法國(guó)預(yù)測(cè)與國(guó)際信息中心-外包脫碳？貿(mào)易如何塑造法國(guó)的碳足跡（2000-2014） Outsourcing Decarbonization How Trade Shaped Frances Carbon Footprint (2000–14)

No2025-09–June2025

WorkingPaper

CEpii

OutsourcingDecarbonization?HowTradeShapedFrance’s

CarbonFootprint(2000-14)

PierreCotterlaz&ChristopheGouel

Highlights

France'semissionsfellby18%(2000-14),butitscarbonfootprintbyonly5%.

Trade-embeddedemissionsincreasedfrom45%to54%ofFrance'stotalcarbonfootprint.

Techniqueeffectsreducedemissionsby28%,mainlythroughefficiencygainsabroad.

Geographicshiftstocarbon-intensivepartnersincreasedemissionsby18%.

Ascountriesdecarbonizedomestically,footprintreductionsbecomeincreasinglydependentonforeignactions.

RESEARCHANDEXPERTISE

ONTHEWORLDECONOMY

CEPIIWorkingPaperOutsourcingDecarbonization?HowTradeShapedFrance’sCarbonFootprint

Abstract

ThisstudyexaminestheevolutionofFrance'scarbonfootprintfrom2000to2014,withaparticularfocusontheroleofinternationaltrade.Duringthisperiod,France'sterritorialemissionsdecreasedby18%,yetitsconsumption-basedfootprintdeclinedbyonly5%.Thismodestreductionreflectsanincreaseinemissionsembeddedinimports,whichgrewfrom45%to54%ofthetotal.Employinganovelstructuraldecompositionanalysis,wedisentanglethecontributionsofscale,composition,andtechniqueeffectsfromaconsumptionperspective.Ourapproachadvancestraditionalmethodsbyexplicitlydistinguishingbetweendomesticandforeigninfluencesandbyseparatelyanalyzingtradeopennessandthegeographicreallocationoftradeflows.Theresultsunderscorethedominanceofthetechniqueeffectinreducingemissions(-28%),drivenprimarilybyefficiencyimprovementsabroad.However,thegeographiccompositioneffectledtoasubstantialincreaseinemissions(+18%),especiallyduetoshiftstowardmorecarbon-intensivetradingpartnerspriorto2008.Thispattern-characterizedbyagrowingrelianceonforeignimprovementsforemissionreductions-likelyforeshadowsdevelopmentsinotherdevelopedeconomiesasdomesticdecarbonizationadvances.Ithighlightstheneedforgreatercoordinationbetweentradeandclimatepolicies.

Keywords

Carbonfootprint,Structuraldecompositionanalysis,Consumption-basedaccounting,Scale,composition,andtechniqueeffects,France.

JEL

F18,Q54,Q56,C67,F64.

WorkingPaper

CEpii

?CEPII,PARIS,2025

ISSN2970-491X

EdItoRIAldIRECtoR:AntoInEBou?t

CEPIIWorkingPaper

Contributingtoresearchininternationaleconomics

June2025

Centredétudesprospectives

etdinformationsinternationales

20,avenuedeSégurTSA10726

75334ParisCedex07

contact@cepii.fr

www.cepii.fr@CEPII_Paris

Presscontact:presse@cepii.fr

CEPII(CentredétudesProspectivesetdInformationsInternationales)isaFrenchinstitutededicatedtoproducingindependent,policy-orientedeconomicresearchhelpfultounderstandtheinternationaleconomicenvironmentandchallengesintheareasoftradepolicy,competitiveness,macroeconomics,internationalfinanceandgrowth.

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Allrightsreserved.Opinionsexpressedinthispublicationarethoseoftheauthor(s)alone.

RESEARCHANDEXPERTISE

ONTHEWORLDECONOMY

CEPIIWorkingPaperHowTradeShapedFrance’sCarbonFootprint

3

OutsourcingDecarbonization?

HowTradeShapedFrance’sCarbonFootprint(2000–14)

PierreCotterlaz

*

andChristopheGouel

t

1.Introduction

Apersistentgapbetweenproduction-basedemissionsinventoriesandconsumption-basedcarbonfootprintscharacterizesmostdevelopedeconomies(

Petersetal.

,

2011

;

Dugastetal.

,

2024

),raisingquestionsaboutwhetherdomesticdecarbonizationrepresentsgenuineprogressortheoutsourcingofemissionstocountrieswithweakerenvironmentalregulations(

Levinson

,

2023

).Franceoffersaparticularlyinstructivecase:itsrelativelylowterritorialemissions—aresultofearlyandextensiverelianceonnuclearpowerandlong-standingde-industrialization—standincontrasttoagrowingshareoftrade-embeddedemissionsinitsoverallcarbonfootprint.Inthiscontext,analyzingtheinfluenceofinternationaltradedynamicsprovidesvaluableinsightsfordesigningeffectiveclimatepoliciesinaglobalizedeconomy.

WhatforceshaveshapedtheevolutionofFrance’scarbonfootprintbetween2000and2014?Althoughinternationaltradeisoftencitedasapotentialdriveroffootprinttrends,itsspecificroleremainsdifficulttodistinguishfromotherfactorssuchaseconomicgrowth,sectoralchanges,andtechnologicalimprovements.Toaddressthisquestion,weadoptaconsumption-basedperspectiveanduseadecompositionapproachtoquantifytherelativecontributionsofscale,composition,andtechniqueeffects.Ourframeworkexplicitlyseparatesdomesticandforeigninfluencesanddifferentiatesbetweentwokeytrade-relatedmechanisms:greateropennesstotradeandthegeographicreallocationoftradeflows.Usingdetailedinput-outputdatafromtheWorldInput-OutputDatabase(WIOD),weprovideanin-depthbreakdownofemissionsbysector,traderegion,andconsumptionpattern.Thisapproachallowsforanuancedunderstandingofhowtradedynamics,inconjunctionwithotherdrivers,haveshapedtheevolutionofFrance’scarbonfootprint.

TheanalysisyieldsthreemainfindingsregardingtheroleoftradeinshapingFrance’scarbonfootprint.First,whileFrance’sterritorialemissionsdeclinedby18%between2000and2014,itsconsumption-basedfootprintdecreasedbyonly5%.Thisunderscoresthegrowingsignificanceofimport-embeddedemissions,whichincreasedfrom45%to54%ofthetotalfootprint—anunusuallyhighsharebyinternationalstandards.Second,thedecompositionrevealsthattrade

*CEPII:

pierre.cotterlaz@cepii

tINRAEandCEPII:

christophe.gouel@inrae.fr

CEPIIWorkingPaperHowTradeShapedFrance’sCarbonFootprint

4

actedasasubstantialcountervailingforcetoemissionreductions.Althoughtechniqueeffects—primarilyimprovementsinemissionintensity—reducedFrance’sfootprintby149MtCO2e,trade-relatedgeographiccompositioneffectsincreaseditby127.3MtCO2e.Thisincreaseoccurredthroughtwodistinctchannels:greatertradeopenness(46.7MtCO2e)andareorientationtowardmorecarbon-intensivetradingpartners(80.7MtCO2e),particularlyChina.Third,andperhapsmoststrikingly,efficiencygainsabroadcontributedmoretooverallemissionreductionsthandomesticimprovements,highlightingtheincreasingexternalizationofmitigationoutcomes.

BeyondtheseFrance-specificfindings,ouranalysisoffersbroaderinsightsforcountriesatvariousstagesofdecarbonization.France’ssituation—characterizedbyextensivenucleardeployment,significantde-industrialization,andahighshareofimportedemissions—likelyanticipateswhatmayawaitotherdevelopedeconomiesastheydeepentheirdomesticdecarbonizationefforts.Ascountriesreducetheirterritorialemissionsthroughcleanerelectricityandindustrialtransformation,therelativeimportanceofemissionsembeddedinimportsnaturallyrises.Ourcomparativeanalysisinsection

5

demonstratesthispatternempirically,showingthatcountrieswithlowerinitialemissionintensitiesfacelargerpositivegeographiccompositioneffectsandgreaterdependenceonforeignemissionintensityimprovements.France’sexperiencethuspreviewsthechallengesthatcountriesfurtheralongtheirdecarbonizationpathwaysmayencounter.

Thisworkengageswiththreestrandsofliterature.First,itbuildsonstructuraldecompositionmethodsfromtheindustrialecologyliterature.Structuraldecompositionanalysisenablesthedisentanglingofanoutcomemeasurefromaconsumption-basedperspectiveintovariousdriversidentifiedviaaninput-outputmodel(

MillerandBlair

,

2009

,Chapter13).Weextendthesemethodsbyseparatelyidentifyingtheeffectsoftradeopennessandgeographicreallocationoftradeflows,andbydistinguishingdomesticandforeigncontributions(inspiredby

Xuand

Dietzenbacher

,

2014

).Unlike

XuandDietzenbacher

(

2014

),whodecomposebothpurchasingandsellingdecisions,ourfocusonconsumption-basedemissionsleadsustodistinguishdomesticandforeigninfluencesfromtheperspectiveofthepurchasingcountry.

Second,wecontributetotheenvironmentaleconomicsliteratureanalyzingemissionsthroughthelensofscale,composition,andtechniqueeffects,asinitiatedby

GrossmanandKrueger

(

1994

)and

CopelandandTaylor

(

1994

).Whilethisframeworkhasoftenbeenusedintradecontexts,itistypicallyproduction-basedandbettersuitedformodel-basedcounterfactuals(e.g.,

Copelandand

Taylor

,

1994

;

LarchandWanner

,

2017

;

PothenandHübler

,

2018

)thanforempiricalanalysisoftrade’smultifacetedrole.Inpractice,empiricalapplicationseitherabstractfromtrade(

Copeland

etal.

,

2022

,Figure6)orfocusnarrowlyonoffshoring(

Antweileretal.

,

2001

;

Levinson

,

2009

),therebyoverlookingbroadertrade-relatedmechanismssuchaschangesintradingpartners,tradedeficits,sector-drivenfluctuationsintradeflows,orefficiencyimprovementsabroad.Arecurringconclusionfromthisliteratureisthedominanceofthetechniqueeffectandthelimitedroleofcompositioneffects(see

CherniwchanandTaylor

,

2022

).Incontrast,wedemonstratehowthescale/composition/techniqueframeworkcanbeoperationalizedwithinaconsumption-basedanalysistoenablearicherdecompositioninclusiveoftrade-relateddimensions.Ourresultsfor

CEPIIWorkingPaperHowTradeShapedFrance’sCarbonFootprint

5

Francerevealamorecomplexpicture:whiletechniqueremainsthelargestdriverofemissionreductions,compositioneffects—especiallygeographicreallocation—contributedsignificantlyandoffsetmuchofthereductionachievedthroughefficiencygains.Moreover,thetechniqueeffect—themaindriverofdecarbonization—isprimarilydrivenbyimprovementsabroad,indicatingthatforacountrywithalargeshareofimportedemissions,decarbonizingthefootprintisstronglydependentonthebehaviorofitstradingpartners.

Third,ourfindingsintersectwiththebroaderliteratureontheenvironmentalimplicationsofglobalizationandthechallengesitcreatesforterritorial-basedclimatepolicy.Agrowingbodyofresearchhasshownthatinternationaltradeenablesdevelopedcountriestoreducedomesticemissionswhileincreasingtheircarbonfootprintabroad(

DavisandCaldeira

,

2010

;

Petersetal.

,

2011

).Thishasgeneratedsustainedinterestinconsumption-basedaccountingasatoolforattributingemissionsmoreaccuratelytofinaldemandandforinformingclimatepolicy(

Jakob

andMarschinski

,

2013

;

WiedmannandLenzen

,

2018

).France’sincreasingrelianceonimportedemissions,alongwiththeprominentimpactofforeignefficiencyimprovementsonitsfootprint,illustrateshowdecarbonizationstrategiesarebeingreshapedbyglobaldynamicsandraisesnewquestionsabouttheeffectivenessandequityofnationalmitigationefforts.

Theremainderofthepaperisorganizedasfollows.Section

2

presentsthemethodologicalframework,detailingthestructuraldecompositionanalysisusedtodisentanglethecontributionsofscale,composition,andtechniqueeffectstotheevolutionofFrance’scarbonfootprint,anddescribesthedatasources,withanemphasisontheadvantagesoftheWorldInput-OutputDatabase(WIOD)forthisanalysis.Section

3

providesdescriptivestatisticsonFrance’semissionsandtheroleoftrade-embeddedemissions,settingthecontextforthedecompositionresults.Section

4

presentsthemainfindings,focusingontheinterplaybetweendomesticandinternationalfactorsandtherelativeimportanceoftheidentifiedeffects.Section

5

offersacomparativeanalysisofthemainresultsacrossthecountriesincludedinWIOD.Section

6

concludes.

2.Methods

2.1.Structuraldecompositionmethodology

ThissectionpresentsthestructuraldecompositionframeworkusedtoanalyzetheevolutionofFrance’scarbonfootprint.Ourobjectiveistoquantifythecontributionsofvariousdriverstochangesinconsumption-basedemissions.Webeginbyintroducingthenotationandstructureoftheinput–outputmodel,beforedetailingthedecompositionoffinaldemandandproductionrequirements.Finally,weexplainhowdomesticandforeigncomponentsareseparatedandhoweachdriverismappedintothescale–composition–techniquetaxonomy.

Comparedtopreviousstructuraldecompositionstudies,ourapproachintroducesseveralinnova-tionstailoredtoaconsumption-basedanalysis.First,weseparatelyidentifytheeffectsoftradeopennessandthegeographicreallocationoftradeflows—twomechanismsoftenconflatedinthe

CEPIIWorkingPaperHowTradeShapedFrance’sCarbonFootprint

6

literature.Second,wedistinguishbetweendomesticandforeigncontributionstoeachdriver,focusingonthelocationofpurchasingdecisions,whichalignsnaturallywithaconsumption-basedperspectiveandcontrastswithapproachesthatconflatebuyingandselling(e.g.,

Xuand

Dietzenbacher

,

2014

).Third,weintroduceGDPexplicitlyinthescaleeffect,allowingustoisolatetheroleoftradedeficitsinenablingconsumptionbeyonddomesticproduction.Together,thesefeaturesprovideamoregranularviewofhowinternationaltradeshapesnationalcarbonfootprints.

Topresentthemethods,wefirsthavetointroducenotations.Ournotationsfollowthestandardsinmatrixalgebraandinput-outputanalysis:lower-caseboldlettersindicatecolumnvectors,upper-caseboldlettersindicatematrices,⊙a(bǔ)nd?indicateelement-wiseproductanddivision,?indicatesKroneckerproduct,and·orjuxtapositionindicateastandardmatricesmultiplication.iisacolumnvectorofonesandIistheidentitymatrix.Whenitisnotambiguous,thedimensionsoftheseelementsarenotspecified.Therearenisectorsindexedbyiandj,andnrregionsindexedbyrands.nri=nrniistheproductofthenumberofregionsandsectors.WedefineιFRAanr-vectorofzeros,exceptforthepositioncorrespondingtoFrancewhereitis1.Wedenote?theoperatoroftimedifference:?x=xt—xt-1,wherextisalwaysthevariablexinyeartatthepriceofyeart—1.

Werelyonamulti-regionalinput–output(MRIO)modeltotraceemissionsacrossglobalvaluechainsandallocatethemtofinalconsumptioninFrance.ThestartingpointoftheanalysisistonotethatthefootprintfcanbecalculatedasthesumofemissionsoccurringduringtheproductionofgoodsconsumedinFranceandtheemissionsoccurringwhenfinaldemandisrealized(e.g.,cooking,carusage)fh.TheemissionsfromproductionareobtainedusinganMRIOmodeland,thus,aretheproductoftheemissionintensity,theLeontiefinverse,andfinaldemand:

(1)

whereyisanri-vectorofFrancefinaldemand(inwhichallfinaldemandtypeshavebeensummed),Lisanri×nri-matrixofLeontiefinverse,Wisanri-diagonal-matrixofemissionintensity(i.e.,thequantityofemissionsassociatedtoonedollarofproductioninacountry-sector),andfpisanri-vectordetailingFrance’sfootprintbyregionandsectoroforigin.

WebeginbydecomposingFrance’sfinaldemandintomacroeconomic,sectoral,andtrade-relateddimensions:

y=p·(g/p)·(y/g)·ysector⊙yopenness⊙yforeign,(2)

wherepispopulation,gisGDP,y=i′yistotalfinalconsumption(correspondingtothegrossnationalexpenditures),ysectoristhevectorofsharesspentoneachsector,yopennessisavectorindicatingthesharespentondomesticandforeigngoods,andyforeignisavectorindicatingthesharespentoneachorigincountriesamongforeignorigins.

1

Inmostconsumption-based

1Thisdecompositioninthreesharesisreminiscentofthepracticeinmanyappliedtrademodelsofusingnested

CEPIIWorkingPaperHowTradeShapedFrance’sCarbonFootprint

7

decompositions,GDPisomitted,andthescaleeffectiscapturedsolelybytotalfinalconsumption.ByintroducingGDPexplicitly,wecandisentangletwodistinctfactors:thewealthgenerateddomestically(GDP)andtheadditionalconsumptionenabledbytradeimbalances,measuredbytheconsumption-to-GDPratio,withy/gexceedingoneinthecaseoftradedeficits(see

Jakob

andMarschinski

,

2013

,foranotherdecompositionhighlightingtheroleoftradedeficits).Doingthisallowstotrackonemoretrade-relatedcomponentinthedecomposition.

Thethreelasttermsoffinaldemanddecompositionareobtainedasfollows.

?ysectorisanri-vectorobtainedbycalculatingtheni-vectorofsectoralshares(inr?Ini)′·y/yandbystackingitnrtimes.

?yopennessisanri-vectorobtainedbycalculatinginafirststepycountry=y?(y·ysector),whichrepresentstheshareofeachcountryoforigin(includingallcountries,domesticandforeign).Inasecondstep,thedomesticshareisextractedfromycountrybymultiplyingit(element-wise)withιFRA?1niandtheforeignsharebymultiplying1—ycountry(element-wise)withιFRA?1ni.Theforeignshareisthenrepeatedequallyforallforeigncountries.

?yforeign=ycountry?yopenness,soitcontainsonesforFranceandforforeigncountriesitcontainstheshareofimportfromeachcountryintotalimports.

Wenowturntothedecompositionofproductioninputs,capturedbytheLeontiefinversematrix.Thisallowsustoisolatehowchangesinintermediatedemandstructures—bothdomesticandforeign—affectthecarbonfootprint.WeobtaintheLeontiefinversefromtherequirementmatrix

A:L=(I—A)-1.Usingtherequirementmatrix,wedecomposetheLeontiefinverseinthreecomponents.Todothis,weusethewell-knownidentity(

MillerandBlair

,

2009

,Chapter13)

?L=Lt(?A)Lt-1=Lt-1(?A)Lt,(3)

andwefollowsimilarstepsasforfinaldemand,decomposingAas

A=Asector⊙Aopenness⊙Aforeign,(4)

where

?Asectorisanri×nri-matrixobtainedbycalculatingthenri×ni-matrixofsectoralshares(inr?Ini)′·Aandbystackingitnrtimes.Itrepresentstheshareofeachsectorintheintermediateconsumptionofagivencountry-sector.

?Aopennessisanri×nri-matrix.Itrepresentstheshareofinputsprocureddomesticallyorfromforeignsources.Thedomesticsharesarepresentontheblock-diagonalmatricesofsizeni.Foragivenimporter,allnon-block-diagonalmatricesarefilledwiththesameforeignshares.ItisobtainedbycalculatinginafirststepAcountry=A?Asector,whichrepresentstheshareofeachcountryoforigininintermediateinputs.Inasecondstep,thedomesticsharesare

CESutilityfunctionswiththreenestswherethefirstnestcontainsthesectoralchoice,thesecondnestthearbitragebetweendomesticandforeigngoods,andthethirdnestthechoiceoforigincountriesforimports.

CEPIIWorkingPaperHowTradeShapedFrance’sCarbonFootprint

8

extractedfromAcountrybymultiplyingitelement-wisewithInr?iniandtheforeignsharesbyelement-wisemultiplication1—AcountrywithInr?ini.

?Aforeign=Acountry?Aopennessisanri×nri-matrixthatrepresentsthesharespentoneachorigincountriesamongforeignorigins.

Thedecompositionofequation(

4

)isillustratedinequation(

5

)inwhichtheworldisassumed

tobecomposedofthreecountries(h,f,andg)andtwosectors(1and2).TheAsarethe

elementsofA,theαaretheelementsofAsectorwith,theβaretheelementsof

Aopenness,andtheγisaretheelementsofAforeignwith.Thisequationclarifiesthat

thisdecompositionallowstoseparatethesectoralshare,theopennesstotrade,andtheshareofeachorigincountry:

β1

β2

1

1

—β1

—β1

1

1

—β2

—β2

1—β1

1—β1

——1I

1—β1

1—β1

1—β2

1—β2

β1

β1

β2

β2

1—β1

1—β1

1—β2

1—β2

I

I

I

I

I

1—β1

1—β1

1—β2

1—β2

1

1

—β1

—β1

1

1

—β2

—β2

β1

β1

β2

β2

」I

「β1β2

II

I

I

⊙III

lI

1I

I

I

I

I.I

II

11」I

「11

III

I

(5)

11

γ

γ

γ

γ

γ

γ

γ

γ

γγ

1

1

γ

γ

γγ

1

1

γ

γ

γγ

γ

γ

1

1

γγ

γ

γ

⊙IIII

lI

Wecannowrewritethefootprintequationusingthesevariouscomponents:

f=i′W(I—Asector⊙Aopenness⊙Aforeign)-1[p(g/p)(g/y)ysector⊙yopenness⊙yforeign]+fh.(6)

Here,wecannotethatthematricesW,Asector,Aopenness,andAforeignmixelementscorrespondingtodomestic(France-related)andforeigndimensions.Toseparatethesedimensions,weexpresseachmatrixasthesumofadomesticandaforeigncomponent,withinthedomesticmatrixthe

CEPIIWorkingPaperHowTradeShapedFrance’sCarbonFootprint

9

columnscorrespondingtoFrance,therestofcolumnsbeingfilledwithzeros,andconverselyfortheforeignmatrix.ForAsector,wehave:

2

Asector=Ar+Ar.(7)

Usingthesamethree-countryandtwo-sectorexampleusedinequation(

5

),andassumingthatFrancecorrespondstocountryh,thisdecompositionbetweendomesticandforeigncomponentsisasfollows

「Ill1I

II

II

Iααα1α2ααIIα1α2α1α2α1α2I

lIll」I

、/

、–

Asector

「αα00001

001I

Iα21α220000I

「00I

I

I

I

IIlI

I

II

00α1α2ααI

00α1α2α1α2I

Iα1α20000I

=Iαα0000I+

I.

II

I

lI」I

、–

ll」I

、/

Asector

、/

、–

FOR

FRA

Asector

(8)

Forconciseness,wedonotpresentthecompleteexpressionofthefootprintwithdomesticandforeignmatrices,butitisclearthatitinvolvesamixofadditiveandmultiplicativeterms.

Thedecompositionofthefootprintiscarriedoutintwosteps.ThisisnecessarybecausechangesintheLeontiefinverse(?L)cannotbedecomposedintothedifferentcomponentsoftherequirementmatrix(Asector,Aopenness,andAforeign)simultaneouslywiththeothercomponentsofthefootprintexpression.Toaccommodatethisconstraint,andgiventhelargenumberofcomponentsinvolvedinequation(

6

),weusetheadditivepolardecompositiondiscussedin

DietzenbacherandLos

(

1998

).Thismethodisoneofthefewapproachesthatpermitsatwo-stepdecomposition—firstisolatingtheelementsoftheLeontiefinverse,thendecomposingtheremainingterms.Amongsuchmethods,thepolardecompositionisespeciallytractable:itavoidsthecombinatorialexplosionthatwouldresultfromaccountingforallpossibleinteractionpathsbetweenthemanycomponentsinourmodel.Sincethepolardecompositionisastandardtechniqueandtheexpressionofthefootprintdecompositionislong,wedonotdetailtheexpressionofthedecompositionhere.

3

2Thisdecompositiontakesinspirationfrom

XuandDietzenbacher

(

2014

).Theyproposesomethingsimilarexceptthatforthedomesticmatrixtheykeepboththerowsandcolumnscorrespondingtothecountryofinterest.Keepingrowsandcolumnsmixessellingandbuyingdecisions.Givenourconsumption-basedperspective,itismorenaturaltokeeponlythebuyingdecisions.

3Foranoutcomeydefinedbyy=Πixi,apolardecompositionof?y=y1—y0isdefinedby

CEPIIWorkingPaperHowTradeShapedFrance’sCarbonFootprint

10

Thefinaldecompositionofthechangeinfootprint?fptakesthefollowingform:

?fp=gW(?W)+gAsector(?Asector)+gAopenness(?Aopenness)+gAforeign(?Aforeign)+gp(?p)

+gg/p(?g/p)+gg/y(?g/y)+gysector(?ysector)+gyopenness(?yopenness)+gyforeign(?yforeign),(9)

wherethefunctiongx(x)returnsanri-vectorcorrespondingtothecontributionofthecomponentxbetweentwoyears.So,theevolutionofthefootprintisexactlydecomposedintothecontributionofthevariouscomponentsidentifiedabove.

Notethatinadditiontotheemissionsfromproduction,wecouldhavedecomposedtheemissionsoccurringatfinaldemandfhintermsofscaleandtechniqueeffects(welackinformationaboutthesectoralorigintohaveacomponentrelatedtocomposition),butgiventhepaper’sfocusontheroleoftradeinthefootprintevolutionweprefertoabstainfromsuchadecompositionthatwouldnotcontributetothepaper’sobjective.

Toeaseinterpretation,weorganizeourdecompositionintothescale,composition,andtechniqueeffectscommonlyusedinenvironmentaleconomics.However,itisimportanttonotethatour

decompositiondiffersfromtheonesusuallydoneinenvironmentaleconomicswherethesethree

effectsarecalculatedfromaproductionperspective(

GrossmanandKrueger

,

1994

),whileherewedothecalculationfromaconsumptionperspective.Wedetailbelowthecontento