Can the Terms of Trade Externality Outweigh Free-Riding?
The Role of Vertical Linkages
Job Market Paper
Christian Bogmans†
This Version: January, 2014.
Abstract
This paper analyzes the role of vertical linkages on the international effects of environmental policy.
Using a simple general equilibrium model of trade, we find that if countries are mutually dependent
on imports to produce exports, domestic environmental policy not only reduces emissions at home,
but indirectly in the rest of the world as well. When national policymakers non-cooperatively determine environmental standards, they do not internalize all environmental benefits and also realize that
trade increases between countries with weaker standards. If pollution is sufficiently transboundary
a race to the bottom ensues, despite the fact that vertical linkages magnify the ability to export the
costs of environmental policy. It is found that whether vertical specialization is good or bad for the
environment depends crucially on whether it is rooted in stronger linkages or a reduction in the costs
of trade.
Keywords: Globalization, Trade and Environment, Carbon leakage, Climate Policy, Input-Output.
JEL classification: F18, Q56, Q58.
This paper is a revised version of chapter 5 of my 2011 Ph.D thesis. Without any implications, I would especially like to
thank Cees Withagen, Sjak Smulders and Brian Copeland for their support and feedback while writing this paper; discussions
with Steven Brakman, Sumeet Gulati, Carol McAusland, Gerard van der Meijden, Thomas Michielsen, John Morrow, Peter van
Oudheusden, Gonzague Vannoorenberghe, Alan Woodland, Aart de Zeeuw and Ben Zissimos also contributed to improve this
paper. I also received valuable comments and suggestions from seminar participants at the Exeter 2012 workshop on ’Resource
Insecurity, International Trade and the Environment’, the Eureka seminar at the VU University Amsterdam, the ETSG 2012
conference in Leuven and the Dutch Economists Day 2012 at the Dutch Central Bank. Any remaining errors are mine.
1
1
Introduction
Going back at least to Leontief (1970), scholars have recognized the importance of accounting for interindustry relationships when tracking the environmental repercussions of economic activities. Now
more than ever, a study of the environmental impacts of production warrants an international perspective in order to shed light on the role of inter-industry relationships. The reason is twofold. First of all,
over the last few decades production processes have become increasingly internationally fragmented.
This trend is associated with a rapid increase in intermediate goods trade and an increase in the degree to which exports are produced with imported inputs. Second, in recent years policymakers have
increased their attention to global environmental problems, such as the control of anthropogenic greenhouse gas emissions. Despite a recent surge in empirical work in the trade and environment literature
that uses input-output (I-O) methods to account for inter-industry dependencies, see e.g., Levinson
(2009), Davis et al. (2011) and Aichele and Felbermayr (2012), their role on the effects of environmental
policy in open economies remains understudied.
This paper analyzes how vertical linkages shape the incentives facing national regulators concerned
with environmental policy. Here we refer to different industries or sectors as being interconnected
through vertical linkages if the production of intermediate goods in one particular sector is enabled
by the input of intermediate goods from another sector. We employ a simple, multi-country general
equilibrium theory containing vertical linkages to examine the marginal costs and benefits of unilateral environmental policy. The results are then used to determine what happens to global pollution in
a world where countries are becoming increasingly interconnected via vertical linkages and set environmental policies non-cooperatively. The outcome of this non-cooperative game is then compared to
the outcome under full cooperation, where countries coordinate their policies so as to maximize global
welfare.
Recent research suggests that the process of globalization has occurred in two consecutive waves.
According to Baldwin (2006), ’the first unbundling allowed the spatial separation of factories and consumers.
The second unbundling spatially unpacked the factories and offices themselves’. Since the end of the 1980s
trade in intermediate goods and business services have increased to a far greater extent than total trade
(WTO, 2008). According to Yeats (2001) intermediate input trade, or ’global production sharing’, already
accounted for roughly thirty percent of world trade in manufacturing goods in 19951 .
Amidst these structural changes there has been a growing concern that trade liberalization will
intensify regulatory competition in national environmental policies, thereby provoking a race to the
bottom with negative consequences for global environmental quality (see Ederington (2010)). This does
not represent a necessary outcome, however, as some have argued that there might be a race to the top
instead. Provided the elasticity of demand for domestic products on world markets is sufficiently low,
a significant fraction of the costs of environmental policy can be passed through to foreigners via higher
prices. McAusland and Millimet (2013) explain that this incentive is stronger the larger the portion of
trade that crosses national borders.
We generalize the Armington type model of Acemoglu and Ventura (2002) by adding vertical linkages, trade costs and transboundary pollution from intermediate goods production. Within this environment we are able to explain how the degree of vertical specialization, which we define as the import
expenditure share of exports, is increasing in the strength of vertical linkages and decreasing in the
level of trade costs. As argued by Hummels et al. (2001) and Yi (2003), both cross-country technological heterogeneity and the dependence of exports on imports are pivotal to vertical specialization.
Whereas the first characteristic is captured by the Armington assumption of extreme technological heterogeneity, with each country producing a unique set of tradable intermediate goods, we incorporate
1 For
a more thorough overview of empirical studies in the field see Antras and Staiger (2012).
2
the second aspect by assuming that tradable intermediate goods are produced with domestic labor and
a CES aggregate of all available intermediates.
In the first part of the paper we analyze both the marginal costs and benefits of unilateral environmental policy. Naturally, the results obtained here are required for the normative analysis in the second
part of the paper, but they also prove to be interesting in their own right. Of primary interest here is the
concept of pollution leakage, defined as the increase in pollution abroad in response to an increase in
the stringency of environmental policy at home (see Babiker (2005)).
We show that once countries are mutually dependent on the import of intermediates through vertical linkages, a novel channel opens up through which domestic environmental policy can influence
emissions abroad. By reducing the net supply of intermediate goods from a given country to world markets, a stricter domestic environmental policy spills over to foreign countries where it indirectly reduces
output in the import-dependent intermediate goods sector. As in the traditional work on input-output
analysis (see Leontief (1970)), this effect sets in motion another round of reductions in all countries
so that the initial effect is magnified. This negative global supply effect is larger if the policy change
originates in a large country and if the elasticity of substitution between different intermediate goods
is small. Our framework serves as a convenient vehicle to study the role of vertical linkages, because
the combination of assumptions implies that without linkages the foreign intermediates supply curve
is completely inelastic and hence leakage is precisely zero.
The first main contribution of the paper is therefore to explain the occurrence of negative leakage,
with pollution in other countries not increasing, but decreasing under unilateral policy. When trade is
costly, however, environmental policy leads to allocative inefficiencies and expenditure shifting. The
latter effect tends to reallocate production and consumption of intermediates to the rest of the world,
diminishing the magnitude of the negative leakage result. We also repeat our analysis in the one-sector
Eaton and Kortum (2002) model and a classic two-sector Ricardian model, two frameworks that are
characterized by less extreme forms of technological heterogeneity than the Armington model, and
show that the negative leakage result is diminished, but not likely overthrown.
In the second part of the paper the comparative statics results are then utilized to study noncooperative and cooperative environmental policies. Under non-cooperation environmental standards
are endogenously determined by benevolent governments, each setting its standard independently. In
the resulting symmetric Nash equilibrium, the standard is distorted relative to the cooperative solution
due to (i) a terms of trade motive and (ii) a free riding motive, two externalities that lie at the heart of
our normative analysis. It is well known that the terms of trade externality tends to lead to a race to
the top, a situation where environmental policy is set too strict from a social point of view, whereas free
riding leads to the opposite situation, resulting in a race to the bottom in environmental standards.
Regarding the marginal costs of environmental policy, we find that vertical linkages not only lower
the net import elasticity of demand, but also raise trade intensity, implying larger terms-of-trade effects
and ceteris paribus lower costs of environmental policy as compared to the cooperative policy regime.
With respect to the marginal benefits, it is shown that vertical linkages, despite of the fact that they are
a precursor to negative leakage, tend to reinforce the free-riding incentive. Naturally, national interests
are assumed to be of paramount importance to domestic regulators. As such, regulators fail to take into
account that a reduction in pollution abroad also spills back to other countries. This so-called spillback
effect dampens the negative leakage effect compared to a cooperative regime where countries fully
internalize all benefits resulting from negative leakage.
Our second main contribution is to prove that in case of global pollutants, e.g., greenhouse gases
emissions, there is always a race to the bottom. In situations where policymakers are dealing with
pollutants that are local in scope, a race to the top is obtained instead. This core result reflects the
fact that pollution spillovers are more substantial when the geographic scope of pollutants is larger.
3
Therefore, when pollution spillovers are strong the incentive to free ride overwhelms the ability to
export the costs of environmental policy to the rest of the world via vertical linkages, countries install
relatively weak environmental standards and a race to the bottom ensues. Somewhat surprisingly, it is
found that vertical linkages can bring the non-cooperative standard closer to the cooperative standard,
but only when pollution is fully transboundary. In the latter case, vertical linkages tend to magnify
the ability to export the costs of environmental policy, which pushes the non-cooperative standard
upwards. When pollution is local in nature, stronger linkages also imply that a larger fraction of the
benefits are exported, which pushes the non-cooperative standard downwards.
In the third main contribution of the paper we show, using a combination of analytical results and
numerical analysis, that the environmental impact of vertical specialization depends on the underlying
force behind vertical specialization. In particular, we find that under non-cooperation the relationship
between vertical specialization and the environment may either be positive or negative. If vertical
specialization is rooted in stronger input-output linkages pollution tends to increase. In this case, both
the increased ability to export the costs of environmental policy and the higher policy responsiveness
of global pollution tend to reduce pollution, but it is also true that vertical linkages directly raise the
productivity of labor, thereby increasing the opportunity costs of environmental policy. However, if
vertical specialization is induced through a fall in the costs of trade, pollution tends to decrease. The
intuition here is that lower trade costs make it easier for producers to export the costs of environmental
policy.
The environmental consequences of trade in intermediate goods are relatively unexplored in the
literature on trade and the environment. Some important exceptions are Benarroch and Weder (2006),
McAusland (2004) and Hamilton and Requate (2004), but none of these studies incorporate I-O linkages
in a multi-country general equilibrium model. Of course, there is a substantial amount of theoretical
research that tries to determine whether trade, directly or indirectly, results in environmental degradation. The usual method of analysis here is to compare levels of pollution under autarky and under
international trade (see e.g., Copeland and Taylor (1995, 2003)). This paper considers the role of vertical
linkages, an empirically relevant aspect of globalization, that so far has been overlooked in the literature
on trade and environment. McAusland and Millimet (2013) use data on intra and international trade
for the US and Canada to examine whether trade, by prompting demand for stricter environmental
regulations, can indirectly be good for the environment. McAusland and Millimet (2013) find robust
evidence that this is the case, with international trade intensity exerting a beneficial causal impact on
environmental quality, while intranational trade intensity is found to have a harmful impact. These
findings are consistent with a terms of trade motive for stricter environmental policy2 .
The rest of this paper is set up as follows. In the next section, we discuss the model’s assumptions
and characterize the equilibrium, paying special attention to the impact of vertical linkages and trade
costs. In section 3 we study both the marginal cost and marginal benefits of a unilateral change in
environmental policy, which forms the core of our analysis. Here, we also explain how negative leakage
can arise in a setting with vertical linkages and perform some numerical analysis to assess its sensitivity.
In section 4 we study a cooperative and non-cooperative approach to environmental policy, compare
their outcomes in terms of global emission levels and analyze the role of vertical linkages. Section 5
extends our analysis in a number of directions. The last section concludes.
2 Broda, Limao and Weinstein (2008) provide strong empirical evidence for terms of trade considerations playing an active role
in the formation of trade policy. Consistent with the theory on optimal tariffs, they find that non-WTO members systematically
set higher tariffs on imports that are supplied inelastically.
4
2
The Model
We enrich the Armington type model of Acemoglu and Ventura (2002) by adding trade costs, vertical
linkages and (transboundary) pollution from the production of intermediate goods. The world economy consists of a (large) number of N countries indexed by j. There is one primary factor of production,
labor L j , that is supplied inelastically and immobile between countries. The size of the world population equals Lw
j= N
∑ j=1 L j . In each country there are three sectors, producing (1) tradable intermediate
goods, (2) a composite intermediate good and (3) a non-tradable final consumption good. The set of
tradable intermediate goods contains a total number of m varieties. Each country produces a unique
j= N
subset n j from this set of varieties with ∑ j=1 n j = m. Countries engage in costly trade in intermediate
goods in order to produce the composite intermediate good. To sell one unit of an intermediate good
in another country a producer must ship t
1 units, which implies that t
1 units melt in transit.
The composite intermediate good is used in the production of the consumption good, but also serves
as an input to the production of tradable intermediates (input-output), as in Eaton and Kortum (2002),
Alvarez and Lucas (2007) and Ramondo and Rodriguez-Clare (2013).
2.1
Welfare, Consumption and Pollution
Per capita welfare v j in country j depends positively on per capita consumption c j
Cj /L and nega-
tively on damages from (transboundary) pollution Zj :
v j = log c j
(1)
ηZj
where η represents the marginal damage from pollution. Let z j denote emissions generated in the
production of one variety in country j. Then total pollution experienced by country j is given by Zj =
n j z j + ∑i6= j ζni zi where the parameter ζ indicates the extent to which pollution disperses geographically:
when ζ = 0, pollution is local (e.g., sulfur dioxide), while when ζ = 1 the damages of the pollutant are
uniformly distributed across the globe regardless of the country of origin (e.g., carbon dioxide).
2.2
Production of Intermediate Goods and Final Goods
The production of intermediate goods requires the input of labor and the composite intermediate good.
In turn, production of the composite intermediate good requires the input of all available intermediate
goods varieties. From this it follows immediately that the production of each variety is enabled by the
production of all the other varieties. In this sense, we refer to the different varieties in the intermediate
goods sectors as being interconnected or vertically linked. The constant returns to scale production
functions of the intermediate good and the composite intermediate good read:
y j = g j (1
N
Xj =
l jy
β
θj)
ε 1
ε
∑ ni yij
i =1
!
β
1 β
x jy
1
β
(2)
ε
ε 1
, ε>1
(3)
where y j , yij , x jy , l jy , g j and ε > 1 represent respectively net output, the input of a typical intermediate
good from country i in country j, the input of the composite intermediate good, the input of labor, total
factor productivity (TFP) in the intermediate goods sector and the elasticity of substitution between
intermediates. In the intermediate goods sector producers spend a constant fraction β of their expenditures on the composite intermediate good. As such, β can be interpreted as a measure of the strength of
5
vertical linkages in the economy.
The production of one net unit of output generates e(θ j ) units of pollution, where θ j is the fraction of
gross output of the intermediate good used for abatement in country j. Following Copeland and Taylor
(2003) we assume a simple iso-elastic specification, e(θ j ) = (1
θj)
1 α
α
with 0 < α < 1. Total emissions
z j of a typical variety then equal:
z j = e(θ j )y j
(4)
The non-tradable final consumption good Cj is produced with the input of the composite intermediate
good X jC and labor L jC :
2.3
1 τ
L jC
1 τ
Cj =
X jC
τ
τ
(5)
Market Equilibrium
Markets for intermediate goods, the composite intermediate good and the consumption good are subject to perfect competition, and therefore unit cost pricing prevails:
pj
Pj
p jC
=
=
1 1
1
w j β Pj
gj 1 θ j
"
+ ∑ ni φpi
n j p1j ε
= wj 1
β
i6= j
(6)
1 ε
#
1
1 ε
(7)
τ τ
Pj
(8)
where p j is the intermediate goods price, Pj is the price of the composite intermediate good, w j represents the domestic wage rate and φ
t1
ε
1 is a parameter measuring the ’freeness’ of trade.
Market clearing for the composite intermediate good in each country requires X j = X jC + X jy , where
X jy
nx jy represents total input of the composite intermediate good in the intermediate goods sector.
In equilibrium the sum of labor employed in the production of tradable intermediates L jy
n j l jy and
the final consumption good L jC should equal the supply of labor, L j = L jy + L jC .
Next, demand by country i for a typical intermediate produced in country j is of the constant elasticity form, q ji = φ ji p j ε Piε
1
Ei , where Ei equals nominal expenditures on intermediates by country i.
Define nominal income in country j as Ij = w j L j . From profit maximization in the intermediate goods
τ
β I j , such
sector and the final consumption goods sector and labor market clearing it follows that Ej =
that global demand for a typical variety can be written as
qj =
∑ q ji = p j ε Pjε
1τ
i
β
Ij + ∑ φp j ε Piε
i6= j
j= N
Next, define world income and relative income as I w
1τ
β
Ii
(9)
I
j
∑ j=1 Ij and λ j
I w respectively. The balanced
trade condition can then be obtained by equating the supply of and demand for country j’s intermediate
goods (see appendix A for a more detailed derivation):
Ij = n j p j 1
where Γ j
nj pj
1 εΓ
j,
Pjε
1
λ j + ∑i6= j φPiε
1
ε
Γj Iw
(10)
λi . In equilibrium, a country’s relative level of income is equal to
which represents the world income expenditure share on commodities from that country.
Next, inspired by Hummels et al. (2001) and Yi (2003) we define the degree of vertical specialization
as the expenditure share on imports in the production of exports. To this end, denote a country’s exports and imports of intermediates by EX j
nj pj yj
n j p j y jj and I M j
6
∑i ni pi yij
n j p j y jj respectively.
(1
Definition 1. The degree of vertical specialization is denoted by π j
β)
I Mj
I M j +n j p j y jj
= (1
β) 1
λj ε 1
Γ j Pj
While stronger input-output linkages (β #) directly raise the upperbound on vertical specialization,
lower trade costs (φ ") essentially deepen the degree of vertical specialization for a given upperbound
1
β.
Next, for comparative statics purposes we will concern ourselves only with a version of the model
that differentiates between two "groups" of countries, group A and group B. Group A consists of only
one country, to which we will refer as country A, which unilaterally adjusts its environmental policy.
Group B consists of N
1 passive countries. We assume that all countries within group B are fully
symmetric, but we do allow for differences in population size and technology between country A on
the one hand and countries from group B on the other hand.
The general equilibrium of the model can be represented by the wage rate in country A (w A ) and
the wage rate in group B (w B ). Taking PA as the numeraire price, using the price index equations (7)
for country A and group B to write PB as a function of w A only, and substituting for intermediate
goods prices and PB (w A ) into country A’s price index equation (7) and balanced trade equation (10),
the equilibrium pair (w A , w B ) then solves the following set of equations (see the appendix):
1 = nA
1
1
β
w
gA 1 θ A A
wA LA = nA
1 ε
+ φ (N
1
1
β
w
gA 1 θ A A
1 ε
1) n B
h
1
1
w B β ( PB (w A ))1
gB 1 θ B
wA LA + φ (N
1) ( PB (w A ))ε
1
1 ε
β
wB LB
(11)
i
(12)
As we show in the appendix, a unique, asymmetric equilibrium exists and in all countries real income
wj
Pj
is higher under trade than under autarky.
Unlike trade liberalization, the impact of vertical linkages on equilibrium real income levels is diffi-
cult to determine. In a number of special cases, however, a closed-form solution to the pair (w A , w B ) is
available, allowing us to make several clear-cut statements regarding the relationship between vertical
linkages and real income. We consider the following special cases: (a) symmetric countries, (b) zero
trade costs and (c) a unitary elasticity of substitution (ε = 1). Let us define the relative real wage rate,
w A /PA
w B /PB ,
ω AB
and consider the following result:
Result 1. Real Income, Trade Liberalization and Vertical Linkages.
(I) Trade liberalization and vertical linkages increase real income and they are mutually reinforcing,
and
d
dt
d(w j /Pj )
dβ
d(w j /Pj )
dβ
<0
> 0 for j = A, B, case (a) and (c). (II) Vertical linkages disproportionately favor the country
with a relatively high income per capita,
dω AB
dβ
7 0 for ω AB ? 1, case (b). (III) Trade liberalization disproportion-
ately favors the country with a relative disadvantage in technology,
dω AB
dt
7 0 for n A ? n B , case (c).
Here we extend a previous result by Yi (2003), who was the first to implicitly recognize that trade
liberalization and vertical linkages are mutually reinforcing, by providing analytical derivations and by
decomposing the effect of vertical linkages on real income in two sub-effects. First, there is a positive
growth effect or factor elimination effect. When linkages are stronger, the better producers are able to
substitute for a non-reproducible factor of production (labor) by using a reproducible factor of production (e.g., machinery, computers, vehicles and generators). This effect is increasing in the initial level
of real income. Second, there is a dependency effect or love for variety effect, which raises real income
in the relatively poor, technology scarce country, while lowering it in the relatively rich, technology
7
.
abundant country. Taken together, vertical linkages reinforce any initial difference in real income.
Although vertical linkages are the hallmark feature of this paper, a few remarks with respect to the
role of trade costs are in order. With trade costs the price indices of country A and group B will generally
differ. This has implications for policymaking. First of all, an increase of the domestic standard will raise
the domestic price. To restore equilibrium, group B’s nominal wage has to fall relative to that of country
A, but since imports are subject to iceberg trade costs they will have to fall more than proportionally
with the factor φ1 . We refer to this effect as the price index effect. Second, when trade is costly producers
sell more in markets where the cost of living is high, trade barriers are low and relative income is high.
These export determinants are captured by the ’sales bias’ term Γ j . Domestic regulation can affect this
bias of sales and shift global expenditures towards domestic intermediates (expenditure shifting effect).
2.4
Equilibrium Pollution
Using profit maximization in the intermediate goods and final goods sectors, the labour market clearing
condition and the income constraint we can derive consumption of the composite intermediate as a
function of real income, x jy =
1 β τ Ij
β n j Pj .
Substituting this result into (4) gives the equilibrium level of
emissions,
1
z j = e(θ j ) g j 1
β
θj
wj
Pj
!1
β
τL j
, j = A, B
nj
(13)
It is also useful to focus on the supply side. In the appendix we show that real income is directly
proportional to production of the composite intermediate good:
wj
λj 1
= Gjβ , Gj = Gj (θ A , θ B ) , j = A, B
Pj
nj
(14)
Via the composite supply term Gj , which is influenced by global environmental policies, a stricter domestic environmental standard spills over to other countries. The latter channel only arises with vertical
linkages (β < 1).
3
Environmental Policy, Terms of Trade and I-O linkages
3.1
The Costs of Unilateral Environmental Policy
We analyze the effects of a unilateral marginal change in domestic environmental policy on wages
and prices. The government is able to indirectly control the intensity of abatement θ j by imposing an
environmental standard (or emission standard) s j = e(θ j ), where θ j is uniquely determined by θ j =
e
1 (s
j ).
In the remaining of this paper we will always refer to θ j when discussing the stringency of
environmental policy in country j.
Next, we define the elasticity of variable x with respect to θ A by eθx
we use
eyx
dx/x
dy/y
let us refer to a
A
dx/x
.
dθ A /(1 θ A )
with y 6= θ A . In addition, let us define net imports as nI M j
1 dp A /p A
β dθ A /(1 θ A )
=
τ
β
λ
1 ΓA
A
IM
ew
A
> 0 and b
dw A /w A
dθ A /(1 θ A )
dp A =0
=
1
β
Ij
In all other cases
nj pj1
εΓ
jI
w
and
> 0 as the elasticity of
country A’s wage rate with respect to the environmental standard, in as far changes in the environmental standard affects country A’s terms of trade (ToT effect), and the elasticity of country A’s wage rate
with respect to the environmental standard at constant prices (TFP effect) respectively. We then totally
differentiate (11)-(12) with respect to θ A , w A and w B while taking θ B as constant, and rearrange:
8
Proposition 1. The Costs of Environmental Policy.
(i) More stringent environmental policy reduces country A’s real wage,
d
dθ A
wA
PA
= (a
b)
1
wA
<0
θA
(15)
as well as the real wage in group B,
d
dθ A
wB
PB
1
0
C w /P
B
= @ aewp AB eθPAB A B B < 0
| {z }| {z } 1 θ A
<0
where
d
φ
2 κ
2 κ
1 1+φ( N 2)+φ 1 κ +φ 1 κ ( N 2)
φ 1+φ( N 2)+ 1 κ κ +φ 1 κ κ ( N 2)
(16)
>0
is the price index coefficient with d
w
measures the strength of backward linkages in group B, and e p AB
1 d λ A ΓB
N 1 φ λB Γ A
dp A
pA
dθ A = βa 1 θ A
1, κ
(1
β) 1
φλ A
ΓB
> 0, eΓwAA ? 0 and eΓwAB < 0.
dp B
< 0 and e PpBA < 0.
> 0, dθ
A
(ii) Suppose countries are symmetric. Stronger vertical linkages increase the terms-of-trade coefficient if trade
da
2
< 0. A sufficient condition reads φ > 21 N
costs are sufficiently small, dβ
N 1.
Prices of intermediate goods increase at home and decrease abroad,
Environmental policy affects the real wage rate via two different channels. First, there is a TFP effect.
Since the net unit labor requirement increases with the stringency of environmental policy, the return to
labor must go down. Second, product differentiation implies that a part of the costs of environmental
policy can be exported via higher prices. A relatively wealthy country has to take into account that
it consumes a non-negligible portion
lowers export intensity,
τ
β
1
λA
ΓA
λA
ΓA
of domestically produced dirty intermediates. This ’burden’
, and reduces the terms of trade (ToT) effect. Stated otherwise, when
the number of countries is large, domestic producers of intermediate goods will ceteris paribus depend
heavily on imported inputs, the more so if vertical linkages are strong, and are therefore less affected by
domestic regulation, enabling stricter environmental policy. The net impact of environmental policy on
the domestic real wage rate is unambiguously negative, because the positive terms of trade (ToT) effect
is always overwhelmed by the negative TFP effect, a
b < 0.
The finding that terms of trade effects are larger in a setting with a large number of countries would
arise in any model with differentiated products. Employing the monopolistic competition model of
Krugman (1980), McAusland and Millimet (2013) explain how a high trade intensity enables regulators
to export the costs of environmental policy to consumers abroad, an effect they coin ’regulatory decoupling’. With vertical linkages, costs of environmental regulation are shifted to producers abroad, the
more so if linkages are strong3 .
In general, trade costs seem to have an ambiguous effect on the ability to export the costs of environmental policy. On the one hand, vertical specialization among group B countries deepens in response to
stricter environmental policy (expenditure shifting effect). In addition, production losses due to trade
frictions are exacerbated (production ineffiency effect). These two effects only occur when trade costs
are positive and country A is large. Numerical analysis indicates that these effects can either lower or
I M . On the other hand, trade costs reduce the fraction of
raise the net import elasticity of demand ew
A
> 0, thereby lowering export intensity4 .
Vertical linkages influence the costs of environmental policy in a number of ways. First of all, vertical
domestically produced intermediates that is exported,
∂Γ A
∂φ
3 Whether the optimal environmental tax should be higher or lower than the standard Pigouvian tax depends on whether the
country is a net exporter (higher) or a net importer (lower) (see Krutilla (1991)). In our setting, as in models of monopolistic
competition, all countries produce a unique set of varieties and as such are net exporters. We relax this assumption in section 5
of the paper.
4 Note that under extreme parameter values (very low β and φ) the magnitude of the expenditure shifting effect and the
production inefficiencies could become so large, that the terms of trade effect turns negative. We discard this possibility.
9
linkages increase the dependence of exports on foreign inputs. In particular, the ’degree of specializa-
< ε (1 β1 )(ε 1) = 1+ β(1ε 1) , such that it becomes more difficult to substitute away
towards other (local) inputs and therefore the ToT effect becomes larger. Second, the introduction of I-O
linkages gives rise to an intermediate goods multiplier β1 that increases the magnitude of both the TFP
effect and ToT effect. Intuitively, a higher standard in country A diminishes production of intermediate
goods in that country. In turn, this fall in supply then also lowers production of intermediate goods
in other countries, which then feeds back into country A etc. This cycle will repeat itself again and
again5 , culminating in the geometric sequence, 1 + (1 β) + (1 β)2 + .. = 1 (11 β) = β1
1. Thus, in
line with the growth effect from Result 1, vertical linkages raise the opportunity cost of environmental
policy. Third, vertical linkages tend to increase the dependence of group B on intermediates produced
in group B, thereby diminishing the price index effect coefficient φd , that is, d 1 for β 16 . By doing
so, vertical linkages weaken the expenditure shifting effect and production inefficiency effect. Provided
trade costs are sufficiently small and countries are symmetric, one can show that via this channel vertical linkages lower the net import price elasticity of demand and subsequently strengthen the ToT effect
(Proposition 1 (ii)).
tion’ increases,
3.2
1
ε
The Benefits of Unilateral Environmental Policy
We are interested in the impact of a unilateral marginal change in environmental policy on equilibrium
pollution, both at home and abroad. Using (13) we totally differentiate z A and z B with respect to θ A ,
w A , w B and PB while taking θ B as given.
Proposition 2. The Benefits of Environmental Policy.
Consider a unilateral marginal increase in the stringency of environmental policy by country A. Pollution is
reduced in all countries,
2
6 1
dz A
=6
4 α + (1
dθ A
|{z}
<0
dz B
= (1
dθ A
3
7 zA
β) ( a b)7
=
| {z }5 1 θ A
z
eθ A
A
1
zA
<0
θA
(17)
zB
<0
θA
(18)
<0
1
0
zB
B
w
P C
β) @ ae p AB eθ B A
=
| {z }| {z A} 1 θ A
<0
z
eθ B
A
1
>0
z
Pollution in group B is unaffected in the absence of vertical linkages, eθB = 0 for β = 1.
A
As one would expect, a more stringent unilateral environmental policy reduces pollution in country
A. Surprisingly, pollution in group B is reduced as well. A discussion of the following examples serves
to illuminate why leakage is negative:
5 In an I-O model of a small open economy with multiple factors of production, Jones (2010) explains how the simple I-O
multiplier is a special case of a general, more complex multiplier where industries differ in the degree to which rely on the inputs
of intermediate goods. Furthermore, using the 2006 edition of the OECD I-O database he concludes that for most countries "one
over one minus the intermediate goods share" represents a good approximation to the true multiplier.
6 Unless vertical linkages are very strong, we find that the trade cost effect is always dominant, d > 1. For example, with
φ
symmetric countries one finds
have
d
φ
d
φ j N =2
=
2 κ
1 1+ φ 1 κ
φ 1+ 1 κ κ
> 1 and lim N
< 1 provided β is sufficiently small.
10
d
!∞ φ
= 1, but for intermediate values of N (e.g., N = 3) we
Example 1. Free trade (φ = t1
ε
= 1). In this case Gj = G, z j =
1
β e(θ j ) g j
1
λ j β1
nj G
θj
1 β
τL j
nj
β
z
(1 β) 1 λ Aλ A a < 0.
Stricter policy in country A reduces pollution via two effects. First, with country A’s relative income
falling while that of group B increasing (λ A #, λ B "), the ’consumption’ and production of intermediates decreases in country A and increases in group B. This market size or allocation effect tends to reduce
pollution in country A while increasing pollution in group B. Second, stricter policies in country A
and
eθ B :=
A
1
reduce the supply of intermediates to domestic and world markets via the term G β . Imports by group
B fall and ceteris paribus output in group B must decrease. This negative supply or technology effect thus
reduces pollution in both country A and group B. The overall impact is a reduction of pollution in both
country A and country B. In the latter, the negative supply effect overwhelms the positive market size
effect. Intermediate goods, like physical capital, represent produced inputs, and by limiting supply of
these inputs, domestic environmental policy then results in a spillback effect in the form of reduced
pollution abroad7 .
z
(1 β) N1 1 a < 0.
When trade costs are positive, the allocation effect in country B is reinforced by expenditure shifting and
the magnitude of the terms-of-trade coefficient a diminishes. Hence, the reduction of pollution in group
B is weakened. Stated otherwise, with the price of country A’s intermediate goods increasing, composite intermediate good producers in group B will shift expenditures towards intermediates produced in
other group B countries. Due to these backward linkages, the ’consumption’ and production of intermediates in group B all increase in response to a stricter policy in country A, and there is more intra-group
trade. In equilibrium the price index PB falls relative to PA . This effect is akin to the factor mobility role
of intermediates that is present in new economic geography models, see Fujita et al. (1999), and it tends
to induce positive leakage.
Example 2. Symmetric countries. In this case
eθ B :=
A
To provide some further guidance to the sensitivity of the leakage rate with respect to key parame∆ZB
ZB
Z
Z
= B,0ZB,0 B,1 , such that
positive values correspond to negative leakage. We then consider the following numerical example:
ters, let us denote the rate of leakage as a function of the standard θ A by
Numerical Example. Baseline parameter values are N = 2, n A = n B = 1, g A = gB = 2, τ = 0.8,
β = 0.5, L A = L B = 1 and θ B = 0. The left and right panel of figure 1 depict leakage rates for different
levels of the elasticity of substitution (with φ = 0.9) and different levels of trade costs (with ε = 3) respectively. A lower elasticity of substitution and higher trade costs are shown to reduce the magnitude
of negative leakage. Although we lack a formal proof, we were unable to find cases where leakage is
7 On a technical level, our results bear a resemblance to Harstad (2012). In a recent, influential study Harstad (2012) has shown
that supply side policies are key in overcoming free riding. Once countries can trade the rights to exploit fossil fuel deposits,
a climate coalition’s best policy is simply to buy foreign deposits and conserve them by using e.g., a carbon tax. Although the
coalition’s policies raise the price of fossil fuels on world markets, they do not result in supply side leakage. This surprising
effect occurs because the foreign fossil fuel supply curve has become locally inelastic after the coalition has acquired the marginal
foreign deposits. In fact, higher prices now reduce fossil fuel consumption in other countries as well. Hence, leakage becomes
negative. In this paper, the foreign intermediates supply curve depends positively on the supply of intermediates from other
countries. With stricter domestic environmental policy reducing the supply of intermediates to world markets, consumption of
these intermediates by intermediate goods producers in all other countries will fall, thereby inducing negative leakage.
11
actually positive.
Figure 1. Sensitivity of Leakage rates.
Unilateral policy resulting in negative carbon leakage is an interesting outcome. Most studies on climate change policies in open economies find the opposite result of positive leakage, see e.g., Babiker
(2005). As far as we know, Fullerton et al. (2011) and Karp (2012) are the only other papers that present a
mechanism for negative leakage using a ’conventional’ trade model8 . In Fullerton et al. (2011) it results
from a so-called abatement resource effect; by increasing its demand for the internationally mobile clean
factor of production, the regulated sector in the mitigating country crowds out production in the unregulated sector abroad. Karp (2012) generalizes an early contribution by Chau (2003) and explains, among
other things, that negative leakage can occur in factor endowment models with a separate abatement
sector. If the abatement sector is the most capital intensive sector and the dirty sector the least capital
intensive sector, a stricter environmental policy will increase the cost of capital, thereby pushing up the
relative price of the clean good and increasing the country’s comparative advantage in the dirty sector.
Similar to Fullerton et al. (2011) we do not claim that carbon leakage actually is negative. Our results
merely illustrate that conventional models might have overlooked certain channels. Interestingly, the
mechanism for negative leakage presented here is purely market driven and different from mechanisms
that rely on strategic interaction and income effects, as in Copeland and Taylor (2005).
8 In contrast to our study, Fullerton et al. (2011) and Karp (2012) do not consider strategic interaction between countries nor do
they derive welfare results in the context of non-cooperative policies.
12
4
Cooperative and Non-Cooperative Environmental Policy in the Global
Economy
4.1
A Variety of Externalities
In this section we study a cooperative and non-cooperative approach to environmental policy and
compare their outcomes in terms of global emission levels. Our focus here is on a arbitrary number of symmetric countries in a world with trade costs. Under the cooperative solution countries coordinate their environmental policies with the objective of maximizing global welfare. In the one-shot
non-cooperative game governments maximize national welfare by choosing environmental standards
unilaterally, while taking the standards in other countries as given. In the resulting symmetric Nash
equilibrium, a number of externalities distort the non-cooperative standard relative to the cooperative
solution. Let us first briefly discuss these externalities, with an emphasis on the role played by vertical
linkages, before continuing with our analysis.
First of all, firms and domestic policymakers do not take into account that pollution spillovers from
domestic production reduce welfare in other countries. A stricter environmental standard reduces emission intensity and the emission of pollutants at home, but domestic policymakers only internalize these
benefits in as much they lower domestic pollution damages. This is the conventional transboundary
pollution externality and it results in too much pollution as compared to the cooperative solution.
The transboundary pollution externality is reinforced in the presence of vertical linkages. By reducing the productivity/supply term Gj in the tradable goods sector (see (14)), environmental policy decreases production and pollution in the rest of the world, which in turn lowers pollution damages in the
domestic country. We refer to this additional effect as a spillback effect, similar to Ogawa and Wildasin
(2009). Without cooperation only a certain portion of the spillback effect is internalized. Hence, we
may refer to the uninternalized fraction of the spillback effect as a spillback externality. For future reference, we define (1) free-riding as the joint incentive underlying pollution policy as shaped by both the
spillback effect and the transboundary pollution externality.
Second, domestic policymakers ignore the negative ramifications of higher prices induced by their
environmental policies for intermediate good producers and final good producers in other countries.
This (2) terms of trade externality tends to lead to too little pollution.
4.2
The Cooperative Equilibrium
∑N
j=1 v j . Substitution of (1), c j =
Let us define global welfare by V w
wj
p jC
=
wj
Pj
τ
and (13) into V w
gives
Vw =
N
∑ log
i =1
wi
Pi
N
τ
η ∑ Zi (θ 1 , θ 2 , .., θ N )
(19)
i =1
When countries cooperate they maximize their joint welfare (19) and as a result each country selects a
1
standard θ j that equates the social marginal cost of the environmental standard, ΩC
S 1 θ , to the social
j
ηnz j
θj
marginal benefit of the standard, Ω B 1
τ
+τ ( N
|
1 θ j dw j
1 θ j dPj
1
w j dθ j
Pj dθ j 1 θ j
1 θ
1 θ j dPi
1
i
1) w j dw
Pi dθ j 1 θ j
i dθ j
{z
1
ΩC
S 1 θ
j
+ (N
1) ΩlB 1
ηnzi
θj :
0
}
1 θ j dz j
z j dθ j
B
B
= ηn B
@ +( N
|
13
1 θ j dzi zi
zj
zi dθ j z j 1 θ j
1
1 θ j dz j z j
j dzi
+
ζ
zi dθ j
z j dθ j zi
A zi
1 θ dzi
1 θj
+ζ ( N 2) zi j dθ
j
+ ζ (N
0 1 θ
1) @
ΩB
ηnz j
1 θj
{z
+( N
1)
ηnz
1)ΩlB 1 θi
j
1
C
C
C
A
}
(20)
A higher standard reduces real income at home and abroad, thereby reducing consumption and utility
in all countries. The social marginal benefit of setting a higher standard in country j results from less
dz j
dθ j
pollution damages at home, which consist of a direct effect via
In addition, there are benefits for all other N
are reduced directly, via
dzi
dθ j ,
and a spillback effect via ζ ( N
1)
dzi
dθ j .
1 countries, because pollution damages in these countries
dz
and indirectly due to various spillback effects, via ζ dθ j + ζ ( N
2)
j
dzi
dθ j .
Be-
fore we present the full solution of the optimal cooperative standard θ C , we analyze the non-cooperative
problem.
4.3
The Non-Cooperative Equilibrium
In the non-cooperative game the problem of country j is to maximize v j = log
wj
Pj
τ
ηZj (θ 1 , θ 2 , .., θ N )
with respect to θ j , taking the standards set by other countries as given. The first-order condition reads:
1
τ
|
θ j dw j
w j dθ j
1
{z
θ j dPj
Pj dθ j
ΩC 1 1θ
!
1
1
θj
}
j
1
= ηn
|
θ j dz j
+ ζ (N
z j dθ j
1)
{z
ΩB 1
1
θ j dzi zi
zi dθ j z j
!
zj
θj
zj
1
θj
}
(21)
for all j = 1, .., N. Each country sets the private marginal cost of meeting the domestic standard (lefthand side term) equal to the private marginal benefit of meeting the domestic standard (right-hand side
term) when determining the optimal standard.
Equation (21) implicitly determines the best response of country j as a function of the standards set
in other countries, θ j = BR j (θ j ). A strategy profile (θ 1 , ..., θ N ) represents a Nash equilibrium if, for
each country j, its equilibrium strategy θ j is a best response to the strategies (θ 1 , ..., θ j
the other N
1 , θ j+1 , ..., θ N )
of
1 players. Since we have assumed all countries to be identical in terms of endowments,
technology and preferences, a symmetric Nash equilibrium exists where each country sets the optimal
non-cooperative standard θ NC . Note that under full symmetry (13) reduces to
_
z ( θ ) = z (1
θ)
1 1 β
α+ β
_
, z
1
g ( w )1
β
β
ly
(22)
_
where z (w) is the maximum level of pollution (wage rate) in a world without environmental policy (see
the proof of Result 1), and Φ
By substituting for
dw j dwi
dθ j , dθ j ,
dz 1 θ
= α1
d (1 θ ) z
dPi dz j
dzi
dθ j , dθ j and dθ j
+
1 β
β
> 0.
from Proposition 1 and Proposition 2 into (20) and (21),
and applying symmetry we obtain respectively the private marginal cost and private marginal benefit
elasticities, ΩC = τ (b
a) and Ω B =
social marginal benefit elasticities,
ΩlB
1
α
+ (1 β ) ( b
tions for θ C and θ NC :
ζ
a) +
1
α
+ (1 β) (b a) + ζ (1 β) a, the social marginal cost and
and ΩSB = Ω B + ( N 1)ΩlB with
ΩC
S = τb
N 2
N 1 (1
θ NC = 1
β) a +
ΩC
ΩB
1
N 1
(1
1
Φ
,
θC = 1
β) a, and subsequently closed-form solu"
ΩC
S
ΩSB
#1
Φ
(23)
In turn, by substituting these solutions into (13) we can obtain the levels of pollution in equilibrium910 .
9 Our
implies
set of assumptions (i.e. symmetric countries and taking the price index Pj of one particular country as the numeraire)
1 dPj
Pj dθ j
= 0 for all j, such that this terms drops out both equations (20) and (21). Of course, ex-ante countries take into
account that their policies can affect price indices in other countries, hence the term
10 Our
dPi
dθ j
that does play a role.
set-up allows for analytical solutions to the optimal standard under alternative specifications as well, e.g., iso-elasticity
utility. For functional forms other than log utility, however, the real wage rate does not vanish from the elasticities in (21) and (20).
In addition, Result 1 tells us that vertical linkages and trade liberalization raise real income. Since we are not directly interested
14
Next, let us refer to a "race to the top" and a "race to the bottom" as situations in which θ NC > θ C and
_
θ NC < θ C hold respectively. Define ζ as the spillover coefficient for which θ NC = θ C . We assume that
trade costs are sufficiently low such that the terms-of-trade effect is increasing in the strength of vertical
linkages, as in part (ii) of Proposition 1. The solutions under (23) then satisfy the following properties:
Proposition 3. Environmental Standards: Race to the Bottom or Race to the Top? The Role of Vertical
Linkages.
(i) When pollution is fully transboundary (ζ = 1) there is always a race to the bottom, that is, θ NC < θ C . Stronger
d
dβ
θ NC
θC
< 0.
(ii) Under purely local pollution (ζ = 0) there is always a race to the top, that is, θ NC > θ C . Stronger vertical linkθ NC
d
? 0.
ages have an ambiguous impact on the gap between the cooperative and non-cooperative standard, dβ
θ
vertical linkages diminish the gap between the cooperative and non-cooperative standard,
_
_
C
_
(iii) There exists a unique ζ, such that that there is a race to the top for ζ < ζ and a race to the bottom for ζ > ζ,
_
provided ζ 2 (0, 1).
Both a race to the bottom, which is typical for the tax competition literature, and a race to the top, where
standards are actually highest in the non-cooperative equilibrium, are feasible, depending on whether
national regulators are dealing with local or transboundary pollutants. To explain this outcome, let us
examine in more detail the incentives underlying the non-cooperative and cooperative solutions.
On the one hand, a comparison of the two solutions under (23) tells us that a national regulator’s
ability to export the costs of environmental policy via higher prices can significantly lower the private
marginal cost of environmental policy relative to the social marginal cost. In a world with a large number of countries, and hence a large number of sovereign governments and international borders, domestic producers of intermediate goods depend heavily on imported inputs, the more so if vertical linkages
are strong, and are therefore less affected by domestic regulation, enabling stricter environmental policy.
In more technical terms, vertical linkages lower the net import elasticity of demand and magnify export
intensity, strengthening the ToT motive. Based on this argument alone, the non-cooperative standard
should be more stringent than the cooperative standard.
On the other hand, in the cooperative regime the spillback externality is fully internalized and so the
marginal benefits of meeting the environmental standard are larger under cooperation. Therefore the
cooperative standard tends to be higher than the non-cooperative standard. For example, in the case of
greenhouse gas emissions (ζ = 1) the social benefits are exactly N times as large than the private benefits, Ω B + ( N
1)ΩlB := NΩ B . By giving rise to spillback effects, vertical linkages reinforce free-riding,
thereby limiting the incentive for national regulators to implement stricter policy. Taken together, when
the terms of trade externality overwhelms the free-riding externality the outcome represents a race to
the top and otherwise we end up with a race to the bottom.
To clarify this result further, consider the case where pollution spillovers between countries are
absent (ζ = 0). Again, we find that national policymakers do not fully account for the reduction in
real income and pollution abroad, thereby underestimating both the global benefits and global costs
of domestic environmental policy. As it turns out, for local pollutants the terms of trade effect always
outweighs the free-riding incentive and a race to the top ensues.
Interestingly, proposition 3 also tells us that stronger linkages tend to weaken the race to the bottom
result. Intuitively, this occurs because stronger linkages magnify the terms of trade externality, but
they have no impact on the degree of free-riding. Hence, stronger linkages bring the non-cooperative
standard relatively closer to the cooperative standard. The story is more complicated, however, for
local pollutants, for which the impact of vertical linkages becomes ambiguous. In that case, stronger
in the role of income, the welfare specification at hand enables us to take a "neutral stance" regarding any vertical specialization
induced income effects that drive the stringency of environmental policy.
15
linkages also magnify the extent to which the benefits of environmental policy are exported. This result
contrasts sharply with transboundary pollutants; reducing greenhouse gas emissions limits damages
from climate change irrespective of the location of these cutbacks.
Notwithstanding the availability of analytical solutions, it turns out to be difficult to unambiguously
sign the absolute impact of I-O linkages on the non-cooperative outcome. For one thing, part (iii) of
_
proposition 4 shows that there exists a threshold value ζ for the spillover coefficient such that for all
_
_
_
ζ < ζ we obtain a race to the top result and a race to the bottom result for all ζ > ζ, but whether ζ
_
is increasing or decreasing in β is not clear. Numerical analysis indicates that ζ tends to be decreasing
in β. In words, in a world where national economies are becoming increasingly interdependent via
I-O linkages we find that the range of pollutants for which inefficiently low levels of environmental
protection result, is decreased.
4.4
Vertical Specialization and Global Pollution
To increase our understanding of the impact of vertical specialization on global pollution across different policy regimes, this section concentrates on the important case of greenhouse gas emissions (ζ = 1).
The equilibrium solutions to real income and pollution can be obtained by substituting for (23) into (22)
and (39) respectively,
w NC = w
wC = w
τ
_
ηnz
τ 1
_
ηnz N
1
α
+ (1
β) b
!1
1
α
b
+ (1 β ) b
!1
b
1
β Φ
a
, nz NC =
, nzC =
1
β Φ
τ
η
b
1
α
τ 1
ηN
+ (1
1
α
a
β) b
b
+ (1 β ) b
(24)
(25)
Inspection of equations (24)-(25) tells us that stronger vertical linkages raise pollution due to a stronger
TFP effect (b "), while reducing pollution via a stronger spillback channel, (1
β) ". Under non-
cooperation, there is also a stronger terms-of-trade effect, a ", which lowers pollution. Proposition 4
then summarizes the net impact of stronger linkages on global pollution:
Proposition 4. Vertical Linkages and Global Pollution.
When pollution is fully transboundary (ζ = 1), stronger vertical linkages strictly increase the cooperative level
of global pollution,
dz NC
dβ
dzC
dβ
< 0, but their impact on the non-cooperative level of global pollution is ambiguous,
? 0.
Proposition 4 explains the impact of β on pollution under free trade. For the cooperative regime it
is found that, since the opportunity cost of environmental policy is increasing in the strength of inputoutput linkages, it is optimal to increase global pollution, despite the increased effectiveness of environmental policy. The latter mechanism arises because pollution becomes more responsive to environmental policy per se when linkages become stronger11 . Because stronger linkages also make it easier to
export the costs of environmental policy under non-cooperation, the impact of β under non-cooperation
is not as clear cut as in the cooperative case and becomes ambiguous.
In general, it turns out to be difficult to characterize analytically the influence of (i) trade freeness
φ and (ii) changes in β when trade is costly. To explore in more detail the impact on global pollution
11 Market structure may thus increase ’international interdependence’ and thereby influence the extent to which countries can
effectively exercise control over local and global environmental quality. See Bagwell and Staiger (2004) for a more general and
formal analysis of international interdependence and national sovereignty.
16
of these two crucial parameters underlying vertical specialization, we resort to numerical analysis to
supplement our analytical results. Our baseline parameter values are: m = 10, g = 1, τ = 0.6, ε = 3,
α = 0.3, Lw = 10 and η = 2. In figure 2 we display the non-cooperative level of pollution under free
trade for different values of N and β. The results here are rather clear. First, due to the strong negative
impact of free-riding on the willingness to reduce emissions, the equilibrium level of pollution is strictly
increasing with the number of countries. Second, figure 2 also illustrates that in the case of free trade
(φ = 1) the impact of β on equilibrium pollution is ambiguous. For a realistic range of parameter
values however (see Jones (2010)), that is, 0
β
0.5, it appears that total pollution is increasing
when vertical linkages become stronger (β #) ZNC "). Apparently, although vertical linkages magnify
both the ToT externality and the responsiveness of environmental policy, which should ceteris paribus
reduce pollution, their impact is overwhelmed by the increase in the opportunity cost of environmental
policy.
figure 2. The non-cooperative level of
pollution - the impact of β and N under free
figure 3. The non-cooperative level of
trade.
pollution - the impact of β and trade costs.
Figure 3 explores the sensitivity of our findings by introducing trade costs. Here we fix the number of
countries at N = 10. Again, vertical linkages increase pollution when their strength is weak, but tend
to diminish pollution once they are sufficiently strong. Another interesting observation from figure 3 is
that a reduction in trade costs lowers the level of global pollution under non-cooperation. This effect
can be rationalized by pointing out that trade intensity increases when trade is less costly, the more so
the stronger the degree of vertical linkages, making it easier to export the costs of environmental policy.
Next, we repeat our numerical experiments for the cooperative policy regime. Figure 4 shows the
positive relationship between β and the cooperative level of pollution, as stated under proposition 4.
When vertical linkages are stronger, labor is more productive, the opportunity costs of environmental
policy are larger, and it is optimal to allow more pollution. Note that in the absence of trade costs,
terms-of-trade considerations do not play a role under cooperation and hence the impact of N is neutral. Figure 5 illustrates the possibility of a negative relationship between vertical linkages and global
17
pollution. This effect appears to occur only when vertical linkages are already quite strong.
0,9
0,9
0,8
0,8
0,7
0,7
0,6
0,6
0,5
0,5
ZC
ZNC
0,4
0,4
0,3
0,3
0,2
0,2
0,1
0,1
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,1
0,2
0,3
0,4
b
0,5
0,6
0,7
0,8
0,9
1,0
b
figure 4: The cooperative level of
figure 5: The non-cooperative level of
pollution - the impact of β.
pollution - the impact of β.
In sum, figures 2-5 show that although the relationship between vertical linkages, trade costs and the
environment is not clear-cut, at least two important lessons can be drawn. First of all, whether one considers cooperative or non-cooperative policymaking, the relationship between vertical specialization and
pollution depends strongly on whether a higher degree of vertical specialization π is rooted in stronger
vertical linkages, which raise the upperbound on vertical specialization, or lower trade barriers, which
deepen the degree of vertical specialization for a given upperbound 1
β (see definition 1). Second,
and closely related to the first lesson, under non-cooperation the relationship between vertical specialization and the environment can either be negative or positive, depending on whether it is induced by
stronger linkages (β #) or lower costs of trade (φ ").
Let us consider the latter finding in more detail. On the one hand, a decrease in β increases the
ability to export the costs of environmental policy, because export intensity increases and the net import elasticity of demand falls, and it increases the responsiveness of global pollution to environmental
policy. On the other hand, a world with a low β (or a large 1
β) is a world where exports are too
a large extent fabricated with produced inputs, thereby increasing the productivity of domestic labor
and raising the opportunity cost of environmental policy. The latter effect appears to dominate the ToT
effect and the responsiveness effect for reasonable parameter values such that pollution increases with
1 β. Similarly, while a reduction in the cost of trade tends to increase the ToT effect, it does not directly magnify the opportunity cost of environmental policy, so that an increase in trade freeness tends
to lower pollution.
5
5.1
Extensions
Endogenous Specialization and Composition Effects
In the Armington model production adjustments take place solely along the intensive margin; by decreasing the supply of produced inputs to world markets, environmental policy indirectly lowers production in import-dependent sectors. By assuming a strong degree of cross-country technological heterogeneity, however, we were able to abstract from any effects induced by domestic labor mobility and
focussed exclusively on the role of the spillback effect (see Table 1). In this section we allow for weaker
18
forms of technological heterogeneity, thereby enabling domestic labor mobility within and between industries. As a result, the pattern of specialization becomes endogenous. We extend our analysis in two
directions. First, we employ the Eaton-Kortum (2002) (E-K) model of trade to stress the role of intraindustry specialization, i.e., the intensive margin. Second, we use a traditional two sector Ricardian
model of trade to explain the impact of inter-industry specialization, i.e., the extensive margin.
Table 1
Model
Effect/Margin
Spillback effect
Intensive margin
Extensive margin
Armington
yes
mute
mute
Ricardian (2-2)
yes
mute
yes (large country only)
Eaton-Kortum
yes
yes
mute
As a preview of our findings, Table 1 lists the different channels that are present in each model. First,
the spillback effect is a distinct channel for negative leakage that is present in all models. The spillback
effect actually enables negative leakage in the Armington model, but it magnifies negative leakage in
the E-K and Ricardian models. Second, intra-industry labor mobility (E-K) and inter-industry labor
mobility (Ricardian) are distinct mechanisms for either positive or negative leakage. Third, a sufficient
condition for negative leakage is the absence of composition effects. A sufficient and necessary condition for negative leakage is that the degree of comparative advantage is sufficiently large compared
to the difference in emission intensity across sectors. Therefore leakage can only be positive in the
Ricardian model, but not in the Armington and E-K models.
5.1.1
Leakage in the Eaton-Kortum Model of Trade
We endogenize the pattern of intra-industry specialization by employing a variation of the one-sector
Eaton-Kortum (2002) (E-K) model without trade costs. Eaton-Kortum (2002) proposed a probabilistic
representation of technologies. Productivity levels are treated as an independent realization of a random variable, independent across goods, with the random variable presented by a country-specific
Frechet distribution. The E-K set-up is richer compared to the Armington model due to the presence of
an additional parameter in the Frechet distribution governing cross-country technological heterogeneity, that is, the degree of comparative advantage. As we show in a supplementary appendix, in the E-K
model stricter environmental policy always leads to negative leakage, but now effects on the intensive
margin also play a role:
Proposition 5. Unilateral Environmental Policy in the E-K model of Trade.
Consider a unilateral marginal increase in the stringency of environmental policy by country A. While the number of varieties produced decreases in country A and increases in country B, pollution decreases in both countries.
Technological heterogeneity across countries is a sufficient condition for negative leakage, even in the absence of
vertical linkages (β = 1).
In the E-K model leakage is negative even without vertical linkages. The reason is as follows. A unilateral change in the environmental standard in country A contracts (expands) the range of commodities
produced in country A (B). Although countries in group B now produce some of the dirty intermediates originally produced in country A, all countries will produce less of each commodity on average; in
country A because of the higher unit labor cost induced by stricter environmental policy and in country
B because producers have now specialized in commodities in which they are on average less produc19
tive. Thus, the "forced" expansion of country B into relatively unproductive marginal commodities
lowers country B’s average productivity and total output. Since emission intensities are uniform, total
pollution in country B must go down as well.
In the presence of vertical linkages, country B’s expansion into relatively unproductive marginal
commodities is magnified, as both countries, but A in particular, suffer from a reduction in the supply of produced inputs. Note that in the Armington model the degree of technological heterogeneity
across countries is infinite, the intensive margin effect is mute and vertical linkages become a necessary
condition for negative leakage.
5.1.2
Leakage in a Two Sector Two Country Ricardian Model of Trade
We have also conducted our thought experiment in a two-country, two-sector Ricardian model with
vertical linkages and different sectoral pollution intensities. In this case, labor can move freely across
sectors with different emission intensities and the pattern of inter-industry specialization becomes endogenous. The comparative statics results depend on the specialization regime. First, consider a situation where country A is relatively small and specialized in one commodity, while the relatively large
country B is imperfectly specialized. If country A raises its standard the production of exports declines
and consequently labor in country B is reallocated from the export sector to the import-competing sector. As a result, country B experiences respectively a decrease of pollution in the export sector and an
increase of pollution in the import-competing sector, the more so if linkages are stronger. The overall
leakage effect is more likely to be negative if (i) country B exports the relatively dirty commodity (since
that is the sector that will contract) and (ii) country B’s productivity in the import-competing sector is
relatively low compared to its export sector12 . Note that a sufficient condition for total leakage in B to
be negative is that composition effects are absent, which is in line with out findings for the E-K model.
Second, let the two countries be of comparable size, such that both are perfectly specialized. This
regime corresponds to the Armington model, with negative leakage occurring if and only if countries
are vertically specialized (β < 1). Third, consider country A to be relatively large such that it is imperfectly specialized whereas B is perfectly specialized. Unilateral policy leads to negative leakage if
the standard is raised in the export sector. A higher standard in the import competing sector causes
positive leakage. If standards are raised simultaneously, leakage is negative provided the increase is
larger in the export sector13 .
5.2
Spiders, Snakes and Asymmetric Dependence
Up to this point, our view of vertical linkages has been quite symmetric. In a very rudimentary fashion
our production technology of the intermediate goods sector resembles that of a spider, to borrow a term
from Baldwin and Venables (2013), where multiple limbs (i.e., intermediate goods) from different countries (a number n j per country) come together to complete the body (i.e., the composite intermediate
good). In practice, global supply chains might also be organized in a more sequential manner, where intermediate goods are processed through a series of steps with value added at each stage of production.
Baldwin and Venables (2013) refer to this alternative set-up as the ’snake’.
We adjust our AV model with vertical linkages to match the snake configuration. Our aim is to
12 Interestingly, in this regime it is also true that if country B initially exports the dirty (clean) commodity, then negative leakage
is more likely if the cross-sectoral differences in pollution intensities are large (small).
13 Even if a marginal change in environmental policy leads to positive leakage, then there always exists a discrete change in the
standard that induces negative leakage, provided country B has a comparative advantage in the dirty commodity. Essentially, if
θ A ! 1 then country A becomes small and country B becomes autarkic. Assuming country B has a comparative advantage in
the production of the dirty commodity, pollution increases when going from autarky to trade and the other way around. More
detailed results regarding the Ricardian model can be found in the supplementary appendix.
20
show that vertical specialization, by making certain countries more dependent on trade than others14 ,
can potentially increase the responsiveness of foreign pollution to national environmental regulation.
In contrast to Baldwin and Venables (2013), Dixit and Grossman (1982) and Costinot et al. (2013), who
analyze respectively a partial equilibrium, a semi-general equilibrium and a full general equilibrium
version of the snake, we take the pattern of specialization as given. On the plus side, we work in a
general equilibrium setting. Our snake is also assumed to be quite ’short’; group B is dependent on
imports from country A to produce exports, but there is no further division of tasks within group B. Let
β j and 1
β j denote the Cobb-Douglas expenditure shares in the intermediate goods sector (see (2)),
then we assume β A := 1 and β B > 0. In the spider configuration an increase in β represents a mutual
increase of interconnectedness between countries. In the snake configuration, however, an increase in
β B makes group B more dependent on imports from A, but not vice versa. For this reason, we refer to
β B as an indicator of the degree of asymmetric dependence.
Let us define s PB
1 βB
β B (1 λ A )
1 β
1+ β B (1 λ A )
B
, which measures total expenditures on intermediate goods by coun-
try B’s intermediate goods sector as a fraction of world expenditures on intermediate goods. In this setting, unilateral environmental policy by country A then reduces the domestic real wage rate as follows
(see the appendix for more detail):
d (w A /P)
dw A
=
=
dθ A
dθ A
"
(1 λ A ) 1 s PB
1 + β B (ε 1) s PB
1
#
wA
= ( aS
1 θA
bS )
wA
<0
1 θA
(26)
d(w B /P)
dθ A
λA
wB
=
1 λ A aS 1 θ A < 0, such that leakage is always negative. Asymmetric linkages
have a remarkable influence on the effects of environmental policy. Most notable, asymmetric dependence can shift the balance of trade in favor of country A such that the ToT effect induced by country’s
A policy is larger than before. There are two opposing effects here. On the one hand, since a certain
share of imports by the consumption goods sector consists of re-imports, it becomes harder to export
the costs of environmental policy. To understand this consumption effect, note that the gross export share
(1 λ A ) is adjusted to account for the fraction of exports 1 s PB that are not re-imported. On the other
hand, country B becomes increasingly reliant on imports from country A to produce its exports. This
production effect reduces country B’s export elasticity of demand, as reflected in the denominator of the
ToT term in (26) and makes it easier for country A to export the costs of environmental policy:
while
Proposition 6. Asymmetric Dependence and the Responsiveness of Pollution.
(i) Consider a situation with λ A = λ constant (partial equilibrium). A marginal increase in the degree of asymmetric dependence (dβ B < 0) will strengthen the role of country B as a ’producer country’ and strengthen the role
d[(1 λ A )(1 s PB )]
ds P
of country A as a ’consumer country’, dβB < 0 and
> 0. As a result, it becomes easier to export
dβ
B
the costs of environmental policy, that is,
foreign pollution is increasing,
d
dβ B
z
eθ B
A
B
d
dβ B
w
eθ A
A
=
daS
dβ B
< 0, and for any given θ A the responsiveness of
> 0. (ii) Consider a situation with λ A variable (general equilibrium).
Then the effects of a marginal increase in the degree of asymmetric dependence are ambiguous. For β B sufficiently
close to 1, the partial equilibrium effects outweigh the indirect general equilibrium effects.
14 Of course, one could easily extend the model by adding Ricardian elements that will ’limit the degree of control’ by country
A over country B. For example, producers in country B might be able to choose from a portfolio of production technologies that
vary in their intensity of imports, including an unproductive, labor-only backstop technology. If prices of inputs from country
A would increase sufficiently, producers in B will find it profitable to switch to the old technology in order to limit dependence
on imports and to increase output. The productivity gap between the import-dependent technology and the import-substitution
technology will then determine the degree of control that country A can exert over B.
21
With pollution originating in production, not consumption, and with country B dependent on A for
the import of crucial inputs, one would expect country A to have a strong incentive to increase the
stringency of its environmental policy, both to raise its terms of trade as well as to decrease foreign
pollution. Indeed, a higher degree of asymmetric dependence not only makes it easier to export the
costs of environmental policy to country B, but it also implies that the reduction of pollution in country
B will be larger. This partial equilibrium type result, however, does not necessarily hold in general
equilibrium. Intuitively, changes in relative income can change the magnitude of the consumption effect and production effect, thereby rendering the overall impact of asymmetric dependence on the ToT
effect ambiguous. Hence, the magnitude of negative leakage could go down and the marginal costs of
environmental policy might go up. Nevertheless, the direction in which vertical specialization takes
place across countries can thus also have important consequences for the incentives facing domestic
policymakers.
6
Conclusion
In this paper we have explored the role of vertical linkages on the international effects of environmental
policy. When countries are mutually dependent on imports to produce exports, domestic environmental policy indirectly lowers pollution externalities in the rest of the world. This mechanism for negative
leakage is robust to the inclusion of trade costs, technological heterogeneity, composition effects and
asymmetric linkages. Vertical linkages also increase export intensity and the degree of international
specialization, both of which make it easier to shift the costs of environmental policy to producers
abroad. Whether strategic interaction between national policymakers leads to levels of pollution that
are inefficiently high, depends on the geographic scope of the relevant pollutant and hence on the
relative strength of the terms of trade motive and the free riding motive. In the context of global externalities the latter incentive is dominant, because regulators fail to internalize the spillback effects that
are enabled by vertical linkages.
The model used in this paper was deliberately simple, thereby allowing for a range of analytically
tractable results. Future work might extend our analysis by explicitly incorporating multinational corporations, as these firms are known to play an active role in establishing vertical linkages between
producers in different countries. For various reasons, studying optimal environmental policies with
asymmetric countries and linkages also constitutes an interesting avenue for future research. It seems
likely, for example, that any agreement on burden sharing in the context of climate policies will depend strongly on cross-country heterogeneity in technology and endowments. At the industry level,
more detailed analysis of pollution intensive sectors might be a fruitful research topic as well15 . This
seems especially interesting in the context of the energy and transportation sectors. These sectors are
of vital importance not only to the world economy, as measured by their degree to which they are (inter)nationally linked to other sectors, but, since they are carbon intensive, also appear to be crucial to
any serious plan that aims to mitigate global carbon emissions.
References
[1] Acemoglu, Daron, Ventura, Jaume (2002), ’The World Income Distribution’, The Quarterly Journal
of Economics, vol. 117 (2), pp. 659-694.
15 A recent paper by Lanz et al. (2013) analyses the effects of climate policies for the global copper industry, thereby emphasing
the role of trade in intermediate goods and geographical considerations.
22
[2] Aichele, R., Felbermayr (2012), ‘Kyoto and the carbon footprint of nations’, Journal of Environmental
Economics and Management, vol. 63, pp. 336-354.
[3] Alvarez, F., Lucas, R. (2007), ’General equilibrium analysis of the Eaton-Kortum model of international trade’, Journal of Monetary Economics, vol. 54 (6), pp. 1726-1768.
[4] Antras, Pol, Robert W. Staiger (2012),’Offshoring and the Role of Trade Agreements’, American
Economic Review, vol. 102 (7), pp. 3140-83.
[5] Babiker, Mustafa H. (2005), ’Climate Change Policy, Market Structure, and Carbon Leakage’, Journal of International Economics, vol. 65 (2), pp. 421-45.
[6] Bagwell, Kyle, Staiger, Robert W. (2004), ’National Sovereignty in an Interdependent World’, NBER
Working Papers 10249, National Bureau of Economic Research, Inc.
[7] Baldwin, R. (2008), ’Globalisation: the great unbundling(s)’, contribution to: Globalisation Challenges for Europe and Finland, Secretariat of the Economic Council of Finland.
[8] Baldwin, R., Venables, A. (2013), ’Spiders and snakes: Offshoring and agglomeration in the global
economy’, Journal of International Economics, vol. 90 (2), pp. 245-254.
[9] Benarroch, Michael, Weder, Rolf (2006), ’Intra-industry trade in intermediate products, pollution
and internationally increasing returns’, Journal of Environmental Economics and Management, vol. 52
(3), pp. 675-689.
[10] Broda, C., Limao, N. and Weinstein, D., ’Optimal Tariffs and Market Power: The Evidence’, American Economic Review, vol. 98 (5), pp. 2032-65.
[11] Chau, S. (2003), ’Does tighter environmental policy lead to a comparative advantage in less polluting goods?’, Oxford Economics Papers, vol. 55, pp. 25-35.
[12] Copeland, Brian R., Taylor, M.S. (1995), ’Trade and Transboundary Pollution’, American Economic
Review, vol. 85 (4), pp. 716-737.
[13] Copeland, Brian R., Taylor, M.S. (2003), Trade and the Environment: Theory and Evidence, Princeton
University Press, New Jersey.
[14] Copeland, Brian R., Taylor, M.S. (2005), ’Free trade and global warming: a trade theory view of the
Kyoto protocol’, Journal of Environmental Economics and Management, vol. 49 (2), pp. 205-234.
[15] Costinot, A., Vogel, J. and Su Wang (2013), ’An Elementary Theory of Global Supply Chains’,
Review of Economics Studies (forthcoming).
[16] Davis, Steven J., Peters, Glen P. and Ken Caldeira (2011), ‘The supply chain of CO2 emissions’,
Proceedings of the National Academy of Sciences, vol. 108 (45), pp. 18554–18559.
[17] Dixit, A.K., Grossman, G.M. (1982), ’Trade and Protection with Multistage Production’, Review of
Economic Studies, vol. 49 (4), pp. 583-594.
[18] Dornbusch, Rudiger, Fischer, Stanley and Samuelson, Paul A. (1977), ’Comparative Advantage,
Trade, and Payments in a Ricardian Model with a Continuum of Goods’, American Economic Review,
vol. 67 (5), pp. 823-39.
[19] Eaton, J., Kortum, S. (2002), ’Technology, Geography, and Trade’, Econometrica, vol. 70 (5), pp. 17411779.
23
[20] Ederington, Josh (2010), ’Should Trade Agreements Include Environmental Policy?’, Review of Environmental Economics and Policy, vol. 4 (1), pp. 84-102.
[21] Fujita, M., Krugman, P. and A. Venables (1999), The Spatial Economy: Cities, Regions and International
Trade, Cambridge, MA: MIT Press.
[22] Fullerton, Don, Karney, Daniel and Baylis, Kathy (2011), ’Negative Leakage’, NBER Working Papers 17001, National Bureau of Economic Research, Inc.
[23] Harstad, B. (2012), ’Buy Coal! A Case for Supply-Side Environmental Policy’, Journal of Political
Economy, vol. 120 (1), pp. 77-115.
[24] Hamilton, S.F., Requate, T. (2004), ’Vertical structure and strategic environmental trade policy’,
Journal of Environmental Economics and Management, vol. 47 (2), pp. 260-269.
[25] Hummels, David, Ishi, Jun and Yi, Kei-Mu (2001), ’The nature and growth of vertical specialization
in world trade’, Journal of International Economics, vol. 54 (1), pp. 75-96.
[26] Jones, Charles (2010), ’Misallocation, Economic Growth, and Input-Output Economics’, Prepared
for the 10th World Congress of the Econometric Society, mimeo.
[27] Jones, Charles (2011), ’Intermediate Goods and Weak Links in the Theory of Economic Development’, American Economic Journal: Macroeconomics, vol. 3 (2), pp. 1-28.
[28] Karp, Larry (2012), ’Carbon Leakage in General and Partial Equilibrium’, mimeo.
[29] Krugman, P. (1980), ’Scale Economies, Product Differentiation, and the Pattern of Trade’, American
Economic Review, vol. 70 (5), pp. 950-959.
[30] Krutilla, K. (1991), ’Environmental Regulation in an Open Economy’, Journal of Environmental Economics and Management, vol. 20, pp. 127-142.
[31] Lanz, B., Rutherford, T., and Tilton, J. (2013), ‘Subglobal Climate Agreements and Energy-Intensive
Activities: An Evaluation of Carbon Leakage in the Copper Industry’, The World Economy, vol. 36
(3), pp. 254-279.
[32] Leontief, W. (1970), ’Environmental Repercussions and the Economic Structure: An Input-Output
Approach’, The Review of Economics and Statistics, vol. 52 (3), pp. 262-71.
[33] Levinson, A. (2009), ’Technology, International Trade, and Pollution from US Manufacturing’,
American Economic Review, vol. 99 (5), pp. 2177-92.
[34] McAusland, Carol (2004), ’Environmental Regulation as Export Promotion: Product Standards for
Dirty Intermediate Goods’, The B.E. Journal of Economic Analysis and Policy, vol. 0 (2).
[35] McAusland, Carol, Millimet, Daniel (2013), ’Do National Borders Matter? Intranational Trade,
International Trade, and the Environment’, Journal of Environmental Economics and Management,
vol. 65, pp. 411-437.
[36] Ramondo, Natalia, Rodriguez-Clare, Andres (2013), ’Trade, Multinational Production, and the
Gains from Openness’, Journal of Political Economy, vol. 121 (2), pp. 273 - 322.
[37] Ogawa, H., Wildasin, David E. (2009), ’Think Locally, Act Locally: Spillovers, Spillbacks, and
Efficient Decentralized Policymaking’, American Economic Review, vol. 99 (4), pp. 1206-17.
24
[38] Ossa, R. (2011), ’A “New Trade” Theory of GATT/WTO Negotiations’, Journal of Political Economy,
vol. 119 (1), pp. 122-152.
[39] WTO (2008), ’World Trade Report 2008 - Trade in a Globalizing World’, Geneva.
[40] Yeats, A. (2001), ‘Just how big is global production sharing?’, in Kierzkowski, H. and Arndt, S.W.
(eds) Fragmentation: New Production Patterns in the World Economy, Oxford and New York:
Oxford University Press.
[41] Yi, Kei-Mu (2003), ’Can Vertical Specialization Explain the Growth of World Trade?’, Journal of
Political Economy, vol. 111 (1), pp. 52-102.
7
7.1
Appendix A: Derivations
The Balanced Trade Condition
From a trade theory point of view, the most intuitive method of deriving the BT condition is by equating
imports and exports. Four steps are needed. First, profit maximization in the intermediate goods sector
results in:
w j l jy = βp j y j and Pj x jy = (1
β) p j y j
Second, profit maximization in the final goods sector gives us w j L jC = (1
(27)
τ ) Ij . Using this result, the
definition of nominal income Ij = w j L = p jC C and labor market clearing, we obtain
n j w j l jy = τ Ij
(28)
Third, combining (27) and (28) then provides us with expressions for l jy and x jy as a function of income,
τ Ij
nj wj
j= N
1 β τIj
β n j Pj , as well as being able to rewrite ∑ j=1
j= N
n j p j y j = ∑ j=1 τβ Ij = τβ I w . Fourth and
finally, with n j intermediates produced by each country and a total number of N 1 trading partners,
l jy =
and x jy =
imports and exports are defined as:
∑ ni pi yij
I Mj
n j p j y jj
i
EX j
nj pj yj
n j p j y jj
Equating imports and exports, substituting for ∑i ni pi yij = τβ Ij and n j p j y j = n j p1j ε Γ j τβ I w while cancelling the term n j p j y jj on both side of the equations, then leads to the balanced trade condition:
Ij = n j p j 1
7.2
ε
Γj Iw
(29)
The Composite Intermediate Good
A country’s consumption share (or import share) of a typical intermediate good equals
sij
yij
=
yi
φij
ε
ε 1
Γi
25
Pjε
1
λj
(30)
1
ε τ w
yi = ∑ N
j=1 yij = pi Γi β I (see (9)) and tij
closed-form solution to X j can then be derived using a number of substitutions:
ε
where we used yij = tij pi
N
ε 1
ε
∑ nyij
=
Xj
1τ
β Ij ,
Pjε
i =1
!
= λ j @ ∑ ni
0
0
N
=
=
=
sij yi
i =1
sij
g (1
λj i
0
sij
B
= λ j @ ∑ n i @ gi ( 1
λj
β
1
β
∑ ni
ε 1
ε
!
β
1 β
λj Xj
1
1
β
λ j Gj
β
θi )
θi )
0
@ ∑ ni
liy
β
β
liy
β
β
1 β
xiy
1
β
1 λi Pj
X
ni λ j Pi j
sij
g (1
λj i
= φij . Using (3), a
ε
ε 1
!ε 1 1ε ε1
ε
sij
A
yi
λj
0
= λ j @ ∑ ni
ε
ε 1
ε
θ i ) liy
β
!ε ε1 1ε ε1
A
!1
β
1ε 1 1ε ε1
ε
A C
A
1 β
λi Pj
ni Pi
!ε 1 1ε ε1
ε
A
where the second equality follows from substitution of yij = sij yi for all i; the third equality follows
φij
from substituting for sij =
ε
ε 1
Γi
Pjε
1
λ j and taking λ j outside brackets; the fourth equality follows
from substitution of the intermediate goods production function, yi = gi (1
θi )
liy
β
β
xiy 1 β
; from
1 β
profit maximization in the intermediate goods sector and the consumption goods sector it follows that
nPi xiy =
1 β
β τ Ii
and Pi XiC = τ Ij . Combined with the constraint Xi = XiC + nxiy and the ratio
one can obtain xiy =
1 β λi Pj
ni λ j Pi X j .
X
∑iN=1 ni
sij
λ j gi
(1
θ i ) liy
=
λi Pj
λ j Pi
Substitution then gives the expression after the fifth equality; For the
sixth equality we rearrange the expression and bring λ j
j
ε
ε 1 !ε 1
Gj
Xi
Xj
λi Pj
ni Pi
β
1 β
1 β
and
ε
1
β
β
outside brackets; By defining
1 β
, bringing the term X j
to the left-hand side
and raising both sides to the power β1 , we obtain the desired closed-form solution to X j .
7.3
Spiders and Snakes
With asymmetric vertical specialization only group B countries require imports to produce exports.
Therefore p A =
1
1
gA 1 θ A w A
and p B =
βB
1
1
gB 1 θ B w B .
The set of equilibrium conditions reads
1 = n A p1A ε + ( N
with X w := τ I w +
1) n B p1B
ε
(31)
τ I A = n A p1A ε X w
(32)
τ
IB = n B p1B ε X w
βB
(33)
1 βB
βB τ ( N
1) IB , which is no longer proportional to world income since the intermediate goods sector in country A is assumed to produce using a labor-only technology. Rearranging
26
the price index equation and the BT conditions, we obtain respectively
wA
=
wB
=
h
h
n A ( g A (1
θ A ))ε
1
n A ( g A (1
θ A ))ε
1
+ nB ( N
( ε 1)
ω AB
LA
n
= A
LB
nB
β B ω AB
wB
(1 β B )(ε 1)
gA 1
gB 1
θA
θB
1
θ B ))ε
1) ( g B (1
(1 β B )(ε 1)
wB
ω εAB1
1) ( g B (1
( ε 1)
(1 β B )(ε 1)
ω AB
wB
1
ε 1
θ B ))ε
+ nB ( N
ε 1
i
1
(34)
i
1
β B ( ε 1)
(35)
(36)
Substitution of (35) into (36) gives us w B (ω AB ) and subsequently w A (ω AB ). Using country A’s BT
condition (32) we can write
wεA 1
1
θ A ))ε
n A ( g A (1
w1A
ε
LA =
n A ( g A (1
1
θ A ))ε
1
(N
βB
1) L B w B
The LHS is strictly positive and increasing in w A while the RHS is strictly increasing in w B . Since
w0A (ω AB ) < 0 and w0B (ω AB ) > 0, the LHS and RHS are respectively decreasing and increasing in ω AB
and the equilibrium is unique.
7.4
Existence and Uniqueness of Asymmetric Equilibrium
First, substitute for n B p1B
ε
=
1 n A p1A ε
φ ( N 1)
equation of country B to obtain PB =
dP1
from the price index equation of country A into the price index
1+ φ ( N 2)
φ ( N 1)
(1
1+ φ ( N 1)
φ ( N 1)
φ)
n A p1A
ε
1
1 ε
ε
= PB (w A ) with dwB > 0. Second, substitute for PB (w A ), prices from (6) and expressions for relative
A
income λ j into the price index equation and the balanced trade condition of country A to get:
h
1 = n A g A (1
w A L A = n A ( g A (1
θ A ) wA
i
β ( ε 1)
+ φ (N
0
θ A ))ε
1
wA
β(ε
B
B
B
1) B
Bw A L A +
B
B
B
@
h
1) n B g B (1
β
θ B ) w B PB (w A )
(1 β )
i(ε
1)
(37)
1
φ ( N 1) w B L B
h
i
β ε 1
φn A g A (1 θ A ) w A
h
β
(1
+ (1 + φ ( N 2)) n B gB (1 θ B ) w B PB
i
β) ε 1
C
C
C
C
C
C
C
C
A
(38)
A general equilibrium is a pair (w A , w B ) that solves equations (37)-(38). To proof existence and uniqueness of the equilibrium, we characterize each equation in (w A , w B )-space, starting with the price index
h
i 1
β ( ε 1)
equation (37). If w A ! ∞ then w B ! w B
PB = w Ba
(1 + φ ( N 2)) n B ( gB (1 θ B ))ε 1
1
h
i 1
1+ φ ( N 2) 1 ε
ε 1 β ( ε 1)
where PB
.
If
w
!
∞
then
w
!
w
n
= w aA . Total
g
1
θ
(
(
))
B
A
A
A
A
A
φ ( N 1)
differentiating (37) with respect to w A and w B and rearranging, we obtain the following derivative:
0
dw B
=@
dw A
1
1+ φ ( N 2)
1 φ 1+ φ ( N 1)
1
n A ( g A (1
where the sign follows from
1
β
θ A ))
1 1+ φ ( N 2)
1 φ 1+ φ ( N 1)
ε 1
wA
β ( ε 1)
1
n A ( g A (1
θ A ))
ε 1
wA
β ( ε 1)
1
A n A p1
A
ε
wB
<0
wA
> 1. Second, we characterize the BT-condition, equation (38).
For w B = 0 we get w A = w A . Furthermore, totally differentiating (38) with respect to w A and w B and
27
rearranging, we get:
λA
ΓA
1
dw B
=
dw A
+ φPε
1 λA
ΓA
λA
ΓA
1
β ( ε 1)
1 λA
+
+ φPε 1 λΓ AA
P
P
We have
dw B
dw A
1 λA
ΓA
β 1 1 κ φPBε
where ewBB > 0 and where we substituted for ewBA
1
1 κ
λA
ΓA
P
1)ewBB Γ1
A
1 (ε
+ φPε
1
(1 λ A )φPε
ΓA
1
φPε
1
ε 1 λA
1
1 κ βφPB Γ A
=
wB
wA
with κ
(1
β) 1
> 0 unless β is very small. Thus, the price index equation and the BT condition slope re-
spectively monotonically downwards and monotonically upwards in (w A , w B )-space. Since the price
index equation starts above the BT condition at w A = w aA a unique equilibrium exists with w A 2
(w aA , ∞) and w B 2 (w Ba , ∞). With w A > w aA , w B > w Ba and PB w A < PB , real income
wj
Pj
is higher in
both countries under free trade than under autarky.
8
Appendix B: Proofs
Result 1. Real Income, Trade Liberalization and Vertical Linkages.
Proof Closed form solutions to wages can be obtained in a number of cases. (a) When countries are
fully symmetric,
w = n (1 + φ ( N
θ ))ε
1)) ( g (1
1
β ( ε 1)
1
= w (1
1
θ) β
(39)
which is obtained by applying symmetry to (11). (b) When trade costs are absent we obtain, after setting
φ = PB = Γ A = 1 in equations (11)-(12) and rearranging,
wA
=
wB
=
h
h
n A ( g A (1
θ A ))ε
1
n A ( g A (1
θ A ))ε
1
ω AB =
+ nB ( N
β ( ε 1)
+ nB ( N
ω AB
n A LB
nB L A
θ B ))ε
1) ( g B (1
gA 1
gB 1
!
β ( ε 1)
ω AB
1) ( g B (1
ε 1
θA
θB
1
θ B ))ε
i
1
1
β ( ε 1)
i
1
β ( ε 1)
1
1+ β ( ε 1)
(c) Setting ε = 1 and rearranging equations (11)-(12) gives the required expressions for wages for the
Cobb-Douglas case,
wA
wB
PB
w
s
2
4 ( g A (1
θ A ))
nA
1
t
(n A n B )
=
ω AB
1
t
=
1
ω AB
1
t
(n A n B )
1+ n A n B
g B (1
θB)
!n B ( N
!n A
!n B ( N
1)
1)
ws
ws
31
(40)
β
5
, ω AB =
n A LB
nB L A
1
t
n A nB
(I) Statement follows directly from the derivatives and cross-derivatives with respect to β and t. For
example, with case (b) we have
dw A
=
dβ
log w A +
1 λA
wA
log ω AB
1 + β ( ε 1)
β
28
φλ A
ΓA
.
dw B
=
dβ
with
dw A
dβ
< 0 and
dw A
dβ
λA
1 + β (ε
log w B
dω AB
dβ
dω AB
dt
=
i
h
β ( ε 1)
dω AB
log ω AB ωβAB
dβ =
1+ β ( ε 1)
n B ) ω tAB we have dωdtAB 7 0 for
< 0 provided g A and gB sufficiently large. (II) Since
7 0 for ω AB ? 1 for case (b). (III) With
n A ? n B in case (c). This completes the proof.
we have
1)
wB
β
log ω AB
(n A
Proposition 1. The Costs of Environmental Policy.
Proof (i) We substitute for n B p1B
ε
1 n A p1A ε
φ ( N 1)
=
from the price index equation of country A into the price
1+ φ ( N 2)
φ ( N 1)
index equation of country B to obtain PB =
(1
φ)
1+ φ ( N 1)
φ ( N 1)
n A p1A
ε
1
1 ε
= PB ( p A )
1 ε
1+ φ ( N 1)
p
< 0. Next, we totally differentiate equations (11)-(12)
(1 φ) φ( N 1) n A PAB
and the price index equation for country B with respect to w A , w B , Γ A and θ A to get:
P
with e pBA =
0 = n A p1A
dw A
dw
= λA A + (N
dθ A
dθ A
PB1
Solving for
dw B
dθ A :
dw A
dθ A
ε
ε
w
1) n B p1B
w A dw B
+ β (1
w B dθ A
ε)
1) λ B
1
d nA pA
N 1 φ n B p1
B
1
ε
ε
> 0 with d
θ A:
Γ
0 and
Γ
εθ A
A
ε)
(41)
wA
w dΓ
+ A A
1 θA
Γ A dθ A
2)) n B p1B
ε
1 dp B
p B dθ A
(42)
(43)
φ2 ( N 1) κ
2) 1 κ
1+ 1 κ κ
1+ 1+ φ ( N
h
= @
0
φ ) (1
1
(N
(44)
β)
s BB
ssBB .
Second, we then totally
1) λ B , with respect to w A , w B and
(45)
(1 λ A ) λ A
φPBε 1
ΓA
A
from (44) and dΓ
dθ A from (45) into
A
P
λ A ) φPBε 1 e pBA
< 0. Next, substitute for
dw A
dθ A
1
dw B
dθ A
and rearrange:
h
Γ w
1) + ( N 1) ewAB e p AB
1
1 λ A Γ1
1 A wA
A
IM
β
1 θA
ew
A
1
1 A wA
(46)
β 1 θA
λ A Γ1
τ 1 + β(ε
τ
(1
λ A + φ ( PB ( p A ))ε
τ
β
β
= @
=1
wB
1 θA
Γ dw B
ΓA
dΓ A
Γ dw A
= eΓwAA A
+ eΓwAB A
+ εΓθ AA
dθ A
w A dθ A
w B dθ A
1 θA
i
1+ φ ( N 1) 2( ε 1) 1
φPBε 1 β(ε 1) (1 φ) N 1 PB
? 0, eΓwAB
Γ
(1 λ A ) λ A
1
ΓA
1
1) (1
Γ A (ε
0
θ A dw A
1
+
w A dθ A
β
1
w
e p AB
the differentiated BT condition (42), solve for
dw A
dθ A
1 dp B
p B dθ A
then proceeds in three steps. First, solve the two price index equations (41) and (43) for
differentiate the sales bias definition, Γ A
where ewAA
ε
dw A
+ (1
dθ A
1 dp A
1 dPB
= φn A p1A ε
+ (1 + φ ( N
PB dθ A
p A dθ A
dw B
=
dθ A
where e p AB
1 dp A
+ φ (N
p A dθ A
A
i
Γ
ewAA + ( N
w
1) λ B e p AB
λA
(47)
Equation (46) reduces to (15) by applying the definitions of a and b. The derivative
dp A
dθ A
= βa 1 p Aθ A
follows immediately.
(1+φ( N 2))λ B PBε 1
λA
.
Γ A and s BB =
ΓB
1+ φ ( N 2)
1 θ A dw A
. Substituting for w dθ
1+ φ ( N 1)
A
A
Next, we define the consumption shares s AA
try these reduce to ssAA =
1
1+ φ ( N 1)
and ssBB =
29
Under full symmeinto (44) and using
1 <
the consumption share equations we obtain
1 + φ ( N 2) s AA d ε
P
N 1
s BB φ B
dw B
=
dθ A
Furthermore, we can write
1
1
wB
θA
(48)
p
= e PpBA eθ AA 1 PBθ A as
dPB
dθ A
dPB
=
dθ A
1
φ
φ 1 + φ ( N 1)
s AA PBε
N 1
1
βa
PB
θA
1
(49)
Finally, combining (48)-(49) we can write:
d (w B /PB )
=
dθ A
d(w B /PB )
dθ A
1
1+ φ
1 and ssB
Since s B
< 0, and
dp B
dθ A
=
w
well, is φ >
1N 2
2 N 1.
IM
dew
A
dβ
β) eθ B
A
A
=
1 s AA ε
P
φ ssAA B
s BB ssBB
s BB
P
βeθ B + (1
IM
dew
A
dβ
s BB ssBB
s BB
φ+
we have
If countries are symmetric then
the second term within
φ+
=
pB
1 θA
1
1+ φ ( N 1)
"
1
1
N
1
a
ssB
sB
φ+1
(ε
φ
1+ φ
φ+
< 0. (ii) We have
da
dβ
a
β
=
φ) + φN )
1) (2 (1
+ N1 1 φ φ
w B /PB
<0
1 θA
φ) + (2φ
(2 (1
shows that a sufficient condition for
IM
dew
A
dβ
φ2
1+ φ
=
1+
#
1) N )
< 0. Hence
IM
β dew A
dβ
? 0.
IM
ew
A
? 0. Rewriting
> 0, and therefore
da
dβ
< 0 as
This completes the proof.
Proposition 2. The Benefits of Environmental Policy.
Proof Straightforward total differentiation of (13) for j = A, B with respect to θ A gives us (17) and (18)
respectively. From
dw A
dθ A
< 0 and
d
dθ A
wB
PB
< 0 we immediately obtain
dz A
dθ A
< 0 and
dz B
dθ A
< 0. This
completes the proof.
Proposition 3. Environmental Standards: Race to the Bottom or Race to the Top? The Role of Vertical
Linkages.
Proof (i) Substitution of the coefficients from definition 1 into (23) results in the following expressions
for the environmental standard:
"
θ NC = 1
2
θC = 1
4 1_
ηnz ez A + ζ ( N
θ
A
where Φ
(1 α ) β + α
αβ
1
τ (b a)
_
ηnz ezθ A + ζ ( N 1)ezθB
A
b a
b
=1
1
N
Φ
(50)
31
Φ
τb
z
z
1) e θ B + ( N
1) ζ e θ A + ( N
A
A
z
2) e θ B
A
+ ezθBA
5
(51)
> 0. Setting ζ = 1 and comparing these solutions shows us that
θ C ? θ NC for
Since
A
#1
φ ( N 1)
1)
IM
ew
A
N 1+ φ ( N
>
φ ( N 1)
1)
N N 1+ φ ( N
N
1
N,
b
a
b
?
1
N
we have θ C > θ NC . Next, differentiating
30
(52)
θ NC
θC
with
respect to β gives
d
dβ
θ NC
θC
=
1 1 θ NC
Φ θC
=
1 1 θ NC
Φ θC
θ NC /(1 θ NC )
θ C / (1 θ C )
where ρ
"
ΩC /Ω B
d
dβ
"
ρ
B
ΩC
S /NΩ
#
g
1
log
h +
m
1/α + (1
ρ ) b2
(1
d IM #
dβ ew A
a
IM
ew
A
β) b
<0
< 1, since θ NC < θ C for ζ = 1. (ii) Setting ζ = 0 and comparing the solu-
tions (50)-(51) reveals that θ C < θ NC ()
Furthermore,
d
dβ
+
ΩC /Ω B
B
ΩC
S /NΩ
d
dβ
θ NC
θC
=
=
1 1 θ NC
Φ θC
"
1
α +(1
b a
β)(b a)
<
ΩC /Ω B
d
dβ
+
ΩC /Ω B
2
(ρ
1 1 θ NC 6
4
Φ θC
+
1) b
d
dβ
(1 β )
d
dβ
b
1
α +(1
β)b
, which is strictly met since a > 0.
B
ΩC
S /ΩS
d
dβ
ρ
B
ΩC
S /ΩS
I M /e I M
ew
w
A
A
(ρ
a
b a
I M /e I M a ( b a ) b
ew
w
A
#
A
+
1/α+(1 β)(b a)
dz/dβ
z
1)
ρb2
1/α+(1 β)b
3
7
5?0
where in this case ρ > 1 because θ NC > θ C for ζ = 0. (iii) Equating θ NC and θ C , using (50) and (51), and
z
_
z
aeθ A +( a b)( N 1)eθ B
1
solving for ζ gives ζ
N 1 (b a)
A
z
eθ A +( N
A
A
z
2) e θ B
.
z
aeθ B
A
A
Proposition 4. Vertical Linkages and Global Pollution.
Proof Consider ζ = 1. Using (24)-(25) one can write
that
d
dβ
z NC
zC
> 0 iff
IM
dew
A
dβ
z NC
zC
=
1a
αb
1
α +(1
of (24)-(25) gives
dzC
dβ
1
β)(b a)
=
b (b
b
1
α +(1
β)b
1
α
a) +
1
zC
β
+ (1
< 0 and
= N b b a . It then follows immediately
1N 2
2 N 1 is a
z NC
b a
zC = b
> 0, for which φ >
proof of Proposition 1. Consider ζ = 0. We have
d
dβ
z NC
zC
1
α +(1 β ) b
1 +(1 β b a
)(
)
α
d IM
dβ ew A
IM
ew
A
I M /dβ
dew
A
I M /β
ew
A
1
b
α +(1 β ) b ( b a ) a α
b +(1 β b b a
)
(
)
α
=
and
? 0. Consider ζ = 1. Differentiation
β) b
dz NC
dβ
sufficient condition, as shown in the
=
a
b a
1 α
α
1
1
α +(1
β)b
z NC
β
? 0.
Proposition 5. The Effects of Unilateral Environmental Policy in the Eaton-Kortum model of Trade
with Vertical Linkages.
Proof In a supplementary appendix I derive solutions to some key variables in the E-K model that only
differ from the standard expressions by the inclusion of the environmental standard θ (see Eaton and
Kortum (2002) and Alvarez and Lucas (2007)):
wA = A
wB = A
1
β
1
β
n A (1
n A (1
1
θ A) ϑ + (N
1
ϑ
1) n B (1
β
ϑ
θ A ) ω AB + ( N
τ
z A = e (θ A ) D A I w
β
τ
z B = e (θ B ) DB I w
β
1) n B (1
θB)
β
,
DA = n A
A wA
gA 1 θ A
DB = n B
A wB
gB 1 θ B
β
,
31
ϑ
β
β
1
ϑ
θ B ) ϑ ω AB
!
!
ϑ
β
1
ϑ
1
ϑ
1
ϑ
where A
hR
∞
0
e
z zϑ (1 ε) dz
i
1
1 ε
dw A
=
dθ A
= A (ϑ, ε) < 1. The various first-order derivatives of interest are
1 ϑ
(1
βϑ+β
dw B
=
dθ A
1 ϑ
λ
βϑ+β A
dz A
=
dθ A
In contrast to the Armington model,
dz B
dθ A
wB
=
θA
1
1
α
dz B
=
dθ A
wA
= (a
1 θA
1
β
λA)
(a
b)
wA
<0
1 θA
λA
wB
a
<0
λA 1 θ A
1
1
b)
zA
<0
θA
1 ϑ
zB
λ
<0
β ϑ + β A 1 θA
< 0 for β = 1. This completes the proof.
Proposition 6. Asymmetric Dependence and the Responsiveness of Pollution.
1 1 λ
( )
d[(1 λ A )(1 s PB )]
β2
ds P
(1 λ) dsPB
B
Proof (i) Assume λ A = λ. Then dβB =
=
2 < 0,
β B dβ B > 0 and
dβ
1
β
B
B
1+ β B (1 λ )
B
(1 λ A ) 1
daS
=
dβ B
1 + β B (ε
s PB (ε 1)
1) s PB
1
β B + (1
z
Hence,
d
dβ B
w
eθ A
A
=
daS
dβ B
< 0 and
d
dβ B
z
eθ B
=
A
z
0, with
d
dβ B
z
eθ B
A
=
λA
1 λ A aS
λA)
1 <0
z
eθ B
A
1 β
est are ambiguous in sign. Differentiating eθB gives
A
λA
β B ) (1
+
eθ B da
S
A
aS dβ B
d
dβ B
> 0 if evaluated in β B = 1.
32
z
eθ B
A
> 0. (ii) In general, all derivatives of inter=
λA
1 λ A aS
(1
βB )
1
a dλ A
(1 λ A )2 S dβ B
+
λ A daS
1 λ A dβ B
?
9
Supplementary Appendix C - Not for Publication
9.1
Leakage in the Eaton-Kortum Model with Vertical Linkages
9.1.1
Production and Technology
We analyze the effects of unilateral environmental policy in the Eaton and Kortum (2002) model of
trade. In contrast to our AV model with vertical linkages, there is a continuum of intermediate goods.
We model the inverse of the TFP level ("costs") across goods as random variables with density ξ. As
in Alvarez and Lucas (2007) the density ξ is exponential with parameter Tj , s˜ exp( Tj ). The random
variables are distributed Frechet. Since intermediate goods differ only in their costs, we use s as a label
for each variety. The production function of intermediate good s in country j reads:
y j ( s ) = g j (1
θ j )s
ly ( s )
β
ϑ
β
xy (s)
1 β
1 β
where g j represents a country-specific TFP term that is invariable across goods. Note that (i) the parameters Tj and ϑ are used to govern absolute advantage and comparative advantage respectively and (ii)
that Tj is identical to the parameter n j in the AV model. The only way in which this production function
differs from E-K is by the inclusion of the terms g j and 1
9.1.2
θ j.
Consumption and Prices
Let x j (s) and X j denote respectively consumption of tradeable good s in country j and consumption of
the composite intermediate good:
Xj =
Z
x j (s)
ε 1
ε
ε
ε 1
ξ (s)ds
The price of the composite intermediate good in country j reads
Pj =
Z
p j ( s )1
ε
1
1 ε
ξ (s)ds
while all producers in country j in this sector buy at the same lowest price
h
i
p j (s) = min sϑ ci
(53)
i
β 1 β
where sϑ ci = sϑ
wi Pi
gi ( 1 θ i )
1
1
. From (53) we note that p j (s) ϑ = mini sciϑ . Since s is exponentially
distributed with parameter Ti , we have ks exponentially distributed with parameter Ti /k where k is
1
an arbitrary constant. Therefore sciϑ is exponentially distributed with parameter Ti ci
1
ϑ
p j (s) exponentially distributed with parameter Φ
∑i Ti ci
1
ϑ
1
ϑ
. This implies
. One can then show (see Eaton-Kortum
(2002)) that the manufacturing price index equals
P = AΦ
hR
∞
0
z zϑ (1 ε) dz
i
1
1 ε
ϑ
= A (ϑ, ε) < 1 is a positive constant. Note that in the absence of trade
costs prices of intermediate goods and the composite intermediate good do not depend on the country
where A
e
33
β
wi P1 β
gi ( 1 θ i )
index. Therefore we can use the fact that ci =
0
β
wi
1
B
P = A β @∑ Ti
9.1.3
for all i such that
gi ( 1
i
θi )
!
1
ϑ
1
ϑ
β
C
A
Market Equilibrium and Trade Balance
Next, let us determine a country’s expenditure share Dij on tradables from country j. In the absence
of trade costs we have Dij = D j , which tells us that all countries will spend the same uniform fraction
of expenditures on intermediates from country j. In other words, D j also measures the fraction of total
global expenditures on intermediates from country j. It can be shown that
Dj =
1
ϑ
Tj c j
= Tj
Φ
1
ϑ
Ac j
P
which states that D j is simply a country’s contribution to the global price parameter Φ. The labor
market equilibrium condition and the factor market condition for the composite intermediate good are
respectively given by
L jC +
X jC +
Z
Z
l jy (s)ξ (s)ds = L j
x jy (s)ξ (s)ds = X j
Trade balance requires that total expenditures on intermediates, PX j ∑ D ji = PX j , equal total revenues from production, ∑ PXi Dij ,such that PX j = ∑i PXi Dij . Substituting for PX j = τβ Ij and noting
that without trade costs Dij = D j , this balanced trade condition can be reduced to:
Ij = D j I w
Taking P as the numeraire we can then use the price index equation and this balanced trade condition
to obtain an expression for the wage rate:
wj = A
1
β
1
ϑ
∑ Ti ( gi (1
θ i )) ω ji
i
2
gj 1
ω ji = 4
gi 1
θj
θi
β
ϑ
1
ϑ
!ϑ
β
3 ϑ
ϑ+ β
Tj Li
5
Ti L j
Next, we are interested in determining the equilibrium level of pollution in country j. Total pollution
R
in country j equals e(θ j )y j (s)ξ (s)ds where the integral is defined over the commodities for which
country j is the lowest cost supplier. Realizing that total supply of intermediate goods must equal
world demand for tradables from country j, z j = e(θ j ) ∑i qij = e(θ j ) ∑i qi Dij = e(θ j ) D j (∑i qi ), total
pollution can be written as
0
1
β
wj
τ
A
A
z j = e(θ j ) D j I w , D j = n j @
β
gj 1 θ j
where we substituted for (∑i qi ) = ∑i τβ Ii =
τ w
βI
1
ϑ
to obtain the expression for pollution.
34
9.2
A Two-Country Ricardian Model with Vertical Linkages
We present a two-country Ricardian model with vertical linkages and two intermediate goods (m = 2).
The production function of the composite intermediate good reads X j =
ε 1
ε
ε 1
ε
y1,j + y2,j
ε
ε 1
. The unit
productivity coefficient of commodity 1 and commodity 2 equal respectively g1,j and g2,j in country
j = A, B. Let us define a1,j
g1,j 1
θ 1,j and a1,j
θ 1,j , for j = A, B. In the remaining part
g1,j 1
of this analysis, we assume the following:
Assumption R-1. Country A has a comparative advantage in commodity 1 while country B has a comparative advantage in commodity 2,
a1,A
a2,A
>
a1,B
a2,B .
In addition, we will sometimes need additional assumptions in order to explain the impact of stronger
vertical linkages:
Assumption R-2. Country A has an absolute advantage in commodity 1 while country B has an absolute
a
a1,A
a1,B
> 1 > a2,A
.
2,B
Assumption R-3. Country A is more productive in commodity 1 than commodity 2 whereas country B is more
a
a1,B
productive in commodity 2 than commodity 1, a1,A > 1 > a2,B
.
2,A
advantage in commodity 2,
In the Ricardian model there are three possible patterns of specialization: (i) perfect specialization
(A1 B2 ), (ii) country A producing both goods and country B only producing commodity 2 (A1 A2 B2 ),
(iii) country B producing both goods and country A only produces commodity 1 (A1 B1 B2 ). Next, let us
characterize the equilibrium of each regime.
9.2.1
Perfect Specialization
First, we analyze perfect specialization (y1,A > 0 and y2,B > 0). The production functions read:
l1,A
β
β
x1,A
1 β
1 β
y1 = y1,A = a1,A
l2,B
β
β
x2,B
1 β
1 β
y2 = y2,B = a2,B
Prices of these goods equal p1 =
β
1
a1,A w A
β
1
a2,B w B
and p2 =
respectively for commodity 1 and 2. Most
equations in this regime are identical to the equations in the Armington model but with some slight
modifications related to notation. The relative wage and wage equations read:
h
w A = ( a1,A )ε
ω AB =
1
+ ( a2,B ))ε
ε 1
a1,A
a2,B
1
LB
LA
β ( ε 1)
ω AB
!
i
1
β ( ε 1)
1
1+ β ( ε 1)
1
Production of the composite intermediate good equals X j = λ j X w = λ j β1 ( G ) β where
G
a1,A (λ A
)1 β
(l1,A )
β
ε 1
ε
+ a2,B (λ B
)1 β
(l2,B )
35
β
ε 1
ε
ε
ε 1
such that pollution in country A
and country B equals:
9.2.2
zA =
1
1
e(θ A ) a1,A λ A ( G ) β
β
zB =
1
1
e(θ B ) a2,B λ B ( G ) β
β
1 β
(l1,A ) β
1 β
(l2,B ) β
Imperfect Specialization
Next, we analyze imperfect specialization (A1 B1 B2 ). Our solution strategy is to impose the specialization pattern and then solve for expressions for wages, production and pollution that are consistent with
this regime. Note that we allow for the possibility of policies to be differentiated across sectors. Since
country B and country A both produce commodity 1, and there are no costs of trade, price equalization
(p1,A = p1,B = p1 ) implies conditional factor price equalization,
1
β
a1,A
a1,B
wA
=
wB
ω AB
Rewriting the price index equation, 1 = p11 ε + p12 ε , provides us with an expression for the wage rate,
i 1
h
β ( ε 1) β ( ε 1)
, which can be further rearranged to get
w A = ( a1,A )ε 1 + ( a2,B )ε 1 ω AB
where H
1+
a2,B
a1,B
1
ε 1
ε 1
1
wA
= ( Ha1,A ) β
wB
= ( Ha1,B ) β
1
= p1 > 1. Since country A only produces commodity 1 we can then
immediately write
=
where we used x1,A = (1
l1,A
β
= a1,A
y1,A
H
1 β
β
1
( a1,A ) β
β)λ A X w , X w
β ) X A = (1
β
1 β
x1,A
1 β
τ
L = y1,A
β A
ε 1
ε 1
y1 ε + y2 ε
ε
ε 1
and X w =
τ w
βI .
Next, total
output of commodity 1 and commodity 2 equal respectively
y1
=
τ
p1 ε I w
β
=
H
1
1
ε
( Ha1,A ) β + ( Ha1,B ) β
τ
y2,B = p2 ε I w =
β
where we used
ε
a1,B
a2,B p1
= p2 ε =
a1,B
a2,B
H
ε
a1,B
a2,B
LB
LA
τ
L = y1
β A
ε
y1
. Next, we determine output of commodity 1 in country
B:
y1,B
=
H
=
H
ε
1 β
β
1
( Ha1,A ) β
H1
ε
1 β
1
1 τ
LA
τ
+ ( Ha1,B ) β
L B H β ( a1,A ) β L A
LB
β
β
1 L
1
τ
1 ( a1,A ) β A + H 1 ε ( a1,B ) β
LB
LB
β
36
(54)
Note that for this regime of imperfect specialization to be feasible we must have y1,B > 0. The expression within brackets in (54) is positive whenever the following condition holds
LB
> Hε
LA
1
1
β
a1,A
a1,B
1
Substituting for H we get the feasibility constraint for this regime with imperfect specialization:
LB
>
LA
ε 1
a2,B
a1,B
1
β
a1,A
a1,B
rB
For the last regime, with country A imperfectly specialized (A1 A2 B2 ), a similar condition for y2,A > 0
can be derived:
LB
<
LA
ε 1
a2,A
a1,A
LB
LA
Thus, there is perfect specialization if r A
LB
LA
1
β
a2,A
a2,B
rA
r B ; imperfect specialization by B if
LB
LA
> r B and im-
< r A . Note that R-1 is a necessary and sufficient condition for r A < r B .
Starting from a regime with imperfect specialization, the following extensive margin results holds:
perfect specialization by A if
Lemma. Vertical linkages and the pattern of specialization.
∂r A
∂r B
∂β > 0 and ∂β < 0.
Then ∂r∂εA < 0 and ∂r∂εB > 0.
(i) Assume R-2 holds. Then
(ii) Assume R-3 holds.
This lemma reveals that if both countries have an absolute advantage in the same commodity in which
they have a comparative advantage, only then is there a tendency for stronger linkages to induce perfect specialization. To be more precise, starting from an initial configuration of imperfect specialization,
stronger linkages can shift the pattern of specialization to perfect specialization, provided the fall in r A
and the rise in r B are substantial enough. Whether such a regime shift actually occurs, will depend on
the initial labor endowments, parameter values and the magnitude of the change in β.
Similarly, a sufficiently large increase in the elasticity of substitution will also induce a move towards
perfect specialization, provided that in both countries the export sector is more productive than the
(dormant) import-competing sector.
9.2.3
Comparative Statics
Pollution in country A and country B reads:
z1,A = e(θ 1,A ) H
z1,B = e (θ 1,B ) H
z2,B = e (θ 2,B )
with 1
H1
ε
1 β
β
H1
a1,B
a2,B
ε
1 β
β
1
( a1,B ) β
1
( a1,A ) β
H
ε
H1
1
ε
τ
L
β A
1
( Ha1,A ) β
ε
H
1+
37
ε 1
!
LA
LB
1
LA
+ ( Ha1,B ) β
LB
> 0. Furthermore, note that
a2,B
a1,B
1
( a1,A ) β
1
ε 1
>1
τ
LB
β
τ
LB
β
dH
dH
<0 ,
>0
dθ 2,B
dθ 1,B
dz2,B
dθ 1,A
dz
< 0 and dθ 1,B > 0, that is, there is negative
1,A
(positive) leakage in the export (import-competing) sector in country B if country A raises its standard
in sector 1, its export sector. Total leakage in country B equals
The following qualitative results follow directly. First,
dz1,B
dz
+ 2,B =
dθ 1,A
dθ 1,A
a1,B
a2,B
ε
e (θ 2,B ) +
a1,B
1
1
e (θ 1,B )
a2,B
β1+ 1
ω
AB
which is negative provided (i) e (θ 2,B ) is large relative to e (θ 1,B ) and (ii)
a1,B
a2,B
LB
LA
y1
1 θ 1,A
small. Note that a sufficient
condition for total leakage in B to be negative is that composition effects are absent; e (θ 2,B ) = e (θ 1,B ).
dz1,A
dθ 2,B
dz
< 0 and dθ1,A
> 0, that is, there is negative leakage in country A if country B raises
1,B
its standard in the export sector and there is positive leakage if country B raises the stringency of environmental policy in the import-competing sector. Naturally, an appropriately designed increase in
environmental standards by country B in both sectors will reduce B’s pollution in both sectors, while
leaving pollution in country A unaffected.
Second,
38