graduapr6 final

8/8/2019 GraduApr6 Final

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Preventing carbon

leakage with

consumption-based

emission policies?

Lauri Myllyvirta

University of Helsinki

Faculty of Social SciencesEconomics

Master's Thesis

April 2010


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Helsingin yliopisto - Helsingfors universitet - University of Helsinki

Tiedekunta-Fakultet-Faculty

Faculty of Social SciencesLaitos-Institution-Department

Department of Economic and Political Studies

Tekij-Frfattare-Author

Myllyvirta, Lauri

Tyn nimi-Arbetets titel-Title

Preventing carbon leakage with consumption-based emission policies?

Oppiaine-Lromne-Subject

Economics: General Economics

Tyn laji-Arbetets art-Level

Master's thesisAika-Datum-Month and year

2010-04-06Sivumr-Sidantal- Number of pages

75

Tiivistelm-Referat-Abstract

Steep and rapid reductions in greenhouse gas emissions are required from industrialized countries. An important policyconcern is that these emission reductions could lead to increases in emissions elsewhere. This leakage effect can be avoidedby suitable choice of policies.

I study the greenhouse gas abatement policy of a large coalition of countries that faces competition from countries with laxeremission policies, comparing the changes in emissions from the rest of the world and in competitiveness of dirty industriescaused by different policy options. My analysis is based on a two-region, two-good model of endogenous growth withdirected technical change.

I compare two approaches to allocation of emissions associated with the supply of internationally traded goods and services:production-based and consumption-based accounting. When technical change and complementary policies are omitted,emission constraints based on either approach cause emissions in the rest of the world to increase, although through differentmechanisms. However, an emission constraint creates incentives for energy-saving innovation and countries' emission policiescan include various complementary measures in addition to the emission constraint. These factors can cause also the rest ofthe world to reduce emissions. Models that omit these factors yield too low recommendations on emission reduction targets.

In order to maximize global emission reductions achieved with unilateral policy, production-based emission constraintsshould be applied on sectors where there are good possibilities to substitute other inputs for fossil energy, and there aredecreasing returns to scale in carbon intensive activities. Consumption-based emission constraints achieve larger globalemission reductions in sectors in which fossil energy and other inputs are strongly complementary and returns to scale on theregional level are not strongly decreasing.

Complementary policies, such as subsidies to energy efficiency investments, subsidies to R&D of energy-saving technologies,transfer of technology to developing countries and relaxing the protection of intellectual property rights, can reduce or reversecarbon leakage. Each of these policies only reduces global emissions under specific conditions. Choosing suitable policies anddifferentiating between economic sectors is of great importance.

If border measures are applied on imported carbon-intensive goods, it is important to account for the relative carbon intensityof individual producers. A regular border tax levied per tonne of product does not encourage producers in the rest of the worldto clean up their production.

Avainsanat-Nyckelord-Keywords

climate policyemissions tradingcarbon leakagecompetitivenesstechnical change

Muita tietoja-vriga uppgifter-Additional information


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Helsingin yliopisto - Helsingfors universitet - University of Helsinki

Tiedekunta-Fakultet-Faculty

Valtiotieteellinen tiedekuntaLaitos-Institution-Department

Politiikan ja talouden tutkimuksen laitos

Tekij-Frfattare-Author

Myllyvirta, Lauri

Tyn nimi-Arbetets titel-Title

Preventing carbon leakage with consumption-based emission policies?

Oppiaine-Lromne-Subject

Kansantaloustiede: Kansantaloustieteen yleinen linja

Tyn laji-Arbetets art-Level

Pro gradu -tyAika-Datum-Month and year

2010-04-06Sivumr-Sidantal- Number of pages

75

Tiivistelm-Referat-Abstract

Teollisuusmaiden tytyy vhent ilmastopstjn nopeasti ja voimakkaasti. Ptksentekijiden huolenaiheena on, ettnm pstvhennykset voisivat aiheuttaa pstjen kasvua pstrajoitusten ulkopuolisissa maissa. Tm vuotovaikutusvoidaan vltt valitsemalla sopivat ohjauskeinot.

Tutkin suuren maajoukon yksipuolisia toimia kasvihuonekaasupstjen rajoittamiseksi tilanteessa, jossa kilpailijamaatharjoittavat lyhemp ilmastopolitiikkaa. Vertaan eri politiikkavaihtoehtojen vaikutusta pstrajoitusten ulkopuolistenmaiden pstihin sek hiili-intensiivisen teollisuuden kilpailukykyyn. Analyysini perustuu kahden alueen ja kahdenhydykkeen kasvumalliin, johon sisltyy suunnattu tekninen kehitys.

Vertaan kahta eri tapaa allokoida pstt, jotka aiheutuvat kansainvlisesti vaihdettujen hydykkeiden tuotannossa:tuotantoperusteinen ja kulutusperusteinen pstlaskenta. Kun pstrajoitusten vaikutus teknisen kehityksen suuntaan sekmuiden ilmastopoliittisten ohjauskeinojen olemassaolo jtetn huomiotta, kumpaan tahansa laskentatapaan perustuvatpstrajoitukset johtavat pstjen kasvuun muualla maailmassa vaikkakin eri vaikutuskanavien kautta. Toisaaltasuunnattu tekninen kehitys sek tydentvt politiikkatoimet mahdollistavat sen, ett mys muu maailma vhent pstjntoimien seurauksena. Niden tekijiden jttminen huomiotta taloustieteellisiss malleissa johtaa liian alhaisiin suosituksiin

pstjen vhentmiseksi.

Yksipuolisilla toimilla saavutettavien maailmanlaajuisten pstvhennysten maksimoimiseksi tuotantoperusteisiapstrajoituksia tulisi soveltaa sektoreilla, joilla mahdollisuudet korvata fossiilisia polttoaineita muilla tuotannontekijillovat hyvt, ja pstj tuottavan toiminnan mittakaavatuotot ovat alenevia. Kulutusperusteiset pstrajoitukset johtavatsuurempiin maailmanlaajuisiin pstvhennyksiin sektoreilla, joilla mahdollisuudet fossiilisten polttoaineiden korvaamiseenmuilla tuotannontekijill ovat hyvin rajoitettuja ja mittakaavatuotot eivt ole voimakkaasti alenevia.

Pstrajoituksia tydentvt ilmastopoliittiset ohjauskeinot, kuten energiatehokkuusinvestointien tukeminen, energiaasstvien teknisten ratkaisujen tutkimus- ja kehitystoiminnan tuet, teknologiansiirto kehitysmaihin sekilmastoteknologioiden patenttisuojan vljentminen, voivat ehkist hiilivuotoa. Kukin nist politiikkatoimista alentaaglobaaleja pstj ainoastaan tiettyjen ehtojen vallitessa, joten talouden eri sektoreille sopivien toimien valinta on erittin

keskeist.

Jos hiili-intensiivisille tuontituotteille asetetaan rajatulleja, on trke, ett yksittisten tuottajien pstintensiivisyysvaikuttaa hiilimaksujen tasoon. Muussa tapauksessa rajatulli ei kannusta pstrajoitusten ulkopuolisia tuottajia toimiinpstjens alentamiseksi.

Avainsanat-Nyckelord-Keywords

ilmastopolitiikkapstkauppahiilivuotokilpailukyky

tekninen kehitysMuita tietoja-vriga uppgifter-Additional information


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Contents

1 Introduction 2

1.1 The importance of spillovers . . . . . . . . . . . . . . . . . . . . . . . 31.2 Denition of spillovers . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Consumption-based emission policies . . . . . . . . . . . . . . . . . . 8

2 The model 10

2.1 General model of directed technical change . . . . . . . . . . . . . . . 102.2 Two-region model with energy and emissions . . . . . . . . . . . . . . 132.3 Adding policy measures and IPR regimes . . . . . . . . . . . . . . . . 14

3 Emission cap on production with complementary policies 16

3.1 Goods markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Supply of machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Market for innovations . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Comparing production and consumption based policies 224.1 Equilibrium with consumer carbon tax . . . . . . . . . . . . . . . . . 22

4.1.1 Goods markets . . . . . . . . . . . . . . . . . . . . . . . . . . 234.1.2 Final output ratio . . . . . . . . . . . . . . . . . . . . . . . . . 264.1.3 Market for innovations . . . . . . . . . . . . . . . . . . . . . . 27

4.2 Equilibrium with producer tax . . . . . . . . . . . . . . . . . . . . . 274.3 Producer carbon tax with border measures . . . . . . . . . . . . . . 28

5 Results 30

5.1 Consumption-based policy . . . . . . . . . . . . . . . . . . . . . . . . 30

5.2 Production-based policy with complementary policy measures . . . . 335.3 Comparison of consumption and production based policies . . . . . . 425.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6 Conclusions and policy implications 49

References 52

Appendices i

A The problem of the household i

B Equilibrium with production-based cap ii

C Log-linearized model with production-based cap iv

D Stability condition v

E Intermediate producers problem with tax vi

F Log-linearized models with taxes vii

F.1 Consumption-based tax . . . . . . . . . . . . . . . . . . . . . . . . . . viiF.2 Production-based tax . . . . . . . . . . . . . . . . . . . . . . . . . . . x

G Summary of model solutions xi


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1

List of symbols

Variables

Yrf Production of intermediate f in region rrL Consumption of intermediate f in region rYrF Production of nal good in region rYr Ratio of the production of energy-intensive and

labor-intensive intermediates, YrE=Yr

L

prf Price of intermediate f in region rp Ratio of the prices of intermediates, prE=p

rL

prkf(i) Price of f-augmenting machine type i in region r

Lrf Labor allocated to production of f-intensive inter-mediate in region r

Er Production of polluting energy in region rNf Level of factor f complementing technologyN Ratio of the technology levels, NE=NLkrf(i) Amount of f complementing machines of type i de-

ployedwrf Factor reward paid to factor fw Relative factor rewards, wrE=w

rL

Sf Supply of factor fS Relative supply of factors, SE=SL ProtEr Use of fossil energy in production of goods con-

sumed in region rLrL Use of labor in production of goods consumed in

region r Ratio of output of nal goods in the abating and

non-abating region

Constants

" Elasticity of substitution between the two interme-diates in the production of the nal good

Marginal cost of production of machines Share of energy and labor in the (Cobb-Douglas)

production function of energy and labor intensive

intermediates, respectively. (Derived) elasticity of substitution between energyand labor

Share of labor in the (Cobb-Douglas) productionfunction of energy

Number of patents resulting from the use of oneunit of nal good in the production of innovations

L Inelastic total labor supply in each region


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Policy parameters

Enforcement of intellectual property rights in thenon-abating region: 0 =no protection; 1 =full pro-tection

d Percentage of the costs of producing an energy-

augmenting innovation covered by a subsidyE Carbon tax applied in the abating regionf Diusion rate of factor f augmenting technology

into the non-abating regionz Border tax on carbon-intensive goods imported

into the abating region

Superscripts (regions)

n Non-abating regiona Abating region

w World

Subscripts

L LaborE Energykf(i) Factor f complementing machineF Final good

Decorations

x Steady-state value of xex Small percentage change of x around the steady-state value1 Introduction

The target of maintaining the increase in global mean temperature below 2 degrees

Celsius, a widely accepted yardstick for international climate policy, requires global

greenhouse gas emissions to peak by 2015 and to be reduced by up to 80 percent

from 1990 levels by 2050 (Barker et al. 2007a, p. 39). Achieving this goal requires,

furthermore, that developed countries cut their greenhouse gas emissions by 25 to

40 percent from 1990 levels by 2020 (Gupta et al. 2007, p. 776). Justied or not,

meeting such targets inevitably raises concerns about competitiveness of carbon

intensive industries and the risk of increases in the emissions of countries not bound

by emission targets, i.e. carbon leakage. It is of great importance to design national

and regional policies in a way that addresses these concerns while delivering the

needed emission reductions.

It has been frequently suggested in the literature that a shift from production-basedto consumption-based emission accounting and regulation would eectively mitigate

carbon leakage. Production-based accounting focuses on emissions from polluting


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activities within a given region, while consumption-based accounting focuses on the

life-cycle emissions associated with nal consumption of goods within a region. I

set two research questions: 1) Would a shift from production-based to consumption-

based emission policy reduce carbon leakage, and under what conditions? And 2) can

other policy measures, such as energy eciency measures, research and development

(R&D) policies, technology transfer eorts and changes in intellectual property right

regimes, be eective in addressing the risk of leakage?

To answer these questions, I build a model of international trade and technology

spillovers of regional climate policy. The model is based on Acemoglus (2002)

depiction of directed technical change and subsequent work by Di Maria and van der

Werf (2008). In the model, an emission constraint creates an incentive for shifting

polluting activity outside the boundary of the emission constraint but simultaneously

stimulates technological change that can counteract or reverse the harmful tendency.

1.1 The importance of spillovers

Since the impacts of GHG emissions are truly global, costly domestic action to curtail

emissions is only justiable if the action leads to decreases in total global greenhouse

gas emissions. Therefore, rational policymakers must consider the spillover eects

of domestic action on other countries emission levels. The more positive the global

impacts of regional actions, the larger emission reductions rational policymakers

should pursue on the basis of self-interest. In this context, it is also of great interest

whether the sign and magnitude of spillovers can be inuenced by careful selection

of policy measures to maximize global benets of action at home.

In the foreseeable future, the involvement of dierent regions or countries in inter-

national eorts to combat climate change is bound to dier widely, for two reasons.

Firstly, international climate agreements need to reect the drastically dierent eco-

nomic capacities and emission levels of countries, and adapt their respective rights

and obligations accordingly. Secondly, there is a risk that some countries continue

to free-ride on the climate, refusing to do their fair share to curtail emissions. Both

in the public discussion and academic literature, a wide range of policy prescriptions

is oered for this situation.

The most pessimistic authors argue that any subglobal action to restrict emissions

can even make the situation worse by driving polluting activity to freeriding regions

where specic emissions are higher due to inferior technology (e.g. Babiker 2005).

In extreme cases, this line of thinking uses the existence of negative spillovers as anargument against action by more progressive regions. (E.g. Korhola 2006; Interna-

tional Federation of Industrial Energy Consumers 2007, p. 3; Federation of Finnish


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Marginal

utility

Emissions

Marginal

benefit from

emission

reductions

Marginal

benefit from

consumption

Positivespillover

Figure 1: Impact of the existence of positive spillovers on optimal emission reduc-tions. The decreasing solid curve depicts marginal benet from increased consump-tion as emissions increase. The increasing solid curve represents marginal benets

from emission reductions when international spillovers are not taken into account.Optimal emission level is given by the intersection of these two curves. If there is apositive international spillover of regional action to limit greenhouse gas emissions,the marginal benet from emission reductions is higher, which is depicted by thedashed curve. In the presence of such spillover, rational policymakers should pursuedeeper emission reductions.

Technology Industries 2007.)

At the other end of the spectrum are optimists who argue that regional action spurs

low-carbon innovation, causing the rest of the world to reduce emissions as well,and that the risk of carbon leakage has been exaggerated (Di Maria and van der

Werf 2008; Grubb et al. 2002). Moreover, even if loss of market share in polluting

products was to occur, it would raise incomes in the receiving regions and hence

lead to increased abatement of emissions (Copeland and Taylor 2005). All of the

aforementioned interactions are examples of international spillovers of unilateral

climate policy.

Grubb et al. (2002) scope the importance of international spillovers through simple

back-of-the-envelope scenarios on the development of carbon intensity in industri-alized and developing regions. They argue that if industrialized countries pursue

a policy of reducing GHG emissions by just one percent per annum, international


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spillovers alone have the potential to halve emissions from developing countries com-

pared to business-as-usual development by 2050.

The European Union has positioned itself as a leader in international climate policy

(Oberthr 2009; Vogler 2008). However, concerns over competitiveness, as well as

inuence of industry pressure groups, have lead to substantial concessions to pol-luting economic sectors, weakening the environmental eectiveness of the unions

domestic policies (Markussen & Svendsen 2005, p. 253; Neuho et al. 2006). Possi-

bly the most important argument against strong unilateral policy is the fear that it

will cause dirty industries to dislocate outside the union. Keeping dirty industry in

the union is seen as a policy goal in itself and, in addition, it is believed that disloca-

tion of companies might oset some of the emission reductions achieved within the

union (e.g. Babiker 2005; International Federation of Industrial Energy Consumers

2007, p. 3).

In the US Congress, two comprehensive pieces of climate and energy legislation were

introduced in 2009, the Waxman-Markey and Kerry-Boxer climate bills. These ini-

tiatives have spurred concerns very similar to those raised in the EU. In a brieng

on cap-and-trade, the U.S. Senate Republican Policy Committee lists its objections

to the provisions of the bills on regulating greenhouse gas emissions. The committee

claims that "While all American businesses would be hurt by higher input prices [...],

American manufacturing would be especially vulnerable and likely to head overseas"

(Republican Policy Committee 2009). In another response to the bills, ten Demo-cratic senators sent a letter to President Obama in August 2009, stressing the need

to "maintain a level playing eld for American manufacturing" as Congress considers

energy and climate legislation (Brown et al. 2009). Both bills place strong emphasis

on maintaining the competitiveness of US energy intensive industries, advocating

subsidies in the form of free allocation of emission credits to companies, as well as

border taxes on energy-intensive imports (U.S. House of Representatives 2009; U.S.

Senate Committee on Environment and Public Works 2009).

The above examples demonstrate that spillovers of unilateral climate policies are

potentially signicant and represent an important policy concern. I examine policies

that could be used to increase the positive spillovers and mitigate the alleged risk of

loss of competitiveness and carbon leakage when a unilateral carbon cap is enforced.

1.2 Denition of spillovers

Grubb et al. (2002) dene spillovers as the impact of mitigation actions by indus-trialized countries on the level of GHG emissions in developing countries. They

distinguish three components of international spillovers:


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spillovers due to economic substitution eects, such as price or terms-of-tradeeects, resulting in a leakage of emissions,

spillovers due to the diusion of technological innovations induced by abatementaction in industrialized countries and transferred to the developing countries, and

spillovers due to policy and political inuence of industrialized countries miti-gation eorts on developing countries abatement actions. Policies that could be

spread by industrialized countries example include abolishing fossil fuel subsidies,

accepting mitigation commitments, liberalizing electricity markets or implementing

other energy eciency enhancing measures.

This denition was also adopted as a basis for the extensive assessment of spillovers

of climate policy by the Netherlands Research Programme on Climate Change (Sijm

et al. 2004).

Economic literature has largely focused on the substitution eect. This has lead to

fears of carbon outsourcing or dumping, i.e. the dislocation of rms due to changes

in environmental and climate policy, in the public discussion. Sijm et al. (2004)

recognize three channels through which the substitution eect can occur: energy

markets; goods and services market; and factor market. The energy market channel

is generally expected to be most important (Sijm et al. 2004, p. 13), while evidence

on leakage through goods, services and capital markets, is sparse at most (ibid.;

Javorcik & Wei 2004).

Another potentially important form of spillover is demonstrated by Copeland and

Taylor (2005), who build a model allowing for an income eect that raises the

demand for environmental quality. They proceed to show that for suciently strong

elasticity of marginal damages with respect to income, the income eect alone can

more than oset the emissions leakage caused by substitution. The authors also

dene a freerider eect as the incentive to increase emissions if marginal damages

of emissions fall as a result of a cut in the rest-of-the-world emissions.

Negative spillovers of climate policy are likely to be dampened or prevented by

responses of other sectoral policies, such as mainstream industrial and economic

policies. E.g. the Intergovernmental Panel on Climate Change argues that coun-

tries have and are likely to adjust their policies to ensure that carbon outsourcing

does not occur (Barker et al. 2007b, p. 666). In the EU, examples of such policy

changes include free allocation of emission permits and cuts in energy taxes tar-

geted at sectors believed to be likely to outsource their production. These policy

responses will mitigate the risk that emission-intensive industries choose to dislocatetheir production. The impact of these policies on global greenhouse gas emissions,

however, can be either positive or negative. Also, real-world market imperfections


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tend to reduce and slow down any potential carbon leakage (Bergman et al. 2007).

One aspect not addressed at all, to the best of my knowledge, in the literature is the

uncertainty related to the macroeconomic costs of emission reductions. Experiences

from deep greenhouse gas emission cuts can greatly decrease the perceived, and

often deliberately exaggerated, risks of pursuing such policies in other countries,thereby signicantly limiting the perceived ex-ante macroeconomic cost. Economic

literature on international spillovers in general is still to incorporate insights from

political sciences on political interaction between countries, the third component in

the denition of Grubb et al. (2002).

For the purposes of this paper, I follow the denition used by the IPCC: "Carbon

leakage is dened as the increase in CO2 emissions outside the countries taking

domestic mitigation action divided by the reduction in the emissions of these coun-

tries" (Barker et al. 2007b, p. 665). If carbon leakage is larger than unity, global

emissions increase as a result of unilateral policies. Negative carbon leakage means

that a unilateral emission reduction induces the rest of the world to reduce emissions

as well.

Carbon leakage = En

Ea; (1)

where Ea and En denote emissions at home and in the rest of the world, respectively,

and x refers to the change in the value of variable x between two periods. Rate

and sign of carbon leakage depend on the chosen policy measure and on the initial

allocation of production and factors before the policy is introduced.

It is entirely conceivable that emission reduction policies induce technical change

that causes the rest of the world to reduce emissions, even if some rms decide to

relocate as a result of that policy. Impacts of emission reduction policies on compet-

itiveness of dirty industry are, however, an important concern for a large number ofpolicy makers, even if the net eect of those policies is to decrease emissions in the

rest of the world. Because of this, I introduce the concept of "carbon outsourcing",

meaning the eect of unilateral emission reductions on the production volume of

dirty industries in the abating region.

The simplest denition of carbon outsourcing would be the elasticity of output of the

dirty good with respect to emissions in the abating region. This denition would,

however, overlook the fact that emission policies are likely to curtail the consumption

of dirty goods. Therefore, according to this denition, carbon outsourcing would

occur even if the degree of self-suciency in the dirty good remains constant. The

denition I choose for the purposes of this paper is:


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carbon outsourcing = (YaE=

aE) = (Y

aE=

aE)

Ea=Ea; (2)

where Ya

E and aE denote the production and consumption of dirty goods in the

abating region. Carbon outsourcing is dened as the elasticity of the degree of self-

suciency in the dirty good with respect to emissions. An alternative approach is

to measure the change in global market share of the producers from the abating

region. When emission policies do not aect the ratio of dirty good consumption

in the abating region and in the rest of the world, as in the equilibrium with a

production-based emission cap studied in Section 3, the two criteria are equal.

1.3 Consumption-based emission policies

Since early 1990s, there has been a lively academic discussion on quantifying carbon

emissions "embodied" in internationally traded goods, i.e. emissions associated with

the production of imported and exported goods. Recent studies indicate that more

than a fth of worlds greenhouse gas (GHG) emissions are associated with the

production of internationally traded goods. Industrialized countries, such as the US

and EU, are net importers of GHG emission intensive goods. (Peters and Hertwich

2008.)

The rapid growth of export-related emissions in China has, in particular, drawn

attention from both Chinese and Western authors. Numerous researchers have sug-

gested that responsibility for carbon emissions should lie more with the nal con-

sumer of goods. (Lin & Sun 2010; Li & Hewitt 2008; Yan & Yang 2010; Bin &

Harriss 2006; Peters & Hertwich 2008; Bastianoni et al. 2004; Ferng 2003; Munks-

gaard & Pedersen 2000; Wycko & Roop 1994.) It appears however that the actual

impacts of consumption-based emission regulation on emissions and trade patterns

have not been systematically studied so far.

Peters and Hertwich (2008) show that while emissions taking place within the bor-

ders of rich countries have often leveled o, emissions associated with imports are

growing rapidly. The other side of this development is most drastically evidenced in

China, where half of emission growth is due to a booming export industry (ibid.).

The results of Peters and Hertwich have two important implications for the relative

merits of production and consumption based GHG policies: Consumption based

measures will have a larger coverage if implemented by industrialized nations. They

are also able to address emission growth in emerging economies like China which is

an important public and policy concern.


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Interest towards consumption-based emission policies has increased rapidly in recent

years. In the United States, The Waxman-Markey bill lays down as an objective

of the country in international negotiations to include in an internationally binding

agreement "provisions by which countries signatory to the agreement agree to apply,

with respect to imports from countries not signatories to the agreement, border

measures designed to minimize or avoid any carbon leakage from the signatory

countries to the non-signatory countries, including border measures that may require

the purchase of allowances [...]" (U.S. House of Representatives 2009, section 903).

In case a satisfactory international agreement is not reached, the bill includes a

provision for the inclusion of importers of carbon-intensive goods into a US emission

trading system, requiring them to purchase emission allowances corresponding to

the volume of emissions embodied in imported goods (ibid., section 905).

In a 2008 review of the European Emission Trading System (ETS), in response tosome member states fears of carbon outsourcing, the European Commission (Com-

mission of European Communities, CEC) scheduled a new review "which could

lead to proposals such as requiring importers to enter ETS auctions to purchase

allowances alongside European competitors, as long as such a system was compat-

ible with WTO commitments" (CEC 2008a, p.11). In another communication, the

Commission reiterated that the possibility of extending carbon policies to importers

is left open, contingent on the outcome of international climate negotiations: "In

light of international negotiations of a global climate change agreement for the pe-

riod post 2012, the Commission will further assess the situation of energy-intensive

industries and might propose adjustments in particular in terms of free allocation

or inclusion of imported products in the Communitys Emission Trading Scheme"

(CEC 2008b, p.9). French president Nicholas Sarkozy has repeatedly called for a

border carbon tax (EurActiv 2009).

There has been some academic interest in the compatibility of carbon border taxes

or carbon quotas on imports with international trade agreements. UNEP and WTO

(Tamiotti et al. 2009) give a cautious approval to border taxes imposed to redresscosts incurred by domestic producers because of emission reduction policies. The

case is most clear-cut when domestic and foreign producers receive the same treat-

ment, as is the case with the entirely consumption-based emission policy studied

here.

There are precedents of trade measures in some international environmental agree-

ments. Border carbon taxes are reasonably certain to be in line with the provisions

of the General Agreement on Taris and Trade (GATT), as long as producers who

use best available technology are not subject to fees calculated assuming worse thanbest available technology (e.g. Ismer and Neuho 2007). This paper focuses on an

approach that meets this requirement.


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The rest of the paper proceeds as follows: In Section 2, I introduce the basic model,

the two-country version of the model and describe the modications I have made.

Section 3 solves the model for a production based cap and extends it to study

complementary policy measures. In Section 4, I derive solutions of the model with

two dierent types of emission taxes. Section 5 studies the comparative statistics of

dierent equilibria, compares the two types of emission constraints, presents results

and discusses their applicability. In Section 6, I present conclusions.

2 The model

2.1 General model of directed technical change

My analysis relies on an extension of a model of directed technical change con-

structed by Acemoglu (2002). Acemoglus work is based on the models of growth

and technological progress by Romer (1990) and Grossman and Helpman (1991). In

this section, I provide an overview of the model and present the choices I have made

in adopting the model to the purposes of this paper.

The Acemoglu (2002) model stands out from its predecessors in describing the di-

rection or bias of technical change with respect to dierent factors of production.

Acemoglus original intention was to study the impacts of increased supply of edu-cated labor on the incentives to innovate. In the model, there are two intermediate

goods that are produced by competitive rms, using one factor of production, ei-

ther labor or an unspecied factor Z. I follow Di Maria and van der Werf (2008)

in taking the factor Z in Acemoglus model to be fossil energy, denoted by E. The

two intermediate goods are combined to produce a single nal good, with constant

elasticity of substitution between the intermediates:

YrF =h

(rL)"1" + (rE)

"1"

i ""1

;

where YrF is the production of the nal good in region r. rE and

rL denote, re-

spectively, the consumption of the energy-intensive and labor-intensive intermediate

goods in region r. " is the elasticity of substitution between the intermediates. The

nal good is chosen as the numeraire.

The nal good is used for consumption by household, as well as invested into theproduction of machines and new machine designs. Production of innovations, ma-

chines and nal good uses the same technology. Therefore, there is a constant rate


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11

of transformation between the three goods and they can be treated as one good,

henceforth called consumption.

The population is assumed to have homogenous preferences, and therefore attention

can be restricted to one representative household. My interest lies with the direction

of technical change and factor allocation. This implies that the utility maximizationproblem of the representative household does not need to be explicitly solved to

obtain the results in this paper. For completeness, the required assumptions and

the solution to the problem is presented in Appendix A.

The two intermediates are produced by competitive rms, in a Cobb-Douglas man-

ner using one factor of production and a specialized set of factor-complementing

machines:

Yrf =1

1 ZNf

0

kf(i)1di

(Sf)

; (3)

where Yrf is the output of f-intensive intermediate in region r, kf(i) is investment in

f-complementing machines of type i and Sf is the factor input. is factor share of

output.

The range of machines available to complement each factor is captured in the above

equation by Nf. The number of installed machines can be adjusted immediately

free of cost and machines cannot be traded once installed. The ranges of machines

are augmented by research and development (R&D) eorts. Innovation is assumed

to be costly and result in a patent held by the innovator.

The source of growth in the model is the addition of new patents into the stock

of technology. This allows the production of intermediate goods and, consequently,

the production of the nal good, to grow in the steady state while factor allocation

stays constant.

When technical change is directed, innovators can decide which type of patents they

want to focus their eorts on. Consequently, the availability of patents that augment

each factor depends on prot-maximizing choices by innovators. The production

functions are:

_NE = (RnE + R

aE) ; and

_NL = (RnL + R

aL) ;

where the dot denotes a time derivative, Rrf represents R&D outlays directed to

factor f in region r. Production of innovations is a stochastic process in which each


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12

unit of input results in a given probability of a successful innovation. When investors

are risk-neutral and risk is diversiable, innovators produce new patents until the

expected prot is equal to the expected entry cost the expected cost of producing

a patent. The expected cost of producing one innovation, 1

, is the same for all

innovations and is known beforehand1.

The nal good is used as the only input into the production of innovations. Inno-

vation directed towards energy eciency is subsidized by the government and, as

a result, the cost of producing one patent of an energy-augmenting machine to the

innovator is (1 d) ; where d is the share of the costs covered by the subsidy.

In order to single out the eect of the directed nature of technical change, I introduce

a specication of endogenous, but undirected technical change. When technical

change is undirected, the technology ratio N = NE=NL is constant and R&D eorts

only inuence the overall level of technology:

_NE = _NL = (Rn + Ra) :

The producer of an innovation obtains a global patent for it, gaining a monopoly over

the production of the machine type. I assume that the owner of the patent caters

to the entire global market by producing all machines by itself. The owner could

also be assumed to sell licenses to other producers, but allowing for this possibility

would not change the equilibrium. Innovators direct their innovation eorts so as

to maximize the present value of the resulting patents. Protability is determinedby marginal productivity of the machine and the number of potential users.

Acemoglu (2002) solves the model for the steady state where technology stock has

had time to adjust to the equilibrium, ignoring transitory eects.

These formulations of the production function of innovations, or the "innovation

possibilities frontier", reect a few key assumptions. They correspond to the "lab

equipment specication" of Rivera-Batiz and Romer (1991), in which only the nal

good is used in the production of innovations. No scarce resources such as laborare needed. Also, the cost of innovation is not state-dependent, meaning that the

amount of existing knowledge does not inuence the cost of innovation. This speci-

cation allows stable economic growth in the steady state. The amount of existing

knowledge could also be assumed to cause a "shing out" eect, in which new ideas

are harder to come up with as the pool of possible ideas is exhausted. Conversely,

the accumulation of knowledge could cause a "standing on shoulders" eect in which

researchers can draw on the existing pool of knowledge to facilitate the creation of

new patents. This latter assumption gives rise to knowledge based specication of

R&D, also described by Rivera-Batiz and Romer (1991).

1 Acemoglu (2002) allows the cost of producing dierent types of innovations to dier, but thiswould be an unnecessary complication for my analysis.


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2.2 Two-region model with energy and emissions

Figure 2: Overview of production and trade in the model. There are two naloutputs - emissions and the nal good.

Di Maria and van der Werf (2008) extend the model by introducing two regions, an

abating and a non-abating region, and allowing for trade between them. Energy is

produced in a Cobb-Douglas manner using labor and a xed factor:

Er = (LrE) ;

where LrE is the amount of labor employed in the production of energy in region r.

Specic emissions from the production of energy are assumed to be xed, so a cap

on emissions is eectively a cap on the amount of energy produced and hence on

the amount of labor employed in the production of energy. represents returns to

scale in energy production on the regional level2. The larger is, the stronger the

tendency of energy intensive industry to conglomerate in a region, instead of being

spread evenly between the regions.

Labor is assumed to be immobile and the production of energy in each region is

assumed to be characterized by decreasing returns to scale. The abating region sets

a unilateral, exogenous cap on its emissions. The non-abating region is assumed to

pursue no climate policy regardless of its income level and the actions of the other

region. This means that the authors abstract from any income eects or policy

interactions that could increase demand for environmental quality.

I assume that both regions comprise a large number of small countries. The abating

region, which could correspond to the EU, the US or a larger coalition of indus-

trialized countries, is assumed to reach an agreement on constraining emissions of

2 In numerical simulations used to illustrate the results obtained in this paper, I follow Di Mariaand van der Werf (2008) in using = 0:4 as the default value. When the qualitative results dependon the value of; simulations are presented for a wide range of values.

Abating

region

Non-abating

Region

Labor Energy

Labor

intensive

intermediateEnergy

intensive

intermediate

Final good

Energycomplementing

machines

Innovation

Laborcomplementing

machines

Emissions

Trade


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14

greenhouse gases and possibly introducing other policy measures. The non-abating

region does not form such an agreement. Harmful impacts of emissions are dis-

tributed globally, regardless of origin, and, hence, it is not in the self-interest of

the individual small states to pursue a strong unilateral emission reduction policy.

Because of lack of cooperation, the countries do not engage in eective retaliatory

measures against the abating region either.

This setting is not intended to deny eorts by some non-industrialized countries to

reduce emissions, but rather to study the impacts of diering levels of participation.

2.3 Adding policy measures and IPR regimes

Instead of simply enforcing an emission cap and leaving the rest to the market, coun-

tries responses to climate change have invariably included a portfolio of dierent

measures. Examples of widespread policies include investment subsidies, R&D in-

centives, voluntary agreements and technology transfer programmes. Many of these

measures are likely to both cause international spillovers by themselves and inuence

the rate of carbon leakage caused by an emission cap.

In order to study the eects of complementary policies, I introduce several policy

parameters into the model: 1) Energy eciency policies are modeled by a subsidy

that lowers the marginal cost of energy saving machines in the abating region by Epercent. 2) Research and development policies are, similarly, modeled by a subsidy

covering d percent of the cost of producing an energy saving innovation. 3) Tech-

nology transfer to the non-abating region is represented by a change in the diusion

rate of energy saving technology. 4) Parameter captures changes in the protection

of intellectual property rights.

Non-distorting, lump-sum taxes or transfers are used to balance the state budget

after emission-related taxes and subsidies.

The enforcement of intellectual property rights can strongly inuence both the

strength and direction of technical change. Since technical change is one of the

key interactions between the regions in the model, the properties of the market for

technology are paramount for its dynamics. There are considerable dierences in

relative greenhouse gas intensities of production technologies employed by dierent

countries and producers. As we shall see, this has implications for rates of carbon

leakage.

Di Maria and van der Werf (2008) assume that intellectual property rights are fully

enforced globally. I extend this model to cover the situation in which the non-abating

region does not protect intellectual property. The extension is based on DiMaria


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and Smulders (2004).

The DiMaria and Smulders (2004) model comprises two regions, one of which is

technically advanced and enforces intellectual property rights (IPRs). The other

region does not enforce IPRs and therefore no technological innovation takes place.

Consequently, the region depends on use of technology developed in the techni-cally advanced region, which diuses only partially. The share of energy and labor

augmenting technologies that are adopted into use in the non-abating region are

measured by E and L: Innovators are assumed to be unable to inuence these

ratios. Impartial diusion can be due to some technologies being too complex or

otherwise unsuitable for the non-abating region or due to time lag in the adoption

of technology.

Protection has two discernible eects: lack of protection prevents patent holders

from exerting monopoly power and hence allows producers in the non-enforcing re-

gion to obtain energy-saving devices at a lower cost. On the other hand, technology

development is driven by prot gained from monopoly pricing and technology de-

velopers consequently ignore the needs of regions where they wield no monopoly

power.

DiMaria and Smulders (2004) include in their model a subsidy to all machines and

generic transfer of technology. The use of these measures does not seem to be likely

to be motivated by climate policy, so I focus on a subsidy targeted at energy saving

machines.

The main formal dierence between my model and that of DiMaria and Smulders

(2004) is in assumptions regarding factors of production. DiMaria and Smulders

(2004) focus on the use of regionally controlled resources or emissions of pollutants

with regional impacts, assuming that the assimilative capacity of the environment is

scarce, and the policy makers set a limit on emissions in both regions. They assume

the exploitation of natural resources does not require labor. In contrast, I follow

Di Maria and van der Werf (2008) in assuming that the non-abating region doesnot regulate pollution at all, but polluting activities require labor. This guarantees

that the optimal level of pollution is nite also in the absence of regulation. The

latter choice is more appropriate when studying global greenhouse gas emissions,

as a small country has little reason to limit emissions unilaterally on the basis of

self-interest, but the production and use of fossil fuels does require labor and other

productive resources.

DiMaria and Smulders (2004) solve explicitly for rates of investment in both phys-

ical and knowledge capital, assuming that investments are nanced from domesticsavings. While there is convincing evidence for the existence of a home bias, its in-

clusion would complicate the analysis without much additional benet. I therefore


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16

follow Di Maria and van der Werf (2008), who omit the dierences in investment

rates between regions.

3 Emission cap on production with complemen-

tary policies

3.1 Goods markets

I start by solving the model for the most widely used policy instrument, a binding cap

on greenhouse gas emissions from a given region. Regional caps form the backbone

of the Kyoto Protocol, have been adopted by Australia and many US states, and

are now under consideration by US federal government.

I abstract from the option included in the Kyoto Protocol of increasing the amount

of emissions permitted under the cap by purchasing emission osets. In an ideal

world, in the absence of transaction costs and methodological shortcomings in the

mechanism, the possibility of funding emission reductions abroad should equalize

the shadow price of carbon in the two regions, eectively mitigating carbon leakage.

In reality, many of the projects implemented to acquire emission osets do not re-

duce emissions from a business-as-usual baseline and therefore represent an increase

in global emissions (Schneider 2009; Wara and Victor 2008). Therefore, emission

targets set by the abating region are not strictly binding. Accounting for the exis-

tence of emission osets would introduce an important dynamic into the model, and

should be studied.

A formal solution of the model is presented in Appendix B. In the following section

I highlight and discuss some key features of the solution.

Producers of the nal good are competitive and hence take the prices of the inter-

mediate goods as given. As shown in Appendix B, cost minimization dictates the

following relative demand for intermediates:

Yr = p"; (4)

where prf is the price of f-intensive intermediate in region r, Yr =

YrE

YrL

and p =prE

prL

:

This is, conversely, the free entry condition for intermediate good producers. Thenal good is chosen as the numeraire.

Intermediate goods producers are competitive and choose factor inputs and machine


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demands according to the following rst-order conditions, derived in Appendix B:

wrf =

1

prfZNrf

0

kf(i)1di

Srf

1; and (5)

kf(i) =

prf

prkf(i)

!1=Srf; (6)

where wrf is the factor reward paid to factor f in region r, Srf is the amount of factor

f used in the production of intermediate goods and prkf(i) is the price of f-augmenting

machines in region r. These equations enable a brief comparison of the model withthat studied by Di Maria and van der Werf (2008). They consider a special case,

in which prices of all machines are equal and, consequently, factor rewards are also

equalized by international trade. When the assumption of harmonized prices of

machines is relaxed, factor productivity and, consequently, factor rewards will also

dier between the regions. One price will prevail for the internationally traded

intermediate goods, and their region superscript can be omitted from now on. The

ratio of factor rewards in the regions is obtained by combining equations (A:4) and

(A:5) in Appendix B:

wafwnf

=

EL

1pakf(i)

pnkf(i)

1

; f = E;L;

where E and L are the diusion rates of energy and labor augmenting technol-

ogy into the non-abating region. Labor productivity depends on the amount of

machines deployed per worker. The abating region has a higher productivity when

pakL(i)=pnkL(i)

< (L)

1 ; i.e. when lower machine prices in the non-abating region

are not sucient to compensate for lower availability of technologies. It also fol-

lows from the above that, if relative prices of machines dier in the two regions,international trade exists in the equilibrium even without emission policies.

In the absence of technical change, when an emission cap is enforced, the prices of

both energy and the energy-intensive good will tend to increase. The abating region

will increase its exports of the labor-intensive good and imports of the energy-

intensive good.

Substituting machine demands (6) into the production function of intermediates (3)

and taking the ratio gives global relative supply of intermediates as:


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Yw = N p1 Sw; (7)

where S

w

is global relative eective factor supply, or supply of factors corrected bythe price of machines available to complement them:

Sw =

pakE(i)

1

(LaE) + E

pnkE(i)

1

(LnE)

pakL(i)

1

L LaE

+ L

pnkL(i)

1

L LnE :

The goods market equilibrium condition is obtained by equating relative globalsupply (7) and demand (4) for intermediates:

p = (NSw)

; (8)

where = 1 + (" 1) is the derived elasticity of substitution between energy andlabor.

Substituting machine demands (6) into the intermediate producers factor demand

condition (5) taking the ratio between goods and using the relative demand for

intermediates (4) yields equilibrium relative factor demands:

wr = N1 (Sw)

1

prkE(i)prkL(i)

! 1

: (9)

Free entry in energy production implies that energy producers increase production

until the marginal production cost of energy equals its price. As shown in Appendix

B, this means

wr =(LrE)

1

: (10)

This is the energy market equilibrium condition, giving, importantly, a relationship

between the factor rewards to energy and labor. To nd equilibrium labor allocation,


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equate the two previous equations, the equilibrium relative factor rewards given by

the energy market and goods market equilibrium conditions, in the non-abating

region to get:

N1 =

EL

pnkE(i)pnkL(i)

! (1)

Sw (LnE)(1) : (11)

This equilibrium condition includes as a special case solution obtained by Di Maria

and van der Werf (2008). To see this, let prkf(i) = 1 and f = 1 for all r and f to

obtain:

2 L LaE LnE = N1h

(LaE) + (LnE)

i

(LnE)(1) ;

where I have made use of the fact that Sw = Ew

LwL

=(LaE)

+(LnE)

2LLaELn

E

. The above equation

is exactly the equilibrium condition derived by Di Maria and van der Werf (2008).

The above is a closed-form solution when the abating region applies a cap on emis-

sions and labor allocation into energy production is, therefore, exogenously given.

For the sake of completeness, I show how the equilibrium is determined in the ab-

sence of a cap. First, use (9) to calculate the ratio of relative factor rewards in the

two regions:

wa

wn=

waEwaL

=wnEwnL

=

EL

1pakE(i)pakL(i)

=pnkE(i)pnkL(i)

! 1

:

Take the ratio of the regional energy market equilibrium conditions, (A:8) and use

the above equation:

LaELnE

=

EL

11 pakE(i)pakL(i)

=pnkE(i)pnkL(i)

! 1(1)

': (12)

Comparative advantage in the production of the two intermediate goods is deter-mined by availability and price of machines to augment inputs needed in their pro-

duction. The easier the adoption of energy augmenting technology is compared to


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labor augmenting technology and the lower the relative price of energy augmenting

machines in the non-abating region, the more that region specializes in the produc-

tion of the dirty good.

Equating the goods market (8) and energy market (10) equilibrium conditions yields

the equilibrium in the absence of directed technical change:

N1 = (LnE)(1)

EL

Ew

LwL: (13)

This equilibrium condition includes as a special case solution obtained by Di Maria

and van der Werf (2008). To see this, let prkf(i) = 1 and f = 1 for all r and f to get:

L LnE = N1 (LnE)(1)+ ;

where I have relied on the fact that in the absence of an emission cap and comple-

mentary policies, the countries are symmetric and Ew

LwL

= En

LnL

=(LnE)

LLnE

.

3.2 Supply of machines

When intellectual property rights (IPRs) are perfectly enforced, the patent to each

machine type kf(i) is held by a monopolist. It is shown in Appendix B that

the patent owner will set the price of the machine as a mark-up over marginal

cost , prkf(i) =1

1 . When there is no enforcement of IPRs, competitive mar-

kets ensue and price of machines equals marginal cost, prkf(i) = . In general,

prkf(i) =

h

1 + (1 )

i: Substituting machine prices, global eective factor allo-

cation becomes:

Sw =(1 m)

1 (LaE)

+ E [1 (1 )]1 (LnE)

L LaE

+ L [1 (1 )]

1

L LnE

:IPRs are assumed to be completely enforced in the abating region. When there is

a subsidy to sales of machines in the abating region, the marginal cost of machines

becomes (1 m) and the price set by patent owners is pa

kE(i) =1

m

1 : Protsgenerated by each type of machine are:

pakE(i) (1 m) = 1 (1 m) ; pakL(i) = 1 ; and pnkf(i) = 1 :


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3.3 Market for innovations

The prots of producers of f-type machines are

wf = pakf(i)

kaf(i) + fpnkf(i)

knf(i); where the rst term represents prof-

its from the abating region and the second from the non-abating region: f featuresin the expression because those blueprints that are not adopted for use in the non-

abating region do not produce any prot there and f is the exogenous probability

that a given machine is used in the non-abating region. It is assumed that the

innovators cannot inuence this probability.

When technical change is directed, innovators can choose which type of machines to

develop. The arbitrage condition is that expected prot from each type of innovation

per unit of investment is equal:wE1

d

=wL1

, where 1

(1

d) represents the cost to

the innovator of producing an energy-augmenting patent, after subsidy, and cost of

producing a labor-augmenting patent is 3. Use machine demands (6) and relative

price of intermediates (8) to get:

N = (1 d) (w) (Sw)1 ; (14)

where w =

pakE(i)

pakE(i)

1 (LaE)

+E

pnkE(i)

pnkE(i)

1 (LnE)

pakL(i)

pakL(i)

1 (LLaE)+L

pnkL(i)

pnkL(i)

1 (LLnE)

: When intellec-

tual property rights are fully protected in the non-abating region, the expressionbecomes:

wj=1 = (1 m) 1

(LaE) + E (L

nE)

L LaE

+ L

L LnE

:Conversely, when IPRs are not enforced,

wj=0 = (1 m) 1

(LaE)

L LaE:

In the above expressions, the subscripts fp and np refer to full protection and no

protection, respectively. w is weighted relative factor supply with prot margins

of machine producers from each type of machine and each region as the weights. In

3 The cost and the revenue entailed by the production of a patent are incurred in dierent timeperiods. Therefore, cost does not equal prot. However, assuming the type of the patent does notaect the time preferences of the innovator, or the time prole of the revenue stream, the ratio ofcost and prot must be equal for the two types of patents.


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general,

w =(1 m)

1 (LaE)

+ E (LnE)

L LaE + L L LnE :This is a complete solution when LaE is determined exogenously by the emission cap.

The equilibrium technology ratio in the case of no emission cap is, again, obtained

by using LaE = 'LnE.

It is seen that technology development is driven by prot, prkf(i) ; derived frommonopoly power. When IPRs are perfectly enforced, the expressions for w and

Sw become identical and incentives to innovate reect the allocation of resources

globally. When = 0; w follows labor allocation in the abating region only, anddemand for machines from the non-abating region is ignored by innovators.

The equilibrium condition (14) is in accordance with a general result obtained by

Acemoglu (2002): An increase in the abundance of a factor leads to technical change

biased towards that factor when the two factors are gross substitutes in production

( > 1). When the factors are gross complements, the reverse holds.

To nd equilibrium labor allocation with directed technical change, equate the in-

termediate goods market and energy market equilibrium relative factor rewards inthe non-abating region:

Sw = EL

(w)1 (LnE)1 : (15)

The comparative statistics of this equation are studied in Section 5.

4 Comparing production and consumption based

policies

4.1 Equilibrium with consumer carbon tax

One way around the perceived problems of carbon leakage and carbon outsourcing

would be to apply the emission cap on emissions originating from consumption of

nal goods consumed in the abating region, regardless of their origin. The policy

would work in much the same way as a value added tax. This approach avoids dis-


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criminating against domestic producers by imposing the same limits on all producers

wishing to cater to the domestic market.

Regulation of emissions from consumption can be implemented either as a part of

an emissions trading system or as a border carbon tax. The tax option envisages

a sales tax, levied on all carbon intensive products regardless of origin. The tax oremission allowance requirement would be proportional to veried carbon emissions

of individual producers up to a product specic ceiling, representing an exceptionally

dirty production method. If the producer of the good fails to provide veried data

on the carbon footprint of the product, the maximum tax would be charged. This

procedure would place a ceiling on transaction costs stemming from provision and

verication of data, while providing importers, who trade substantial quantities of

energy intensive products, with an incentive to supply data.

I restrict my attention to the case in which technology diuses fully between regions,

intellectual property rights are fully enforced and prices of machines are equalized.

In the rest of the section, I focus my attention on carbon taxes. A tax is chosen

for the purposes of this section only for the sake of analytical tractability. In fact,

I also present the solution for a carbon quota in order to derive some of the results

in Section 5.

As explained in Section 2, revenue generated by the tax is returned to households in

the form of non-distorting, lump-sump transfers. No assumptions on the distributionof tax revenue between regions is required for the model solution presented here, as

the distribution ratio is included in the solution as a parameter. However, a more

restricting assumption needs to be made in order to derive some of the analytical

results: tax revenue is assumed to accrue evenly to the two regions, implying that tax

revenue does not change the relative income levels of the regions. This can happen

e.g. as a result of international funding obligations, such as those agreed in the

Copenhagen Accord (UNFCCC 2009), or as a part of unilateral policy initiatives.

For example, national climate legislation under consideration in the US Congressforesees a substantial allocation of funds to overseas projects.

The implications of dierent tax revenue distribution ratios between regions are

studied in Section 5, Proposition 5. Formal analysis is complemented by numerical

simulations covering dierent tax revenue distribution ratios.

4.1.1 Goods markets

I assume that the abating region levies a carbon tax tE per ton of carbon embodied

in goods consumed in the region. The producers that are subject to the tax pay


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wE + tE for the fossil energy they use. It is shown in Appendix E that their prot-

maximizing condition becomes:

wE + tE =

1 NE (paE)

1

: (16)

Other producers still follow the decision rule derived in Appendix B:

Since there is free trade in both intermediate goods and all machines, factor rewards

wf are equalized across regions. There is also no asymmetry in the model that could

give rise to dierentiation in the price of the labor-intensive intermediate good. The

mix of industries is identical in the two regions, as the location decisions of rms do

not aect the input or output prices they face.

Carbon-intensive intermediate good producers located in either region can choose

whether to supply to the abating or the non-abating region. This decision depends

on whether the higher after-tax energy price is oset by the higher price of the

product. Naturally, pre-tax price of energy does not depend on the market that a

producer sells to. The arbitrage condition for the suppliers of the carbon intensive

intermediate is:

wE =

1

NE (p

aE)

1

tE =

1

NE (p

nE)

1 :

For all tax-based solutions of the model I choose pnE as the numeraire4. This allows

me to write paE as:

paE =

1 +

1

tENE

(1 + E) : (17)

I will treat E as an exogenous variable. This assumes that individual innovatorsdo not consider the change in E accompanied by their innovations large enough to

inuence the protability of those innovations.

Let Ea and En denote the amount of energy consumed in the production of the

energy-intensive intermediate for use in the abating and in the non-abating region,

respectively, regardless of where the use of energy occurs. I dene LaL and LnL ;

similarly, as labor employed in the production of labor-intensive intermediate for

use in each region.

4 This choice of numeraire implies that the cost of producing innovations, ; cannot be inter-preted as the amount of the nal good needed to produce one innovation, as in Acemoglu (2002).However, as we shall see, the cost of producing innovations does not aect the equilibrium as longas it is positive, nite and equal for the two kinds of innovations.


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The higher after-tax energy price, faced by producers targeting the abating region,

provides an extra incentive to invest in energy-complementing machines in produc-

tion of intermediate goods, as well as to substitute away from the energy-intensive

intermediate in the production of the nal good.

Take the ratio of supply of the intermediates to the two regions:

YafYnf

=

pafpnf

!1 Saf

Snf; (18)

where Srf refers to the allocation of input f deployed in the production of interme-

diate f for use in region r, i.e. either Er or Lr:

Equate relative supply and demand to get market clearing conditions for each in-

termediate good:

Ea = (1 + E) En; and (19)

La = Ln: (20)

Ratio of inputs of each factor to the two regions is given by model parameters.

Rearranging the rst equation shows that when E > 0; carbon intensity of nal

good production is lower in the abating region:

Ea

YaF

= (1 + E) En

YnF

< En

YnF

:

Factor market equilibrium condition remains wr = (Nr)1 (Sr)

1 and energy

producers prot maximization rule is, as before, wr =(LrE)

1

= 1 (Er)

1 :

Equating the two expressions for relative factor rewards in the non-abating region

gives

N1 = En

LnL(LnE)

(1) : (21)

Energy sectors in the two regions are symmetric. It follows that the amount of labor

employed in the production of energy in each region is obtained as


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26

LrE =

Ea+En

2

1=; r = a;n:

Substituting this into the goods market equilibrium condition (21) and using equa-

tion (19) yields

N1 = En

LnL

(1 + E)

+ 12

En(1)=

: (22)

To express LnL in terms of En; note that:

LaL + LnL = 2L LaE LnE = 2

hL Ea+En

2

1

i:

Then, use (19) and (20) to write:

LnL =2

1 +

"L

(1 + E)

+ 12

1

(En)1

#: (23)

4.1.2 Final output ratio

When studying the producer carbon cap model, I was able to abstract from changes

in real income of the regions, as wage levels and prices of both intermediate and

nal goods were equalized across regions by trade. The consumer carbon tax causes

prices of nal goods in the two regions to dier, aecting relative real incomes.

I assume that capital income accrues to the regions in proportion to their wage

levels, which is the case i.a. when there is a uniform global saving rate and uniform

preferences regarding investment. It is shown in Appendix A that this is the case

in the steady state.

The total income of the labor force in each region is wLL. In addition, the carbontax generates a revenue oftEE

a: I use to denote the share of tax proceeds kept by

the abating region and assume that the rest is channeled to the non-abating region.

Because the price of the energy intensive intermediate diers between the regions,

the price of the nal good in the two regions also diers. The ratio of real incomes

in the two regions is determined by the production costs, given by a standard CES

unit cost function:

prF = (prE)

1" + (prL)1"

1=(1")

;

where prF is the price of the nal good in region r.

Given the assumption of uniform saving rate, the regions use the same proportion


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27

of their income on production of the nal good. Therefore, nal output ratio can

be written as =YaF

YnF

= Ia

paF

: In

pnF

, where Ir is the income of region r, and further,

substituting the expressions for prices and incomes:

= (pnE)

1"+(pnL)

1"

(pa

E)

1"

+(pa

L)

1"1=(1")

wLL+tEEa

wLL+(1

)tEEa:

Using (A:7) and (19), this becomes:

=YaFYnF

=

YaFYnF

"(N En)

(1") +(LnL )

(1")

(NEa)(1")

+(LaL )(1")

#1=(1")wLL+tEE

a

wLL+(1)tEEa ; and further

=

"(1 + E)

1 (NEn)1 + (LnL )

1

(N En)1 + (LnL )

1

# 1

wLL + tEEa

wLL + (1

) tEEa

: (24)

As discussed in the beginning of this Section, I will assume in most proofs in Section

5 that tax revenue accrues evenly to the two regions, i.e. = 12

:

4.1.3 Market for innovations

The prots of machine producers are

kE = [kaE(i) + knE(i)] = (pnE)1 En 1 + (1 + E)1 and

kL = (pL)1 Ln (1 + ) ;

where I have used machine demands (6) ; demands for intermediate goods (A:2)

and normalized machine production cost to 1 , implying prkf(i) = 1. Protmaximization in innovation requires kE = kL giving the equilibrium condition for

innovations:

N =

"(1 + E)

1 + 1+ 1

# En

LnL

1; (25)

where I have used the relative price of intermediates, (8) :

4.2 Equilibrium with producer tax

To allow comparisons with the consumer tax, I solve the model for a producer carbon

tax instead of the emission constraint modeled in previous section.


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28

Using individual factor rewards (A:3) ; the ratio of factor rewards in the regions is

given by

waEwnE

= 1 tEwnE

= 1 1

tENE

= 1 E;

where tE and E denote the absolute and relative tax levels, respectively. E can be

treated as an exogenous variable with the same condition as in subsection 4.1.

Wages will be equalized in the two regions and wn =(LnE)

1

, which means that

wa

wn=

LaE

LnE

1= 1 E; and, further,

Ea = (1

E)

1 En: (26)

This equation shows that the tax causes the non-abating regions share of global

emissions to increase. Whether or not this implies carbon leakage depends on the

change in global emissions achieved by the tax.

Substituting the above equation into the equilibrium conditions derived in the pre-

vious section and setting prkf(i) = 1, E = L = 1 and d = 0 gives the equilibrium

with a producer tax. Global factor allocation as a function of tax level and energy

production in the non-abating region becomes:

Sw =

h(1 E)

1 + 1

iEn

2L h

(1 E)1

1 + 1i

(En)1

(27)

Otherwise, the equilibrium conditions remain as before. Given the assumptions

made in the beginning of this section, global relative factor allocation equals the

prot ratio of innovators, Sw = w:

4.3 Producer carbon tax with border measures

The consumer carbon tax model studied in this section is potentially demanding to

implement. Another option that the abating region could choose to pursue in or-

der to limit carbon outsourcing are traditional countervailing border taxes or other

countervailing restrictions on imports of the polluting good. Per tonne border taxesdier from the consumer tax studied in the previous section in one important re-

spect: they do not depend on the specic emissions of the production of an imported


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29

good. While this signicantly reduces the demands towards information on produc-

tion processes, it removes any incentive of the foreign producers to clean up their

production.

A border tax not based on actual veried emissions has an additional protectionistic

element which could render it harder to defend under international trade agreements.Another limitation of this approach is that the level of the tax or the amount of

emission credits required from importers needs to be based on the cost increase

incurred by a domestic producer using best available technology (Ismer and Neuho

2007). This means that if foreign producers employ production methods that are

substantially more polluting than best available technology, the system will impose

too low costs on importers.

Applying an import tax z causes the price of the energy-intensive intermediate in

the two regions to diverge. The price increases in the abating region and decreases

in the non-abating region. Both consumption and production patterns in the non-

abating region will become more pollution-intensive, as the traditional border tax

gives producers in the non-abating region no incentive towards cleaner production.

Producers of the energy-intensive good in the abating region experience an increase

in demand, while their counterparts in non-abating region experience a decrease.

This will drive energy prices up in the abating region and down in the non-abating

region, which also contributes to dirtier production and consumption patterns in

the non-abating region.

As before, I assume that the abating region levies an emission tax which raises

the price of energy to intermediate producers: waE + tE = wnE; which, under the

same conditions as in the previous subsection, can be expressed aswaEwnE

= 1 E;where wrE refers to energy price before taxes. The cost minimization problem of the

intermediate good producer, with machine prices normalized to unity, is

minEr;krE

wrEEr + krf (i) s.t.

11 NE

krf (i)

1

(Er) = 1:

Optimum factor use is krf (i) = wrEE

r: Unit cost is obtained by dividing total cost

by the production function:(wrE)

11 NE

: Markets for intermediate goods are assumed to

be competitive, which implies that prices equal marginal costs. Taking the ratio of

costs in the two regions yields paE = (1 + E)pnE: This relationship holds as long as

some trade takes place.

Naturally, the level of a countervailing import tax is set so as to cause an equal

increase in the price of the domestic and the imported good, 1 + z = (1 + E).

The producer prices of energy as well as wages are equalized, which implies that

energy consumptions in the two regions are equal and move in tandem. Therefore,


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30

the border taxes give rise to a dynamic very similar to that created by consumer

carbon taxes.

There is one important dierence. Imposing dierent kinds of taxes on domes-

tic and foreign producers adds an asymmetry that inuences location decisions by

rms. Firms located in the non-abating region are deprived of the option to increasetheir energy eciency in order to lower the level of tax they are subject to. There-

fore, all rms in the non-abating region are discouraged from investing in cleaner

production and the incentive to develop clean technology to be deployed in the non-

abating region is also weakened. This dierence is of importance, if the two regions

have diering characteristics that need to be paid attention to when technologies

are developed and commercialized. Conversely, rms in the abating region cannot

choose to avoid the tax by specializing in exports to the non-abating region. This

could induce some companies to dislocate, which entails extra adaptation costs.

5 Results

5.1 Consumption-based policy

Proposition 1 A consumer carbon tax in the abating region causes global emissions

to decrease when technical change is undirected.

Proof. Using the relationship between emissions in the abating and non-abating

region (19) and the fact that global emissions are the sum of the emissions associ-

ated with the consumption of the two regions, Ew = Ea + En; the goods market

equilibrium condition (22) can be written as:

N1 = 1 + 2

1(1 + E)

+ 1Ew

L Ew2

1

Ew2(1)= : (28)

When E increases, the value of the right side of the equation decreases. As shown in

Appendix F.1, an increase in E will also cause to decrease. The partial derivative

of the right side of the equation with respect to is

@@ "

1+2

1(1+E)

+1Ew

L

(Ew2 )

1

Ew

2 (1)=

#=

h1 1+

2(1+E)

(1+E)+1

i1

(1+E)+1

Ew

L(Ew2 )1

Ew

2

(1)=:


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When < 1; this derivative is positive. When N is held constant, an increase in

the tax must be accompanied by a decrease in global emissions in order for the

equivalence to be maintained. This Proposition is illustrated in Figure 3.

Proposition 2 In the absence of directed technical change, a consumer carbon taxcauses carbon leakage.

Proof. Based on the previous proposition, when E increases, Ew decreases. Ac-

cording to Appendix F.1, decreases. From (A:12), it is seen that this implies an

increase in LnL : The goods market equilibrium equation (22) shows that En must

increase to maintain equivalence. A decrease in Ew and an increase in En imply

a decrease in Ea; which, according to (1) ; means that carbon leakage is positive.

This Proposition is illustrated in Figure 3.

Proposition 3 Directed technical change reduces carbon leakage.

Proof. The change in emissions from the non-abating region can be decomposed

as

@En

@EjDT C= @En@E jU T C + @E

n

@NdN

dE:

From the technology market equilibrium (25) ;

N =h

(1+E)1+1

+1

i En

LnL

1=

Ew

LwL

1;

where I have used (19) and (20) :

Based on previous propositions, an increase in the carbon tax causes Ew to decrease,

which implies that the ratio Ew

LwL

decreases and, consequently, dNdE

is positive exactly

when < 1. From the goods market equilibrium (22) ; it is seen that @En

@Nis

positive when and only when > 1: Therefore, @En

@N

dN

dEis always negative and

@En

@EjDT C< @En@E jU T C : This Proposition is illustrated in Figure 3.

Proposition 4 When energy and labor are strongly complementary and technical

change is directed, introduction of a consumer carbon tax leads to emission reductions

in the non-abating region, i.e. negative leakage.

Proof. Appendix C presents a log-linearized version of the equilibrium condition

with directed technical change:h( 2)

1 + 1

LnELwL

1

i eEn =


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32

+h

( 1)2 (1+E)(1+E)

1+1E +

h( 2) LnE

LwL

(1 )i

(1+E)

(1+E)+1

E1+E

i eEh

( 1) (1+E)1(1+E)

1+1+

1+ ( 2)

LnE

LwL

(1+E)

1+(1+E) +

1

(1+E)

1+(1+E)

i e:The coecient of

e for the introduction of a marginal tax is

12h ( 2)

LnELwL

+ 1i ; which is negative when < 2 and becomes positive as

approaches innity. Since it is known from Appendix F.1 that d < 0 when the

tax increases, this implies that the term is positive for < 2: When approaches

zero, the coecient ofeE becomes positive and that of eEn is negative, indicatingnegative carbon leakage. For values of around 2, there is also a possibility of

negative leakage.

More exact thresholds can be derived for the introduction of a small tax and assum-

ing constant returns to scale in carbon intensive industries ( = 1). It is shown inAppendix C that, under these conditions, the equilibrium condition becomes:

32

( 2) eEn = 224+12

EeE + 142 e:The coecient ofe is negative when 0 < < 4: The roots of the coecient ofeEare 1 1p

2 1 0:7; which implies that there is negative leakage when 2 ]0; 0:3]

or 2 [1:7; 2:0] : This Proposition is illustrated in Figure 3.

Proposition 5 Increasing the share of revenues from the carbon tax that accruesto the abating region reduces global emissions, as income level in the non-abating

region decreases.

Proof. Dierentiating (24) with respect to gives

dd

=

"(1+E)

1(N En)1 +(LnL )

1

(NEn)1 +(LnL )

1

# 1

2wLL+tEEa

[wLL+(1)tEEa]2 tEE

a;

which is always positive. This shows that, naturally, an increase in the share ofproceeds kept by the abating region increases income in the abating region and

decreases income in the non-abating region. From equation (22) ; it is seen that

when increases, En must decrease to maintain the equality.

Numeric simulations also indicate that leakage rates are lower when a larger propor-

tion of tax proceeds accrue to the abating region. These simulations are illustrated

in Figures 4 and 5.


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33

Figure 3: Rate of carbon leakage in the case of consumption-based carbon tax thatreduces emissions in the abating region by 50 %. Leakage is low or even negativewhen energy and labor are strongly complementary. When the elasticity of substitu-tion between energy and labor increases and technical change is undirected, leakagerate increases. In contrast, with directed technical change and for moderate andhigh elasticities, rate of leakage decreases when elasticity increases. The equationsused in numerical simulations are presented in Appendix G. (Parameter values:

= 0:4; = 0:66:)

5.2 Production-based policy with complementary policy mea-

sures

Because of the complexity of the model solution associated with a consumption-

based policy, I was only able to model the impacts of complementary policy measures

in the presence of a production-based emission constraint.

Proposition 6 When technical change in undirected, unilateral emission reductions

always cause some carbon leakage. Global emissions increase, if the availability of

clean technology in the non-abating region is markedly worse than in the abating

region.

Proof. It is straightforward to see from (11) that whenever LaE decreases and N

stays constant, LnE must increase to maintain equality.

Global emissions decrease when(LaE)

eLaE+(LnE)

eLnEeLa

E

> 0: Solve eLnE from the log-linearized model, keeping other variables than LaE constant to get:

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3

Carbonl

eakage

Elasticity of energy-labor substitution ()

Undirected

technical

change

Directed

technical

change

dEn

dEa


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Figure 4: Rate of carbon leakage as a function of when the abating region reducesemissions by 50%. The curves depict dierent shares of tax proceeds kept by theabating region. The higher the share, the lower the rate of leakage. The equationsused in numerical simulations are presented in Appendix G. ( = 0:4; = 0:66:)

eLnE = (1m) 1 (LaE)Ew +LaELwL[1+(1)]

1

E

(LnE)

Ew +L

LnE

LwL

+(1)

eLaE:Substituting into the condition given above yields:

(1 ) LaE + [1 (1 )] 1 E(LnE)Ew + L (LnE)LwL >(1 m)

1

(LaE)

Ew +

(LaE)LwL

:

Substitute the equilibrium values in the absence of a cap,

LaELnE

=

EL

11(1 m)

1(1) ; to get

n[1 (1 )] 1 E (1 m) 1 o 1Ew + LE (LnE)1LwL > (1 ) :If the availability of energy augmenting machines in the non-abating region is markedly

worse than in the abating region, it is possible that emissions increase

graduapr6 final

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