KIEL
WORKINGPAPERNew Trade Models,Same Old Emissions?

No. 2267 April 2024
Robin Sogalla, Joschka Wanner, and Yuta Watabe

Kiel Institute for the World Economy
ISSN 1862–1155

KIEL WORKING PAPER

NO. 2267 | APRIL 2024

ABSTRACTNEW TRADE MODELS, SAME OLDEMISSIONS?
Robin Sogalla, Joschka Wanner, and Yuta Watabe
This paper investigates the elusive role of productivity heterogeneity in new trade models in the tradeand environment nexus. We contrast the Eaton-Kortum and the Melitz models with firm heterogeneity
to the Armington and Krugman models without heterogeneity. We show that if firms have a constantemission share in terms of sales — as they do in a wide range of trade and environment models — thethree models’ emission predictions exactly coincide. Conversely, if firms have a constant emission
intensity per quantity — a prominent alternative in the literature — the emission equivalence between
the three models breaks. We provide a generalization that nests both constant emission shares in sales
and constant quantity emission intensities as special cases. We calibrate the models to global
production and trade data and use German firm-level data to estimate the key elasticity of how emission
intensity changes with productivity. Our multi-industry quantification demonstrates that the role of firm
heterogeneity depends both on the model and the estimated parameters. Moving from the Armington
model to the EK model increases the emissions effect on trade, while moving from the Krugman modelto the Melitz model decreases the emission effects on trade.
Keywords: International trade; carbon emissions; firm heterogeneity
JEL classification: F11; F12; F18

Robin Sogalla

Joschka Wanner

Yuta Watabe

German Institute for Economic
Research (DIW),
Email: rsogalla@diw.de
www.diw.de

University of Wuerzburg,
Kiel Institute for the World Economy
CESifoEmail: Joschka.wanner@ifw-kiel.de
www.ifw-kiel.deInstitute of Developing
Economies, JETRO
Email: yuta_watabe@ide.go.jp
www.ide.go.jp/English

The responsibility for the contents of this publication rests with the authors, not the Institute. Since working papers are of apreliminary nature, it may be useful to contact the author of a particular issue about results or caveats before referring to, or
quoting, a paper. Any comments should be sent directly to the authors.

1

Introduction

Are exporting firms cleaner than domestic producers? How do different firms react toepisodes of trade liberalization? Do firms’ international sourcing decisions affect theiremissions intensity? The focus on firm heterogeneity by “New New Trade Theory” ’ andthe availability of firm-level data has strongly influenced the literature on the relationshipbetween international trade and environmental outcomes. Here, the focus has shifted
toward new micro-level questions. However, for the “pure” trade models, the implicationsof micro-level insights for macro-level outcomes deserve special attention: Do new models
with firm heterogeneity deliver different predictions for aggregate emissions? In theirseminal paper, Arkolakis, Costinot, and Rodríguez-Clare (2012) (henceforth ACR) showthat a broad class of trade models with very different micro-foundations — including
Armington (1969)-type models, Krugman (1980), Eaton and Kortum (2002), and Melitz(2003) (henceforth Armington, Krugman, EK, and Melitz) — yield the same expression
for gains from trade. Hence, even though firm heterogeneity offers a new source of gains
from trade — the reallocation of production towards more productive firms — this newchannel does not translate into larger overall gains. The ACR insight begs the questionof whether heterogeneous firm-level responses to trade liberalization could potentiallychange overall environmental outcomes or, in a similar vein, are neutralized in aggregate
consideration.
The first key contribution of our study is an ACR-type equivalence result for singleindustry models: if the emissions of firms are proportional to the value of their production
and if this proportion is common across firms, the aggregate emission predictions of theArmington-, Krugman-, EK-, and Melitz-type models are identical. The equivalence
condition applies to production emissions in the majority of new quantitative trade andenvironment models, including models based on Armington (e.g. Larch and Wanner, 2017,2024; Klotz and Sharma, 2023), Krugman (Farrokhi and Lashkaripour, 2024), EK (e.g.
Egger and Nigai, 2015; Duan et al., 2021; Caron and Fally, 2022; Mahlkow and Wanner,2023), and Melitz (Shapiro and Walker, 2018; Sogalla, 2023).1 The intuition behind thisequivalence is straightforward: the EK- and Melitz-type models do take into account a
1All examples given here are multi-industry models. We will return to this distinction below but havealready prefigured that a broad equivalence result will continue to hold.

1

crucial insight from the empirical trade and environment literature (see e.g. Cole, Elliott,
Okubo, and Zhou (2013), Richter and Schiersch (2017), and Forslid, Okubo, and UlltveitMoe (2018), as well as Cherniwchan, Copeland, and Taylor (2017) and Copeland, Shapiro,and Taylor (2022) for recent surveys), which is that exporters have lower emission intensities. Trade liberalization induces a reallocation of production towards these cleaner firms,
leading to an environmentally beneficial technique effect. However, as these models also
capture the key feature that exporters are more productive (see, e.g. Bernard, Jensen,
Redding, and Schott, 2007), they produce more, resulting in an emission-increasing scaleeffect. In this class of models, these two effects exactly offset each other when the relativeemissions price is fixed.
An alternative specification to model emissions in trade models is to link them to produced quantities with fixed proportions. A prominent example is Shapiro (2016). Our second main contribution is showing that the Armington-, Krugman-, EK-, and Melitz-typemodels are not all equivalent in this case. Instead, models with heterogeneous producers
may lead to worse emissions outcomes in the case of trade liberalization. The intuition canbe linked to the previously mentioned scale and reallocation effects: Productivity differences are still considered, and the resulting scale effect drives up emissions, while emission
intensity differences are absent in this case. Hence, there is no counteracting reallocation
effect. Trade liberalization may lead to a shift in production to high-productivity firms
and, therefore, to larger quantities produced and, in turn, higher emissions. In the specificcase of movement from an economy in autarky to equilibrium with trade, we show that
global emissions increase in the models with firm heterogeneity.
Third, we consider a generalized modeling strategy for emissions in trade and environment models along the lines of Kreickemeier and Richter (2014) (henceforth KR). In thiscase, emissions are linked to the quantities produced, but more productive producers areallowed to be cleaner. The productivity-emission intensity relationship is disciplined by anadditional parameter: the productivity elasticity of emissions. We derive expressions for
aggregate emissions in Armington, Krugman, EK, and Melitz models with KR-type emission intensities. Similar to the quantity-based approach, the different models do not yield
the same emission outcomes. The EK and Melitz models imply a scale effect that drives
emissions up and a counteracting technique effect due to reallocations between producers.

2

The magnitude of the latter depends on the KR elasticity parameter. If the emission
intensity bonus of highly productive firms becomes sufficiently strong, firm heterogeneity
may lead to lower aggregate emissions in response to trade liberalization. In this setting,
we can show that when emissions are elastic [inelastic], moving from autarky to a tradeequilibrium results in lower [higher] global emissions. Note that the KR approach nests
the value- and quantity-based approaches as special cases. If the KR elasticity equals
one, emission outcomes correspond to the case in which emissions are proportional tovalues, and the corresponding equivalence results hold. If the KR elasticity equals zero,
the emission outcomes equal the ones from the case in which emissions are proportional
to quantities.
Conditional on equal trade outcomes, our (non-)equivalence results for the three emission modeling strategies carry over to multi-industry models. In multi-industry environments, reallocations across sectors induce an additional composition effect on emissions:
Some countries specialize in emission-intensive industries and face higher emissions, whileothers focus on clean industries and hence reduce their emissions. Central to pollution
haven and carbon leakage concerns, this mechanism is crucially important and should be apart of full-fledged quantitative trade and environment models. However, our distinction
between different types of trade models is decisive for scale and technique effects within
sectors.
Due to economies of scale, trade outcomes for multi-sector Armington and EK models
differ from those of the multi-sector Krugman and Melitz models. Hence, in the valueemission case, The Armington and EK models again imply the same emission responses totrade, and these two models have different emissions responses compared to the Melitz andKrugman models only because the trade responses are different. In the flexible emission
specification, emission effects again vary across models, with the emission effect of firm
heterogeneity depending on the sectoral KR elasticities.
In our quantitative exercise, we calibrate the flexible emissions version of the multiindustry Armington, Krugman, EK, and Melitz models. The key parameter is the elasticity with which the emissions intensity reacts to a firm’s productivity. We use a German
firm-level data estimation procedure to identify this parameter. Otherwise, the Armington, Krugman, and EK models only rely on readily available trade and production

3

data, and the Melitz model comes with only one additional data requirement, namely thecountry-industry level share of exporting firms.
We simulate a global reduction in trade costs to quantify the effect of trade on global
emissions. In the Armington model (and equivalently, in an EK model with unit KR
elasticities in all sectors), global emissions increase only mildly in response to sectoral
production shifts across countries. Using the estimated elasticities in the EK setup instead, the global emissions increase in response to trade liberalization triples. The increaseindicates that the emission-increasing scale effect induced by firm heterogeneity is stronger
than the emission-decreasing technique effect. In other words, in the perfect competition
models, once we incorporate firm heterogeneity in a way that can influence how tradeaffects emissions, our quantification suggests that firm heterogeneity turns out to be bad
news. The opposite is true in the monopolistically competitive frameworks. The Krugman model (and hence, equivalently, the Melitz model with unit KR elasticities) yields amild global emission increase similar to that of the Armington model. If, however, we use
the estimated elasticities in the multi-sector Melitz model, global emissions decrease in
response to the trade liberalization shock, implying that in this case, reallocation acrossfirms induces a stronger technique than scale effect. These results indicate the importance of the model structure in terms of both competitive environment (and hence scaleeconomies) and firm heterogeneity, as well as of the specific parametrization.
Our work is related to several strands of literature. First, it contributes to the literatureon the interplay between international trade and the environment (recently surveyed e.g.
by Copeland et al., 2022).
Second, it relates to the new quantitative trade literature (see Costinot and RodriguezClare, 2014; Caliendo and Parro, 2022, for overviews) and, more specifically, environmental extensions of quantitative trade models (see e.g. Egger and Nigai, 2015; Larch andWanner, 2017; Shapiro and Walker, 2018). We clarify how modeling choices in the tradecomponent affect the environmental effects they predict.
Third, we contribute to a strand of literature that studies the role of firm heterogeneity
in the trade and environment context, which has been very active in terms of both theory(e.g. Kreickemeier and Richter, 2014; Cherniwchan, Copeland, and Taylor, 2017; Forslid,
Okubo, and Ulltveit-Moe, 2018; Egger, Kreickemeier, and Richter, 2021; Chang, Cheng,

4and Peng, 2022) and empirics (e.g. Cole, Elliott, Okubo, and Zhou, 2013; Holladay, 2016;
Cherniwchan, 2017; Richter and Schiersch, 2017; Rodrigue, Sheng, and Tan, 2022). In
this firm heterogeneity literature, we take a bird’s-eye view of how incorporating (some)insights from the micro-level into a macro-level quantitative framework affects aggregate
outcomes.
Finally, there is a long tradition in the trade and environment literature of decomposing emission changes into scale, composition, and technique effects (Grossman andKrueger, 1993; Copeland and Taylor, 1994; Levinson, 2009; Shapiro and Walker, 2018).
We elucidate how different trade modeling strategies shape these effects and whether
differences in decomposition translate into different aggregate outcomes.
The rest of the paper proceeds as follows. Section 2 shows a simple example of incorporating emissions into the Melitz model. Section 3 establishes our general (non-)equivalence
results and applies them to three types of trade and emissions modeling choices. Section
4 describes the multi-industry extension and the corresponding analytical results. In Section 5, we introduce flexible versions of the models to the data and quantify how firm
heterogeneity alters the emission effects of international trade. Section 6 concludes.

2

A primer on trade and emissions with firm heterogeneity

To gain an intuition for our equivalence result, we start with a single-industry Melitz
model with two emission settings: endogenous abatement in the spirit of Copeland andTaylor (2003) and emissions linked to quantities in a fixed proportion.
Emissions proportional to value – In the model, firms have heterogeneous productivity
φ. The physical output from country i for market n is produced using labor lni :qni (φ) = (1 − ξi (φ))φlni (φ),
where ξi is the share of labor devoted to abatement. The emissions in the production

5

process are given by:zni (φ) = (1 − ξi (φ))1/αi lni (φ),
where αi is the elasticity of the pollution emissions intensity with respect to pollution
abatement intensity. With this abatement function, emissions can be equivalently expressed as a second factor of production (Copeland and Taylor, 2003):
qni (φ) = φ(zni (φ))αi (lni (φ))1−αi .
Given a price for emissions, ti , and wages, wi , the firm-level emissions embodied in the
trade flow from i to n are a constant share of the revenues, xni (φ) = pni (φ)q̃ni (φ), :zni (φ) = αixni (φ),σ̃tiwhere q̃ni is the quantity of goods consumed in country n and σ̃ is the markup ratio,
which is common and constant. The aggregate emissions embodied in the trade flow fromi to n are obtained by aggregating the emissions of each exporting firm.2 Under standard
assumptions on the relative magnitude of fixed costs, a unique productivity cutoff exists
for every market, φ∗ni , that determines the set of firms that export from i to n. Only firms
with productivity greater than or equal to this cutoff export. The emissions embodied in
the total exports from i to n are given by:
Zni = Mni E[zni (φ)|φ ≥ φ∗ni ] = Mni

Z

αi
αi
xni (φ)dG(φ ≥ φ∗ni )dφ =Xni
σ̃ti
φni∗ σ̃ti(1)Rwhere Xni ≡ Mni φni∗ xni (φ)dG(φ ≥ φ∗ni )dφ is the aggregate export value from country i
to country n. Mni is the mass of firms producing in i and selling to n. It is evident from
(1) that the change in the aggregate bilateral export value is a sufficient statistic for thechange in embodied emissions.
Emissions proportional to quantities – We now provide an alternative assumption
2
We assume fixed costs of exporting are not associated with emissions, or we can also allow the fixed
cost to be paid in terms of goods.

6regarding the generation of emissions. Specifically, we assume that emissions are proportional to the quantity produced:zni (φ) = µi qni (φ).
With an analogous calculation as in the previous case, the emissions embodied in exports
from i to n are given by:
Zni = Mni E[zni (φ)|φ ≥ φ∗ni ] = Mni

Zβi qni (φ)dG(φ ≥ φ∗ni )dφ = µi Qni

(2)

φni∗

R
where Qni ≡ Mni φni∗ qni (φ)dG(φ ≥ φ∗ni )dφ is the aggregate quantity of goods produced
to export from i to n. This quantity includes an iceberg component. In this case, thechange in the aggregate export quantity is a sufficient statistic for the change in embodied
emissions.
There are two main differences in the treatment of the two cases. The first concerns
how firms’ productivity is related to their emission intensity. When emissions are proportional to the value, more productive firms use less labor and emit less per output unit.3
In contrast, when emissions are proportional to quantity, more productive firms may use
less labor but emit the same amount per output unit. Trade liberalization changes the
productivity composition of firms, which, in the value case, affects both the quantity andemissions per unit of output. However, in the case of quantity, it only changes the quantity produced. Regarding the decomposition of emission changes (Grossman and Krueger,
1993; Copeland and Taylor, 1994), trade in both cases induces an emission-increasing scaleeffect. It is the sole effect in the quantity case but counteracted by an emission-decreasing
technique effect in the value case.4
The second difference lies in the applicability of the ACR results. In a scenario whereemissions are proportional to the trade value, the model benefits from the ACR findingthat changes in trade value coincide across a range of models. If emissions per value
are common across different models (e.g., Armington, Krugman, EK, and Melitz) andthe ACR result of equal changes in aggregate trade flow holds, the changes in aggregate
34Emission per quantity inversely proportional to productivity (zni /qni ∝ 1/φni ).
The exact decompositions for each case and each model are shown in Section 3.5.

7

emissions will be identical. However, in a scenario where emissions are proportional toquantity, even though the emission intensity is the same across models, the changes intrade quantity differ, breaking emission equivalence. In the next section, we formalize thisintuition and present the analytical results for changes in aggregate emissions associatedwith trade shocks.

3(Non-)Equivalence of emission effects

3.1

General model set-up

This section introduces a general model encompassing the Armington, Krugman, EK,
and Melitz models with different emission mechanisms, including endogenous abatement
as in Copeland and Taylor (2003). In this section, we consider a single-industry setting.
We will show how this Section’s results can be embedded into a multi-sector setting in
Section 4.
The global economy comprises i = 1, ..., N countries. Each country has a mass of
consumers li , each supplying a unit of labor inelastically. There is a mass of varieties Ω,which is potentially endogenous.5 A variety can be produced by multiple firms or a single
firm.
Preferences – The preference of a representative consumer in country i are of the
Dixit-Stiglitz form, maximizing utility from consuming a variety of goods. The associatedprice index isZPi =pi (ω)1−σ

1/(σ−1)
d(ω)
,

i∈Ωi

where Ωi is the set of varieties available in country i and σ is the elasticity of substitution
between varieties.
5

Following ACR, Ω may include either a continuum or a discrete number of goods. This allows us toinclude the Armington model and models with heterogeneous producers.

8

Production and emissions – If a firm in country i produces variety ω, it requires labor:qi (ω) = fi,ω (lip (ω)),
where lip (ω) is a labor input for production. We allow the production technology of variety
ω to be country-specific. Emissions are associated with production and can be partiallyabated by labor input:zi (ω) = gi,ω (qi , liz (ω))
where liz (ω) is the labor input for abatement of variety ω in country i. Again, we allow
this abatement technology to be country-specific. We assume gi,ω is increasing in yi andnonincreasing in liz .6 Firms have to pay a carbon tax, ti , per emission. The firm’s cost
minimization problem is:Ci,ω (wi , ti , q̄) = minlp ,lz ,z wi (lp + lz ) + ti z
subject to q̄ = fi,ω (lip )z = gi,ω (q̄, liz ),where wi and ti are the wage and emission taxes in country i, respectively. The solution tothis minimization problem is characterized by a cost function, Ci,ω (wi , ti , q), labor demand
function, li,ω (wi /ti , q) and the emission output function, zi,ω (wi /ti , q).7
Trade – Firms face an iceberg trade cost τni and a fixed cost fni when exporting.
Specifically, as variable trade costs, firms in country i have to produce τni amount ofgoods to sell one unit to country n. For a fixed cost, firms have to pay fni amount oflabor in the destination country.8 We denote the shipped quantity and the value of export
as qni (ω) and xni (ω), respectively, and denote associated emissions as zni (ω).
6

We allow the case where firms cannot abate emissions.
Because li,ω (wi /ti , q) and zi,ω (wi /ti , q) are factor demand functions, they only depend on the factor
price ratio.
8
We assume there is no emission associated with fixed costs. We can allow fixed-cost payments
involving abatement and emissions, like in the variable cost.
7

9

Market Structure – The market structure can be either (i) perfect competition or (ii)monopolistic competition. In the case of perfect competition, anyone can produce variety
ω, and there are large numbers of potential firms and consumers. Firms and consumers
take the prices, wages, and emission taxes as given. In this case, there are no fixed costsof exporting (fni = 0).
For monopolistic competition, we consider both free and fixed entry. In free entry,
each firm can produce a unique variety ω by paying a fixed entry cost Fi > 0 in termsof labor. This fixed entry cost is not associated with emissions.9 Firms enter until their
expected profit from entry is zero. We denote the mass of firms in country i by Mi . In thecase of fixed entry, each country has a fixed mass of firms, each producing a unique variety
ω. The profits earned by the firms in i in the fixed entry case are given to consumers in
the country. Firms take the aggregate price index and wage as given in both free andfixed entry, and maximize their profit.
Equilibrium – The carbon tax in country i is exogenously given, and tax revenue isrepatriated to consumers in the country. In the equilibrium, the labor and goods markets
clear.
Before discussing specific assumptions on how emissions are related to production, we
briefly state how the three canonical trade models we consider throughout the paper fit
into the general model structure outlined thus far.
Armington – The Armington model arises as a special case of the general model
structure if we assume perfect competition and a fixed discrete number of varieties, namely
one per country.
Krugman – In the Krugman case, firms engage in monopolistic competition; the number of firms in each country is endogenous, and each firm produces its unique variety. The
production technology is the same for all firms within a country.
EK – The EK model is the second perfect competition special case with a fixed setof varieties. In this case, the set of varieties is a unit interval, and every variety can be
9

We can allow entry costs and the export fixed cost to have emissions. In that case, we have to haveequal emission intensities for fixed and variable costs.

10

produced in every country. Countries differ in their efficiency of producing these varietiesand draw their productivities from a Frechet distribution with location parameter Ti anddispersion parameter θ.
Melitz – The Melitz model is similar to Krugman’s, but firms differ in their productivity. Firms in every country draw their productivities from a Pareto distribution withscale parameter Ti and shape parameter θ.

3.2

Emissions linked to values

We explain the assumptions necessary for our propositions. The first assumption is thatwithin a country, emissions embodied in sales are proportional to the output value, andthis proportionality is constant across varieties (firms).

Restriction 1. Denote the export value of a variety ω from country i to country n as
xni (ω). The first assumption is that the emission embodied in the export of variety ω fromcountry i to country n is proportional to the export value, and the proportion is common
across varieties:
zni (ω) =βi (wi /ti )xni (ω),ti(3)

where βi can be fixed or depend on the country’s wages relative to the emission cost.
A simple interpretation of this formula is that the proportion of emissions embodied
in trade is common across firms and can be written as the emission cost share divided
by the emission cost. First, we discuss the three assumptions that achieve this restriction
when combined. Notice that these assumptions are slight generalizations of the example
we discussed in the previous section:
Common cost share – In country i, for any variety ω, the emission (tax) cost share iscommon and constant for different quantities:
ti zi,ω (wi /ti , q)
= αi (wi /ti ),Ci,ω (wi , ti , q)11where αi (wi /ti ) is a cost share function that only depends on the relative wages.10
Constant marginal cost – In any country and any variety, the marginal cost is constant:Ci,ω (wi , ti , q) = ci,ω (wi , ti )q,
where ci,ω (wi , ti ) is the marginal cost function, which differs across the country of production and depends on the factor prices.
Constant markup – The factory gate price of variety ω in country i is as follows:pi,ω (wi , ti ) = σ̃ci,ω (wi , ti ),where σ̃ is a markup ratio in the economy.
Constant markup and constant marginal cost jointly imply that the price of variety ω
produced in country i and sold in country n is:
pni,ω (wi , ti ) = σ̃τni ci,ω (wi , ti )These assumptions indicate that the emissions per monetary unit of export sales from ito n are constant across varieties:
zni (ω)zni (ω)=xni (ω)σ̃ci,ω (wi , ti )qin (ω)αi (wi /ti )=.
σ̃tiThese common assumptions in the literature result in Restriction 1 with βi (wi /ti ) =αi (wi /ti )/σ̃. Examples include the endogenous abatement modeling a la Copeland andTaylor (2003) in Shapiro and Walker (2018) and the Cobb-Douglas or CES energy input
with proportional emissions in Larch and Wanner (2017) and Farrokhi and Lashkaripour(2024).
10

Notice that the cost function is homogeneous of degree one with respect to the factor prices
t zi,ω (wi ,ti ,q)ti zi,ω (wi /ti ,q)zi,ω (wi /ti ,q)(Ci,ω (wi , ti , q) = ti Ci,ω (wi /ti , 1, q)). Therefore, we have Ci i,ω
(wi ,ti ,q) = ti Ci,ω (wi /ti ,1,q) = Ci,ω (wi /ti ,1,q) .
This implies that the cost share is only a function of the relative factor price.

12

3.2.1Aggregate implications

Denote Zni as the total emissions associated with the exports from country i to country
n. This can be written asZZzni (ω)dω =

Zni =
ω∈Ωi

where Xni ≡Rω∈Ωβi (wi /ti )βi (wi /ti )xni (ω)dω =
Xni
ti
ti
ω∈Ωi

xni (ω)dω is the total export from country i to country n. This equationsuggests that the emissions associated with trade do not depend on the micro-compositionof emissions.
Building on the ACR, we introduce the notion of trade shocks and explore their impact
on aggregate emissions.
Definition 1. A trade shock with constant carbon tax is a change from {τ } to {τ ′ }, while
fixing the relative price of emission (t/w = t′ /w′ ).
We choose a constant relative emission price to fix the climate policy and focus on
trade liberalization.11 We fix the emission tax relative to the wages because ti is a nominal
variable, and t = t′ is not a meaningful policy rule.12 We denote the economic variable v
after trade shock as v ′ , and denote use v̂ ≡ v ′ /v as the relative changes in the economic
variable v following Dekle et al. (2007, 2008). Using the trade shocks, we show that thechanges in emissions can be derived only by tracking the aggregate trade flows, wages,
and emission taxes:
Proposition 1. Suppose Restriction 1 is satisfied. The change in the aggregate emission
for country i through a trade shock can be written asẐi =where Ri ≡

R̂i
ŵi

(4)

PN

n=1 Xni is the total revenue in country i .

11Similar assumptions are discussed in Copeland and Taylor (2003, pp. 112, 146)
When t = t′ , the emission outcome crucially depends on the normalization of wages. Note that
this rules out any factor price-driven within-firm emission intensity changes. Any technique effect will,
therefore, come from reallocation between firms with different productivities (see Egger, Kreickemeier,and Richter, 2021, for a discussion of these two different sources of the technique effect).
1213

Proof. By Restriction 1, we showed that:Zni =βi (wi /ti )
Xni ,
ti

and this implies

Zi =

N
X

Zni =

n=1

βi (wi /ti )Ri .
ti

Notice we fix the relative wages (wi /ti ), and the emission tax moves proportional to thewages (ŵi = t̂i ). Taking the ratio between the emissions of the baseline equilibrium andthe equilibrium after a trade shock yields:

Ẑi =

3.2.2

R̂i
R̂i
.
=
ŵi
t̂i

Combining the restriction with ACR

The results of Theorem 1 are complemented with the restrictions imposed in Arkolakis,
Costinot, and Rodríguez-Clare (2012) (henceforth ACR). These are macro restrictions
that models may satisfy.13 .We slightly modify their restriction (to introduce an emissiontax) and state the restrictions similar to R1, R2, and R3’ in ACR.
ACR R1: Trade balance – For any country i, trade is balanced:
N
X

Xni =

i=1

N
X

Xin .

i=1

This assumption implies that the total revenue Ri is the same as total expenditure Yi ≡PN R
14
ACR further imposes a constant aggregate profit share for eachn=1 ω∈Ω xin (ω)dω.
country:
ACR R2: Constant aggregate profit – Denote the aggregate profit of country i by13
14

In all the models we discuss, these restrictions are satisfied.
We could include trade deficits as an exogenous transfer between countries.

14

Πi ≡

R
ω∈Ω

πi (ω)dω, and the aggregate revenue of country i by Ri . For any country i,

Πi /Ri is constant.
For the third assumption, we introduce a slightly modified version of R3’ in ACR toincorporate carbon taxes:
ACR R3’: CES import demand – The import demand system is such that for any
exporting country i and importing country n, the expenditure share of country n on
goods from country i is:
λni = PN

χni · Mi · (c̃i (wi , ti )τni )εk=1 χnk · Mk · (c̃k (wk , tk )τnk )ε.

where χnk is a parameter, Mi is a number of varieties, and c̃i (wi , ti ) is a function thatcombines wages and the emission tax, which is homogeneous degree of one. The tradeelasticity is denoted by ε.
We can show that as in the ACR, the changes in trade flows associated with trade
shocks are the same across models. Combining this result with our proposition 1, we
obtain the following proposition:
Proposition 2. Consider a model that satisfies Restriction 1, ACR R1, ACR R2, andACR R3’. The relative change in emissions associated with trade shocks with constantcarbon tax isẐi = 1
where variable changes are determined by:(τ̂ni ŵi )ϵλ̂ni = PN,(5)

Ri = ŵi Ri ,
1 X
′
ŵi =
λ̂ni λni Rn ,
Ri j

(6)

ε
k=1 (τ̂nk ŵk )′(7)where Ri is the total revenue of country i.
The proof is provided in Appendix A. The result is striking; the proposition shows that15

global emissions remain constant following any trade shocks.15 Our result highlights thatin a single-industry trade model with emissions proportional to values, trade shocks do
not change the aggregate emissions. We briefly discuss the rationale behind the absenceof an emission effect in the Armington, EK, and Melitz models.
Armington – In the single-industry Armington model, trade only affects where goods
are sold and leave production unaffected. As there are no heterogeneous producers, thesame quantity is produced using the same technology (and hence emission intensity),
irrespective of trade openness. In terms of the emission decomposition discussed in theprimer, there is a zero scale effect and a zero technique effect (and — in the absence of asectoral structure for now — a zero composition effect).
Krugman – As in the Armington case, trade only affects the destination products are
sold to, not the overall quantity produced. In the Krugman case, this is less obvious
because each firm features a production firm with an increasing return to scale. However,if the ACR Restrictions hold, the mass of active firms does not change with trade, andthe scale economies hence are not affected, and the overall quantities and production
techniques stay the same.
EK – In EK, trade allows countries to focus on goods they can produce efficiently.
Hence, X trade increases the overall quantity produced. Simultaneously, specializationin goods for which a country has high productivity implies specialization in goods thatthe country can produce at a low emission intensity. These two effects — a positive scaleeffect and a negative emission effect — perfectly offset each other.
Melitz – In Section 2, we discussed that in the Melitz model, trade leads to a reallocation towards highly productive firms and, hence, to higher quantities but lower emission
intensities. Proposition 2 implies that, as in the EK case, the scale and technique effects
cancel each other out exactly. Notably, while EK and Melitz share this property, themagnitudes of the scale and technique effects do not coincide across the two models.
15

While it is possible to generate changes in emissions by fixing t and changing w, the aggregate effecton emissions crucially depends on the wage normalization scheme. In Appendix B, we show that any
changes in global emissions can be realized by choosing the appropriate normalization.

16

3.3

Emissions linked to quantities

In an environmental context, physical units naturally play an important role, as we areinterested in how much firms pollute rather than how much they spend on pollution.
Hence, a clear alternative suggestion for introducing emissions into trade models is to linkthem directly to physical output.
Restriction 2. Denote the export quantity of a variety ω from country i to country n as
qni (ω). Emissions embodied in the export of variety ω from country i to country n areproportional to the export quantity, and the proportion is common across varieties:
zni (ω) = µi qin (ω),(8)

where µi is fixed.
3.3.1

Aggregate implications

The aggregate implication is similar to the common value assumption case:ZZµi qni (ω)dω = µi Qni ,zni (ω)dω =

Zni =

(9)

ω∈Ωin

ω∈Ωin

where Qni is the aggregate quantity produced to export from country i to country n.16
For a trade shock, we propose the following:
Proposition 3. Suppose Restriction 2 is satisfied. The change in the aggregate emission
for country i in response to a trade shock can be written as:

Ẑi =

N
X

ιni Q̂ni ,

(10)

k=1

where ιni ≡ ZZnii , and in this specific case, we also have ιni = PQni.
Qkik

The change in export quantity in the Armington and Krugman models is derived asQ̂in = X̂in /p̂in . However, as discussed, it is not trivial to derive changes in the quantity
in the EK and Melitz models.
16

To be clear, the quantity includes the amount of goods used to pay the iceberg costs.

17

We adopt another restriction to Restriction 2 so that the model is compatible with
ACR:
No emission tax – Producers do not pay a price for their emissions:ti = 0.
This assumption implies that labor is the only relevant cost in production.17 We
combine these assumptions with the ACR restrictions:
Proposition 4. Consider a model that satisfies Restriction 2, ACR R1, ACR R2, andACR R3’. The percentage change in emissions associated with any change in variable
trade costs in country i can be expressed as

Ẑi =

N
X

ιni · Q̂ni

i=1

Variable changes are determined by:(τ̂ni ŵi )ϵλ̂ni = PN
,
ε
(τ̂
ŵ
)
nk
k
k=1
′

Ri = ŵi Yi ,
1 X
′
ŵi =
λ̂ni λni Rn .
Ri jThe change in the quantity, Q̂ni , and hence the emission change varies across different
models (e.g., Armington, Krugman, EK, and Melitz).
The key insight is that although trade values are common in the ACR class of models,trade quantities differ across models. Combining Restriction 1 with ACR restrictions gives
rise to specific and common emission predictions. Meanwhile, combining Restriction 2
with ACR restrictions is insufficient to pin down the emission response to a trade shock.
There is no general solution for Q̂ni , and a closed-form solution may not exist. Fortunately,
we can show that there are closed-form solutions for the canonical models we consider(i.e., Armington, Krugman, EK, and Melitz).
17

With positive emission taxes, the model cannot be reduced to the ACR class of trade models.

18

Armington – In the case of the Armington model, we haveQ̂ni =

X̂ni
.
ŵi

(11)

and ιni = XYni
. The equation implies Ẑi = R̂i /ŵi = 0, which coincides with the caseiof emissions associated with values. In the Armington model, emissions do not changewith trade shocks. Without a change in technology, the production quantity remains unchanged. Trade shocks only change the allocation of goods used for iceberg transportation
costs and consumption.
Krugman – The expressions for the quantity change Q̂ni and the emission share ιni
in the Krugman model coincide with the Armington case. Intuitively, as all producers
use the same technology, the sales share coincides with the emission share, as there is no
selection of exporters. Also, as trade liberalization does not affect the mass of active firms
or their prodution technologies, aggregate emissions do not change.
EK – For the EK model, the quantity of production is not only a function of tradevalues but also of the import share λni = XXnin . Specifically, changes in the production
quantities associated with trade shocks are:
Q̂EK
ni =

X̂ni −1/θλ̂,ŵi ni(12)

where θ is a parameter of the Frechet distribution. The quantity share is given by:−1/θιni = P

Xni λni−1/θ.

k=1 Xki λki

Appendix C provides the derivation of these results. When comparing to the Armington
model, it’s important to note that the EK model accounts for endogenous changes in
productivity due to the selection of more productive varieties. In the EK framework,
λni represents the import share and the proportion of varieties that country i exports tocountry n. A key implication is that a lower λni indicates a higher quantity for a given
trade value Xni , reflecting the export of only highly productive varieties charging lower
prices. Furthermore, when calculating changes in quantity (and consequently emissions),19

it is essential to recognize that value shares do not precisely equate to quantity shares.
This distinction is critical and is incorporated into the computation of ιni .
Melitz – For the Melitz model, the quantity of production is a function of the export value, domestic productivity cutoff φ∗ii , and share of exporting firms to a particular
destination, Sni = Mni /Mi :X̂ni −1/θ ∗Ŝ
φ̂iiŵi ni

elitz
=
Q̂M
ni

(13)

where θ is a shape parameter of the Paret distribution. and the quantity share is:
−1/θ

Sni

Xni
−1/θ
Xki
k=1 Skiιni = PN

elitz
, Ŝni and φ̂∗ii are delegated to the appendix. Compared to the
The derivation of Q̂M
ni

Armington model, changes in quantities in the Melitz model must again consider endogenous productivity changes due to selection. Changes in Sni represent the productivity
changes due to the selection in country i of being an exporter to country n. In addition to
the changes in Sni , we must consider the change in the domestic productivity distributionof producers, which is represented by the changes in φ∗ii . Like the EK model, we need toconsider that the quantity share differs from the value share.
Using these results, we derive the emission effects of trade opening:
Definition 2. Trade opening is a change in trade costs from autarky (infinite iceberg
trade costs) to finite trade costs.
Proposition 5. Consider a model that satisfies Restriction 2, ACR R1, ACR R2, andACR R3’. Trade opening(i) leaves aggregate emissions in Armington and Krugman models unaffected(ii) increases emissions in the EK and the Melitz models.
The proof is in appendix D.
For example, the quantity-based emission specification is used in Shapiro (2016) who
embeds it into an Armington trade model. While the value-based approach is more
20

common and has the advantage of allowing flexibility in substituting emissions/energy
against other production inputs, there are some contexts in which a focus on quantities
arises naturally. This includes transportation emissions (what matters is the physicalquantity shipped from one country to another) and process-related emissions (different
from emissions from fossil fuel combustion, they cannot be avoided by shifting inputs
away from fossil fuels).
Next, we introduce an emissions specification that links emission intensity to productivity more flexibly and nests the value and quantity specifications as special cases.

3.4

A flexible emission specification

The two emission modeling approaches considered so far have very different implications.
In the quantity-based setting, more productive firms are not at the same time cleaner
than less productive firms. Hence, nothing counteracts the scale effect in the case of tradeliberalization. In the value-based setting, more productive firms are cleaner firms, introducing a counteracting reallocation effect on emissions. However, for the value case, themagnitude of this effect turns out to be identical to the scale effect and, therefore, neutralizes the role of firm heterogeneity. In this section, we follow Kreickemeier and Richter(2014) and consider an emission-generating process linked to the produced quantities andlink emission intensity to productivity with a technology parameter.
Restriction 3. Assume that the production function is a simple one-factor function andemissions are generated according to the following expression:zi (ω) =µi qi (ω).
[φ(ω)]γi(14)

The relationship between the physical emission intensity and firm productivity now
depends on the value of γi . If γi < 0, more productive firms are dirtier than less productive
firms. Conversely, γi > 0 relates to the empirically more relevant case in which highly
productive firms produce less emission-intensively. Whether the associated reallocation
effect suffices to offset the scale effect entirely depends on the precise value of γi rather
than just on its sign. Unlike in Sections 3.2 and 3.3, as emission intensity across firms isconstant neither in value nor quantity terms, we cannot write useful general expressions
21

for aggregate national emissions or their relative change. Instead, we directly consider the
implications of the third emission modeling approach in the three trade models.18 Thechange in the aggregate emissions is again shown as a change in emissions weighted by
the initial weight:
Ẑi =

X

ιni Ẑni .

n=1

Armington – The change in emissions is equal to the change in the quantity of production, which is given byArmington
Ẑni
=

X̂ni
,
ŵi

(15)

and the emission share again equals the sales share (ιni = XYni).
i
Krugman – As any differences in the KR case from the quantity case arises due tothe heterogeneity of producers and firms are homogenous in the Krugman framework, itArmington
Krugmanagain simply coincides with the Arimington model (Ẑni= Ẑni).

EK – For the EK model, the quantity of production is not only a function of tradevalues but also of the import share λni = XXnin . The changes in emissions associated withtrade shocks are:
EK
Ẑni
=

X̂ni −(1−γi )/θλ̂,ŵi ni(16)

and the emission share, ιEKni , is−(1−γ )/θXni λni i
EKιni = P.
−(1−γi )/θ
k=1 Xki λki

Melitz – For the Melitz model, the quantity of production is a function of the domestic
18

We derive the exact expressions in appendix C

22

productivity cutoff φii and a share of firms serving a particular destination, Sni = Mni /Mi :M elitzẐni=

X̂ni −(1−γi )/θ ∗ 1−γi,Ŝ(φ̂ii )ŵi ni(17)elitz
and the emission share, ιM, isni−(1−γ )/θSni i Xni
M elitzιni= PN.
−(1−γi )/θ
Xki
k=1 SkiUsing these results, we state the following proposition for the emissions effect of trade
openings:
Proposition 6. Consider a model that satisfies Restriction 3, ACR R1, ACR R2 andACR R3’. Trade opening(i) leaves aggregate emissions in Armington and Krugman models, as well as in EK
and Melitz models with γi = 1 unaffected(ii) increases emissions in EK and Melitz models with γi < 1(iii) lowers emissions in EK and Melitz models with γi > 1.
The proof is in appendix D.

3.5

Decomposing emission changes

As discussed above, the different effects in models with and without firm heterogeneity canintuitively linked to emission decompositions. We discuss the four cases by decomposing
the changes in emissions into scale and technique effects. Log-linearizing the emissions
embodied in trade yields:Zni
d ln Zni = d ln Qni + d ln.
| {z }
Qni|{z}scale effecttechnique effect23

In the value case, we can show that:
Arm/Krugd ln Zni= d ln Xni − d ln wi +|{z}scale effect

0
|{z}

,

technique effect1
1
EK
d ln Zni= − d ln λni + d ln Xni − d ln wi + d ln λni ,{z}| θ|θ {z }
scale effecttechnique effect1
1
Melitz= − d ln Sni + d ln φ∗ii + d ln Xni − d ln wi + d ln Sni − d ln φ∗ii .
d ln Zni
| θ
{z
} |θ
{z
}
scale effecttechnique effectSumming over all the destinations yields:
Arm/Krug

dlnZi

=

N
X

ιni (dlnXni − dlnwi ) + 0,

n=1
N
X


 X
N
1
1
ιni − dlnλni + dlnXni − dlnwi +ιni dlnλni ,
θ
θ
n=1
n=1




N
N
X
X
1
1
M elitz∗∗dlnZi=
ιni − dlnSni + dlnφii + dlnXni − dlnwi +dlnSni − dlnφii ,
ιni
θ
θ
n=1
n=1
dlnZiEK =where usingPN

19
i=1 ιni (dlnXni − dlnwi ) = 0 , we obtain:

Arm/Krugd ln Zi

=

0
+
|{z}

scale effect

0
|{z}

,

technique effect

N
X


 X
N
1
1
EK
d ln Zi =ιni − d ln λni +ιni d ln λni ,
θ
θ
|n=1
{z
} |n=1 {z}scale effecttechnique effect


 X


N
N
X
1
1
Melitz∗∗ιni − d ln Si + d ln φii +ιnid ln Sni − d ln φii .
d ln Zi
=
θ
θ
|n=1
{z
} |n=1{z}
scale effecttechnique effect

The result indicates that in the Armington and Krugman models, the scale and technique effects are zero, whereas for the other two, the effects cancel out exactly. In thequantity case, the technique effect is absent, and only the scale effect is present.20 For
PN
PN
dlnXni − dlnwi = dlnRi − dlnwi = 0
This is from i=1 ιni (dlnXni − dlnwi ) = i=1 XRni
i
20
In addition, ιni is different between the value case and the quantity case, since in the value caseιni = Xni /Rn while in the quantity case ιni = Qni /Qn .
1924

the flexible emission specification, the decomposition is expressed as follows:
Arm/Krug

dlnZi

=

N
X

ιni (dlnXni − dlnwi ) + 0

n=1
N
X



N
X
1
1
ιni dlnλni
ιni − dlnλni + dlnXni − dlnwi − γi
θ
θ
n=1
n=1




N
N
X
X
1
1
M elitz∗∗dlnZi=
ιni − dlnSni + dlnφii + dlnXni − dlnwi − γiιnidlnSni − dlnφii
θ
θ
n=1
n=1
dlnZiEK =where the sign and the magnitude of the technique effect now depend on the parameterγi .21 When γi = 0, the model is equivalent to the quantity case, where no technique effectexists, and only the scale effect exists. When γi = 1, the model collapses to the value
case, where the technique and scale effect cancel out.

4

Multi-industry extension

4.1

General model set-up

We extend the model in Section 3 to multiple sectors S. The production technology andmarket structure in each industry are the same as in the aggregate consideration above.
Additionally, we follow Kucheryavyy et al. (2023), Farrokhi and Lashkaripour (2024),
and Lashkaripour and Lugovskyy (2023) and assume that consumers have a three-tiernested CES utility. The upper-tier is Cobb-Douglas across sectors with spending shareκns . The second tier is CES across different origins within industries, with the elasticity
of substitution ηs , and the last tier aggregates varieties within a country of origin withthe elasticity of substitution σs .22 This model implies the following expenditure share of
consumers in n on products from i, sector s (see Appendix E for the derivation):

λins = P(βis (wi /ti )Lis )δs (cis (wi , ti )τnis )−ϵs ξnis

δs
−ϵs
ξnls
l∈N (βls (wl /tl )Lls ) (cls (wl , tl )τnls )

21

,

(18)

Also, as mentioned in the previous section, ιni depends on γi .
We introduce the nest compared to Section 3 to ensure a unique equilibrium in the monopolisticcompetition versions of the model (see Kucheryavyy et al., 2023, for a discussion).
22

25

where ϵs is the trade elasticity, ψs is the scale elasticity, and δs = ψs ϵs is the product of
the scale and trade elasticities and ξins is a constant. We now briefly outline how the four
canonical models deliver special cases of Equation (18).
Armington – In the multi-industry Armington model, the three-tier nested utility
function reduces to two nests because every country produces a single variety per country.
The trade elasticity simply relates to the elasticity of substitution across varieties within
one sector from different countries (εs = σs − 1). δs = 0 because there are no scaleeconomies in this framework.
EK – In the multi-industry EK model, the three-tier nest reduces to two tiers. In
this case, it is because firms from different countries produce varieties from the same
unit interval per sector rather than distinct varieties. The trade elasticity coincides withthe sectoral Frechet dispersion parameter (ϵs = θs ). As in the other perfect competition
framework, there are no scale economies, and hence δs = 0. Note that for a given tradeelasticity, trade adjustments will be identical in the multi-sector EK and Armington model
because they only differ in the constant ξins , which does not affect the equilibrium inchanges.
Krugman – In the multi-sector Krugman model, substitutability has to differ between
varieties from different firms, countries, and sectors to ensure a unique equilibrium. The
trade elasticity is directly linked to the elasticity of substitution across different varieties
in a given sector from the same country (ϵs = ηs − 1). Further, in this monopolisticallycompetitive framework, scale economies are present and linked to the elasticity of substitution between varieties from different countries, specifically νs = 1/(σs − 1) and henceδs = (ηs − 1)/(σs − 1).
Melitz – In the multi-industry Melitz model, substitutability again has to differ acrossthe three layers of firms, countries, and sectors. The trade elasticity is linked to boththe Pareto shape parameter θs and the elasticities of substitution between varieties fromboth different firms and countries, specifically ϵs = θs /(1 + θs ηs1−1 − σs1−1 ). As inthe second monopolistically competitive framework, there are scale economies, which inthis case are linked to the Pareto shape parameter, specifically νs = 1/θs and hence26δs = 1/(1 + θs1
− σs1−1ηs −1

). Note that trade responses are identical in the multi-sector

Melitz and Krugman models for given values of trade and scale elasticities.

4.2

Emissions linked to values

Following the same lines as in 3.2, it is straightforward to show that emissions in sectors, country i are given by:Zis =βis (wi /ti )
Ris ,
ti

(19)

where revenues are equal to:
Ris =

X

λnis Ens ,n∈Nand the sector-level expenditure is defined as:
Ens = κns (wn Ln + tn Zn ) .
Proposition 7. Suppose we have a model where Equation (18) and Restriction 1 hold.
Following a trade shock as in Definition 1,(i) Emission changes in country i are:
Ẑi =

X Zis
s∈S

Zi

L̂is =X Zis

X
1
λ̂nis λnis Êns Ens ,Zi ŵi wi Lis n∈N
s∈S

(20)

where the change in the trade share is δs(ŵi τ̂ins )−ϵs
λ̂nis = P,  δs
−ϵs
λ
L̂
(
ŵ
τ̂
)
ls
l lns
l∈M ljsL̂is(21)

and the counterfactual expenditure is given by:Êns Ens = κns ŵn wn Ln + Ẑn tn Zn ,where ϵs is the trade elasticity, ψs is the scale elasticity, and δs = ψs ϵs is the productof the scale and trade elasticities.
27

Proof. See Appendix F.
Corollary 1. Suppose the model structure that satisfies equation (18) and that Restriction
1 holds. We further assume common trade elasticity across four models, and common
scale elasticity for Melitz and Krugman (which is zero for Armington and EK). Following
a trade shock as in Definition 1,(i) the canonical Armington and EK model lead to the same emission changes, Ẑi .
(ii) the Melitz and Krugman model lead to the same emission changes, Ẑi , which isdifferent to the emission changes for EK and Armington due to scale economies.
(iii) Ẑi = 1 for all models if ZZisi = LLisi∀i ∈ N s ∈ S.

Proof. See Appendix G.
In the multi-industry case, a trade shock affects emissions even when the emission
price is fixed to the wage rate. The reallocation of labor across sectors fully explains theseemission changes. As is evident from equation 21, the trade response, which determines
the magnitude and the direction of labor reallocation, differs across models. As scaleeconomies are absent in the canonical Armington and EK models, the change in expenditure share depends only on the changes in iceberg trade costs and the wage rate. The
monopolistic competition models of Krugman and Melitz generate external economies ofscale, implying that the expenditure share also depends on sectoral employment. These
differences in trade responses have been shown elsewhere (see e.g. Costinot and RodriguezClare, 2014). Moreover, proposition 7 shows that emission responses are solely driven by
the shift in the industry composition. A special case arises when the emission per employed labor is common across industries within the country, Zis /Lis = Zi /Li . In thiscase, the composition effect is absent because the reallocation of labor does not alter the
relative importance of emission-intensive and cleaner sectors. Hence, trade shocks do notaffect emissions as in the single industry economy, regardless of the model considered.
Note that part (i) of Corollary 1 is of practical relevance because for a range of models
used in the literature (including e.g., Egger and Nigai, 2015; Larch and Wanner, 2017,2024; Duan et al., 2021; Caron and Fally, 2022; Mahlkow and Wanner, 2023), it implies
that they could switch back and forth between an Armington representation without firm28heterogeneity and an EK model with heterogeneous producers without any changes totheir aggregate outcomes. The same is not quite true for the Melitz models by Shapiro andWalker (2018) and Sogalla (2023): Switching them to Armington models would change
aggregate emission outcomes, however, only because the trade responses are different in
the Melitz case, not because of the within-industry reallocation between more or lessemission-intensive producers.

4.3

Flexible emission specification

The basic model structure is similar to Section 4.2. Moreover, Restriction 3 is assumed
to hold for each sector, with sector-varying emissions intensities and elasticity µis and γis .
The emission changes due to a trade shock according to Definition 1 is given by:Ẑi =X Zis X Zinss∈S

Zi n N Zis

Ẑins .

(22)

The changes in emissions are given by the sector level equivalent of (15) to (17) as wellas the corresponding embodied emission shares ιnis . 23 .
The remaining equilibrium conditions in the changes are given by equation 21 and thefollowing equations:Êns Ens = βns ŵn wn Ln ,

(23)

ŵi =

1 XX
λ̂ins λins Êns Ens ,wi Li s∈S n∈N(24)

L̂is =

X1
λ̂ins λins Êns Ens .
ŵi wi Lis n∈N(25)

When γ = 0 , the formulation collapses to the quantity case with multiple industries.
Unlike in the single industry case, the flexible model with γ = 1 differs from the modelthat links emissions to values. This is because collected emission taxes, which respondto the trade shock in multiple industry cases, are absent in the flexible model. If one
assumes that environmental tax revenues are lost in rent-seeking as, e.g., Shapiro andWalker (2018), the two models are again isomorphic.
As the multi-sector model features, composition effects, and the role of firm hetero23

The change in embodied emissions in Melitz is a function of the change in the exporting share, which
is presented in Appendix H

29geneity may differ across industries, general statements on the emission effects of trade
shocks and trade opening and the role of firm heterogeneity become harder. Nevertheless,we still reach sharp conclusions for the relative emission effects between EK and Armington for a set of interesting special cases concerning the range of values that γis takes,
summarized in the following proposition:Comparing Krugman and Melitz models is notstraightforward, since trade liberalization may lower the productivity of certain industries
in a multi-industry setting.
Proposition 8. Consider a model that satisfies Equation 18 and Restriction 3. Trade
opening(i) leads to equal aggregate emissions in Armington and EK models if γis = 1 ∀i, s.
(ii) increases emissions in EK relative to Armington models if γis < 1 ∀i, s.
(iii) lowers emissions in EK relative to Armington models if γis > 1 ∀i, s.
The proof is in appendix I. Note that generally, γis will be above one in some sectors
and below one in others. Whether firm heterogeneity leads to relatively higher or lower
emissions associated with trade liberalization then has to be answered by quantitative
simulations.

5

Quantification

5.1

Data and parameters

Our main data source is the World Input-Output Database (WIOD) from Timmer et al.
(2015), which contains trade flows and expenditure shares. CO2 emissions consistent
with WIOD classifications are provided by Amores et al. (2019). To quantify emission
changes in the Melitz model, we require data on the shares of exporting firms. We
gather these data from various sources. The number of active firms is given by the OECD
Structural Statistics of Industry and Services database. For the number of exporting firmsby partner country, we rely on the OECD Trade by Enterprise Characteristics Database,Eurostat, and the World Bank Exporter Dynamics Database. We limit the number ofexporting/active firms to those operating in manufacturing. Unfortunately, we do not30have data on the share of exporting firms for all trading pairs. We impute the remaining
export shares to retain as many countries as possible (see Appendix J for details).
We rely on estimates from the literature for the standard model parameters. We obtain
the demand substitution parameters, σs and ηs , from Lashkaripour and Lugovskyy (2023).
We use the Pareto shape parameter estimate θs from Shapiro and Walker (2018). The
translation of these parameters into the trade and scale elasticities, ϵs and δs , is modelspecific. We calculate ϵs and δs in line with the multi-sector Melitz model structure. We
then fix the resulting trade elasticities across all four canonical models. Similarly, we fix
δs across the two monopolistically competitive models but put it equal to zero for the two
perfectly competitive models as they do not feature scale economies. While this procedure
implicitly assumes different values for underlying parameters (such as σs and θs ) acrossmodels, it ensures maximal comparability across models in the quantitative results. We
want all differences to stem from model differences rather than from differently calibrated
elasticities.
The key parameter for how firm heterogeneity affects the effects of trade on emissions is
the productivity elasticity of emissions. We estimate γs using administrative German firmlevel data. We combine different modules of the official German manufacturing census
AFiD-Panel (Amtliche Firmendaten für Deutschland). The main module is the AFiD
Panel Industrial Firms. It covers the universe of German manufacturing and mining
firms with 20 or more employees and provides data on sales and employed labor. Fora representative sample, we further observe material expenditure, different costs of thefirm, and investments. We complement this module with the module Energy Usage,
which contains the energy inputs in physical quantity. We combine these data with fuelspecific emission factors from Juhrich (2022), which enables us to calculate firm-level
CO2 emissions from fuel combustion. This method of calculating carbon emissions has
been applied in several other studies such as Richter and Schiersch (2017) or Rottner and
Von Graevenitz (2022). Finally, we combine these two modules with a customs data set
to obtain firm-level exports.

31

5.2

Estimation of γ

Hereafter, we assume γis is common across countries but varies across sectors. We estimate
γs by exploiting the relationship between domestic sales and the emission intensity. Here,
we provide a derivation through the perspective of the Melitz model, while the estimationis also consistent with the EK model. Expressing emissions in terms of sales leads to:−γszis (ω) = (φ(ω))

Pn∈N τnis xnis (ω)µispnis (ω)

1−γs= (φ(ω))


µis

σs
wi
σs − 1−1 Xxnis (ω),

n∈Nand the emission intensity is then given by:zis (ω)eis (ω) == (φ(ω))1−γs µis
xis (ω)σswi
σs − 1−1.

Firm productivity is linked to the sales in the domestic market as follows:
σs −1

φ


(ω) = xiis (ω)σswi
σs − 1σs −1−1
Biis,where Biis is the real market size of sector s in country i. This leads to the following
expression of the emission intensity in terms of domestic sales:eis (ω) = (xiis (ω))

1−γs
σs −1



σs
wi
σs − 1

−γs

γs −1
σs −1
Biis
.

(26)

Hence, we can estimate γs by regressing emission intensity on the domestic sales:ln eω,is = β0 + β1OLS ln xω,iis + ϵω,is ,(27)

where ϵω,is is an idiosyncratic component capturing measurement errors. With an additional estimate of σs , we can obtain an estimate for γs from the estimated coefficient:γ̂s = 1 − β̂1OLS (σs − 1).
We include direct emissions and those embodied in the electricity usage in our emission
intensity measure. We estimate (27) by the whole sample (Mining and Manufacturing)and each WIOD sector. Table 1 shows the estimation results and the parameters sourced
32

from the literature. Note that we calculate γ̂s based on the Melitz-consistent σs values
from Lashkaripour and Lugovskyy (2023) and then fix γs across all models considered —again ensuring that quantitative differences across models stem from model differences,rather than differences in the calibration of key elasticities.
The aggregate γ, estimated using manufacturing and mining firms, is 1.2. This value
is close but above unity, which implies that the technique effect is stronger than the scaleeffect in the models with firm heterogeneity. In individual industries, while γs is always
positive (more productive firms are not dirtier), the value of γs widely differs across sectors. In industries like the manufacture of basic metals (C24) and the manufacture ofpaper and paper products (C17), the value of γs is close to zero, which indicates thatthese industries exhibit emissions almost proportional to quantity. Conversely, industries
like the manufacture of motor vehicles, trailers, and semi-trailers (C29) and repair andinstallation of machinery and equipment (C33) have γs above 2, indicating a strong positive relationship between productivity and emission intensity.24 The relative strength of
the scale and the technique effect differs by industry, and the aggregate implications are
a-priori unclear. To further investigate the aggregate implications, we plot the relationship between emission intensity and γs in figure 1. In general, higher emission intensity is
associated with lower γs , and these industries occupy a significant fraction of the global
emissions. This overall tendency suggests that trade liberalization may increase aggregate
emissions.

24

Note that, as mentioned in Section 5.1, this is calculated using only combustion emissions.

33

Table 1: Parameter Estimates
SectorEstimate
C10-C12-0.09
C13-C15
-0.19
C16
0.08
C17
0.21
C18
0.12
C19
0.13
C20
0.09
C21
-0.15
C22
0.02
C23
0.08
C24
0.16
C25
-0.03
C26
-0.07
C27
-0.05
C28
-0.13
C29
-0.15
C30
-0.12
C31-C32
-0.11
C33
-0.29
Total
-0.05

Std. Err.
(0.008)(0.027)(0.033)(0.026)(0.02)(0.122)(0.024)(0.042)(0.014)(0.023)(0.024)(0.01)(0.019)(0.017)(0.01)(0.02)(0.038)(0.016)(0.028)(0.004)

γ
1.62
1.48
0.64
0.07
0.61
0.59
0.92
1.64
0.91
0.45
0.04
1.14
1.34
1.09
1.24
2.22
1.95
1.88
2.92
1.20

Note:
Estimation of γ according to(27). The first colum presents the estimation result. The second column
presents the corresponding standard error. The implied γ is calculated basedon the value of σ from Lashkaripour andLugovskyy (2023).

34

Figure 1: Emission intensity and γs

Note: The figure shows the estimated γ and the emission intensity for all manufacturing sectors
and mining. The size of the points reflects the sector’s share in global emissions.

5.3

Results

5.3.1

Single Industry

To quantitatively illustrate the role of firm heterogeneity in shaping the emissions effectof international trade, we simulate a uniform 40% decrease in iceberg trade costs. We
need a multi-industry model to fully understand the effects of trade on emissions. We
nevertheless start with an aggregate consideration as it can accentuate the role of firm
heterogeneity within the industry.
Figure 2 shows the global emission response for the different models and varying valuesfor γ. Recall that γ captures the relationship between emission intensity and productivity:
The larger γ, the cleaner and more productive firms are. The figure displays the effects
for γ ∈ [0, 3]. The left end (γ = 0) corresponds to the quantity-based emission case inwhich the physical emission intensity is independent of the productivity. The two dashedvertical lines indicate the special case when emissions are proportional to value, i.e., γ = 1,35

and when γ lies at our estimated aggregate value of 1.2. The red line shows the emission
effect in the aggregate Armington (and, by equivalence, Krugman) model. The blue andgreen curves refer to the Melitz and EK models.
In line with the intuition from Propositions 2 and 6, emissions do not change in
response to the trade liberalization shock in the Armington and Krugman models for any
value of γ, as well as in the EK and Melitz models if γ = 1. In the quantity case (γ = 0),
consistent with the intuition from Proposition 5, emissions increase in the EK and Melitz
models. The increase in global emissions is considerable: More than a quarter in EK
and more than a third in Melitz. Global emissions increase in the two models with firm
heterogeneity for all γ < 1. However, as γ increases, the emission increase becomes weakerbecause the scale effect (the only active effect in the quantity case) gets increasingly offset
by the technique effect.
For all γ > 1, global emissions decrease in the EK and Melitz models in response totrade liberalization. While the production scale increases, reallocating production towards
more productive firms significantly reduces the average emissions intensity. This techniqueeffect is stronger than the scale effect, which reduces the aggregate emissions. For theestimated γ = 1.2, global emissions decrease by approximately 7% in Melitz and 5% in
EK. However, it is premature to conclude that firm heterogeneity positively affects theemission effects of trade or that trade generally lowers global carbon emissions. First, theprevious section shows that the aggregate estimated γ hides considerable heterogeneity
across sectors. Second, a full quantification of the trade effects needs to consider sectoral
reallocations — which can alter global emissions irrespective of sectoral differences in γ.
The Melitz model’s emission response is slightly stronger than EK for all values of γ.
However, the difference between this group of two models with producer heterogeneity
and the two homogenous producer models with a zero-emission response is much more
pronounced than the difference within the heterogenous producer model group.

36Figure 2: Changes in emissions for different γ

Note: The figure shows the changes in global emissions due to a 40% uniform tradeliberalization for different values of γ.

Table 3 in Appendix L additionally shows the national emission changes in EK and
Melitz for the two cases in which emissions are assumed to be proportional to the physicalquantity produced (γ = 0) or γ taking the estimated value of 1.2. As expected, emissions
increase for all countries in the quantity case and decrease for γ = 1.2. However, there
is significant heterogeneity across countries. In the quantity case, the emissions increase
ranges from 17.79% in the US to 81.97% in Cyprus in the EK model and from 10.51%
in Luxemburg to 51.21% in Cyprus in the Melitz model. For the case of γ = 1.2, theemission reductions range from 3.06% in the US to 15.05% in Lithuania in the EK modeland from 4.32% in the US to 13.21% in Ireland in the Melitz model. Importantly, thecomposition effect of international trade, which involves shifting the industry composition,is inherently excluded from these results.

37

5.3.2Multiple Industries

As discussed in Section 4, the emission response to trade liberalization can differ acrossmodels in multi-industry settings for two distinct and potentially interacting reasons:Firm heterogeneity as in the single-industry models and differential trade responses due
to scale economies. We compare the multi-industry Armington, Krugman, EK, and Melitz
models, and for the models with firm heterogeneity, consider four cases with γs = 0, γs = 1,
γs = 1.2, and estimated γs . As with the aggregate quantification, we simulate a uniform
cut in international trade costs by 40%.
The results are illustrated in Figure 3. Just as in the aggregate consideration, thechoice of γs does not affect the results in the Armington and Krugman models because
there is no firm heterogeneity. Therefore, only one result bar is shown for each of thesemodels. However, global emissions are affected by trade liberalization, which is different
from the single-industry case. The global emissions increase mildly by less than one
percent (Armington) and 1.6% (Krugman).
Increased emissions in these models are driven by a global composition effect, i.e.,
trade liberalization induces countries to specialize in more emission-intensive industries.
However, these findings suggest that these compositional shifts play a relatively minor rolein global emissions for this specific counterfactual. Even though both the Armington and
the Krugman models feature no heterogenous productivity, the results are not identicalacross these two models. This difference is because trade outcomes and the associatedemission effects from sectoral reallocation are not identical, as the Krugman model features
scale economies.
In line with Proposition 7, if γs = 1, the emission response is identical within the twogroups of perfect competition models without scale economies (Armington and EK) andmonopolistic competition models with scale economies (green bars in Figure 3). Withinevery industry, productivity heterogeneity does induce additional scale and techniqueeffects. Still, as in the single industry case, these cancel out if the KR elasticities areunity.
Further focussing on the EK model, when we use the estimated γs for each industry,
a 40% reduction in trade costs leads to a 3.4% increase in global emissions (purple bar).
Accounting for productivity heterogeneity, hence, in this case, more than triples the global
38

emission increase associated with the trade liberalization shock. Note that this contrasts
with the result of a single industry, where the trade liberalization resulted in a decrease inglobal emissions. This stresses the importance of taking the heterogeneity in the relationship between productivity and emission intensity across sectors. We can further illustrate
this by using the aggregate γ estimate of 1.2 for all sectors in the multi-sector EK model(turquoise bar). In this case, within-sector reallocations across firms induce a net emission
reduction and emissions decrease in response to the trade liberalization shock by 1.7%.
As a final multi-sector EK consideration, assuming emissions are directly proportional to
output (γs = 0), EK models would forecast a substantial increase in global emissions byover 16%.
Turning to the multi-industry Melitz case with emissions proportional to quantities(i.e. γs = 0), emissions increase dramatically by almost 80%. On the other hand, taking
the optimistic γs = 1.2 case leads to an environmentally beneficial reallocation acrossfirms that reduces global emissions by 3.4%. These two effects are qualitatively in linewith the EK case, but the effects are considerably stronger. In the case in which we
use the sectoral estimates of γs , even the qualitative prediction is different in the Melitz
model: Global emissions decrease by 1.4% in response to the trade liberalization shock.
These contrasting results illustrate the effect of scale economies and firm heterogeneityinteract in a non-trivial way. Adding only scale economies (i.e. moving from Armington
to Krugman) slightly increases the emission effect. Only adding firm heterogeneity (i.e.
moving from Armington to EK) considerably increases the emission effect. However,adding both scale economies and firm heterogeneity (i.e., moving from Armington to
Melitz) in a setting with flexible and sectorally varying KR elasticities alters the emission
prediction altogether, turning the increase into a decrease.
The stark differences in global emissions prediction across models underscore the quantitative significance of firm heterogeneity and the importance of accurately modeling theemissions-productivity relations. Both the exact model specification and the parametrization make a sizable difference in the quantitative results.
The country-level results are shown in Table 4 in Appendix L. When we look at
the individual countries, there is a huge heterogeneity in emission changes. When we
use the estimated γs , while some countries like Denmark and Poland witness a stark39

increase in emissions, countries like Luxembourg and Malta witness a stark decline inemissions. Overall, we observe different models (i.e., Armington, Krugman, EK, andMelitz) with different γs values, resulting in quantitatively significant global and countrylevel differences.
Figure 3: Changes in global emissions by model and γs

Note: The figure shows the changes in global emissions due to a 40% uniform tradeliberalization for Armington and EK. Values are shown for the quantity case γs = 0, the value
case γs = 1, and the estimated values of γs from Table 1.

40

6Conclusions

In their seminal paper, ACR raise the question to how much the rise of new trade models
has altered the answer to the field’s central question of how large the gains from tradeare. Their answer is: “So far, not much.” A decade later, we investigate how strongly new
trade models have affected the key question in the trade and environment subfield: What
are the effects of trade on emissions?
We initially arrived at a conclusion similar to ACR’s. While new trade models add
interesting mechanisms via which trade affects environmental outcomes, they tend to
be incorporated into quantitative models, leaving aggregate emission effects unaltered.
If emissions are linked to production value, the emission-saving effect of reallocating tocleaner producers is perfectly offset by an emission-increasing impact of higher overall
production.
However, upon closer inspection, the answer is more nuanced. Even in cases where
the ACR’s trade equivalence holds, emissions equivalence breaks whenever emissions arelinked to quantities rather than values. We further generalize the relationship between
quantity and emissions to be productivity-dependent. Depending on how clean the productive firms are, accounting for firm heterogeneity can shed a better or worse light on
the environmental consequences of international trade.
The basic intuition holds for multiple industries but requires additional caution because the ACR’s trade equivalence no longer generally holds in multi-industry settings.
In the model of multiple industries with emissions linked to value, the Armington and
EK models still yield identical aggregate emission effects because the ACR-type tradeequivalence continues to hold. A multi-industry Melitz model yields different aggregate
emission effects, however, only because the trade effects and associated global changes in
sectoral composition differ due to the presence of scale economies. It, therefore, coincides
with a multi-sector Krugman model. If the emission intensity across industries is uniform,
trade liberalization does not change global emissions in either model. We also provide ageneralized multi-industry case in which emissions are flexibly linked to quantities, andfirm heterogeneity matters for aggregate emission outcomes. Our quantitative exercises
illustrate the importance of the elasticity with which emission intensity depends on productivity. If the link is relatively weak, firm heterogeneity worsens the emission effects of41

trade. If it is strong, firm heterogeneity can make trade environmentally beneficial. We
estimate the key elasticity using German firm-level data and quantify our multi-industry
model. Our results illustrate that the emission effect of firm heterogeneity and scaleeconomies interact non-trivially. Firm heterogeneity fosters the emission increase inducedby trade liberalization in a perfect competition environment while lowering global emissions in a monopolistically competitive world. These contrasting results illustrate thequantitative importance of getting both the model structure and the parametrizationright.

42

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45

Appendix
A

Proof for the exact hat algebra

We start with the change in the trade shares λ̂ni . For all i. We take the ratio of tradevalues:PN′ ε)χkj · Nk′ · (c̃(wk′ , t′k )τki
χij · Ni · (c̃i (wi , ti )τni )ελ̂ni = PN
· k=1
′
′ ′
ε
ε
χij · Ni · (c̃i (wi , ti )τni′ )k=1 χkj · Nk · (c̃(wk , tk )τki )= PN

N̂i (τ̂ni ĉi )εε
k=1 λnk N̂k (τ̂nk ĉk )c (w′ ,t′ )where ĉi = cii (wii ,tii ) . Notice that ci is homogeneous degree of one, and t̂i = ŵi . Therefore,
we can simply calculate the change in costs as follows:ĉi =ci (wi′ /ŵi , t′i /ŵi )ci (wi , ti )ci (wi′ , t′i )
= ŵi
= ŵi
= ŵi .
ci (wi , ti )ci (wi , ti )ci (wi , ti )Furthermore, as discussed in ACR, the first two restrictions imply M̂i = 1. Using these
relationships, we have:
λ̂ni = PN(τ̂ni ŵi )εε
k=1 λnk (τ̂nk ŵk ).

Now we discuss the goods market clearing. The goods market clearing assumption implies:X
λ̂ni λni Rk′ .
R̂i Ri =n=1

The change in the revenue (output) can be written as
wi li
ti Zi
Πi
+ t̂i Ẑi+ Π̂i
wi li + ti Zi + Πi
wi li + ti Zi + Πi
wi li + ti Zi + Πi
wi li
ti Zi
Πi
= ŵi
+ R̂i
+ R̂i
wi li + ti Zi + Πi
wi li + ti Zi + Πi
wi li + ti Zi + ΠiR̂i = ŵiwhere the second equality uses the fact that Ẑi = R̂i /t̂i and Π̂i = R̂i . This derivation
implies R̂i = ŵi .

BFixing absolute emission taxes

We focus on the global emissions, which is a summation of emissions across countries:
Z=

N
X
i=1

46

Zi .

The changes associated with trade shocks are:
Ẑ =

N
X

ρi Ẑi =i=1NXρi β̂i (ŵi , wi /ti )R̂i

i=1

where ρi is the share of emissions from country i (Zi /Z) and β̂i (ŵi , wi /ti ) ≡ βi (wi′ /ti )/βi (wi /ti )is a change in the emission intensity. We will need to calculate R̂i given that t̂i is fixednow:ŵi wi Li
Ẑi ti Zi
Π̂i Πi++wi Li + ti Zi + Πi wi Li + ti Zi + Πi wi Li + ti Zi + Πi
β̂i (ŵi , wi /ti ) R̂i βi (wi /ti )RiR̂i Πiŵi wi Li++=
wi Li + ti Zi + Πi
wi Li + ti Zi + Πi
wi Li + ti Zi + ΠiR̂i =which implies:
R̂i =ŵi wi Li
wi Li − β̂i (ŵi , wi /ti )βi (wi /ti ))Ri

and hence:
Ẑ =

N
X
i=1

si β̂i (ŵi , wi /ti )ŵi wi Li
wi Li − β̂i (ŵi , wi /ti )βi (wi /ti ))Ri.

We also need to reconsider the trade share equations since now the changes in wages andtaxes do not coincide:
λ̂ni = PN(τ̂ni ĉi )εε
k=1 λnk (τ̂nk ĉk ).

c (w′ ,t )where ĉi = cii (wii ,tii ) . Using these equations, we construct an example where the global
emissions depend on the normalization scheme. We choose the normalization scheme
where we fix the wage change of country one as ζ. If ζ = 1, the normalization scheme
fixes the wages of country 1 to be the same before and after the counterfactual experiment.
For the example, we use a symmetric two-country model with β fixed (this corresponds
to the Cobb-Douglas emission function, which is common in the literature). Figure ??
shows the changes in global emissions for a 40% reduction in trade costs for various valuesof ζ. The figure indicates that the normalization scheme matters when we fix the absoluteemission tax level. Especially the result suggests that increasing the price of the numeraireof goods results in higher global emissions.

C

Deriving emission for the quantity case and the flexible specification case

Since the quantity case is a special case of the flexible specification with γi = 0, we omit
the proof and only exhibit the proof of the flexible specifications.
47

Figure 4: Comparing emissions for different normalization schemes

C.1

EK

We start from the fact that the price of goods exported from country i to country n also
follows a Frechet distribution. Specifically, the price distribution of goods exported fromcountry i to country n ,Gni (p), only depends on the destination country:
P r (pin (ω) = p|pin (ω) ≤ mink=1,...,N pki (ω))= Gni (p) = exp(−Φn pθ ),θ/(1−σ) −θ
R∞Pn = 0 p1−σ dGni (p) is a function of the price index inwhere Φn = Γ θ+1−σθτni, and hence the emissions
country n. The productivity of a product with price pni is wpiniof a particular producer with price pni is

γi
pni
pni (ω)−σzni (pni (ω)) = 1(pni (ω) ≤ mink p(ω)nk )µi
τni Xi .
wi τniPn1−σ48

Hence, the aggregate emissions are
Z 1
zni (ω)dω
Zni =
0

γi
Z 1
pni
µi pni (ω)−σ
1(pni (ω) ≤ mink pnk (ω))µi=
Xn dω
wi τniPn1−σ0Z ∞µi pγi −σ−γi= λni (wi τni )τni Xn dGni (p)
Pn1−σ
0
Z ∞
1
−γi
(σ−1)/θ Φnpγi −σ dGni (p)= Xni µi τni (wi τni )
θ+1−σ
Γ
0
θ


θ + γi − σ1−γi(σ−1)/θ (γi −σ)/θ
 Φn
Φn
Γ
= Xni µi τni (wi τni )θΓ θ+1−σθΓ θ+γθi −σ (γi −1)/θ Φn= Xni µi τni (wi τni )−γiΓ θ+1−σθθ+γi −σ(γi −1)/θ −1 (1−γi )/θ Γ−θ −θθ Φn(γi −1)/θ
= Xni µi wi τni Ti
wi Ti
θ+1−σ
Γ
θ

 (1−γi )/θθ+γi −σ
Γ
Xni
Ti
θ
.
=
µi
wi
λni
Γ θ+1−σθThis leads to the following exact hat algebra:
EK
Ẑni
=

X̂ni (γi −1)/θ,λ̂ŵi niand the corresponding emission share ιni is given by(γ −1)/θ
λnii
Xni
EK
ιni = P.
(γi −1)/θ
Xki
k=1 λki

C.2

Melitz model

We start by expressing the physical quantity in terms of revenues, i.e.:qni (ω) =xni τnipni,ω (wi , ti )Then emissions embodied in the trade flow of variety ω from i to n can be expressed interms ofµi τni xni (ω)
zni (ω) =.
τni σ̃wi (φ(ω))γi
In Melitz, the only firm-specific component of the unit costs is the productivity, φ(ω), i.e.
ci,ω =

wi
.
φ(ω)

49

Thus, emissions embodied in trade flows from i to n:
Z
µi
Zni =
Mni
(φ(ω))1−γi xni (ω)dG(φ(ω)|ω ∈ Ωni ).
σ̃wi
ω∈Ωni
With exports of firm ω from i to n ofxni (ω) = (φ(ω))σ−1 (σ̃wi τni )1−σ wn Ln Pnσ−1 ,To enter the foreign market, firms have to pay a fixed cost of wn fni , which leads to aunique productivity cut-off of(φ∗ni )σ−1 =fni(σ̃wi τni )σ−1 .
σ−1L n PnBecause φ(ω) is the only parameter that varies at the firm level, we henceforth only index
firms by their productivity. The embodied emissions are given by
Z ∞
µi
σ−1
wn Ln Pn Mni
φσ−γi dG(φ|φ ≥ φ∗ni ).
Zni =
σ̃wi
φ∗ni
With the assumption of Pareto distributed productivity, i.e. Gi (φ) =
Zni =

 θ
Ti
φ

we get:µiθwn Ln Pnσ−1
Mni (φ∗ni )σ−γi .
σ̃wi
θ + γi − σExpressing (φ∗ni )σ−γi in terms of revenues and the share of exporting firms:

Sni =

φ∗ni
φ∗ii

−θ
,

yields:Zni =µi −(1−γi )/θ ∗ 1−γiθ(φii )Mni
Sni
xni (φ∗ni ).
σ̃wiθ + γi − σNoting thatMniθxni (φ∗ni ) = Mni E[xni |φ ≥ φ∗ni ] = Xni ,θ + γi − σyields:Zni =θµi−(1−γ )/θSni i (φ∗ii )1−γi Xni .
σ̃wi θ + γi − σThis leads to the exact hat algebra expression of:
M elitzẐni=

X̂ni −(1−γi )/θ c∗ 1−γiŜ(φii ),ŵi niwhich yields (17) and for γ = 0 (13). The corresponding weights to calculate aggregate

50

emissions are given by−(1−γ )/θSni i Xni
M elitz= PN
ιni.
−(1−γi )/θ
Xki
k=1 SkiD

Proof for proposition 5 and 6

We discuss the Armington, EK, and the Melitz model sequentially. We only prove thecase for γi < 0 since we can prove the case of γi > 0 and γi = 1 in a similar manner. The
proof of the quantity case is omitted since it is a special case with γi = 0.

D.1

Armington model

Because there is only a single variety in each country, we omit the notion of ω. The total
emission of country i is proportional to the quantity produced:
Zi = µi φ−γi Qi ,and the produced quantity is:
Qi = φi Li .
Notice that the trade shocks that move the economy from autarky to trade economy
do not alter the labor endowment li and the productivity φi . Therefore, the changes inoverall emission of country i before and after the autarky are:i
ZiT RADE = µi φ1−γ
Li = ZiAU T .
i

D.2

EK modelFor the EK model, we utilize the expression for emissions embodied in trade: (1−γi )/θΓ θ+γθi −σ
Xin Ti.
Zni =wi λniΓ θ+1−σθand the aggregate emission is
N
1/θ X


θ+γi −σXni (γi −1)/θ Γ
θ

λin
θ+1−σ
Y
Γ
i
θ
n=1

θ+γi −σX1/θ(γi −1)/θ Γθ,= li Ti
sin λin
θ+1−σ
Γ
θ
n=1

Yi Ti
Zi =
wi

where sni = XYni
. Since λii is unity in autarky, we havei
1/θ Γ
ZiAU T = li TiΓ51

θ+γi −σ
θ
.
θ+1−σ
θ



because sii = 1 and λii = 1 in autarky. Notice that with finite trade costs,
P 0 < λin < 1.
(γ −1)/θ
If γi < 1, we have hence λini
> 1 . Combining these questions and N
n=1 sin = 1, we
have:

N
X
Γ θ+γθi −σ
1/θ
1/θ
AU T

sin
Zi
= li Ti = li Ti
θ+1−σ
Γ
θ
n=1

N
θ+γ
i −σ
X
1/θ
(γi −1)/θ Γθ = ZiT RADE .
< li Ti
sin λin
θ+1−σ
Γ
θ
n=1
We can prove the case for γi = 1 and γi > 1 in a similar manner.

D.3

Melitz model

We start by rewriting emissions embodied in trade flows as
Zi =X (1−γ )/θ Xniµi L i
θSni i(φ∗ii )1−γi.
σ̃ θ + γi − σ
wi Li
n∈N

(28)

By the zero profit condition of exporting the domestic productivity cut-off is
φ∗ii =

fiiwi σ̃τii .
Pi

Hence φ∗ii ∝ wPii . As shown by Arkolakis et al. (2012) trade opening increases the real wage
T
RADE
and thus must rise the domestic productivity cut-off. Hence φ∗,AU< φ∗,T. Further,
ii
ii
Xii
under Autarky wi Li = Sii = 1 and under conventional parameter restrictions, Sni < 1. AsP(γ −1)/θ
> 1. In combination with n∈N wXinia consequence,if γi < 1, Snii
= 1 we get:Li
ZiAU T =
1−γi1−γi X X
µi L i
θµi L iθ
ni
T∗,AU T
φ∗,AU
=
φ
ii
ii
σ̃ θ + γi − σσ̃ θ + γi − σ
w
L
i i
n∈N


X
1−γi
µi L iθ(1−γ )/θ Xni
RADE
<
φ∗,T
.
Sni i
ii
σ̃ θ + γi − σ
w
i Li
n∈N

The proof works similar for γi = 0 and γi = 1.

E

Derivation of (18)The multi-sector environment in Section 4 assumes the following nested demand structure. The upper nest is Cobb-Douglas with spending share ζis on sector s in country i.
Consumers have CES preferences within each sector across goods from different countries
with elasticity ηs and varieties from a specific origin with elasticity σs . Hence, consumers
in i spend on variety ω from n in s:

1−ηs
Pnis
1−σs
σs −1
pnis (ω)qnis (ω) = pnis (Pnis )
Eis ,
(29)
Pis
52

with the price indices:!1/(1−ηs )
X

Pis =

1−ηs
Pnis

n∈N

Z
Pnis =

pnis (ω)

1−σs1/(1−σs )dωω∈ΩnisHence, the spending share of consumers in i on sector s country n is given by:R
p1−σs (ω)dω(Pnis )σs −ηsω∈Ωnis nis
Rλnis = P1−σsσs −ηsl∈N ω∈Ωlis plis (ω)dω(Plis )(30)With the definition of the price index, this implies:
1−ηs
Pnis
λnis = P
1−ηsl∈N Plis

E.1

(31)

Armington

In Armington, the price index is
Pnis =

τnis c(wn , tn )φns

As a consequence, the expenditure share is given by1−ηs
λnis = Pτnis cn (wn ,tn )
φns

l∈N



τlis cl (wl ,tl )
φls

1−ηs

(32)

which implies equation (18) by setting the trade elasticity to ϵs = ηs − 1 and ξins = φηnss −1 .

E.2

EK

In the EK model, there are only two nests (ηs = σs ) since there is no distinction between
the foreign and the domestic varieties. The expenditure share is given by
λnis = P(τnis c̃i (wi , ti ))−θs Tis−θsTlsl∈N (τnls c̃l (wl , tl ))which implies equation (18) by setting the trade elasticity to ϵs = θs and ξins = Tls .

53

(33)

E.3

Krugman

In Krugman, firms are homogeneous and engage in monopolistic competition. This market
structure implies the following constant markup price for all varieties ω ∈ Ωnis
pnis (ω) =σs τnis cn (wn , tn )σs − 1φns(34)e
To enter the market, firms have to pay a fixed cost of wn fns. Free entry implies that firms
enter as long as they earn positive profits, i.e.:Xpnis qnise
Mns wns fns
=
Mns
σs
i∈N

Because labor is the only factor of production, aggregate revenues equal labor payments.
Hence, the number of firms is given by:Mns =γn (wn /tn )Lns
e σ
fns
s

(35)

Thus, the price index becomes:
Pnis =

γn (wn /tn )Lns
e σ
fns
s

1
 1−σ

s

σs
τnis )wn
σs − 1(36)

and the expenditure share can be expressed as:
λnis =

γn (wn /tn )Lis
e
fis

P

l∈N



Lls
e
fls

1−ηs 
 1−σs

1−ηs 
 1−σs

τnis cn (wn ,tn )φns

τlis cl (wn ,tn )
φls

1−ηs

1−ηs
equation (18) can be obtained by setting ϵs = ηs −1, δs = 1−σand ξins =
s

E.4

(37)

1−ηs



γn (wn /tn )
e
fis

1−ηs
 1−σ

s

(φns )ηs −1 .

Melitz ModelIn Melitz, firms are heterogeneous in their productivity φ(ω), which leads to a firm-spefic
price of:σs τnis cn (wn , tn )pnis (ω) =(38)σs − 1φ(ω)
Productivity is Pareto distributed with cumulative density
Gns (φ(ω)) = 1 −

Tns
φ(ω)

−θs

e
Firms face two different types of fixed costs. First, they pay wn fns
to enter the economy.
Second, for each market i, which they serve, they need to pay wn fnis . This second fixed
cost type implies that only firms with productivity higher than φ∗nis serve market i from54

n, s. Thus, the equilibrium price index is determined by:1−σs Zσs1−σs∗Pnis = Mnis (1−G(φnis ))τnis cn (wn , tn )φ(ω)σs −1 dG(φ(ω)|φ(ω) ≥ φ∗nis )∗σs − 1
φnis
With the Pareto distribution, the price index can be simplified to:
1−σs

σs
1−σs
τnis cn (wn , tn )θs Tisθs (φ∗nis )σs −1−θsPnis = Mnis
σs − 1(39)

Free entry into markets implies the following cut-off productivity:φ∗nis =

σs
τnis cn (wn , tn )σs − 1

σs wi fnis
Bnis

where
Bnis = (Pnis )

σs −1



Pnis
Pis

1/(1−σs )
(40)

1−ηs
Eis

s
Plugging into the expression for the price index and defining ζs = θsσ+1−σ
leads to:
s −1

1−σs
Pnis
= Mnisσsτnis cn (wn , tn )σs − 11−σs

θs Tisθsσsτnis cn (wn , tn )σs − 1σs −1−θs 

σs wi fnis
Bnis

ζs

s
, this can be expressed as:
Defining ζs = θsσ+1−σs −1

1−σ +ζ (σ −η )Pnis s s s s = Mnis



−θs

ζ
σs wi fnis sσsθsτnis cn (wn , tn )θs Tisσs − 1
Eis Pisηs −1

Now, note that1 − σs + ζs (σs − ηs ) = 1 − ηs + θs

1 − ηs−1 +1 − σs= (1 − ηs ) 1 + θs11−ηs − 1 σs − 1,then the price index can be rewritten as:δs1−ηsPnis = Mnis
where δs = (1+θscondition:

σsτnis cn (wn , tn )σs − 11( ηs1−1 − σs1−1 )

 −θ
s δs
1−η
s

θs Tisθs

δs
 1−η
s



σs wi fnis
Eis Pisηs −1

ζs δs
 1−η

s

(41)

. The number of firms can be calculated from the free entrye
Mns wn fns
=

X
i∈N

Mns

pins qins
σs(42)

Firms enter the economy as long as they make positive profits in expectation, i.e:


X
1
e
∗
∗
wn fns =(1 − G(φnis ))E[pins (ω)qnis (ω)|φ ≥ φins ] − wi fins
(43)
ηs
i∈N

55

With the Pareto distribution, the average revenues are given by

1−σs
θs
σ
∗
E[pnis (ω)qnis (ω)|φ ≥ φnis ] =cn (wn , tn )(φ∗nis )σs −1 Bnis
θs + 1 − σs σs − 1
and fixed costs of entry must equal the revenues of the marginal firm, i.e.:

1−σs
σ
wn fnis =ci (wi , ti )(φ∗nis )σs −1 Bnis
σs − 1(44)(45)

Hence, the free entry condition implies:
!1−σs
σ X
ci (wi , ti )(φ∗nis )σs −1 Bnis
σs − 1 i∈N

σs − 1e
wn fns=θs + 1 − σs

(46)

or expressed in terms of aggregate revenues Xns :e=
Mns wn fns

σs − 1Xns
θs + 1 − σs(47)With the labor market clearing condition, we get the following:e
Mns fns= γn (wn /tn )σs − 1Lns
θs + 1 − σs(48)

Hence, the expenditure share is given by


 δs


θs δs
(τins cn (wn , tn ))−θs δs Tns(fins )ζs δs ξins
λins = P δs−θs δsγl (wl /tl )Lls
θs δs
(τ
c
(w
,
t
))
T
(fils )ζs δs ξils
e
lns
l
l
l
ls
l∈N
f
γn (wn /tn )Lns
e
fns

(49)

ls

Definingξins =

γn (wn /tn ) δs θs
ζs δs) Tns finsefns

and ϵ = θs δs yields (18)F

Proof of proposition 7

PPart (i) The change in country level emissions is Ẑi = s∈S ZZisi Ẑis . From (??), thecounterfactual change in emissions in sector s country i is given byẐis =\β(wi /ti )
R̂is
t̂i

(50)

Fixing t̂i = ŵi and noting that from the labor market clearing condition R̂is = ŵi L̂isyields:Ẑis = L̂is
(51)

56

and
P thus the first expression of (20). Because aggregate revenues are given by Ris =n∈N λins Ems the change i the labor allocation can be expressed as:
1
L̂is =ŵiPn∈N λ̂ins λins Êns Ens

wi Lis(52)

which directly yields the second equality of (20). The change in expenditure in the
expenditure is obtained by applying the exact hat-algebra to (18)G

Proof of Corollary 1

Part (i) From the derivation of (18), the change in the trade share for an Armington
and EK model is obtained by setting δs = 0 in (21). Hence, the trade share response isexactly the same across models. From proposition 7, the difference in emissions acrossmodels is fully captured via differential responses in the trade share. Thus, the emission
response is the same for Armington and EK.
Part (ii) The derivation of equation (18) shows that the change in expenditure shares, which is larger than zero because ηs > 1
in Krugman is obtained by setting δs = σηss−1−1
and σs > 1. Hence, there is an additional term affecting expenditure changes. From (18),these scale economies are also operative in Melitz. Moreover, ζs is generally different fromzero.
Part (iii) If ZZisi = LLisi , the change in emission is given by:
Ẑi =

X Lis
s∈S

Li

L̂is

(53)

Because the labor endowment is fixed, for any trade shock L̂i = 1∀i. Hence,
X Lis
s∈S

H

Li

L̂is = L̂i = 1

Counterfactual exporter share

The change in the exporter share is given by:Ŝnis =

∗
d
φ
nis
∗
d
φ
iis

!−θs

The change in the productivity cut-off is equal to:∗dφnis = τ̂nis ŵi



ŵn
B̂nis

57

1/(σs −1),(54)with the counterfactual value of aggregate market level for goods in sector s shipped fromi to n given by:B̂nis = (P̂nis )σs −ηs (P̂ns )ηs −1 Êns ,(55)
with the change in price indices of: −ζs δsδs−ϵsP̂nis = (L̂is ) (1−ηs ) (τ̂ins ŵi ) (1−ηs ) P̂ns
,
# −1
ϵ

"
P̂ns =(56)s

X

λnis Lδiss (τ̂nis ŵis )−ϵs

.

(57)

i∈M

I

Proof of proposition 8

AU T
We start from the same observed autarky equilibrium with ZisAU T and Ris. We only
prove the statement (ii), since proving (i) and (iii) is a straightforward extension.

I.1

EK

We first prove that if γi < 1, trade opening implies higher emissions in the EK than in
the Armington model. Denote the industry’s emissions per output in autarky as µ̃i =
AU T
AU T
are emissions and revenue in autarky for industry s
where ZisAU T and Ris
ZisAU T /Risin country i, respectively. The emissions under trade opening in the Armington modelare:
ZisARM = µ̃i Ris
where Ris is a revenue of industry s in country i after the trade opening. Notice that Ris
is common across the two models. In the EK model, the emissions after trade openingare:
ZisEK =

NX

(γ −1)/θ

Xnis µ̃i λnisi> ZisARM Ris = ZisARM .

i=1

Aggregating this over industries will result in the proposition 8 (ii).

J

Imputation of the exporting share

We impute the share of exporting firms based on a model-driven gravity equation. Recall
that the share of exporters from n to i in sector s is given by
Snis =

Mnis
Miis

(58)

The number of exporters can be expressed as the ratio of total to average exports, i.e. :Mnis =
58

Xnis
x̄nis

(59)

and thus

Xnis x̄iis(60)
Xiis x̄nis
In the Melitz-Chaney model, the ratio of the average sales is equal to the ratio of fixed
costs:
fnis
x̄iis
=
(61)
x̄nis
fiis
Snis =

We proxy the relative fixed costs by the distance between n and i, distni . Hence, we get
the following estimation equation:log(Snis ) = log(λxnis ) + log(distni ) + ξn

(62)

nis
where λxni = X, and ξn are destination fixed effects. We drop all internal trade flows forXiis
the estimation and estimate the equation for each WIOD sector and the entire economy.

K

Parameter calibration

Calibration of parameters for the multiple industries is done as follows. We take σs and ηsfrom Lashkaripour and Lugovskyy (2023) and θs from Shapiro and Walker (2018). Using
these parameters, we construct trade elasticity and scale elasticity using the formula from
the Melitz model (ϵs = (1+θ 1θs − 1 , δs = θϵss ). We use the trade elasticity deriveds ( η −1
σs −1 )sfrom the Melitz model for other models. For the scale elasticity, we use the derived scaleelasticity for the Melitz model while setting the parameter to zero for the Armington andthe EK. The parameter γs is calculated from the estimate in column 9 and the same σs
we use to calculate elasticities. Apart from γs the counterfactual emissions in EK and
Melitz depend on the value of θs , which is different for these two models. For Melitz we
use the value presented in table 2, whereas for EK, θs equals the trade elasticity, i.e. weset θsEK = ϵs .
We acknowledge that this is not internally consistent. If we take the parameters
seriously, we should have different trade elasticity across the model. If we fix the tradeelasticity, we should use the implied σs and θs to calculate γis and the counterfactual
emissions, which will differ across models. We keep our calibration this way to highlightthe key differences from the firm heterogeneity while keeping the elasticity intact.

59

Table 2: Parameters
Sector

δ

ϵ

θ

η

σ

A01
A02
A03
B
C10-C12C13-C15
C16
C17
C18
C19
C20
C21
C22
C23
C24
C25
C26
C27
C28
C29
C30
C31-C32
C33
D-E
F
G
H
I-U
Total

0.00 1.85
7.23
0.00 0.52
7.23
0.00 11.98
7.23
0.00 13.97
7.23
0.86 3.35 3.89 3.30
0.74 3.55
4.8 4.36
0.85 5.29
6.2 4.90
0.77 4.00 5.21 3.65
0.77 4.00 5.21 3.65
0.22 2.21 9.91 1.64
0.93 3.27
3.5 4.97
0.93 3.27
3.5 4.97
0.80 3.70 4.62 6.16
0.92 3.71 4.05 6.28
0.45 4.47 10.01 4.00
0.63 3.01
4.8 4.00
0.42 2.24 5.32 2.24
0.45 2.14 4.77 2.24
0.96 4.04 4.19 8.75
0.44 2.46
5.6 3.81
0.53 2.06 3.87 3.81
0.96 3.61 3.75 7.17
0.96 3.61 3.75 7.17
0.00 4.00
4.00
0.00 4.00
4.00
0.00 4.00
4.00
0.00 4.00
4.00
0.00 4.00
4.00
4.00

7.99
7.99
7.99
7.99
3.54
5.46
5.37
4.12
4.12
1.82
5.31
5.31
8.14
6.99
5.78
5.78
2.81
2.81
9.33
8.75
8.75
7.58
7.58
5.00
5.00
5.00
5.00
5.00
5.00

Note:
Parameters used in the analysis. σs andηs are sourced from citeLashkaripour2023
and thetas from citeShapiro2018. The remaining parameters are calculated basedon these estimates and consistent with the
Melitz model, i.e ϵs = (1+θ 1θs − 1 ,s ( η −1
σs −1 )sϵs
δs = θs . For sectors outside manufacturing
and without an estimate of θs we take theestimated trade elasticity from Fontagné
et al. (2018).

60

LCountry-level results

61

Table 3: Changes in emissions by country
γ=0

γ = 1.2

Country

EK

MelitzEKMelitz

AUS
AUT
BEL
BGR
BRA
CAN
CHE
CHN
CYP
CZE
DEU
DNK
ESP
EST
FIN
FRA
GBR
GRC
HRV
HUN
IDN
IND
IRL
ITA
JPN
KOR
LTU
LUX
LVA
MEX
MLT
NOR
POL
PRT
ROU
ROW
RUS
SVK
SVN
SWE
TUR
TWN
USA

47.72
50.89
38.80
69.38
42.28
43.13
48.38
18.21
81.97
46.00
30.80
52.67
45.77
60.06
65.60
39.59
40.34
67.19
73.38
40.45
56.02
42.20
20.40
41.63
34.95
43.62
50.86
20.47
78.09
46.06
42.75
54.20
48.96
66.25
64.59
20.78
43.52
48.96
59.00
51.37
52.53
42.67
17.79

44.66
34.91
28.59
45.28
48.04
30.31
38.76
35.49
51.21
42.45
37.58
32.73
42.76
32.80
43.51
43.60
38.86
44.41
42.97
35.47
44.57
39.03
16.89
37.07
39.08
41.62
30.97
10.51
40.62
36.00
31.58
38.75
49.08
45.70
47.43
48.20
42.55
31.94
29.27
40.97
48.72
32.45
27.10

-7.91
-10.78-10.64-13.92-6.17-8.95-12.33-3.71-14.68-11.57-8.35-12.93-8.30-13.97-11.92-7.24-7.28-10.43-14.69-12.23-9.42-6.89-14.34-7.77-6.00-10.29-15.08-12.98-14.14-9.29-13.73-12.69-9.81-11.84-11.74-3.33-8.45-12.88-14.77-10.79-9.93-13.19
-3.06

-7.55
-8.12
-8.17
-9.18
-6.46
-6.54
-10.59-5.61-9.24-11.52
-9.99
-9.16
-8.14
-7.86
-8.81
-7.99
-7.25
-7.24
-9.20
-11.46-7.96-6.50-13.21
-7.28
-6.44
-9.66
-9.52
-9.34
-7.99
-7.53
-9.36
-10.28-10.35
-8.69
-9.22
-8.10
-8.40
-8.33
-7.63
-9.49
-9.33
-10.46-4.32

Note:
Changes in emissions by country in the single industry case. Results shown for theEaton-Kortum (EK) and Melitz model andthe quantity case γ = 0 and the estimatedγ = 1.2. All values in percentage changes
compared to the baseline.

62

Table 4: Changes in emissions by country
Armignton

Krugman

EK

MelitzCountry

γ=1

γ=1

γ=1

γ=0

γ̂

γ = 1.2

γ=1

γ=0

γ̂

γ = 1.2

AUS
AUT
BEL
BGR
BRA
CAN
CHE
CHN
CYP
CZE
DEU
DNK
ESP
EST
FIN
FRA
GBR
GRC
HRV
HUN
IDN
IND
IRL
ITA
JPN
KOR
LTU
LUX
LVA
MEX
MLT
NOR
POL
PRT
ROU
ROW
RUS
SVK
SVN
SWE
TUR
TWN
USA

8.73
4.42
15.63
12.97
5.65
6.56
-5.54
-0.18
12.29
5.87
3.53
31.93
6.07
24.63
4.16
1.21
-1.98
-3.67
10.08
5.24
-0.40
-4.79
-13.35
-3.39
-0.01
-0.45
19.32
-28.405.51
0.15-31.31
32.70
-3.03
11.05
-2.21
-0.49
1.62
-3.21
23.69
2.93
10.83
-1.62
5.45

15.61
-1.11
7.90
26.16
8.78
2.02
-7.07
1.14
558.73
11.79
2.61
19.90
66.16
25.48
15.91
-23.88
5.23
1.64
-0.41
12.55
-7.84
1.45
-22.45
0.54
-3.24
-4.36
22.47
-38.37
19.37-12.64-31.95
32.74
-7.22
18.63
-13.54
-2.94
-0.62
-3.47
14.68
1.12
35.45
-18.35
8.75

8.73
4.42
15.63
12.97
5.65
6.56
-5.54
-0.18
12.29
5.87
3.53
31.93
6.07
24.63
4.16
1.21
-1.98
-3.67
10.08
5.24
-0.40
-4.79
-13.35
-3.39
-0.01
-0.45
19.32
-28.405.51
0.15-31.31
32.70
-3.03
11.05
-2.21
-0.49
1.62
-3.21
23.69
2.93
10.83
-1.62
5.45

23.11
37.38
43.49
77.07
26.76
30.75
39.16
8.80
57.01
54.42
35.98
60.39
33.08
87.42
56.70
28.62
22.56
45.60
60.46
57.09
17.73
9.71
8.17
25.60
15.36
29.73
47.73
4.43
52.58
21.51
0.99
59.77
34.95
52.47
45.19
10.69
15.26
30.36
78.50
41.25
41.35
27.50
23.83

9.48
13.87
17.44
15.00
14.34
7.95
-2.48
2.11
22.56
7.64
5.92
32.65
11.75
26.95
7.46
5.49
-2.28
0.54
15.43
6.91
2.07
0.36
-10.64
0.87
5.26
8.04
21.83
-25.568.28
4.84-31.47
33.64
-0.23
16.48
4.04
0.08
5.95
-0.05
26.39
7.44
16.15
5.85
6.54

6.17
-2.66
8.47
0.70
1.66
2.15
-13.59
-1.61
3.89
-2.39
-2.32
24.67
0.56
10.81
-4.21
-4.25
-6.11
-10.34
-1.02
-5.46
-3.44
-7.28
-18.33
-8.31
-2.82
-5.44
9.67
-36.58-4.60-3.38-38.22
26.97
-8.88
2.47
-9.73
-2.68
-0.68
-9.08
10.05
-4.25
6.00
-7.38
2.28

15.61
-1.11
7.90
26.16
8.78
2.02
-7.07
1.14
558.73
11.79
2.61
19.90
66.16
25.48
15.91
-23.88
5.23
1.64
-0.41
12.55
-7.84
1.45
-22.45
0.54
-3.24
-4.36
22.47
-38.37
19.37-12.64-31.95
32.74
-7.22
18.63
-13.54
-2.94
-0.62
-3.47
14.68
1.12
35.45
-18.35
8.75

53.85
7.92
22.77
51.18
37.40
25.65
38.74
101.85374.17
56.45
89.15
33.47
98.54
57.82
63.57
17.97
60.80
90.32
36.59
51.59
22.01
15.95
12.19
72.25
40.46
94.85
8.40
-24.7842.93
34.70-18.62
16.10
66.62
61.83
36.71
88.26
53.37
28.43
29.33
38.95
119.14
49.47
92.01

1.98
-21.61
0.53
23.68
-3.82
-3.32
-11.36-2.06
344.24
3.38
-0.42
20.66
55.61
21.52
-13.08-27.30
-8.99
-3.94
-6.15
7.92
-10.02-1.02-18.65-4.31-8.84-10.8716.40-40.0616.04-14.29-32.02
19.50
-9.57
11.12
-15.15-2.74-4.82-23.149.29-11.1830.12-21.15
7.62

13.72
-1.16
-1.18
-1.57
6.06
-5.68
-18.65
2.57
348.95
-4.14
-6.23
-7.81
63.02
-3.09
9.22
-31.00-0.51-7.17-12.03-7.74-14.39-5.51-34.71
-0.86
-4.05
-7.06
1.02
-53.154.73-15.00-61.21
22.05-19.1710.30-27.55-11.22
-6.04
-0.57
-2.66
-8.76
31.32
-25.95-3.40

Note:Changes in emissions by country in the multi industry case for Armington and EK. Results shown for thequantity case γ = 0, the value case, γ = 1, the estimated one, γ e , and if γ = 1.2 for all sectors. All values inpercentage changes compared to the baseline.

63