficiently small. On ∆t = ∆bt, it holds that bN − bS = −2θ and bN + bS =b2(1 + ∆t). We thus have W |A=N, ∆t=∆bt ≥ W |A=S, ∆t=∆bt+ε if τ ≥ τb∗∗ ≡ 2βθ/(2γ + 1) and
W |A=N, ∆t=∆bt < W |A=S, ∆t=∆bt+ε otherwise. It can be also checked that τ a < τb∗∗ < τ b .
With these in hand, we will derive the socially optimal taxes in each case.
Case (i) τ < τ a .

In this case, we have
W |A=S, ∆t=∆t|A=S > W |A=S, ∆t=∆bt > W |A=N, ∆t=∆bt .

The socially optimal outcome is the unconstrained maximum with assembly in S.
Case (ii) τ a ≤ τ < τ b .
As τb∗∗ is in between τ a and τ b , this case is further divided into
two subcases.
Case (ii-a) τ a ≤ τ < τb∗∗ .
We have
W |A=S, ∆t=∆bt+ε > W |A=N, ∆t=∆bt .
The socially optimal outcome is that assembly takes place in S and the tax difference is set
at ∆t = ∆bt + ε.
Case (ii-b) τb∗∗ ≤ τ < τ b .
We have
W |A=N, ∆t=∆et ≥ W |A=S, ∆t=∆bt+ε .
The socially optimal outcome is that assembly takes place in N and the tax difference is set
at ∆t = ∆bt.
Case (iii) τ ≥ τ b .

In this case, we have
W |A=N, ∆t=∆t|A=N > W |A=N, ∆t=∆bt > W |A=S, ∆t=∆bt+ε .

The socially optimal outcome is the unconstrained maximum with assembly in N .
In sum, the socially optimal tax difference is∆t|A=S = − 2γ(β + θ) if τ < τ a
2γ + 1



∆b
t+ε
if τ a ≤ τ < τb∗∗
∆t =
,
τ

∆b
t=
−β
if τb∗∗ ≤ τ < τ b


2θ


2γ(θ − β)∆t|A=N =if τ ≥ τ b
1 + 2γ2θ(β − 2γθ)2βθ2θ(2γθ + β)where τ a ≡, τb∗∗ ≡, τb ≡,
2γ + 12γ + 12γ + 1
as given in the main text.

25

A3 Nash equilibrium outcome under high unbundlingcosts
As noted in Appendix A2.1, under high unbundling costs, the indirect utility of the representative agent in each country is given by(
VN |A=S = ue − CS + 1 + X
if τ < τ ∗VN =,VN |A=N = u
e − CN + tN (b − b) − (γ/2)(b − b)2 + 1 + X if τ ≥ τ ∗(VS |A=S = tS (b − b) − (γ/2)(b − b)2 + 1 + X if τ < τ ∗VS =,VS |A=N = 1 + X
if τ ≥ τ ∗where CN = (b − b)(1 + tN ); CS = τ + (b − b)[(b + b)/2 + tS ]; τ ∗ ≡ (b − b)(β + ∆t). The
unbundling thresholds degenrate: bN = b; bS = b.
(i) First, we investigate S’s best responses given N ’s pollution tax. Evaluating the switching
point τ ∗ at taxes making the locations indifferent to S (i.e., VS |A=S = VS |A=N ), we get thethreshold tax rate: btN = τ /(b − b) − β + (γ/2)(b − b).
If tN ∈ [0, btN ], S imposes a pollution tax satisfying tS ≥ tN − τ /(b − b) + β so as to induce
A = N and VS |A=N = 0. Or else, S’s welfare is negative (A = S, VS |A=S < 0).
If tN ∈ (btN , ∞), S imposes a pollution tax satisfying tS < tN − τ /(b − b) + β − ε so as toinduce A = S and positive welfare where ε is a sufficiently small constant.
(ii) Second, we investigate N ’s best responses given S’s pollution tax. Similarly, evaluating
the switching point τ ∗ at taxes making the locations indifferent to N (i.e., VN |A=S = VN |A=N ),we get the threshold tax rate: b
tS = −τ /(b − b) + β + (γ/2)(b − b).
If tS ∈ [0, btS ), then VN |A=S > VN |A=N holds. N imposes tN > tS + τ /(b − b) − β andchooses A = S.
If tS ∈ [btS , ∞), then VN |A=S < VN |A=N holds. N imposes tN < tS + τ /(b − b) − β andchooses A = N .
(iii) Third, we combine (i) and (ii) together to get the Nash equilibria as follows.
If τ /(b − b) − β < 0, or τ < τb∗ , both locations can be the Nash equilibria, i.e., AN E ∈{N, S}. The Nash equilibrium tax differences at AN E = N are ∆tN E < 2[τ /(b − b) − β], andthose at AN E = S are ∆tN E = τ /(b − b) − β.
If τ /(b − b) − β = 0, or τ = τb∗ , the tax differences and the assembly location at the Nashequilibria are respectively ∆tN E ≤ 0 and AN E = N .
If τ /(b − b) − β > 0, or τ > τb∗ , the tax differences and the assembly location at the Nashequilibria are respectively ∆tN E < τ /(b − b) − β and AN E = N .
From Appendix A2, we can see that the Nash equilibria coincides with the socially optimal
outcomes for τ ≥ τb∗ , which are shown in Fig. A10.

26

Fig. A10. Nash equilibrium tax difference (shaded area and ∆t = τ /(b − b) − β) andassembly location under high unbundling costs

A4 Nash equilibrium outcome under low unbundlingcosts
As noted in Appendix A2.2, the indirect utility of the representative agent in each country
is given by(if τ < τ ∗∗VN |A=S = ue − CS + tN (b − bS ) − (γ/2)(b − bS )2 + 1 + X,
VN =VN |A=N = u
e − CN + tN (b − bN ) − (γ/2)(b − bN )2 + 1 + X if τ ≥ τ ∗∗(VS |A=S = tS (bS − b) − (γ/2)(bS − b)2 + 1 + X
if τ < τ ∗∗VS =,VS |A=N = tS (bN − b) − (γ/2)(bN − b)2 + 1 + X if τ ≥ τ ∗∗where Ci is defined in (6) and (7); and τ ∗∗ ≡ 2θ(β + ∆t); bN = 1 − θ + ∆t; bS = 1 + θ + ∆t.
(i) First, we derive the best responses of each country with exogenous assembly location.
N ’s best response given tS and A = N ist̃BR
N (tS )|A=N ≡ tN =

γ
γ
tS +
(b − 1 + θ).
1+γ
1+γ

27

N ’s best response given tS and A = S ist̃BR
N (tS )|A=S ≡ tN =

γ
γ
tS +
(b − 1 − θ).
1+γ1+γ

S’s best response given tN and A = N ist̃BR
S (tN )|A=N ≡ tS =

1+γ
1+γ
tN +
(1 − θ − b).
2+γ2+γ

S’s best response given tN and A = S ist̃BR
S (tN )|A=S ≡ tS =

1+γ
1+γ
tN +
(1 + θ − b).
2+γ2+γ(ii) Second, we allow for endogenous location and derive S’s best response with endogenous
assembly given tN .
BR
if tN < bt∗Nt̃S (tN )|A=N
tBRtS |A=S = tN − τ /(2θ) + β if bt∗N ≤ tN ≤ t1N ,S (tN ) =
 BRt̃S (tN )|A=S
if tN > t1Nq∗bwhere tN = τ (2+γ)/(2θ)+(3+γ)θ+(γ/2)(b−b)+(b−1)− 2(2 + γ)τ + 2θ(2 + γ)(b − b + 2θ)is the switching point of assembly location at which S is indifferent to where assembly takes
place; t1N = (2 + γ)[τ /(2θ) − γ] + (1 + γ)(1 + θ − b).21 It is illustrated in Fig. A11.

Fig. A11. S’s best response with endogenous assembly location (red curve).
21

We need to assume that θ < (b − b)/2(1 + γ) to avoid the case where the switching point falls between
the two exogenous best response lines. The assumption is reasonable since we restrict our attention to thecase of low unbundling costs.

28

(iii) Third, we allow for endogenous location and derive N ’s best response given tS .
 BR
t̃N (tS )|A=S



t |
N A=S ≡ tS + τ /(2θ) − βtBR
N (tS ) =
tN |A=N ≡ tS + τ /(2θ) − β BRt̃N (tN )|A=N

if tS < t1S
if t1S ≤ tS ≤ b
t∗S
,
if b
t∗S < tS ≤ t2S
if tS > t2S

where bt∗S ≡ γ(b − 1) − (1 + γ)[τ /(2θ) − β] is the switching point of assembly location atwhich N is indifferent to where assembly takes place; t1S ≡ γ(b − 1 − θ) − (1 + γ)[τ /(2θ) − β];t∗S = (t1S + t2S )/2. N ’s best response ist2S ≡ γ(b − 1 + θ) − (1 + γ)[τ /(2θ) − β]. Note that b
illustrated in Fig. A12.

Fig. A12. S’s best response with endogenous assembly location (blue curve).

(iv) Fourth, we derive Nash equilibria with endogenous assembly location. We only need to
combine the best responses of the two countries together and then to see whether there exist
intersections or overlapping lines. Fig. A13 draws the cost-indifference line at τ = 0, i.e.,τ ∗∗ ≡ 2θ(β + ∆t) = 0, or tN = tS − β. Note that the cost-indifference line locates aboveBRthe intersection of t̃BR
N (tS )|A=S and t̃S (tN )|A=S . Therefore, there are two types of Nashequilibria depending on τ : one characterized by the cost-indifference line; the other by theBRintersection of t̃BR
N (tS )|A=N and t̃S (tN )|A=N , i.e., point B.

29

Fig. A13. Cost-indifference line at τ = 0.
We have seen that N is indifferent to where assembly takes place if tN = t∗N , so is S atb∗tS = bt∗S , or equivalently tN = bt∗∗
N ≡ tS + τ /(2θ) − β. Noting that the two countries’ switching
22
points are bt∗N and bt∗∗
N , the two switching points are equalized at
q

2
2
θ
θ(2 + γ){2γ (θ + b − b) + γ(2 + 2b − 4b + θ)} + 2(1 − b) − (γ + 3γ + 1)θ − (b − 1)(1 + γ)
τ1 ≡.
(1 + γ)2E
Then, for τ < τ1 , the Nash equilibria occur on the cost-indifference line where ∆t|N
A=S =
τ /(2θ) − β (see Fig. A15). At point B, N ’s and S’s pollution taxes aretB
N =γ(2 + γ)γ(b − 1 + θ) + (1 − θ − b),2(1 + γ)
2

tB
S =

γ2
1+γ
(b − 1 + θ) +(1 − θ − b).
22b∗
Equalizing tB
N and tN givesq2θ 2θ(1 + γ) γ 2 (b − b) + γ(θ + 1 + 2b − 3b) + 2(1 − b) − θ(2γ 2 + 3γ + 2) − (b − 1)(2 + γ)
τ2 ≡(1 + γ)(2 + γ)
EThen, for τ > τ2 the Nash equilibrium occurs at point B where ∆t|N
A=N = γ(b − 1 + θ)/[2(γ +1)] − (1 − θ − b)/2 (see Fig. A18).
For τ1 ≤ τ ≤ τ2 , there are two possible cases: (a) both countries still impose pollution
taxes along the cost-indifference line, but they choose different assembly locations (see Fig.
22

b∗
b∗∗
It can checked that ∂ bt∗N /∂τ > 0; ∂ bt∗∗N /∂τ < 0; and tN < tN holds at τ = 0.

30

A16); (b) their best-response curves have neither intersections nor overlapping parts (see Fig.
A17). In both cases, there is no Nash equilibrium.
To conclude, we haveNE
if τ < τ1
∆t|A=S ≡ τ /(2θ) − βNE∆t= No Nash equilibrium
if τ1 ≤ τ ≤ τ2 ,
 NE
∆t|A=N ≡ γ(b − 1 + θ)/[2(γ + 1)] − (1 − θ − b)/2 if τ > τ2
which is shown in Fig. A14. The Nash equilibria coincides with the socially optimal outcomes
only for τ ∈ (τ a , τb∗∗ ), which is narrower than τ ≥ τb∗ . We can thus conclude that thedecentralized policy outcomes are more likely to deviate from the socially optimal ones in
the age of the second unbundling.

Fig. A14. Nash equilibrium tax difference (blue line) and assebly location under low
unbundling costs.

31

Fig. A15. Nash equilibrium for τ < τ1 .

Fig. A16. Case (a) for τ1 ≤ τ ≤ τ2 : overlapping line with different assembly location.

32

Fig. A17. Case (b) for τ1 ≤ τ ≤ τ2 : no intersections.

Fig. A18. Nash equilibrium for τ > τ2 .

33

References
Abe, K., Hattori, K., and Kawagoshi, Y. (2014). Trade liberalization and environmental
regulation on international transportation. Japanese Economic Review, 65(4):468–482.
Andonova, L. B. and VanDeveer, S. D. (2012). EU expansion and the internationalizationof environmental politics in Central and Eastern Europe. In Steinberg, P. F. and VanDeveer, S. D., editors, Comparative Environmental Politics: Theory, Practice, and Prospects,
chapter 11, pages 287–312. The MIT Press.
Arbolino, R., Carlucci, F., De Simone, L., Ioppolo, G., and Yigitcanlar, T. (2018). The policy
diffusion of environmental performance in the European countries. Ecological Indicators,
89:130–138.
Baldwin, R. E. (2016). The Great Convergence: Information Technology and the New Globalization. Harvard University Press, Cambridge, MA.
Baldwin, R. E. and Venables, A. J. (2013). Spiders and snakes: Offshoring and agglomerationin the global economy. Journal of International Economics, 90(2):245–254.
Cherniwchan, J. (2017). Trade liberalization and the environment: Evidence from NAFTA
and US manufacturing. Journal of International Economics, 105:130–149.
Cherniwchan, J., Copeland, B. R., and Taylor, M. S. (2017). Trade and the environment:
New methods, measurements, and results. Annual Review of Economics, 9:59–85.
Copeland, B. R. and Taylor, M. S. (2005). Trade and the Environment: Theory and Evidence.
Princeton University Press, Princeton, NJ.
Dijkstra, B. R. and De Vries, F. P. (2006). Location choice by households and polluting
firms: An evolutionary approach. European Economic Review, 50(2):425–446.
Duranton, G. and Puga, D. (2005). From sectoral to functional urban specialisation. Journalof Urban Economics, 57(2):343–370.
Fink, C., Mattoo, A., and Neagu, I. C. (2005). Assessing the impact of communication costs
on international trade. Journal of International Economics, 67(2):428–445.
Forslid, R., Okubo, T., and Sanctuary, M. (2017). Trade liberalization, transboundary
pollution, and market size. Journal of the Association of Environmental and Resource
Economists, 4(3):927–957.
Freund, C. L. and Weinhold, D. (2004). The effect of the internet on international trade.
Journal of International Economics, 62(1):171–189.
Fujita, M. and Thisse, J.-F. (2006). Globalization and the evolution of the supply chain:
Who gains and who loses? International Economic Review, 47(3):811–836.
Gokan, T., Kichko, S., and Thisse, J.-F. (2019). How do trade and communication costs
shape the spatial organization of firms? Journal of Urban Economics, 113:103191.
34

Hamilton, S. F. and Requate, T. (2004). Vertical structure and strategic environmental trade
policy. Journal of Environmental Economics and Management, 47(2):260–269.
Holzinger, K., Knill, C., and Sommerer, T. (2008). Environmental policy convergence: The
impact of international harmonization, transnational communication, and regulatory competition. International Organization, 62(4):553–587.
Ikefuji, M., Itaya, J., and Okamura, M. (2016). Optimal emission tax with endogenous
location choice of duopolistic firms. Environmental and Resource Economics, 65(2):463–
485.
Ishikawa, J. and Okubo, T. (2017). Greenhouse-gas emission controls and firm locations innorth–south trade. Environmental and Resource Economics, 67(4):637–660.
Ishikawa, J. and Tarui, N. (2018). Backfiring with backhaul problems: Trade and industrial
policies with endogenous transport costs. Journal of International Economics, 111:81–98.
Keen, M. and Kotsogiannis, C. (2014). Coordinating climate and trade policies: Pareto
efficiency and the role of border tax adjustments. Journal of International Economics,
94(1):119–128.
Lai, Y.-B. and Hu, C.-H. (2008). Trade agreements, domestic environmental regulation, andtransboundary pollution. Resource and Energy Economics, 30(2):209–228.
Levinson, A. and Taylor, M. S. (2008). Unmasking the pollution haven effect. International
Economic Review, 49(1):223–254.
Markusen, J. R., Morey, E. R., and Olewiler, N. (1995). Competition in regional environmental policies when plant locations are endogenous. Journal of Public Economics,
56(1):55–77.
Obashi, A. (2019). Trade agreements with cross-border unbundling. Journal of the Japaneseand International Economies, 53.
Ogawa, Y. and Yanase, A. (2019). Pareto-efficient international taxation in the presence ofenvironmental externalities. FinanzArchiv: Public Finance Analysis, (Online First):1–16.
Pflüger, M. (2001). Ecological dumping under monopolistic competition. Scandinavian Journal of Economics, 103(4):689–706.
Sanctuary, M. (2018). Border carbon qdjustments and unilateral incentives to regulate theclimate. Review of International Economics, 26(4):826–851.
Shapiro, J. S. and Walker, R. (2018). Why is pollution from US manufacturing declining? The
roles of environmental regulation, productivity, and trade. American Economic Review,108(12):3814–54.
Sterner, T. and Köhlin, G. (2003). Environmental taxes in Europe. Public Finance &Management, 3(1):117–142.
35

Ulph, A. (1996). Environmental policy and international trade when governments and producers act strategically. Journal of Environmental Economics and Management, 30(3):265–
281.
Voßwinkel, J. and Birg, L. (2018). Emission taxes, firm relocation, and quality differences.
mimeo, University of Göttingen.
Wan, R., Nakada, M., and Takarada, Y. (2018). Trade liberalization in environmental goods.
Resource and Energy Economics, 51:44–66.
Wan, R. and Wen, J.-F. (2017). The environmental conundrum of rare earth elements.
Environmental and Resource Economics, 67(1):157–180.
World Bank (2020). World Development Report 2020 : Trading for Development in the Ageof Global Value Chains. World Bank, Washington, DC.
Yomogida, M. and Tarui, N. (2013). Emission taxes and border tax adjustments for oligopolistic industries. Pacific Economic Review, 18(5):644–673.
Zeng, D.-Z. and Zhao, L. (2009). Pollution havens and industrial agglomeration. Journal ofEnvironmental Economics and Management, 58(2):141–153.

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