Shared Producer and Consumer Responsibility

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METHODS

Shared producer and consumer responsibility Theoryand practice

Manfred Lenzen a, , Joy Murray a,1 , Fabian Sack b , Thomas Wiedmann c aISA, School of Physics A28, The University of Sydney NSW 2006, AustraliabSydney Water Corporation, 115 123 Bathurst St, Sydney NSW 2000, AustraliacStockholm Environment Institute - York, University of York, Heslington, York, YO10 5DD, UK

A R T I C L E I N F O A B S T R A C T

Article history:Received 7 March 2006Received in revised form15 May 2006Accepted 26 May 2006

Over the past decade, an increasing number of authors have been examining the nexus of producer versus consumer responsibility, often dealing with the question of how to assignresponsibility for internationally traded greenhouse gas emissions. Recently, a similar problem has appeared in drafting the standards for the Ecological Footprint: While themethod traditionally assumes a full life-cycle perspective with full consumer responsibility,a large numberof producers(businessesand industry sectors) have started to calculatetheir own footprints (see www.isa.org.usyd.edu.au ). Adding any producer's footprint to other producers' footprints, or to population footprints, which all already cover the full upstream

supply chain of their operating inputs, leads to double-counting: The sum of footprints of producers and consumers is larger than the total national footprint. The committee incharge of the Footprint standardisation process was hence faced with the decades-old non-additivity problem, posing the following dilemma for the accounting of footprints, or anyother production factor: if one disallows double-counting, but wishes to be able to accountfor producers and consumers, then one cannot impose the requirement of full life-cyclecoverage;the supplychains of actorshave to be curtailedsomehow in order to avoid double-counting. This work demonstrates and discusses a non-arbitrary method of consistentlydelineating these supply chains, into mutually exclusive and collectively exhaustiveportions of responsibility to be shared by all actors in an economy.

2006 Elsevier B.V. All rights reserved.

Keywords:Producer responsibility

Consumer responsibilityShared responsibilitySupply chainsEcological footprint

1. Introduction: a brief history of producer andconsumer responsibility

It is perhaps because of the tendency of economic policy inmarket-driven economies not to interfere with consumers'preferences that the producer-centric representation is thedominant form of viewing the environmental impacts of

industrial production: In statistics on energy, emissions, water etc., impacts are almost always presented as attributes of industries ( on-site or direct allocation) rather than asattributes of the supply chains of products for consumers. Ona smaller scale, most existing schemes for corporate sustain-ability reporting include only impacts that arise out of opera-tions controlledbythereportingcompany, andnot supplychain

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Corresponding author. Tel.: +61 2 9351 5985; fax: +61 2 9351 7725.E-mail addresses: [email protected] (M. Lenzen), [email protected] ( J. Murray), [email protected]

(F. Sack), [email protected] (T. Wiedmann).URL: http://www.isa.org.usyd.edu.au (M. Lenzen).

1 Tel.: +61 2 9351 2627; fax: +61 2 9351 7725.

0921-8009/$ - see front matter 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolecon.2006.05.018

a v a i l a b l e a t w w w. s c i e n c e d i r e c t . c o m

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to demonstrate that there exists a ubiquitous need for aconsistent and robust, quantitative concept of producer and consumer responsibility (Section 2);

to explain the shortcomings of existing accounting meth-ods, using an example of a simple supply chain involving producers and consumers (Sections 3.1 and 3.2);

to explain in plain terms the concept of shared responsi-bility as a solution to assigning responsibility to bothproducers and consumers, in a mutually exclusive andcollectively exhaustive way (Section 3.3);

to derive an allocation principle for responsibility sharing across single supply chains that is independent of thedelineation (classification, aggregation and boundaries) of supply chain participants (company branches, corpora-tions, industry sectors etc.; Section 4);

to discuss the implications of this allocation principle for shared responsibility (Section 5.1); and

to document experiences from applying the shared re-sponsibility principle to Australian organisations, andoutline challenges ahead (Section 5.2).

2. Conceptualising producer and consumer responsibility attempts and problems

2.1. Previous attempts to quantify producer and consumer responsibility

An early attempt to develop an impact measure that dealswithproducers and consumers in a supply chain formulationis Szyrmer (1992); based on the total flow concept by Jeong (1982, 1984). Szyrmer's motivation for developing total flowarose out of the inabilityof Leontief's classical final-demand-driven inter-industry model to account for total industrialoutput, but only for the fraction of output that is deliveredinto final demand. Taking this approach, the responsibilityfor downstream impacts of some mining industries is negli-gible, since most ores enter other industries rather thanbeing absorbed by final consumers, and all environmentalconsequences of mining would be passed on to metal worksand downstream manufacturers and their customers (com-pare Milana, 1985, p. 284). Thus, Szyrmer sought to formulatea measure that would account for transactions amongstproducers as well as between producers and consumers, inother words for intermediate as well as for final demand.Szyrmer thought the total flow concept to be particularlyapplicable to firms, existing or new, and for identifying keysectors .

Szyrmer (1992, p. 928) correctly points out an importantdisadvantage of the total flow concept, which is also at theheart of the argument pursued in this article: A computa-tional consequence of the non-causal nature of the total flowmodel is its non-additivity feature. As is well known, in thestandard Leontief model, each unit of final demand has itsown support network , that is, its own direct and indirectinputs that are perfectly separable from other inputs requiredby other final demand units. Thus, the whole productionsystem becomes a collection of mutually exclusive andcollectively exhaustive production inputs required by a givenfinal demand mix. In the total flow model the mutual

exclusiveness of inputs is not present. The same quantity of input i may be required at the same time by gross output of two(or more) different sectors, say j and k independently. Thisnon-additivity property results in a number of computational(and conceptual) inconveniences. The total flow coefficientmatrix cannot be expressed as the sum of an infinite power series. When using a total flow model for impact analysis, weshould consider, in principle, only one sector at a time.

Non-additivity was already recognised as a problem for determining indirect requirements for gross output by Milana(1985). Based on Miyazawa (1966) formalism for partitionedinput output matrices, Milana and later Heimler (1991) con-structedmultipliers forthe grossoutput of an industrysector or acompanybyseparatingthatsectororcompanyfromtherestof the economy. Milana(1985)(p.289), writes that thesum of totaloutput and primary input requirements for gross output [ ]leads to a double-counting procedure because some indirectrequirementsof oneindustryareindirectrequirementsof other industries which use part of that output of that industry as anintermediate input . Similarly, Heimler (1991) (p. 263) acknowl-edges that gross output of different industries cannot besummed because of double-counting of intermediateconsumption .6

Ferng (2003) production-benefit principle involves double-counting for similar reasons. Even her shared-responsibilityformulation A+(1 )B, where A and B are allocations of responsibility according to the consumer- and producer-benefit principles and 0<


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Recently, Rodrigues et al. (inpress) have definedan indicator of environmental responsibility that accounts for transactionsbetween countries in a fair manner. Based on normativeconsiderations, they derive environmental responsibility as ameasure that takes indirect effects into account, followseconomic causality, is additive across actors and normalisedto the world total, is monotonic on direct environmentalpressure and is symmetric with regard to consumption andproduction behaviour. 8

The last property symmetry requires further attention.First, Rodrigues et al. (in press) (p.4) state that eacheconomic agent is simultaneously both a consumer and aproducer . In a closed economy the total of full producer andof full consumer responsibility is indeed the same andtherefore symmetrical. However, this cannot be said for asingle business or industry, because these entities may useprimary inputs while not supplying final consumers at all, butonly intermediate consumers (i.e. other firms). Similarly, sub-national sets of final consumers (people) may not be part of the labour force, and therefore not generate primary inputs.Hence, in this sub-national perspective, there may be actorswho are only producers, and actors who are only consumers.The problem becomes asymmetrical.

Second, it is only by enforcing symmetry as a requiredproperty that the proposed indicator of environmental re-sponsibility becomes unique. Rodrigues et al. (in press) statethat if one does not consider symmetry, then manypossibilities arise regarding how to weigh the environmentalpressure from consumption and from production. Whilsttrue, this is not a sufficient justification for requesting thatsymmetry be essential property.

Third, Rodrigues, Domingos, Giljum, and Schneider (inpress) already make one qualification of their argument for imposing symmetry in conceding that (p.6) there aresituations of asymmetry in which a country is more con-strained in the choice of its production activities than on itsconsumer choices . We bring their view into question byassertingthat asymmetry in economic transactions is not theexception, but rather the rule, especially in a sub-nationalperspective: Actors belonging to different industry sectorshave a very different (and limited) choice of choosing operating inputs and output destinations (see Cerin andKarlson, 2002). Hence, the relations between the actors [in asupply chain] may be characterised by considerable asym-metries in information and power (Cerin, 2006b, p. 217).

In Appendix 3 we show that the concept for an indicator of sharedresponsibility that we propose in this paper satisfiesallfive properties suggested by Rodrigues et al. (in press) exceptfor the condition of symmetry which we don't accept. Neither is symmetry a requirement for a unique solution, as we showin Section 4.2.

2.2. A recent example: the standardisation process of theecological footprint

The debate described in the previous two sections providesample evidence for both the practical importance and thechallenges of a robust attribution method that includes bothproducers and consumers. Perhaps the most recent examplefor this ongoing problem is the discussion surrounding theecological footprint standards. 9

In 2004, three committees were set up by the GlobalFootprint Network 10 , with the task of drafting a set of standards for ecological footprint practitioners, dealing withNational Footprint Accounts, application standards, andcommunication standards. 11 While the method traditionallyassumes a full life-cycle perspective with full consumer responsibility, a large number of producers (businesses andindustry sectors) have started to calculatetheir ownecologicalfootprints. As a result, various parts of the applicationstandards draft reflect the following requirements:

A: producers (businesses, industrysectors)canbe assessed, inaddition to consumers (populations in cities, regions, nationsetc.);

B: there shouldbe no double-countingof ecological footprintsofsub-nationalentities;theecological footprintsummedover cities, regions, companies and industries of a nation mustmatch the national ecological footprint as listed in the GlobalFootprint Network's National Footprint Accounts;

C: ecologicalfootprintsshould encompass thefull life-cycleof products. 12

In the following section we argue that: 1) strictly speaking,only two of the three requirements can be fulfilled at any onetime; 2) this dilemma is identical to the problems previousauthors had in conceptualisingproducer responsibility (Section2); and 3) shared responsibility provides a way of meeting mostof all three requirements. In the following sections, we use theexample of theEcological Footprint,andwelookupstream from

8 Mathematically, this turns out to be the arithmetic averagebetween the environmental pressure generated to produce thefinal demand and the primary inputs of an agent. Thus, theenvironmental responsibility of any country is a linear combina-tion of the upstream environmental pressure of the final demandof that country and of the downstream environmental pressure of the primary inputs of that same country. In a practical applicationRodrigues and colleagues apply this indicator to the trade of materials between countries ( Rodrigues et al., 2004; see alsoRodrigues and Giljum, 2004, 2005). In order to distribute totalmaterial responsibilities between both consumers and producers,they introduce Total Material Production (TMP) as a mirror indicator to Total Material Consumption and define a fair indicator of total material requirements (TMF) as the arithmeticaverage of TMC and TMP.

9 For further information on ecological footprints, and itsconnection with input output analysis, see Lenzen and Murray(2003), http://www.isa.org.usyd.edu.au/publications/documents/Ecological_Footprint_Issues_and_Trends.pdf .10 www.footprintnetwork.org .11 www.footprintstandards.org .12 Some of the critique of the draft standards was aimed at thelife-cycle reporting requirement for companies. Life-cycle ac-counting, it was pointed out, was too complex and too compli-cated: For business to embrace the ecological footprint it had to beeasy, affordable and practical, and it had to adhere to the sameboundary as the financial annual report, i.e. the companypremise. While this is also a topical discussion within the GlobalReporting Initiative and elsewhere (see Dey et al., 2002), this workuses the three requirements above as a given starting point.

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final consumption. However, the same principles hold for quantities other than the Ecological Footprint, and for down-stream impacts. 13

3. Life-cycle accounting and sharedresponsibility

3.1. The problem of double-counting

In the same way as traditional Life-Cycle Assessment (LCA),the Ecological Footprint adds up all upstream impacts embod-ied in consumer goods. In the example supply chain (food in aglass jar) in Fig. 1, this is the footprint caused by the foodmanufacturer, plus the footprint caused by the manufacturer of the glass containers that the food manufacturer buys, plusthe footprint caused for making the glass for the containers,plus the footprint caused by mining sand to make glass, etc.

Assume for the sake of illustration that the participants of this supply chain do not supply anyone other than their successor. Imagine that the producers of food and containers,plus the glass maker and the sand mining company all usetraditional LCA to calculate and publicise their ecologicalfootprint. The footprint caused by the food manufacturer supplying the consumer with food would appear in thepopulation's ecological footprint, plus they would appear inthefoodmanufacturer's ecological footprint. It is hence double-counted.

The footprint caused by mining sand appears in the ecolo-gical footprint of the sand mining company (as an on-siteimpact), in that of the glass maker, the container producer,the food company, and the final consumer (as an upstreamimpact). Hence, it is multiple-counted ( Fig. 1). If everybusiness and consumer in the economy used traditionalLCA to calculate their ecological footprint, the sum would bemuchgreater than the total national ecological footprint. TheNational Footprint Accounts would not balance. This canobviously not be right.

3.2. Consumer or producer responsibility?

LCA is a method that assumes full consumer responsibility : itsperspective of analysis is that of the consumer placed at thevery end of the supply chain. All impacts incurred during production are heaped onto the consumer of products. 14 Thisis because LCA is intended to assess the environmentalimpact of competing technical options to supply products or services. Therefore, if double-counting is to be avoided, LCAcan only be used for the final consumers in an economy: theimpacts of any producer must be zero. This is also theperspective taken by traditional Footprint estimates such asthe National Footprint Accounts (NFA). After looking at thetotal impact of production, imports and exports, the NFAcalculations result in one figure, the Footprint of the finalconsumer of a nation in (global) hectares per capita. This is afull consumer responsibility account.

Other approaches assume full producer responsibility . For example, every country has to report their greenhouse gasemissions to the Intergovernmental Panel for Climate Change(IPCC). Some countries like Australia emit a lot during theproduction of goods that are exported. However the IPCC asksthat these emissions appear in Australia's report, not in thereport of the country that imports and consumes these goods.The literature contains some interesting debates about whichapproach is best.

Full consumer and producer responsibility are consistentwith the principles of National Footprint Accounting in thesense that they do not lead to double-counting ( Fig. 2).

Returning to the requirements for ecological footprintstandards, the LCA approach ( Fig. 1) fulfils conditions A(producer assessment) and C (full life-cycle), but fails B (double-counting). Full producer responsibility ( Fig. 2) fulfils A and B, butfails C. Full consumer responsibility ( Fig. 2) fulfils B and C, butfails A. Hence,neither approachsatisfiesall three requirements.

A particular disadvantage of full producer or consumer responsibility is that neither allows for both producers andconsumers to evaluate their ecological footprints withoutdouble-counting. Full producer and consumer responsibility

Fig. 1 Multiple-counting of ecological footprints, for one particular supply chain.

14 What we mean here with consumer is not necessarily thefinal consumer, but any consumer of products. If that consumer isa producing entity, then LCA adds the impacts of upstreamsupply chains originating from that producer.

13 An example for downstream impacts are health effects fromconsuming tobacco or alcohol, end-use of products such as spraycans, or combustion of fuels in cars and home appliances. The

shared apportioning of downstream impacts is described in detailin Gallego and Lenzen (2005).

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therefore appears somewhat unrealistic in their extremeness.Both producers and consumers wish to report their ecologicalfootprint,and it is intuitively clear thatresponsibilityis somehow

shared between the supplier and the recipient of a commodity,because the supplier has caused the impacts directly, but therecipient has demanded that the supplier do so.

When thinking about environmental impacts of producersand consumers, crucial questions arise such as: who isresponsible forwhat, or: howis the responsibility to be shared,if at all? For example: Should a firm have to improve the eco-friendliness of its products, or is it up to the consumer to buyor not to buy? And further: should the firm be held responsiblefor only the downstream consequences of the use of itsproducts, or through its procurement decisions also for theimplications of its inputs from upstream suppliers? And if so,how far should the downstream and upstream spheres of

responsibility extend? Similar questions can be phrased for the problem of deciding who takes the credits for successfulabatement measures that involved producers and consumers:Who has the best knowledge of, or the most influence over how to reduce adverse impacts associated with the transfer of a product from producer to consumer?

3.3. Shared responsibility

As with many other allocative problems, an acceptable consen-sus probably lies somewhere between producer and consumer responsibility. In order to assign responsibility to actors partic-ipating in these transactions, one has to know the respectivesupply chains or inter-industry relations. Hence, a problemposes itself in form of the question: How can one devise anaccounting method that allows apportioning ecological foot-prints (or any other quantity) to both producers and consumerswhile avoiding double-counting? This problem has beenaddressed in a recent publication by Gallego and Lenzen (2005).

The result is that in reality, both the final consumers andtheir upstream suppliers play some role in causing ecologicalfootprints: The suppliers use land and energy in order toproduce, andmake decisionson howmuch land andenergy touse, while consumers decide to spend their money onupstream suppliers' products. And this role-sharing probablyholds for many more situations in business and in life. Theconcept of shared responsibility recognises that there arealways two (groups of) people who play a role in commodities

produced and impacts caused, and two perspectives involvedin every transaction: the supplier's and the recipient's. Hence,responsibility for impacts can be shared between them. Naturally,

this applies to both burdens and benefits.Theidea of sharedresponsibility is not new. However shared

responsibility has only recently been consistently and quanti-tatively conceptualised by Gallego and Lenzen (2005). Sharing impacts between each pair of subsequentsupply chain stages for example on a 50%50% basis between the supplier and therecipient gets rid of the double-counting problem ( Fig. 3).

Adding up all ecological footprints in Fig. 3 above gives8.8ha, which is requiredforaccountingconsistency. Returning once again to the ecological footprint standards requirements,shared responsibility fulfils A (producer assessment) and B(double-counting). With respect to C (full life-cycle), all stagesof the supply chain are present in the ecological footprint

allocatedto both producersand consumers, albeiteachstageissharedat varyingdegreeswithothersupplychainparticipants.

4. Invariance properties of sharedresponsibility

4.1. Mathematical formulation of shared responsibility

A mathematical formulation of shared responsibility asillustrated in Fig. 3 has been developed by Gallego and Lenzen(2005). Its centerpiece is a modification of the traditionalinput output identity

x L y with L IA 1 I T x 1 1 1

to

L I f A 1and y f y

|ffl{zffl} consumers 1 f y 1 f T 1

|fflfflfflfflfflfflfflfflproducers; 2

where I is the identity matrix, A the matrix of input outputcoefficients, T holds intermediate inter-industry transactions,and where the Leontief inverse L links final demand y withgross output x=T1 + y (diagonalised to x

). In the modifiedformulation in Eq. (2), the tensors and represent

Fig. 2 Full producer and consumer responsibility in ecological footprints, for one particular supply chain. The sum of allecological footprints reported on is 8.8 ha.


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responsibility shares amongst industries, and between indus-tries and consumers, respectively. The symbol # meanselement-wise multiplication. Essentially, of any impact that aproducer i receives from upstream, or causes on site, thisproducer i passes on a fraction ij to other producers j, and afraction i to consumers. The same producer i retains theresponsibility for fractions 1 ij and 1 i. Hence, the para-meters (the producer responsibility share ) and (the consumerresponsibility share ) are numbers between 0 and 1.

While Eqs. (1) and (2) are expressed in purely monetaryterms, they can be generalised to represent a system of inputs and outputs for physical factors, for exampleecological footprints. Let f =FFx 1 be a vector of ecologicalfootprints Fi of industry sectors i per gross output x i. Then, f t L( )is a vector of total ecological footprint intensities of commodities bought by final consumers, including respon-sibility shares in all supply chain links. The ecologicalfootprint (scalar) of a final consumer with a commoditybundle y is then f t L( )( # y), while direct and upstreamproducers of the same commodity bundle retain anecological footprint f t L( )((1 )# y +[(1 )#T]1). The totalecological footprint F is f t L( ) y( ).

At the limit ij = i =0 i, j, where L( )=I and y( )=x, we recover the full producer responsibility formulation F= f t x. At the other

extreme where ij = i=1 i, j, we have L( )=L and y( )= y, andrecover the full consumer responsibility formulation F= f t L y.The shared responsibility thus provides a seamless transitionbetween full producer and full consumer responsibility, whilesumming up to the correct total ( F) for any setting of the res-ponsibility shares ij and i.

One question that remained unresolved in the expositionby Gallego and Lenzen (2005) was what value the responsibil-ity shares ij and i should assume. In this work we provide aunique solution to this problem, which we derive by imposing a number of invariance conditions.

4.2. Invariance with respect to disaggregating the supplychain

Consider the responsibility scheme in Fig. 4, which is equalto that in Fig. 3, except that the food manufacturer does notsell directly to final consumers, but through an agent (for example a retailer, or a food outlet). Assume that the agentdoes not transform the food manufacturer's output, butsimply on-sells the product that could equally be distrib-uted by the manufacturer. For the sake of simplicity alsoassume that the agent causes negligible on-site ecologicalfootprint.

Fig. 3 Shared producer and consumer responsibility in ecological footprint reports, for one particular supply chain.

Fig. 4 Shared producer and consumer responsibility in ecological footprint reports, for one particular disaggregated supplychain.


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While this disaggregation changes nothing in terms of realcommodity flows, the final consumer is allof a suddenassigned0.35 ha of ecological footprint, instead of 0.7 ha as in Fig. 3. This

dependence of responsibility allocations on the vertical inte-gration of sectors is inconsistent and undesirable, because itcreates incentives for de-merging in reporting practice.

In Figs. 3 and 4, suppliers and recipients shared ecologicalfootprints on a 50% 50% basis. It is this fixed ratio that actuallyleads to the inconsistency: by arbitrarily breaking up supplychains into moredisaggregatedcomponents,the impact ateachstage gets halved, so that in a more extensive representation(Fig. 4), the final impact is necessarily smaller than in a shorter representation ( Fig. 3).

A solution to this problem is to peg the percentage split of responsibilityretained bythesupplier (1 )toaquantitythatisindependent of sector classification. Value added is such a

quantity: No matter whether a supply chain is represented asmany or few stages, total valueadded is always thesame at theend of the chain. In this work we propose to use

1 a ij 1 b i vixi T ii

; 3

where vi is value added of industry sector i, and xi T ii is grossoutput minus intra-industry transactions, in other words netoutput. Intra-industry transactions T ii have to be understood as

transactions between different branches of the same industrysector. Note that both and are now only a function of thesupplying industry i,sothatin Fig.5andfollowingthevariable

will not be used anymore.In the left part of Fig. 5, ecological footprint (EF) and financial

characteristics of the supply chain participants are added for illustration. Assumethe sand mine supplies1.6$m worth ofsandto theglassmaker, to which thelatter adds 1.6$mof value(VA)toproduce 3.2$m worth of glass net output (NO). To this, the glasscontainer manufacturer adds 4.8$m of value, producing 8$mworthofglass containers. To this, thefood manufacturer adds 14$m of value, producing 24$m worth of food.

Thesandminewill add 50% of value to sandstone by turning it into sand. Its owners will hence retain 50% of their ecologicalfootprint (4 ha) and send the remaining 50% (4 ha) down thesupply chain to the glass manufacturer. The glass maker will

add50%ofvaluetosandbyturningitintoglass.Theglassmaker is hence assigned 50% of 4 ha of ecological footprint passeddown from sand, plus 50% of 0.4 ha used while manufacturing glass. Theremainder is passed on to glass containers. Theglasscontainer manufacturer will add 60% of value to glass, and isassigned 60% of land embodied in glass containers, and so on.Finally, the food manufacturer adds 64% of value to glasscontainers,and isassigned 64%of ecologicalfootprintembodiedin packed food. Final consumers (households, the government)

Fig. 5 Shared, value-added-allocated producer and consumer responsibility in ecological footprint reports, for one particular supply chain. NO= net output, VA =value added.

Fig. 6 Shared, value-added-allocated producer and consumer responsibility in ecological footprint reports, for one particular disaggregated supply chain.


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are at the end of the supply chain, and receive the remaining remainder (0.42 ha).

The logic of this allocation scheme (as opposed to a 50% 50% split) is that an organisation that controls its productionto a high extent, retains a high share of the responsibility for the ecological footprint. High control, or influence over theproduct can be approximated by high value added: Produc-tion processes that add a high percentage of value ontoinputs usually transform these to a high extent, while low-value adding entities operate more like an agent of their inputs.

In contrast to the fixed 50% responsibility sharing depicted inFig.4, addingan agent to thefood manufacturerdoes notchangethe allocation of shared responsibility. The final consumer isassigned 0.42 ha, irrespective of the number of actors, or generally, the disaggregation of sectors involved in the produc-tion process ( Fig. 6).

4.3. Invariance with respect to aggregating the supplychain

Every supply chain consists of trading entities, such ascompanies. In statistical databases, or economic models,these entities are classified into industry sectors. Generally,industry sector classifications vary from year to year, betweencountries, and across applications. In particular, some classi-fications are more aggregated than others.

Leontief-type input output calculations are generally notinvariant with respect to industry sector aggregation. This isbecause the aggregate sector is assumed to produce onehomogeneous product. This product of the aggregate sector however is generally different to the products of the disag-gregated sectors it comprises. Assuming that the disaggre-gated sectors generally all have a different input and outputstructure, aggregation leads to mis-representation of com-modity flows.

As in the standard Leontief system, the dependence of shared responsibility allocations on the sector classificationand aggregation is inconsistent and undesirable, because

it leads to results for one and the same economy being dependent on the model resolution;

economies with different sector classifications not being comparable.

There are however situations in which aggregation does notchange commodity flows: In the special case of an exclusivelinear supply chain, the standard Leontief formulation is in-variant with respect to industry sector aggregation. For theshared responsibility formulation we ask that it is invariant toaggregation at least in this case where the standard Leontief formulation is invariant. If the responsibility shares are set as inEq. (3), the shared responsibility formulation acquires the sameinvariance propertyas the standard Leontiefformulation. This isproven in Appendix 1.

4.4. Invariance with respect to gross or net accounting

Input output accounting distinguishes between gross and nettransactions tables. Net tables differ from gross tables simply

in the fact that net tables have all diagonal elements (intra-industry transactions) set to zero. A number of authors havecriticised the practice of gross accounting based on thestandard assumption in input output modelling of sectoroutput homogeneity . The argument is that if an industry sector produces only one commodity, then there is no reason whyestablishments in the same sector should trade any of their own output, since they are producing that commoditythemselves. Moreover, there is no unambiguous delineationof intra-industry transactions: They could theoretically cover inter-company, inter-branch, or even intra-branch transac-tions. Depending on their delineation, intra-industry transac-tions, and thus gross output, could assume any arbitrarymagnitude. 15

Fortunately, Weber (1998) has shown that multipliers of the form x 1L, based on the traditional input output rela-tionship (Eq. (1)), are invariant with respect to net or grossrepresentation. This invariance is a useful property, andshould also hold for the shared responsibility formulation inEq. (2). In Appendix 2 we show that this invariance holds if ii =1 i. Thus, Eq. (3) and ii =1 i fully defines the tensor inEq. (2).

5. Discussion: shared responsibility theoryand practice

5.1. Some implications of shared responsibility

The main differences between the principle of shared respon-sibility, and that of either full producer or full consumer responsibility are:

15 In his Entropy Law and the Economic Process, Georgescu-Roegen(1971) (pp. 253262) elaborates on what he calls internal flows inLeontief s input output table ( Leontief, 1941, pp. 1518), and posesthe burning question of what place we should assign to thediagonal of an input output table . He provides an illustration of the issue for the example of consolidating two sectors of a flowmatrix, with the respective processes being aggregated into oneindustry or the products into one commodity group: Even if thediagonal elements of the initial flow matrix were zero, those of the consolidated matrix are in general positive. Georgescu-Roegen argues that after consolidation these diagonal elementsmust be suppressed, and the total output netted out, becausefrom an analytical point of view, flows are associated withcrossing a boundary. Since after consolidation these boundarieshave disappeared, the now internal flows must be eliminated aswell. On the other hand, Leontief (1941), in spite of having advocated zero diagonal elements, presents fully populated flowmatrices. Many other authors support the practice of gross flowmatrices with the understanding that diagonal elements repre-sent output that is used by the producing industry itself (such ascoal for powering coal mining machinery). For example, Isard(1951) includes intra-regional flows in his multi-regional input output framework, which contravenes Georgescu-Roegen s posi-tion that only trade between regions should feature. Dorfman,Samuelson, and Solow (1958) (p. 205) add: we find it convenientto include the possibility that the industry does require some of its own product as necessary input in its production process. Theimportance of this is that in a dynamic model in whichproduction takes times, the stocks of coal to be used in coalmining must be available before any new coal can be produced .


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in contrast to full producer responsibility, in sharedresponsibility,every memberof thesupplychainis affectedby their upstream supplier and affects their downstreamrecipient, hence it is in all actors' interest to enter into adialogue about what to do to improve supply chainperformance. There is no incentive for such a dialogue infull producer responsibility. In shared responsibility, pro-ducers are not alone in addressing the impact (ecologicalfootprint) issue, because their downstream customers playa role too.

in contrast to full consumer responsibility, shared respon-sibility provides an incentive for producers and consumersto enter into a dialogue about what to do to improve theprofile of consumer products.

The latter point is acknowledged for example by Bastianoniet al. (2004) (p. 255) who write that assuming a consumer responsibility viewpoint, producers are not directly motivatedto reduce emissions, while consumers, instead, should intheory assume responsibility for choosing the best strategiesand policy by showing a preference for producers who areattentive to GHG reductions. However, without adequateincentives or policies, consumers are not likely to be sensitivewith respect to their environmental responsibilities [ ].

An interesting aspect of the value-added pegging of sharedresponsibility is that it facilitates a trade-off between the rolesof people as workers and as consumers. Assume a producer of a labour-intensive consumer good, retaining a considerablepart of responsibility because of a high proportion of wagesand salaries for workers. If this producer mechanised produc-tion and laid off staff, much of this responsibility would bepassed on to final consumers. 16

Another interesting feature arising out of applying theshared responsibility principle is that the upstream responsi-bility for a given impact decreases with increasing distancebetween actors in the supply chain. In Fig. 5: the finalconsumer's demand of food entails an ecological footprint atthe sand mine. The sand mine is five transactions away fromthe final consumer, and hence its ripple impact is hardlynoticeable (0.42 ha out of an initial 8 ha). However, the sandmine is only two transactions away from the glass container manufacturer, andhence therippleimpact is higherat 1.44 ha.Finally the sand mine operator has the highest control andinfluence over how much land is used in mining and isassigned 4 ha. Diminishing influence is an interesting featuresince it seems logical to assume that the further a receiving sector is located from the producer of the impact, the lesscontrol it has over that impact.

Generally put, different (groups of ) economic agentsoccupy overlapping spheres of social, economic and politicalinfluence [ ], a quantification of [these] influences [ ] wouldbe a precondition for an allocation of environmental respon-sibilities to specific actors (Spangenberg and Lorek, 2002 , p.128). Accordingly, choices of responsibility shares shouldideally reflect suppliers' and recipients' financial control,innovation potential and business relations, as well as their influence over production processes and their options to

substitute suppliers or buyers. 17 Valueaddedindicates wheth-er or not a producer has transformed operating inputs in anysignificant way, and is therefore a good proxy for control andinfluence over production. A logical step onwards fromasserting responsibility is to implement actual legal obliga-tions, or property rights.

5.2. Shared responsibility and property rights

Steenge (2004) (p. 48) has created an interesting link betweenthe concept of shared responsibility, and the Coase Theorem(based on Coase, 1960). Using Leontief's abatement model(Leontief and Ford, 1970 ), Steenge quantitatively confirms thatoverall allocation of resources will be efficient independent of allocation of property rights, given no income effects and zerotransactioncost. Nevertheless, Steenge acknowledges that thenature of shared responsibility, or reciprocity in Coase'sterminology, depends on the allocation of property rights:Indeed, the Coasean prescription of allocating property rightshas consequences at the individual level which often areviewed as unfair and unjustified. However, Steenge alsopoints out that traditionally, Coase's point was only exempli-fied for a few actors at any one time. In reality, there will be amultitude of actors that are interconnected in the sense thatthey use each other's outputs, either directly or indirectly. Insuch a context, the idea of offenders and victims seems less justified. The reason is not difficult to see: A smoke emitting factory produces this smoke precisely to satisfy demand fromanother sector which itself may be quite clean. So who wouldbe considered as being responsible for the smoke? In a sense,it rather is the entire economy (because of the existing interconnections) that should be held responsible. But thatmeans that each sector in an indecomposable economicsystem can be given (part of) the blame. This also meansthat, in this context, a distinction on moral grounds betweenpolluting and non-polluting sectors makes less sense. In factwe might say that interconnectedness makes every oneresponsible (Steenge, 2004, p. 73; see also Steenge, 1997).

According to Steenge (p. 48), Coase proposed that, basically,public authorities should confine themselves to establishing and maintaining a system of property rights , rather than asystem of corrective taxes and subsidies ( Pigou, 1920). In thisrespect, Steenge suggests that (p. 73) the blame thereforeshould not be put arbitrarily at those points where, as aconsequenceof activitiesof entireproductionchains,emissionshappen to occur. The [input output] model expresses this bytelling us that changes in the production process of any sector

16 This point was made by an anonymous reviewer.

17 The Global Reporting Initiative (2005) (p. 2; see also GlobalReporting Initiative (2002), p. 26) states that the organisation'sdegree of control or influence over the entities involved in theseactivities and their resulting impacts ranges from little to full.While financial control is a common boundary for disclosure, therisks to the organisation's assets and the broader community andopportunities for improvement are not limited to financialcontrol boundaries. Therefore reporting only on entities withinthe boundary used for financial reporting may fail to tell abalanced and reasonable story of the organisation's sustainabilityperformance and may fall short of the accountability expecta-tions of users. This is one of the key messages underlying thelogic of this protocol .


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can be passed on straightforwardly to thenextsectors, which intheir turn can pass it on to further ones, and so on .

Taking Steenge's argument further, Cerin and Karlson(2002) and Cerin (2006b) suggest actively re-arranging corpo-rate legal ownership of production processes, or propertyrights, in order to provide incentives for extended producer responsibility for environmental impacts. They argue thateven if major environmental impacts occur outside producers'legal boundary, they often possess the control over, and thebest competence to reduce those impacts, but they are neither obliged nor stimulated to abate because they do not ownproperty rights over upstream and downstream stages of theproducts' life-cycle (stewardship). In this case, if other actors(for example consumers) wanted to abate they would firsthave to acquire the necessary information, thus incurring transaction costs that could be avoided if the actor with thebest abatement competence (the producer) was given theproperty rights over the respective part of the product life-cycle.18 In this respect, Cerin (2006a) again uses the Coasetheorem to explain the necessity of giving the rights toresources to those who can use them most productively inorder to keep transaction costs down and to increase overallefficiency. This control-based delimitation of productionownership would also correspond directly to control over financial risk, for example from new environmental policies,or resource price increases (cf. Cerin, 2002, p. 59).

The shared responsibility approach advocated in this workembraces both Steenge's and Cerin and Karlson's views. Infact, using value added as a proxy for allocating responsibilityfor environmental impact across production chains, we createa rigorous and justifiable methodology, which can inform anefficient spread of property rights to establish extendedconsumer and producer stewardship. By ensuring that own-ership of impacts is equivalent to the responsibility share, weensure that those producers or consumers with the mostdirect influence have a clear economic interest in reducing environmental impact.

5.3. Applying shared responsibility: experience from reporting practice

During the course of developing this approach the authorshave road-tested the idea of aligning responsibility shares andvalue added with a wide range of organisations. Some of thesewerepart of a two-year action research project to examine the

sustainability reporting support needs of business, industry,government and non-government organisations. 19 This road-testing has revealed a number of positions: While some werecritical of the approach for a range of practical reasons otherstook an academic interest in examining possible solutions.The general discussion sparked interest in the philosophicaldilemmas inherent in the construct of responsibility and itsapportioning.

Behind several of the arguments was a practical consider-ation of cost in time, money and energy associated withstakeholder education or re-education. For example, somenon-government organisations with an interest in bringing about change through buyer activism had invested heavily incommunity education programs that rely on the end-user taking responsibility for environmental or social problemsassociated with the production of some goods. For example,the 2004 No Dirty Gold20 campaign conducted by Earthworksand Oxfam and aimed at Valentine's Dayjewelry buyers reliedon the passion of activists and their ability to convince buyersof their responsibility for the health and safety of mineworkers. Organisation with a strong consumer focus may bereluctant to embrace a methodology that could, in the sharing of responsibility, diffuses the focus for activism.

Another organisation had, a fewyearsearlier,begunto reporton greenhouse gas emissions, accepting full upstream respon-sibility, andpublicisingabatementplans andtargets.Theyfelt,anew approach that provided a distinct drop in emissions andassignedsomeof the blame tootherswouldbe viewed withtheutmostsuspicion amongexternal stakeholders. It wouldrequirea considerable investment in education to explain this newposition. A related position was voiced by a member of a largeindustry, who felt that the time and effort required to convinceinternalstakeholders, inparticular theBoardof Directors, wouldbe considerable, andunless there was some outside pressure toadopt shared responsibilityas a reporting methodology supportfor such a campaign would not be considered.

Some organisations responded primarily to the academicargument: Producer and consumer footprint should never bemixed, or added up, and the full producer and full consumer responsibility view ( Fig. 2) should just be taken as the samenumber looked at from a different perspective (compare alsoDietzenbacher, 2005 ).

One criticism of the shared responsibility solution was thatfinancial value added reflects both consumer preferences(demand) and resource or service scarcity (supply), and thattherefore it does not serve as a direct causal basis from whichto assign producer responsibility. It was argued that a morepragmatic approach would be to assign responsibility sharesthat ensurebest possible influencein thesenseof best possible financial abil ity to abate adverse impacts. Based on thisrationale, the responsibility share could be pegged to grossoperating surplus as the only discretionary component of value added. However, a disadvantage of the surplus-pegging method is that it does not have the same invariance propertyas the standard Leontief formulation (see Section 4.3).

18 For example, drivers do often not possess the technicalknowledge required to operate a car at minimum fuel consump-tion and emissions. On the other hand it is not the obligation of car manufacturers to maintain the car in optimum working order,once sold. The result is either drivers shouldering transactioncosts (efforts to acquire technical knowledge, workshop bills) inorder to keep fuel consumption low, or cars running atsuboptimal performance. Assuming that drivers do not reallywant a car as such, but mobility, it would be more efficient if car manufacturers sold mobility (kilometres) rather than cars. In sucha scenario, manufacturers would own and hire out car and petrol,rather than sell or even hire out only cars. Since manufacturershave better product knowledge, cars would operate efficiently inorder to keep mobility cost low and the manufacturer competi-tive. Drivers would not worry about which model car to buy, andhow to maintain it.

19 A full report of this project can be found at http://www.isa.org.usyd.edu.au/research/TBLEPA.shtml .20 http://www.wrm.org.uy/bulletin/80/Africa.html and http://www.nodirtygold.org/dirty_metals_report.cfm .


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Another argument cited destructive production methodsthat add very little value, resulting from various forms of market failure or regulatory intervention. The proposedsolution to the allocation problem would fail to assignresponsibility shares as might seem intuitively appropriatein such cases. This view was guided by an intuitive linkbetween impact severity and responsibility. However, in our approach as in Cerin and Karlson (2002), responsibility isassigned according to process knowledge and influence, notimpact : It may therefore be the case that an industry with alarge environmental impact and little value added in itsproduction shares little responsibility. An example would be asector that largely driven by downstream demand simplyextracted, and passed on an intensively impacting low-priceresource. Most of the responsibility would lie with thosedownstream value-adding industries which created the de-mand for extraction.

It was also pointed out that other less tangible types of influenceshouldbe included in a responsibility measure, suchas advertising 21 , or other mechanisms that create and driveconsumer preferences, and hence generate surplus and valueadded.

Despite the above arguments some took the position thatwhat goes into the black box of methodology was of no realconcern to them. They were happy to leave the academicdiscussion to the experts and were willing to trust whatever the resulting consensus. Their need was for an acceptedstandard that produced reliable and comparable results.

5.4. Shared responsibility and value judgment

The points raised during road testing all serve to indicate thatallocating responsibility always involves value judgments.The judgements inherent in the proposed methodology centreon the assumption that activities which increase economicvalue demonstrate a degree of control and that this influenceover process is tantamount to moral responsibility.

Some organisations canvassed during this researchwarned against the use of moral and value judgments, andpreferred reporting what is, and not what should be. Somerecommended the use of non-judgmental terms such asfootprint of activities or impact embodied in commodities rather than naming actors (producers and consumers). It wasalso suggested not to use the term responsibility because itcould be seen as pre-assigning blame, but rather to use lesscontentious phrases such as allocation or attribution withcertain impacts. 22 The motivation behind these comments is

partly the perceived arbitrariness of any delineation of fair shares between different actors, partly negative experiencesor concern of disaffecting certain segments of the population,and partly the assertion that people would draw their ownconclusions when presented with factual information.

Inthis context,wenotethat ifone wantsto beabletocalculate(environmental) impacts for intermediate as well as final supplychain entities at the same time, one must split the life-cycle atsome point, independent of whether one deals with actors, or with activities/commodities. Without such a split there will bedouble-counting. If oneassumes that anysplit will be based on avalue judgment, then this means that if one wants to be able tocalculate consistent (environmental) impacts for intermediateand final entities, one has to make a value judgment.

Value judgement cannot be avoided merely by avoiding allocation and adopting either a full consumer or producer model. Forexample, the ecological footprint chooses toreport inalife-cycle perspective. This choice is in fact based on a value judgment: In life-cycle thinking no matter whether implemen-ted using the Leontief input output framework or another method ecological footprints, or any other production impact,is passed on downstream until it ends at the final consumer andthe end of commodities' life. Hence, life-cycle thinking choosesthe full consumer responsibility paradigm: it chooses to heap allimpact onto final consumers, and to exclude intermediateproducers from responsibility.

We believe that it is impossible to think of a sustainabilityindicatorthat merelyreportsa state ofaffairs without invoking a value judgment. However formulated, any sustainabilityindicator will at least embody the message that the worldshould move towards a sustainable state which in itself isvalue-based, and ultimately debatable. Moreover, in accepting the use of say, the ecological footprint, we are accepting theoutcome of myriad decisions, judgments made about inclu-sions and exclusions, strategies and calculations, all of whichhave come out of a particular view of the world.

At last, how can people understand a statement of theecological footprint of producing cars , or the ecologicalfootprint of the commodity car , other than as a message thatthey bear some responsibility for the act of producing or consuming this car, and the consequences thereof? Activitiesandcommoditiescannotact,onlypeoplecan.Any sustainabilityindicator does inherently, and must, address people in their capacity to accept responsibility, and invite them to actaccordingly in order to bring about changes towards a particular set of goals and values. For this very reason, many companieshave already started to calculate their ecological footprint .They want, and they are expected by shareholders, to takeresponsibility for the production processes that they own andinfluence.

6. Conclusions

Over the past decade, an increasing number of authors haveexamined the nexus of producer versus consumer responsibil-ity, often dealing with the question of how to assign responsi-bility for internationally traded greenhouse gas emissions.Recently, a problem has appeared in drafting the standards for theecological footprint:Whilethe method traditionally assumes

21 A reviewer of this work actually pointed out that part of theeffect of advertising is captured in the value added of Fig. 6's foodagent , because effective advertising.increases the agent's mark-up and operating surplus.22 Note that using footprint embodied in commodities withoutfurther qualification can lead to ambiguity: Embodiments areusually calculated for final consumer goods and services. Hence,within full consumer responsibility, the footprint embodied in100$ worth of paper relates only to paper bought by a finalconsumer. In this perspective, the footprint of paper bought by abook publisher is zero, because this embodiment is passed on todownstream customers of books, and is part of the footprint of books. As a result, one cannot get around naming actors.


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a full life-cycle perspective with full consumer responsibility, alarge number of producers (businesses and industry sectors)have started to calculate their own footprints. Adding anyproducer's footprint to other producers' footprints, or topopulation footprints, which all already cover the full upstreamsupplychain of their operatinginputs, leads to double-counting:Thesum of footprints of producersandconsumersis larger thanthetotal national footprint. Thestandardisationcommitteewashence faced with the decades-old non-additivity problem,posing the following dilemma for the accounting of footprints,oranyother production factor: if onedisallows double-counting,but wishes to be able to account for producers and consumers,then one cannot impose the requirement of full life-cyclecoverage; the supply chains of actors have to be curtailedsomehow in order to avoid double-counting.

This work demonstrates and discusses a method of consis-tently delineating these supply chains, into mutually exclusiveand collectively exhaustive responsibilities to be shared by allactors in an economy. More generally, the method is anapproach to allocating factors across actors in a fully inter-connectedcircularsystem. In turningon using valueaddedas anallocative proxy for responsibility shares, the method achievesdesirable invariance properties, and leads to a unique assign-ment scheme. As an example we demonstrate how upstreamenvironmental impacts are shared between the actors in asupplychain. Thesame approach canbe applied to downstreamimpacts, asdescribedin GallegoandLenzen (2005). Although our formulation of shared responsibility is developed here for businesses as actors in a national economy, it can also beapplied in a multi-region input output setting to trade betweencountries and regions.

Webelieve that ourapproach of peggingresponsibilitysharesto value added not only has desirable invariance properties, butthat it makes intuitive sense as well, in that it places responsi-bilitywhere the influenceandcontrol over production processesand operating inputs resides. Organisations that are alreadyengaging in Extended Producer Responsibility have starteddialogues with their closest upstream suppliers and customers,or have appraised changes to procurement policy. 8 The fact thatshared responsibility diminishes with increasing distance be-tween the point of impact and the point of product use directlyreflects and supports this practice, since in general, the further users of a product are located from the producer of the impact,the less control they have over that impact.

At a meetingof theaction researchparticipants mentioned inSection 5.3, it was generally agreed that the building of criticalmass was the real issue. Were shared responsibility to becomeembedded in a methodology that became the standard then itwould be accepted because everyone was doingit . Moreover theburden of stakeholder education would be taken from thembecausetheywould beable to pointto thestandard . Andthereinlies theheart of theproblemfor manypractitioners. Thetimeandbudget needed to provide an education strategy are prohibitiveespeciallywhen the issue is onethat most wouldconsider irrele-vant to their corebusiness.Yet until a coregroupoforganisationstake up a standard methodology, developed out of academicdebate and feedback from practitioners then there will be nocritical mass.

There is, therefore, a need to present, in a range of media andin language accessible to a variety of disciplines and stake-

holders, the issues and dilemmas, inherent in accounting fairlyfor the environmental, social and economic effects of doing business. At the same time work must proceed on developing accounting and reporting standards that provide long termsolutionsto theoutstanding accounting problems,solutionsthatwork at all levels and across individual, organisation, city, stateand national boundaries.

The ecological footprint, and sustainability indicators ingeneral,as concepts,arenot simplyabout promotinga particular kind of understanding of our impact on the environment. Theyareimplicitlyaboutpromotingsomeone'snotionof rightaction based on that understanding. Similarly, users of the ecologicalfootprint, or any reporting methodology, are not operating in avalue-free zone. They are using the methodology in order toinfluence people and effect change. Again, presumably theyhavein minda notion of rightaction that they hope will follow.Thus to design a methodology and to use that methodology arealready value-laden actions. In using this or any methodologywetakeresponsibilityforthechoiceandallthatitimpliesbywayof underlying assumptions. Someone produced the methodol-ogy, someoneelse usedit. Justas inthe broaderargumentof thispaper any actoris part of a web of interactions for whichthere isnobeginningandno endpoint nowhere to apportionultimateresponsibility.

Acknowledgements

This research and its applications were supported in parts, bythe Fisheries Research and Development Corporation (FRDC),and the NSW Environmental Trust. Richard Wood (ISA, Uni-versity of Sydney) cleared up mathematical inconsistencies inan earlier allocation model. Mathis Wackernagel (GlobalFootprint Network), Mark McElroy (Sustainable Innovation,USA), Bert Steenge (University of Twente, the Netherlands), Joel Fleming (ClimateFriendly, Australia), Rowena Joske (Aus-tralian Conservation Foundation), and Christopher Dey (ISA)provided valuable comments on earlier drafts. Glen Peters(Norwegian University of Science and Technology) pointed outSteenge's work on the connection of the Leontief model withthe Coase Theorem.

Appendix A

Usingthe standard Leontief inverse (Eq.(1)), the totalecologicalfootprint F causedby a final consumption bundle y={ yn}canbewritten as F = f t L y, where f is a vector of ecological footprintsby sector per unit of gross output. Using the Taylor expan-sion of the Leontief inverse L=I+A+A2 +A3 + , F can beunravelled as

F Xi;n f iLin yn Xi;n f i din Ain X j Aij A jn X jk Aij A jk Akn N 0@ 1A yn :

A1

Each terms f i Aij A jk Akl Alm Amn yn etc., of the nested sum iscalled a structural path ( Lenzen, 2002; Treloar, 1997), with the


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2. The indicator is monotone, since F

f i XkI a# A 1ik yk P j1 akjT kjh i > 0.3. The indicator is additive (or mutually exclusive) over

actors, since

Xi Fi Xi f tI #A 1 yai Xi f tI #A1 yai f

tI # A

1

Xi yai :

4. The indicator accounts for indirect effects, because itemploys either the Leontief or the Ghosh model of tracing indirect effects.

5. The indicator follows economic causality, because of theintrinsic assumption within generalised input outputanalysis that physical flows of an external variable areproportional to the monetary inter-industry transactions.

6. Symmetry does not hold, because ij ji.

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