Two different indicators of “environmental responsibility”were independently proposed by
Article history:Received 16 November 2006Received in revised form9 December 2007Accepted 12 December 2007Available online 16 January 2008
Rodrigues et al. [Rodrigues, J., Domingos, T., Giljum, S., Schneider, F., 2006. Designing anindicator of environmental responsibility. Ecological Economics, 59 (3): 256–266.] and Lenzenet al. [Lenzen, M., Murray, J., Sack, F., Wiedmann, T., 2007. Shared producer and consumerresponsibility — theory and practice. Ecological Economics, 61: 27–42.]. These indicators areboth supposed to reflect the indirect effects of consumer and producer behavior in thegeneration of environmental pressure. In this paper we compare their mathematicalproperties and interpretation. We conclude that they have different implications forenvironmental policy.
Keywords:Environmental indicatorsEnvironmental responsibilityProducer and consumerIndirect effectsInput–output (I–O) analysis
1. Introduction
Solving an environmental problem requires using an indicatorto assess the severity of the problem and to monitor progresstoward its resolution. Direct environmental indicators aremostly used, e.g., according to the UNFCCC (2005) the green-house gas (GHG) emissions of a given country are thoseemissions occurring within its borders. However, manyauthors believe that environmental indicators should takeindirect effects into account (Ferng, 2003; Bastianoni et al.,2004; Gallego and Lenzen, 2005; Rodrigues et al., 2006;Hoekstra and Janssen, 2006).
Authors in this area typically propose an indicator and expost defend its virtues vis-à-vis other indicators (Ferng, 2003;Bastianoni et al., 2004; Gallego and Lenzen, 2005). Given theoften competing properties that it is convenient for anindicator to possess it is not surprising that this approachhas so far not led to a consensus.
3; fax: +351 21 841 73 85.. Domingos).
er B.V. All rights reserved
Given this state of affairs, in a recent paperwritten togetherwith François Schneider and Stefan Giljum (Rodrigues et al.,2006) we have taken another approach to address thisproblem. We proposed ex ante the properties that an environ-mental indicator should possess, andmathematically checkedwhether such an indicator existed.
We proved that there exists one and only one indicator –environmental responsibility – which possesses all theproperties we proposed. Environmental responsibility is theaverage between the upstream embodied emissions ofdomestic final demand (which we interpret as the consumerresponsibility) and the downstream embodied emissions ofdomestic primary inputs (which we interpret as the producerresponsibility). In an input–output (I–O) framework (Miller andBlair, 1985), upstream embodied emissions are computedusing the Leontief matrix (Leontief, 1970) and downstreamembodied emissions are computed using the Ghosh matrix(Ghosh, 1958).
534 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
Recently, Lenzen et al. (2007), based on Gallego andLenzen (2005) proposed a new indicator. The indicatorproposed is constructed by considering that, when aneconomic flow crosses a sector, a sector-specific fraction ofupstream embodied emissions are retained by that sector.The total upstream embodied emissions thus retained bythat sector is interpreted as the “producer responsibility”and the fraction of the upstream embodied emissionseventually reaching domestic final demand is interpretedas the “consumer responsibility”. Added value is used todefine the fraction of upstream emissions retained by asector.
These two indicators of environmental responsibilitydiffer in two main points: the total vs. partial transfer ofindirect effects and the consideration or not of downstreamindirect effects. The aim of the present paper is to comparethe two indicators regarding these points, and theirimplications.
Section 2 summarily reviews the two indicators, focusingon their mathematical definitions. Section 3 compares theindicators, exploring their mathematical properties and dis-cussing their implications. Section 4 concludes.
2. Review of the indicators
The notation followed in the present paper differs fromstandard I–O notation (UN, 1994) and from the originalnotation of either of the papers compared (Rodrigues et al.,2006; Lenzen et al., 2007). Scalars are denoted in italic, vectorsand matrices are denoted in bold. Matrix transpose is denotedby superscript ′.
Each italic letter corresponds to a different type of variable:t denotes an economic flow (in monetary units), e denotesemissions (in physical units); m denotes environmentalintensity (physical/monetary units); U denotes environmentalresponsibility; i, j and k are indices, S denotes an integer; Ψdenotes a set and α denotes a real number, 0≤α≤1.
Subscripts denote sector, flow or region. Superscripts C andP denote consumer and producer. Superscripts L, U and Ddenote local, upstream and downstream quantities. Othersuperscripts are context specific.
2.1. Monetary input–output analysis
The System of National Accounts 1993 (UN, 1994, hereafterreferred to as SNA 1993) proposes a consistent nomenclatureand a set of standardized procedures for the compilation ofnational accounts, of which I–O tables are part. In order toclarify the subsequent discussion we now review a few basicconcepts.
According to SNA 1993 (IV.A.4.2), an institutional unit is “aneconomic entity that is capable, in its own right, of owningassets, incurring liabilities and engaging in economic activitiesand in transactionswith other entities”. Institutional units canbe grouped in institutional sectors (SNA 1993, IV.A.4.6) and forthe purposes of the present paper we consider only threeinstitutional sectors: firms; government and households.
According to SNA 1993 the firms sector can be disaggre-gated into different levels (local units, establishments and
industries). In the present paper we consider an industry to“consist of a group of establishments engaged in the same, orsimilar, kinds of production activity” (V.B.5.5). We alsoconsider that each industry produces a homogeneousproduct, where “[g]oods and services, also called products,are the result of production (II.B.2.49)”.
For the purposes of the present paper the world ispartitioned into a set of mutually exclusive regions (e.g.,countries or composite regions such as “rest of the world”),and each institutional unit is resident in some region (SNA1993, IV.A.4.15).
The institutional units considered in the present paper areS industries, the government and the household sectors. Thefollowing theory can be applied to a single region model(whichmeans that a “rest of the world” institutional unitmustbe defined) or to a multi-region model (where a “rest of theworld” is not necessary).
According to SNA 1993 (III.C.3.12) a “monetary transactionis one in which one institutional unit makes a payment(receives a payment) or incurs a liability (receives an asset)stated in units of currency” (III.C.3.16). For the purpose of thepresent paper we identify economic flows (III.C.3.9) withmonetary transactions.
According to SNA 1993 (VI.B.6.15) “production may bedefined as an activity carried out under the control andresponsibility of an institutional unit that uses inputs oflabour, capital, and goods and services to produce outputs ofgoods or services”. Consumption is an activity in whichinstitutional units use up goods or services and that caneither intermediate or final. Intermediate consumption consistsof inputs into processes of production.
Let tij denote the magnitude (in monetary units) of theeconomic flow from sector i to sector j. If i, j=1,…, S, tij is aninter-industry flow. If i and j belong to different regions thisflow is an import or export.
Final expenditure consists of final consumption (performedboth by households and firms) and gross fixed capitalformation (performed only by firms) (SNA 1993, I.H.1.49).
Let ti0 denote the flow of final expenditure of product/industry i. This flow can be further decomposed into householdconsumption, government consumption and investment (“grossfixed capital formation”). Sector 0 therefore comprises notonly households and government but also industry i in therole of the institutional unit that owns the capital beingaccumulated.
In the production account of an industry (SNA 1993, I.B.1.6)gross value added “is defined as the value of output less thevalue of intermediate consumption”. Gross added value can bedecomposed into wages, taxes, profits and interests (SNA1993, VII.A.7.2 and VII.A.7.13).
Let t0i denote the flow of added value of product/industry i.This flow can be decomposed into the flows mentioned in theprevious paragraph. These flows, in turn, can be decomposedinto secondary income (after paying taxes) which can beassigned to the institutional sectors of households, govern-ment and firms.
An input–outputmodel (Miller and Blair, 1985) is defined bythe set of flows tij, with i, j=0,1,…, S (and the decompositionsof flows t0i and ti0 referred above). Flow t00 is not defined in anI–O model.
535E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
Let ti be the total input or output of industry i. Themain I–Oidentity is:
ti ¼XSj¼0
tij and ti ¼XSj¼0
tji:
Composite sector 0 can be seen as an external sector, actingas a source and sink for the inter-industry economic network.Sectors i=1,…, S are industries.
Let eiL be the local or direct emissions of some environmentalpressure (EUROSTAT, 2004) of industry i.
Let T denote the matrix of inter-industry trade (whose ij-entry is tij); let x denote the column vector of total input/output (whose i-entry is ti); let y denote the column vector ofdomestic final demand (whose i-entry is ti0); let v denote therow vector of primary inputs (whose i-entry is t0i); and let eL
denote the row vector of on-site or direct emissions (whose i-entry is eiL). This is the I–O base data common to bothindicators. Let 1 denote the column vector whose i-entry is 1.In standard vector/matrix notation the main I–O identityreads:
x ¼ T1þ y and xV¼ 1VTVþ v:
The Leontief matrix is matrix A, whose ij-entry is (tij / tj)(Leontief, 1970) and the Ghosh matrix is matrix A′, whose ij-entry is (tji / tj) (Ghosh, 1958). Let I be the identity matrix. TheLeontief and Ghosh matrices verify the identities:
x ¼ I �Að Þ�1y and xV¼ v I�AVð Þ�1:
We shall also use the row vector of local or directintensities mL, whose i-entry is (eiL / ti).
In summary, the source data of the single or multi-regioninput–outputmodel considered in the paper consists ofmatrixT and vectors x, y, v and w. The concepts of that basic modelare those of institutional unit (industries, households andgovernment), economic flows (inter-industry, final expendi-ture or added value) direct emissions.
There are other frameworks besides the present one tocompute environmental indicators. Some environmentalindicators are based on physical (rather than monetary) I–Oanalysis (Hubacek and Giljum, 2003; Suh, 2004; Giljum et al.,2004; Weisz and Duchin, 2006; Hoekstra and van den Bergh,2006).
The monetary I–O model can also be expanded to a socialaccounting matrix (SAM), that records all economic flowsbetween all institutional units in the economy (that is, it closesthe loop between added value and final expenditure), andconsiders both industry and product accounts linked by use“make” and “use” tables (SNA 1993). Physical I–O tables andSAMs require even more data than that required to build amonetary I–O table.
2.2. Environmental responsibility
Environmental responsibility of region k according toRodrigues et al. (2006), Uk, is defined by a set of 6 properties:additivity, normalization, monotonicity, total transfer ofindirect effects, economic causality and consumer–producersymmetry.
By additivity it is meant that if region k is partitioned intoregions k′ and k″, then
Uk ¼ UkVþ UkW :
By normalization it is meant that the environmentalresponsibility of the world should equal total direct emissions.
By monotonicity it is meant that AUk=AeLi N0, for all directemissions eiL which are arguments of Uk.
By total transfer of indirect effects it is meant that theenvironmental responsibility of a region can only be afunction of upstream and downstream total embodied emissions
of some economic flows, involving the sectors that compose a
given region. Formally, Uk ¼ Uk eUijn o
ijð ÞaWUk
; eDijn o
ijð ÞaWDk
� �, where
WUk ;W
Dk pWT
k and ΨkT is the set of all flows involving at least one
of the sectors that compose region k.Quantity eijU (resp. eijD) denotes the upstream (resp. down-
stream) total embodied emissions of the flow from i to j.Total upstream embodied emissions of the outputs of a
given sector equals the upstream embodied emissions of theinputs plus direct emissions of that sector (downstreamembodied emissions follows an analogous definition):
eUi ¼XSj¼0
eUij ¼ eLi þXSj¼1
eUji ; i ¼ 1; N ; S; ð1Þ
and
eDi ¼XSj¼0
eDji ¼ eLi þXSj¼1
eDij ; i ¼ 1; N ; S:
By definition e0iU and ei0D are 0 (neither primary inputs cancarry upstream embodied emissions nor final demand cancarry downstreamembodied emissions since all emissions areassigned to some production sector).
The terminology of upstream and downstream is set by thedirection of the flow of goods and services: from primaryinputs to firms, from firms to final demand (the expressions“backward” and “forward” are sometimes used).
The term “total” is required to distinguish from total frompartial embodied emissions, which are introduced in the nextsubsection.
By economic causality it ismeant the following. LetmiU (resp.mi
D)denote the upstream (resp. downstream) intensity of sector i.Upstream and downstream intensities relate to upstream anddownstream embodied emissions as:
eUij ¼ mUi tij; i ¼ 1; N ; S; and j ¼ 0;1; N ; S: ð2Þ
and
eDji ¼ mDi tji; i ¼ 1; N ; S and j ¼ 0;1; N ; S:
All the outflows (resp. inflows) of sector i have the sameupstream (resp. downstream) intensity. Therefore the totalupstream (resp. downstream) embodied emissions of theoutflows (resp. inflows) of a given sector are distributedamong individual flows proportionally to the economic valueof those flows.
We formalize symmetry of upstream/downstream indi-rect effects by imposing that Uk eUij
n oijð ÞaWU
ik
; eDijn o
ijð ÞaWDik
� �¼
536 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
Uk eDjin o
ijð ÞaWDik
; eUjin o
ijð ÞaWUik
� �. This is the same as requiring Uk to
remain the same if the I–O table is transposed (T is transposedand v is interchanged with y, or alternatively, tij is inter-changed with tji), as proved in Rodrigues et al. (2006).
In Section 3 the intuition behind the properties ofaccounting of indirect effects and symmetry is explored atlength. The motivation for the remaining properties can befound in Rodrigues et al. (2006).
Rodrigues et al. (2006) prove that there is only one indicatorthat fulfils these six properties, defined as follows. Let Ψk
S bethe set of sectors that compose region k. The environmentalresponsibility of region k, Uk, is given by:
Uk ¼12
UCk þ UP
k� �
;
where UCk stands for consumer responsibility, defined as
UCk ¼
XiaWS
keUi0; ð3Þ
and UPk stands for producer responsibility, defined as
UPk ¼
XjaWS
keD0j: ð4Þ
Upstream and downstream emissions, entering Eqs. (3)–(4),are computed as ei0U=mi
Uti0 and e0jD =mjDt0j respectively.
IntensitymiU (resp.mj
D) is the i-entry of row vectormU (resp.j-entry of column vector mD). As shown in Rodrigues et al.(2006), vectors mU and mD are computed as:
mU ¼ mL I� Að Þ�1 and mD ¼ I�AVð Þ�1mL:
Vector mL and matrix A are defined in Section 2.1. There issome discussion regarding the application of the Ghoshmodelin economic analysis (Oosterhaven, 1996; Dietzenbacher,1997). However, that discussion is not relevant here since wederived the Ghosh matrix from first principles (the down-stream counterparts of Eqs. (1)–(2) and did not use the Ghoshmodel (i.e., the set of assumptions used in Ghosh, 1958).
In words, environmental responsibility according toRodrigues et al. (2006) is the average between consumerand producer responsibility, defined respectively as theupstream embodied emissions of final expenditure and thedownstream embodied emissions of added value of thesectors that compose region k.
2.3. α-environmental responsibility
Lenzen et al. (2007) propose an indicator based on workoriginally developed in Gallego and Lenzen (2005). In Gallegoand Lenzen (2005) a family of indicators is proposed thatsatisfies some of the conditions of Rodrigues et al. (2006) byconstruction (additivity, normalization, monotonicity andeconomic causality), but that differs in important ways. First,those indicators verify partial instead of total transfer ofindirect effects. Second, those indicators accounted either forupstream or downstream indirect effects, but not both at thesame time. Crucially, the parameters of transfer of indirecteffects were not specified, which is the same as saying that theindicator of Gallego and Lenzen (2005) is not unique.
Lenzen et al. (2007) propose to obtain a unique (i.e., fullyspecified indicator), by specifying the transfer parameters,
using added value as an allocation rule. An important ideabehind the choice of the added-value rule is that added valueis a proxy for the degree of control and knowledge on theproduction process. Another justification for this rule was tomake the indicator invariant to aggregation in a specific typeof linear supply chain (Lenzen et al., 2007, p. 8).
We shall refer to the indicator proposed in Lenzen et al.(2007) as α-environmental responsibility, Uk
α. Let ΨkS be the set of
sectors that compose region k, and let UαCk and UαP
k denote,respectively, the α-consumer responsibility and the α-producerresponsibility of region k. The latter are related to Uk
α as follows:
Uak ¼ UaC
k þ UaPk ;
UaCk ¼
XiaWS
keai0; ð5Þ
and
UaPk ¼
XiaWS
k1� aið Þeai : ð6Þ
Term 1−αi in Eq. (6) is the “producer responsibility share” ofsector i, defined as:
1� ai ¼t0i
ti � tii: ð7Þ
The fraction of upstream embodied emissions that isretained by a sector is equal to the fraction of added value inthe total net inputs of a sector.
Term eiα in Eq. (6) is the α-embodied emissions of sector i,defined as the eijα of the inputs of that sector plus directemissions of that sector:
eai ¼ eLi þXSj¼1
eaji; i ¼ 1; N ; S: ð8Þ
Quantity eijα denotes the α-embodied emissions of the flowfrom i to j.
Eq. (8) is an assumption of accounting of indirect effects,analogous to Eq. (1). However Eq. (8) does not specify how theα-embodied emissions of the sector is distributed among theoutput flows. In fact, Uk
α is constructed by considering thatonly a sector-specific fraction αi called “consumer responsi-bility share” of eiα is distributed:
XSj¼0
eaij ¼ aieai ; i ¼ 1; N ; S: ð9Þ
Eqs. (8)–(9) define what we call partial transfer of indirecteffects.
Ukα becomes fully determined if a rule is specified to
allocate the α-embodied emissions among individual outputflows. The rule chosen is economic causality, i.e., individualoutput flows are allocated α-embodied emissions in propor-tion to themagnitude ofmonetary flows, and is formalized asfollows.
Let miα denote the α-upstream intensity of sector i, which
relates the α-upstream embodied emissions of a flow to itsmonetary value as:
eaij ¼ aimai tij; i ¼ 1; N ; S and j ¼ 0;1; N ; S: ð10Þ
Fig. 1 – (a) Upstream environmental load. Sector 1 has directemissions, e1o, receives an input from sector 2, t21, anddelivers an output to sector 3, t13. The upstream environ-mental load of the output 1→3, e13U , equals the upstreamenvironmental load of sector 1, e1U=e21U +e1
U. (b) Downstreamenvironmental load. Sector 1 has direct emissions, e1L,receives an input from sector 2, t21, and delivers an output tosector 3, t13. The downstream environmental load of theinput 2→1, e21D , equals the downstream environmental loadof sector 1, e1D=e14D +e1L.
Fig. 2– (a) Upstream economic causality. Sector 1 has directemissions, e1L, receives an input from sector 2, t21, and deliversoutputs to sector 3, t13, and to sector 4, t14. The upstreamenvironmental load of sector 1, e1D=e21D +e1L, is allocated to thesum of output flows, 1→3 and 1→4, following economiccausality. That is, the ratio of upstream environmental load tomonetary value of each flow (its environmental intensity) is thesame: e13D /t13=e14U /t14=m1
U. (b) Downstream economic causality.Sector 1 has direct emissions, e1L, receives inputs from sectors 2,t21, and 3, t31, and delivers an output to sector 4, t14. Thedownstream environmental load of sector 1, e1D=e14D +e1L, isallocated to the sum of input flows, 2→1 and 3→1, followingeconomic causality. That is, the ratio of downstreamenvironmental load to monetary value of each flow (itsenvironmental intensity) is the same: e21D /t21=e31D /t31=m1
D.
537E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
Note that both αi and miα are sector-specific and therefore
α-upstream intensity could alternatively have been defined asαimi
α but Eq. (10) is more convenient (otherwise Eq. (6) wouldbecome cumbersome). Eqs. (9) and (10) can be combined as:
eai ¼ mai ti; i ¼ 1; N ; S:
In summary, partial transfer of indirect effects leads to afraction αi of the α-embodied emissions of sector i beingpassed downstream (Eqs. (8)–(9)), and the remainder beingkept by the sector as α-producer responsibility, Eq. (6).Economic causality (Eq. (10)) specifies how the α-embodiedemissions of sector i is distributed among output flows andthe fraction eventually reaching final demand is α-consumerresponsibility (Eq. (5)). Share α is defined by Eq. (7).
α-embodied emissions of the flow to final expenditure fromindustry i, entering Eq. (5), and α-embodied emissions of industryi, entering Eq. (6), are computed respectively as ei0α=αimi
αti0 andeiα=mi
αti from Eq. (10).Intensity mi
α is the i-entry of row vector mα, computed as:
ma ¼ mL I�Aað Þ�1;
where the (ij)-entry of matrix Aα is αitij / tj.In Appendix A we show how the original formulation of
Lenzen et al. (2007) relates to the above formulation.In the present SectionUα
kwas described as accounting onlyfor upstream indirect effects. However, in the exposition of Uk
α
in Lenzen et al. (2007), it is mentioned in passing that “[t]hesame approach can be applied to downstream impacts, asdescribed in Gallego and Lenzen (2005)”, and Lenzen (personalcommunication) states that downstream effects were omittedfrom Lenzen et al. (2007) because of restrictions on the lengthof the manuscript.
Unfortunately, the extension of the approach developed inLenzen et al. (2007) to downstream indirect effects requires twomajor specifications which are not hinted at in the paper. Oneproblem is the specification of the downstreamversion of Eq. (7):the downstream fraction α could be a function of the fraction ofadded value (given the strong emphasis on added valuemade inthat paper) or, instead, it could be a function of the fraction offinal demand,which is thenatural analogueof addedvalue inandownstreamcontext. A secondproblemconcernsunicity: if bothupstream and downstream indirect effects were considered,there would be two α-consumer and two α-producer responsi-bilities for each sector, but one of the aims of Lenzen et al. (2007)was to obtain a unique indicator. The solution to this contra-diction would be to combine both α-producer responsibilitiesandα-producer responsibilities in twosingle indicators, but thenit is further necessary to specify how they would be combined.
Given these inconsistencies, it is hard to see how “the sameapproach can be applied to downstream impacts, as describedin Gallego and Lenzen (2005)”. Therefore we consider theupstream-only Uα
k to be the only fully specified indicatorproposed in Lenzen et al. (2007).
2.4. Illustration
The intuition behind the indicators is as follows. Eacheconomic flow is assumed to carry embodied emissions. The
Fig. 4 –α-environmental load. Sector 1 has direct emissions,eL1, receives an input from sector 2, t21, and delivers an outputto sector 3, t13. The α-environmental load of the output 1→3equals a fraction α1 of the α-environmental load of sector 1,e1α=e21α +e1L.
538 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
environmental responsibility (either consumer or producer) ofa given agent is a function of the embodied emissions ofeconomic flows involving that agent.
Environmental responsibility is based on upstream anddownstream embodied emissions, which follow total transferof indirect effects meaning roughly “all that goes in must goout”. In the case of upstream (resp. downstream) effects what“goes in” are the embodied emissions of inputs (resp. outputs)plus direct emissions and what “goes out” are the embodiedemissions of outputs (resp. inputs). Fig. 1 illustrates totaltransfer of indirect effects (Eq. (1)).
When a sector has more than one output (resp. inputs) arule must be specified to allocate the upstream (resp. down-stream) embodied emissions of the sector to its outputs (resp.inputs). According to economic causality (Eq. (1) and itsdownstream analogue), the share of total embodied emissionsallocated to a given flow is equal to the share of total economicoutput (or input) of that given flow. Fig. 2 illustrates economiccausality.
The consumer (resp. producer) responsibility of a region isthe upstream (resp. downstream) embodied emissions of theeconomic flows leaving the I–O network, i.e., final demand(resp. primary inputs). Fig. 3 illustrates consumer andproducerresponsibility (Eqs. (3) and (4)). Environmental responsibility isthe average of consumer and producer responsibility.
α-embodied emissions follow partial transfer of indirecteffects, and only a sector-specific fraction α of what “goes in”does also “go out”, and the remainder is retained by the sector.Fig. 4 illustrates the partial transfer of indirect effects inα-embodied emissions (Eqs. (8)–(9)).
Fig. 3 – (a) Consumer responsibility. Sector 1 has directemissions, e1L, receives inputs from sectors 0 (primary input),t01, and 2 (intermediate input), t21, and delivers outputs tosectors 0 (final demand), t10, and 3 (intermediate demand), t13.The consumer responsibility of sector 1, U1
C, is the upstreamenvironmental load of final demand, e10U . (b) Producerresponsibility. Sector 1 has direct emissions, e1L, receivesinputs fromsectors 0 (primary inputs), t01, and2 (intermediateinput), t21, anddeliversoutputs to sectors 0 (final demand), t10,and 3 (intermediate demand), t13. The producer responsibilityof sector 1, U1
P, is the downstream environmental load ofprimary inputs, e01D .
α-embodied emissions also use economic causality as arule to allocate the α-embodied emissions of a sector to itsoutputs. According to economic causality (Eq. (10)), the shareof total embodied emissions allocated to a given flow is equalto the share of total economic output of that flow. Fig. 5illustrates economic causality.
The α-consumer responsibility of a region is the α-embodiedemissions of final demand and the α-producer responsibility isthe fraction (1−α) of the α-embodied emissions of the sector.Fig. 6 illustrates α-consumer and producer responsibility(Eqs. (5) and (6)). α-environmental responsibility is the sum ofα-consumer and producer responsibility.
3. Comparison of the indicators
In this section we compare environmental responsibility Uk
(proposed by Rodrigues et al., 2006) and α-environmentalresponsibility Uk
α (proposed by Lenzen et al., 2007).Both indicators attempt to fulfill the same goal: to assign
the responsibility for environmental pressure to sub-regionalinstitutional units, distinguishing their role as consumers andproducers.
The data required is the same, and the computation effortis similar. Both indicators allocate consumer responsibility tothe final consumers of an industry if it delivers outputs to final
Fig. 5 –α-economic causality. Sector 1hasdirect emissions, e1L,receives an input from sector 2, t21, and delivers outputs tosector 3, t13, and to sector 4, t14. A fractionα1 of theα-upstreamenvironmental load of sector 1, e1α=e21α +e1L is allocated to thesum of output flows, 1→3 and 1→4, following economiccausality. That is, the ratio of α-upstream environmental loadto monetary value of each flow is the same: e13α / t13=e14α /t14=α1m1
α.
Fig. 6– (a) α-consumer responsibility. Sector 1 has directemissions, e1L, receives inputs fromsectors 0 (primary input), t01,and 2 (intermediate input), t21, and delivers outputs to sectors 0(final demand), t10, and 3 (intermediate demand), t13. Theα-consumer responsibility of sector 1, UαC
1, is the α-upstreamenvironmental load of final demand, eα10. (b) α-producerresponsibility. Sector 1 has direct emissions, eL1, receives inputsfromsectors 0 (primary input), t01, and2 (intermediate input), t21,and delivers outputs to sectors 0 (final demand), t10, and 3(intermediate demand), t13. The α-producer responsibility ofsector 1,Uα
1P, is the fraction (1−α1) of the α-environmental load of
sector 1, e1α=e21α +e1L.
Fig. 7 – (a) Comparison of embodied emissions using total andpartial accounting of indirect effects in a supply chain:scenario A. (b) Comparison of embodied emissions usingtotal and partial accounting of indirect effects in a supplychain: scenario B. (c) Comparison of embodied emissionsusing total and partial accounting of indirect effects in asupply chain: scenario C.
539E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
demand; and producer responsibility to an industry or itsprimary suppliers if it receives inputs from value added.
Conceptually, both indicators satisfy 4 of the properties im-posed in Rodrigues et al. (2006) for environmental responsibility:additivity, normalization, monotonicity and economic causality.(The latter is verified by construction, Eqs. (2) and (9), the formerthree conditions can be easily checked by the interested reader.)
Hence, there are two main points in which the indicatorsdiffer:Uk verifies total transfer of indirect effects and considersboth upstream and downstream indirect effects (using sym-metry to ensure uniqueness); Uk
α verifies partial transfer ofindirect effects (using the fraction of added value to ensureuniqueness) and only considers upstream indirect effects.
Total transfer of indirect effects, within a purely upstreamapproach, leads to a complete allocation of responsibility toconsumers.
Uk manages to allocate both to producers and consumersby combining upstream and downstream formulations. It isthen necessary to balance the two allocation procedures,which is done using symmetry.
Ukα manages this by maintaining the purely upstream
approach, but “diverting” environmental responsibility toproducers through partial transfer of indirect effects. Thefraction of “diverted” responsibility must then be stipulated,which in Lenzen et al. (2007) is done in such a way thatconsumer responsibility is decreasing for emissions which arefarther away from the consumer along the production chain.
We now compare the indicators regarding these two mainpoints, regarding the assignment of the indicator to specificinstitutional units, and regarding policy implications.
3.1. Total vs. partial transfer of indirect effects
Both indicators are defined as sums of embodied emissions ofsomeeconomic flows.However, thewayembodiedemissionsaredefined for each indicator is different. Uk is derived using totalembodied emissions (upstream or downstream), defined byEq. (1) and thus verifying total transfer of indirect effects, whileUkα is derived using partial (or α-)embodied emissions, defined by
Eqs. (8)–(9), thus verifying partial transfer of indirect effects.Themainmotivations for partial transfer of indirect effects
in Lenzen et al. (2007) was to be able to allocate some form ofresponsibility to sectors without final demand or primaryinputs (a claim examined in Section 3.3), and to providedecreasing responsibility with increasing distance in thesupply chain. That is, to make final consumers (who are allo-cated the α-embodied emissions of final demand) less “res-ponsible” for direct emissions occurring farther upstream inthe supply chain than for direct emissions occurring closer tofinal demand.
540 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
However, for policy purposes embodied emissions(whether partial or total) of products are important becausethe choice of the products they buy (and that they sell in thecase of Uk) is one way for institutional units to alter theirenvironmental responsibility (whether Uα
k or Uk). Thus it isimportant to compare (total and partial) embodied emissionsper se.
We now look at an example with supply chains.Fig. 7 shows a two-sector supply chain, where sector 1
receives no input from other sectors, sells its product to sector2 for 50$ and delivers 50$ of added value. Sector 2 sells itsproduct to the final consumer for 100$ and also delivers 50$ ofadded value. We consider three scenarios: in scenario A sector1 and sector 2 both emit 5 kg of CO2 equivalent; in scenario Bonly sector 2 has emissions, with a total of 10 kg of CO2
equivalent; in scenario C both sectors emit 10 kg of CO2
equivalent.Table 1 shows the upstream embodied emissions, e2U, and
the α-embodied emissions, e2α, of the consumer good (product2) in the several scenarios. In scenarios A and B the same totalemissions occur (10 kg) while in scenario C more emissionsoccur (20 kg), thus from an environmental point of view theconsumer goods of scenarios A and B are equally good whilethat of scenario C is markedly worse.
Upstream embodied emissions, computed with totaltransfer of indirect effects, report the relative environmentalperformance of the consumer good in the different scenarios.α-upstream embodied emissions, provide a different picture:the consumer good of scenario A transfers less environmentalresponsibility to its consumer than the one of scenario Bbecause its emissions occur further upstream, and becausethe producers of that chain need to be levied with upstreamresponsibility. Consumer goods of scenarios B and C transferequal environmental responsibility to their consumers, eventhough the total emissions of scenario C are double those ofscenario B.
A problem resulting from partial transfer of indirect effects(that therefore affects Uk
α but not Uk) is the need to specify thefraction of accounting (parameter α). Lenzen et al. (2007)proposed Eq. (7) arguing that Uk
α should remain invariant toaggregation, when applied to supply chains.
We fully agree that invariance to aggregation would be animportant property for environmental responsibility, whenapplied to an I–O model with an arbitrary structure. However,this is in general not possible, because aggregation leads toloss of information. Lenzen et al. (2007) proposed invariance toaggregation not with an arbitrary structure but, with a linearsupply chain.
Unfortunately, the claim that Ukα is in general invariant to
aggregation in a linear supply chain (according to Lenzen
Table 1 – Comparison of embodied emissions using totaland partial accounting of indirect effects in a supply chain
Scenario Total emissions e20U e20α
A 10 10 2.5B 10 10 5C 20 20 5
et al., 2007) is not true. We prove in Appendix A that Uαk is
only invariant to the disaggregation of a supply chain if thedownstream disaggregated sector has no emissions or if theupstream disaggregated sector produces no added value.That is, the statement of Lenzen et al. (2007) that Eq. (7)ensures the invariance of the indicator to the disaggregationof supply chains is only true in very particular conditions.However, given that embodied emissions in a demandchain are in general never aggregation-invariant, someinvariance is already an improvement (Lenzen, personalcommunication).
In Appendix A we also examine the behavior of Uk
regarding invariance under the disaggregation of supply anddemand chains. Uk
C is invariant under disaggregation in asupply chain and Uk
P is not. In a demand chain the situation isreversed.
Lenzen et al. (2007) have proposed many other verbal (i.e.,non-mathematical) arguments in support of the added-valuerule (Eq. (7)) such as the idea that it respects “processknowledge and influence” (p. 38, line 9).
3.2. Accounting of downstream indirect effects
Uk is derived accounting both for upstream and downstreamindirect effects, while Uk
α only accounts for upstream effects.Accounting of upstream indirect effects is formalized in eijU,
the embodied emissions of economic ij. This quantity is thesum of all direct emissions that occur to generate the product(good or service) ij. For example, consider the flow of chocolatefrom a factory to a store chain. The corresponding upstreamGHG load takes into account the emissions due to combustionin the factory, the methane emissions of the cow whose milkwas processed in the factory, etc. (but not the emissions due totransport from the store chain's central warehouse to thestore, which occurs downstream from the transaction beingexamined).
Accounting of downstream indirect effects is formalized ineijD, the embodied emissions of economic ij. This quantity is thesum of all direct emissions that generate the payment of theproduct (good or service) ij. Using the example above, considerthe flow of milk from the farmer to the factory. Thecorresponding downstream GHG load takes into account theemissions due to combustion in the factory, the emissions dueto transport from the factory to the final consumer, etc. (butnot frommethane emissions from the cow, upstream from thetransaction being examined).
The literature on environmental impacts (LCA, I–O analy-sis, MFA, industrial ecology) almost exclusively takes anupstream perspective. That we are aware of, only Rodrigueset al. (2006) and Gallego and Lenzen (2005) consider down-stream indirect effects, and they are mentioned in Lenzenet al. (2007), as referred in Section 2.3.
Accounting of downstream emissions, if almost absentfrom the literature on environmental impacts, is not absentfrom the minds of economic agents.
The Equator Principles (http://www.equator-principles.com/) are a set of principles to which financial institutionscan voluntarily adopt “to ensure that the projects we financeare developed in a manner that is socially responsible andreflect sound environmental management practices” (from
541E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
the Preamble, in http://www.equator-principles.com/princi-ples.shtml).
Likewise, the Association of British Insurers reports that “[i]n 2001 […] a third of [financial] analysts said social andenvironmental policies were important in helping themassess companies” and that accumulated evidence in thepast three decades lends overwhelming weight to the viewthat “investors can enhance risk/return performance througha better understanding of the social and environmental riskscompanies face and their skills in managing their risks” (ABI,2004, p. 5).
The Equator Principles and the Association of BritishInsurers espouse the concept of accounting of downstreamindirect effects since the financial institution (which sells afinancial product) is concerned about the environmentalimpacts occurring downstream (that is, resulting from theactions of the buyer of that product).
If we change the focus from environmental to social issues,responsibility for downstream effects becomes much morefamiliar: some people oppose the manufacture and trade ofweapons, tobacco or illegal drugs. Such products have adversesocial effects (war, addiction, crime) downstream along theeconomic process, thus if an individual refuses to engage inmanufacture or trade of such products – and thus refuses toreceive “dirty money” – that individual is acknowledging theprinciple of accounting of downstream indirect effects.
We therefore consider that environmental responsibilityshould be both a function of upstream and downstreamemissions.
Rodrigues et al. (2006) and Gallego and Lenzen (2005)consider both upstream and downstream effects. Rodrigueset al. (2006) require an assumption to guarantee a uniquesolution and the assumption chosen was upstream–down-stream symmetry. Symmetry is a property of the indicatordefined as follows.
If the upstream emissions of the flow ( ji) that agent iconsumes are interchanged with the downstream emissionsof the flow (ij) that agent i produces, for all flows j, then theresponsibility of agent i remains unchanged. This assumptionformalizes the idea that the indicator of environmentalresponsibility should not care whether an agent's embodiedemissions stemfromhis actions as a consumeror as aproducer.
Consider a hypothetical economic agentA, that consumes aset of productswhose upstream emissions are eUjA
n ojAð ÞaWU
A
andhe produces a set of products whose downstream emissionsare eDAj
n ojAð ÞaWD
A
, where ΨAU and ΨA
D are sets of flows. Nowconsider an economic agent B, whose upstream emissionsexactly match the downstream emissions of agent A and vice-
versa: eUiBn o
iBð ÞaWUB
¼ eDAjn o
Ajð ÞaWDA
and eDBin o
Bið ÞaWDB
¼ eUjAn o
jAð ÞaWUA
.
That is, the upstream and downstream indirect effects of theconsumer and producer behavior of agents A and B aresymmetrical.
For example, consider that agent A can sell products withhigh indirect (upstream) emissions and buy products with lowindirect (downstream) emissions, and that the reverse hap-pens for agent B. Should agent A or agent B be charged withmore environmental responsibility?
In an economic transaction, there will likely be anasymmetry in bargaining power and information betweenbuyer and seller (Cerin, 2006). In the definition of an indicator
of environmental responsibility the problem introduced bythese asymmetries is that the disadvantaged economic agentis not allowed to express his environmental preferences.However, either the buyer or the seller can be the disadvan-taged agent.
In the case of bargaining power, a monopolist can set theprice and therefore constrain buyers' choices (e.g., a dominantelectricity company in a small country can set the final price ofrenewable energy relative to fuel-generated energy thusconstraining domestic consumers). However, a monopsonistcan also set the price and therefore constrain seller's choices(e.g., that same electricity company now buying electricityfrom the owners of small hydropower stations).
Regarding asymmetry in information the situation issimilar. The seller of a private transport vehicle may notdisclose the true fuel consumption of the vehicle, thuspreventing the buyer from expressing his environmentalpreferences. But the same seller does not know how thebuyer is going to use the vehicle, and most emissions from atransportation vehicle occur during the use (and not theproduction) phase.
The existence of bargaining power and informationasymmetries between a buyer and a seller is tangential to bethe problem at hand: the weighting of upstream emissionsembodied in consumption and downstream emissions embo-died in production of the same agent in that agent's environ-mental responsibility.
Symmetry according to Rodrigues et al. (2006) means thatwhen we interchange the whole structure of the economy,responsibility of agents should not change. For example, withthis interchange, a monopolist becomes a monopsonist. Isthere any reason to consider that his responsibility shouldchange? Note that his bargaining power is still the same, onlynow it occurs as a consumer and not as a producer.
Symmetry is a weak property, which is sufficient to ensurethe uniqueness of environmental responsibility only if it isconsidered together with the remaining five properties. Forexample, if additivity is not considered, environmentalresponsibility can be symmetrical without being a weightedaverage of upstream load of final expenditure and down-stream load of value added.
If partial (instead of total) transfer of indirect effects wereconsidered, together with the remaining five properties,environmental responsibility would be a weighted sum ofupstream emissions of final expenditure, downstream emis-sions of value added and direct emissions where the weight ofupstream and downstream embodied emissions would beequal. In this case, however, the indicatorwould not be uniqueand a further assumption would be required to specify thefractions of the retained emissions (α's) in order to satisfyuniqueness.
Such a general situation is close to the one reported byGallego and Lenzen (2005), that presents an indicator account-ing for upstream partial indirect effects and another indicatoraccounting for downstream partial indirect effects, both withunspecified weightings. However, Gallego and Lenzen (2005)donot combine them in a single indicator. According to Lenzen(personal communication) this can easily be achieved bycombining the idea of Rodrigues et al. (2006) and Gallego andLenzen (2005) into Uk
542 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
3.3. Assignment of the indicator to institutional units
Consumer responsibility has a similar definition according toboth indicators: it is the total (inUk) or partial (inUα
k) upstreamembodied emissions of final expenditure.
However, producer responsibility is defined in a differentway for each indicator, although in both cases based on valueadded. Environmental responsibility identifies producerresponsibility with the total downstream embodied emissionsof added value while α-environmental responsibility identifiesproducer responsibility with a fraction α, calculated as afunction of the value added of sector, of the α-upstream em-bodied emissions of the inputs of a sector.
The terminology used by Lenzen et al. (2007) seems to dateback to Munksgaard and Pedersen (2001) who identified theCO2 direct emissions of Denmark with its “producer” respon-sibility. However, the focus of Munksgaard and Pedersen(2001) was at the level of regions while the focus of Lenzenet al. (2007) is at the level of industries. That is, as stated in thebeginning of Section 2.3, the aim of Lenzen et al. (2007) was tomake a clear distinction between producer= firm and consu-mer=population. They did so by assigning α-producer respon-sibility to the industry and α-consumer responsibility to finalexpenditure.
The interpretation of Lenzen et al. (2007) is misleadingbecause investment is a component of final expenditure(according to the definition of SNA 1993, reviewed in Section2.1) that is performed by industries (unfortunately this error iscommon, cf. Tukker and Jansen, 2006, p. 161, first paragraph).Therefore, a part of α-consumer responsibility should beassigned to industries. This inconsistency can be solved bymodifying the Leontief matrix (Lenzen, 2001), incorporatinginvestment in intermediate inputs.
However, just as a fraction of final expenditure isperformed by firms, also a fraction of the payments to primaryinputs is delivered to households (in the form of wages, rentsand interests) and government (in the form of taxes). Thus, inour opinion, to be consistent with the goal of distinguishingproducer= firm, all payments to primary inputs to eitherhouseholds or the government should be removed fromEq. (7), to deallocate such payments from α-producerresponsibility.
The way Uk is assigned to different institutional units isquite different. Each institutional unit receives income andmakes expenditure, and therefore each institutional unit k isassigned a certain producer responsibility Uk
P and a certainconsumer responsibility Uk
C.Using Uk there is no distinction in the treatment of
households, government and firms. The procedure for thecalculation of the environmental responsibility is the same forall institutional units.
One of the motivations of Lenzen et al. (2007) was to allowpurely intermediate sectors to capture some environmentalresponsibility. A purely intermediate sector is one that eitherdoes not supply products to final demand and/or does notsupply payments to primary inputs.
The qualitative treatment of intermediate sectors by bothindicators is the same. If there is no final demand there are noupstream embodied emissions in final demand (Eqs. (2) and(10)), and therefore no consumer responsibility (Eqs. (1) and
(5)). If there is no added value there are no downstreamemissions in added value (downstream analogue of Eq. (2) andtherefore no producer responsibility in the case of Uk (down-stream analogue of Eq. (1); in the case of Uk
α absence of addedvalue implies that α=1 (Eq. (7)) and therefore that producerresponsibility is 0 (Eq. (6)).
However, the qualitative treatment of a sectorwithout finaldemand by both indicators is the same (the flow of addedvalue must be positive for both UαP
k and UkP to be positive) but
for different reasons. In the case of Ukα, α-producer responsi-
bility is accounting for indirect emissions occurring upstreamwhile in the case of Uk producer responsibility is accountingfor indirect emissions occurring downstream (Lenzen, perso-nal communication).
3.4. Environmental policy
Wenow address the implications of the choice of the indicatorfor environmental policy. We focus on environmental policythat can be done directly by institutional units (directabatement by firms and indirect abatement through choiceof inputs and outputs) as opposed to policy mandated by thegovernment (such as setting taxes or allocating permits).
Corporate social responsibility (CSR) programs, in whichfirms voluntarily try to reduce environmental and socialnegative impacts, are increasingly popular (Heal, 2005). Firmscan adopt a CSR program and “over-comply” with environ-mental regulation for several reasons, two of which seemparticularly strong. One ismoving ahead of an expectable trendof both legislation and consumer's preferences becomingstricter. This can be interpreted as risk management. Anotheris branding, in which firms use environmental reputation togain market share from less environmentally friendly compe-titors. It is not incidental that CSR programs are more popularamong firms whose image is more exposed (Heal, 2005).
Consumer environmental preferences therefore play in animportant role in this context, as reported by Cerin (2006) forthe adoption of environmentally friendly technology. Cerin(2006) reports that firms are usually reluctant to adopt greentechnology due to its higher-than-average costs. However,small groups of environmentally-minded consumers who arewilling to pay higher costs for green products can provide amarket niche for green firms with a small market share,eventually forcing overall adoption of the greener technologyin an industry.
The case studies reported by these authors usually consideronly first-order indirect effects, in which (typically) the buyertries to influence the seller to reduce its direct emissions.Another example of this approach is the “greenhouse gasprotocol” (WRI and WBCSD, 2004) a corporate accounting andreporting standard, to which firms can voluntarily adhere.According to this protocol, firms should report their direct GHGemissions and theGHG emissions of the energy they consume.Thus, this protocol advocates the accounting of first-orderindirect effects from the energy sector. The protocol allows butdoes not demand the compilation of an inventory of upstreamindirect emissions (scope 3).
The use of Uk or Ukα as environmental indicator is a natural
extension of these several approaches, since it would allowconsumers (either intermediate or final) to decide which
543E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
products to buy based on their total (or partial, in the case ofUkα)
upstream indirect effects.Here, we believe, lies the major strength of an indicator of
indirect effects, the possibility that it offers institutional unitsof balancing their economic and environmental preferences.For example, an environmentally-minded consumer canchoose if he is willing to pay more for a product with a lowerupstream environmental intensity.
Uk has a consistent connection between the responsibilityof the consumer and his information of the total upstreamembodied emissions of the products he is consuming. Uk
α,gives less weight to emissions that occur farther away fromthe consumer in the supply chain. Gallego and Lenzen (2005)explain the less-weight-with-distance property as an intuitiveway to assign indirect responsibility to purely intermediatesectors.
By accounting both upstream and downstream indirectemissions, Uk offers the possibility of reducing indirect emis-sions both by the choice of inputs (fromwhom to buy products)and by the choice of outputs (whom to sell products).
In Section 3.2 we referred two initiatives, the EquatorPrinciples and the Risk Return and Responsibility (ABI, 2004),where downstream analogues of CSR are proposed. Using Uk
all institutional units are allowed to reduce both upstreamanddownstream indirect emissions by choosing inputs (whom tobuy from) and outputs (who to sell to) with low upstream anddownstream environmental intensity.
4. Conclusions
In this paper we reviewed two recently proposed environ-mental indicators: environmental responsibility and α-envir-onmental responsibility.
Environmental responsibility, Uk, is the average betweenproducer and consumer responsibility of an institutional unit,where the former is the downstream embodied emissionsembodied in value added and the latter is the upstreamembodied emissions embodied in final expenditure.
α-environmental responsibility, Ukα, is the sum of α-
producer responsibility of an industry and the α-consumerresponsibility of the households and government to which theindustry sells its products. α-producer responsibility is afraction (1−αi) of the α-upstream embodied emissions embo-died in the outputs of a sector and α-producer responsibilityis the α-upstream embodied emissions embodied in finalexpenditure.
These indicators are similar in a number of aspects: theyboth attempt to account for both producer and consumerindirect effects in the generation of environmental pressure,they are additive, normalized, monotonic in direct emissionsand follow economic causality. They are both grounded inmonetary I–O analysis, require the same data and are roughlyof the same computational complexity. Both indicatorsallocate consumer responsibility to an industry or its finalconsumers if it delivers outputs to final demand; and producerresponsibility to an industry or its primary suppliers if itreceives inputs from value added.
They differ in the transfer of indirect effects (total vs. partialtransfer), in the accounting of downstream indirect effects, and
in the assignment to institutional units, with importantconsequences for environmental negotiation and policy.
Regarding accounting of indirect effects, Uk is based on theaccounting of total indirect effects while Uk
α is based on thepartial transfer of indirect effects, being only a fraction αi of theindirect emissions occurring upstreamof an industry passed onto outputs. Total transfer of indirect effects allows for themeaningful comparison of the total environmental impact of aproduct along its life cycle while partial accounting does not,since it is sensitive to the distance (in terms of number oftransactions) at which emissions occur. In order to be unique,Ukα requires a choice of the sharing parameter α, which is
achieved through asking for invariance with regard to sectoraggregation in linear supply chains. In Appendix A we provethat this invariance is only true in a limited number ofsituations.However, this limited invariance “is an improvementsince an input–output specification does not in general lead todisaggregation invariance in supply chains” (Lenzen, personalcommunication). Lenzen et al. (2007) support partial transfer ofindirect effects in order to be able to assign responsibility topurely intermediate agents, which in turn leads to decreasingresponsibility with increasing distance along the supply chain.However, the value-added α-rule (Eq. (7)) can also be justifiedbecause added value is a proxy for “process knowledge andinfluence”, among other justifications.
Uk considers both upstream and downstream indirecteffects while Uk
α considers only upstream indirect effects.Upstream indirect effects are the emissions embodied in aproduct while downstream indirect effects are the emissionsembodied in the payment of a product. Downstream indirecteffects are usuallyneglected in the literatureonenvironmentalimpacts, but several business initiatives have appeared point-ing toward its accounting. In order to be unique,Uk requires thespecification of the assumption of symmetry of upstream–downstream indirect effects. Symmetry imposes that theenvironmental responsibility of an institutional unit isunchanged if the upstream embodied emissions in theproducts it buys is interchanged with the downstreamembodied emissions in the products it sells. Regarding theassignment to institutional units, Uk defines both a producerand a consumer responsibility for each institutional unit(firms, households and government). UαP
k is applied to firmsand UαC
k is applied to final expenditure, which consists both ofinvestment (that is performed by firms) and final consumption(that is performedbyhouseholds andgovernment). It is possibleto modify the Leontief matrix to deallocate α-embodied emis-sions from investment, thus assigning UαC
k only to householdsand government. However, a fraction of payments to primaryinputs is delivered to households and government (wages,rents, interests and taxes) and according to α-environmentalresponsibility are assigned to firms.
The above differences have implications in the applicationto environmental policy. In particular, Uk allows for the possi-bility of upstream and downstream indirect abatement by thechoice of inputs and outputs with low environmental inten-sity. Uk
α only allows for upstream indirect abatement throughthe choice of inputs.
We consider that there are still some theoretical problemsconcerning environmental responsibility: we identify three asparticularly important and as directions of future research.
544 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
One problem is the estimation of international indirecteffects. I–O data is typically presented at the national levelonly and even databases of international trade (such as theGTAP database) present international trade flows at a veryaggregated level. Since we already know that internationalindirect effects are important (Munksgaard and Pedersen,2001) and environmental responsibility is sensitive to the levelof data aggregation (Lenzen et al., 2004), it is important todevelop a solid methodology to estimate disaggregatedinternational intersectoral trade data (a recent review ofmulti-regional I–O models is found in Wiedmann et al., 2007).
A related problem is that of error estimation. I–O sourcedata have errors, but graver errors appear, in the calculation ofenvironmental responsibility, from aggregation and the esti-mation of international intersectoral data. The estimation oftotal errors affecting computational results is crucial ifenvironmental responsibility is to be of any policy relevance.
A final problem is the generalization of environmentalresponsibility from an I–O to a SAM framework. In an I–Oframework all direct environmental pressuremust be assignedto a production sector. However, for some relevant types ofenvironmental pressure it is reasonable to consider directassignment to the consumption sector (e.g., greenhouse gasemissions from private transportation or household heating).Unfortunately, the definition of environmental responsibilityin a SAM framework poses important theoretical problemsthat take us well beyond the scope of the present paper.
Acknowledgements
We acknowledge the support of FCT via scholarship SFRH/BD/9055/2002 (to J. R.) and grant POCI/AMB/55701/2004 (to T. D. andJ. R.).
We would like to thank Manfred Lenzen and an anon-ymous reviewer for detailed comments, and Stefan Giljum forproviding relevant references.
Appendix A. Formulation of the indicator ofLenzen et al. (2007)
The original formulation of UαCk and UαP
k are, respectively(Lenzen et al., 2007, pp. 6–8):
UaCk ¼ f tL að Þ bfyð Þ
and
UaPk ¼ f tL að Þ 1� bð Þfyþ 1�αÞfTð �1½ Þ;ð
where superscript t denotes transpose; # denotes element-wise multiplication; f is the vector of emissions of sector i pergross output xi.
Vector β and matrix α have entries defined as:
1� bi ¼ 1� aij ¼vi
xi � Tiiu1� ai;
where vi is added value, xi is gross output and Tii isintrasectoral flows.
T is the matrix of intersectoral flows, y is the vector of finaldemand and 1 is a vector of 1's.
Matrix L(α) is defined as:
L að Þ ¼ ðI�αfAÞ�1;
where I is the identity matrix and the entries of matrix A aredefined as:
Aij ¼Tij
xj:
In the notation followed here, f→mL, the remaining matrixnotation remains unchanged (T, y, v, x and A), but scalarnotation follows the nomenclature defined at the beginning ofSection 2. Thus, converting notation we obtain:
UaCk ¼
XiaSk
mai aiti0 ðA1Þ
and
UaPk ¼
XiaSk
mai 1� aið Þti; ðA2Þ
where α-upstream intensity, miα, verifies:
mα ¼ mL I�Aαð Þ�1;
where mα and mL are the row-vectors whose i-entry are,respectively, eiα / ti and eiL / ti andAα is thematrix whose (ij)-entryis αitij / tj. The last equation can be transformed into:
mα I�Aαð Þ ¼ mL
and
mα ¼ mL þmαAα
or
mai ¼
eLjtiþXSj¼1
maj aj
tjiti
0@
1A:
Substituting Eqs. (9) and (10) in the previous expression weobtain:
eaiti
¼ eLitiþXSj¼1
eajitji
tjiti
and Eq. (8) is recovered:
eai ¼ eLi þXSj¼1
eaji:
Eqs. (5) and (6) are recovered by combining, respectively,Eqs. (A2) and (A1) with Eqs. (9) and (10).
Invariance of Ukα to the disaggregation of supply
chains
For concreteness consider a 1-sector chain, to be laterdisaggregated. Sector 1 has direct emissions eiL≥0, provides aflow to final expenditure, t10, receives a flowof value added, t01,and a flow from an external sector, tE1 (to ensure consistencywith the formulation of Lenzen et al., 2007, Figs. 5 and 6).
Fig. A1 – (a) The aggregated supply chain: α1=1–14/22 ande10α =0.56(0.2+0.96). Bold arrows represent flows of goods and
services and dashed arrows represent direct emissions andα-upstream load. (b) An invariant disaggregation of the supplychain of Fig. 1a: α1′=1–10/18; α2′=1–4/22, e1′2′α =0.44(0.2+96) andE2′0α =0.82(0+0.51). Note that e2′0=e10α . (c) A disaggregation of the
supply chain of Fig. 1a that is not invariant: α1′=1–10/18,α2′=1–4/22, e1′2′α =0.44(0+0.96) and e2′0
α =0.82(0.2+0.42). Notethat e2′0α ≠e10α .
545E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
Nowconsider a disaggregation of sector 1 into sectors 1′ and2′. A set of disaggregation constraints that must be verified:e1o=e1′o +e2′o (direct emissions are conserved), t01= t01+ t02′ (addedvalue), t01= t2′0 (final demand), tE1′+ t01′= t1′2′ (I–O equation ofsector 1′) and t1′,2′+ t02′= t2′0 (I–O equation of sector 2′). FromEq. (8) the α-consumer responsibility in the 1- and 2-sectorchains is respectively:
ea10 ¼ a1eL1
ea2V0 ¼ a2V eL2Vþ a1VeL1V� �
:
For α-consumer responsibility to be invariant to disaggre-gation, the following must hold: e10α ≡e2′0α . This is equivalent to:
a1eL1ua2VeL2Vþ a2Va1VeL1V: ðA4ÞFrom Eq. (7) and the supply-chain formulation:
a1 ¼ 1� t01t10
; a1V¼ 1� t01Vt1V2V
and a2V¼ 1� t02Vt2V0
:
Together with the disaggregation constraints, the previousexpressions can be recast as:
a1V¼ 1� t01Vt10 � t02V
and a2V¼ 1� t02Vt10
:
In turn we find that:
a1Va2Vu 1� t01Vt10 � t02V
� �1� t02V
t10
� �¼ t10 � t02Vþ t01Vð Þ
t10 � t02V
� �t10 � t02V
t10
� �
¼ 1� t02Vþ t01Vt10
¼ 1� t01t10
ua1:
thus, we can recast Eq. (A4) as:
a1eL1ua2VeL2Vþ a1 eL1 � eL2V� �
which is only true if:
a2V� a1ð ÞeL2V¼ 0:
This condition is true if e2L≡0, that is, if the downstreamdisaggregated sector has no emissions, or if α2′=α1. The lattercondition, from Eq. (7), the supply-chain formulation and thedisaggregation constraints, is the same as t01= t02 or t01′=0,that is, the condition is also true if the upstreamdisaggregatedsector produces no added value.
If none of these two conditions is verified, the indicatorapplied to supply chains is not invariant to disaggregation. Acounterexample to the example reported by Lenzen et al. (inpress) in Figs. 5 and 6 is presented in Fig. A1c, where thedownstream disaggregated sector has direct emissions. Onlythe last aggregated sector (food, here renamed 1) of theoriginal example is considered, since the upstream part of thesupply chain is irrelevant for the invariance check (for as longas the α-upstream emissions from the glass container sectorto the food sector, eE1α , are considered).
Invariance of Uk to the disaggregation of supplyand demand chains
Consider an S-industry supply chain. Each industry i, withi=1,…, S−1 can only have flows from value added, t0iN0, and
output flows to the next industry in the chain, ti,i+1iN0. Thefinal sector of the chain has a flow from added value, t0SN0,and to final expenditure, tS0N0. Each industry i, with i=1,…, Scan have direct emissions, eiL≥0.
From Eq. (3), the environmental responsibility of consump-tion in a supply chain is US
C=eS0U.Given the supply-chain formulation, each industry has
only a single output and therefore, total transfer of indirecteffects Eq. (1) implies:
eU1 ¼ eU1;2 ¼ eL1
eUi ¼ eUi;iþ1 ¼ eLi þ eUi�1;i; if i ¼ 2; N ; S� 1;
and
eUS ¼ eUS0 ¼ eLS þ eUS�1;S:
Summing up recursively, the upstream emissions of finaldemand are the sum of all direct emissions, irrespective ofwhere those emissions took place:
eUS0 ¼XSi¼1
eLi :
546 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 5 3 3 – 5 4 6
A demand chain is an S-industry chain in which eachindustry i, with i=2,…, S can only have flows to finalexpenditure, ti0N0, and input flows from the previous industryin the chain, ti−1,iN0. The primary sector of the chain has aflow from added value, t01N0, and to final expenditure, t10N0.No other transaction is allowed in a demand chain. Eachindustry i, with i=1,…, S can have direct emissions, eiL≥0.
From Eq. (4), the environmental responsibility of produc-tion in a demand chain is U1
P=e01D .Given that each industry has a single inputs, the down-
stream analogue of Eq. (1) implies:
eDS ¼ eDS�1;S ¼ eLS
eDi ¼ eDi�1;i ¼ eLi þ eDi;iþ1 if i ¼ 2; N ; S� 1;
and
eD1 ¼ eD01 ¼ eL1 þ eD1;2:
Summing up recursively, the downstream emissions ofadded value are the sum of all direct emissions, irrespective ofwhere those emissions took place:
eD01 ¼XSi¼1
eLi :
Summarising, in a supply chain the upstream emissions offinal demand are invariant to aggregation, while downstreamemissions of added value are not invariant. In a demand chainthe downstream emissions of added value are invariant toaggregationwhile upstreamemissions of final demand are notinvariant.
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