Environmentally important paths, linkages and key sectors in the Australian economy

Structural Change and Economic Dynamics 14 (2003) 1 /34 www.elsevier.com/locate/econbase

Environmentally important paths, linkages and key sectors in the Australian economy Manfred Lenzen * School of Physics, A28, The University of Sydney, 2006 Sydney, NSW, Australia Received 1 May 2001; received in revised form 1 April 2002; accepted 1 June 2002

Abstract Traditional work on linkages, fields of influence and structural paths is extended to include environmental and natural resource parameters. The theoretical basis for the generalisation of all three concepts is presented. Recent empirical data on energy consumption, land disturbance, water use and emissions of greenhouse gases NOx and SO2, is used to reveal the interdependence of industries in the Australian economy in terms of environmental pressure and resource depletion. Grazing industries, electricity generation, metals, chemicals, textiles, meat and dairy products, wholesale and retail, non-residential building and hospitality exhibit above-average linkages. A considerable part of environmental and resource pressure is exerted along paths for providing exports. # 2002 Elsevier Science B.V. All rights reserved. JEL classification: C67; L16; Q32; Q43 Keywords: Key sectors; Linkages; Field of influence; Structural path analysis; Environment; Australia

1. Introduction The idea of forward and backward inter-industry linkages as measures of structural interdependence was introduced by Rasmussen (1956). Their use in the identification of key sectors was subsequently suggested by Hirschman (1958), who postulated that economic development and structural change proceed predominantly along above-average linkages, so that a relatively small number of industries * Tel.:
/61-2-9351-5985; fax:
/61-2-9351-7725 E-mail address: [email protected] (M. Lenzen). 0954-349X/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 5 4 - 3 4 9 X ( 0 2 ) 0 0 0 2 5 - 5

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M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

accelerate and amplify initially small changes, which eventually affect the whole economy. Therefore, the identification of key sectors is seen to be useful for economic planning, especially in developing countries, aimed at generating aboveaverage local increases in economic activity and thus stimulating overall economic growth. As a recipe for stimulating development, Hirschman (1958) proposed creating initial disequilibria by selectively investing in key sectors that would facilitate production impulses (capacity expansion and/or imports substitution) through (1) above-average input requirements from upstream supplying industries (induce upstream supply of inputs through backwards linkages); and (2) excessive and therefore cheap supply of inputs to an above-average downstream demand (induce downstream utilisation of outputs through forward linkages). As a consequence of these mechanisms, the sectors growing most rapidly are not necessarily the key sectors themselves, but may be the sectors most closely tied to them. Alternative linkage measures were subsequently proposed by Hazari (1970), Cella (1984) and Clements (1990). Hirschman’s and Rasmussen’s idea was further elaborated by Sonis and Hewings (1989), Sonis et al. (1995a), Sonis and Hewings (1999) and Sonis et al. (2000) in their studies on the hierarchies of backward and forward linkages, and economic landscapes of multiplier product matrices. The latter authors emphasise that these alternative perspectives on economic interdependence should not be regarded as exclusive, but as complementing each other. The meaning of key sectors for economic development and their measurement, and especially Hirschman’s prescription of unbalanced growth, have been the subject of debate (Yotopoulos and Nugent, 1973; Diamond, 1975b; Laumas, 1975b,a; Schultz and Schumacher, 1975; Boucher, 1976; Jones, 1976; Laumas, 1976; Riedel, 1976; Yotopoulos and Nugent, 1976). Furthermore, rather inconclusive evidence has resulted from empirical studies on the correlation between linkages or linkagefocused development policy and actual growth (Panchamukhi, 1975; BulmerThomas, 1982; Hewings, 1982; Hewings et al., 1984; Clements and Rossi, 1991). Criticism is, for example, based on the experience that economic growth is often determined by constraints on production, international comparative advantages, imports and balance of payments, institutional and policy settings, technical and skill endowment, income distribution and final demand structure. Therefore, linkage rankings and correlations appear to be too simplified for assisting development policy (Bharadwaj, 1966; Panchamukhi, 1975; McGilvray, 1977). As a consequence and in accordance with Rasmussen’s initial approach, the focus of more recent research is on linkage measures as a descriptive rather than empirical tool. Previous work on key sectors and linkages is most often formulated entirely in monetary terms.1 Given today’s increasingly pressing environmental problems, it is 1 Diamond (1975a), Meller and Marfa´n (1981), Groenewold et al. (1987), Groenewold et al. (1993) and Kol (1991) examine employment linkages for Turkey, Chile, Australia and for Indonesia, South Korea, Mexico and Pakistan, respectively. Gould and Kulshreshtha (1986) calculate energy and employment forward and backward multipliers for the Saskatchewan economy.

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of interest to examine economic structure in terms of resource use and pollutant emissions and thus identify key sectors and linkages which are associated with above-average environmental impacts in the form of resource depletion and ecosystem degradation. The ranking sequence of environmentally important sectors and linkages should, in general, be different from that obtained from a purely monetary analysis (compare Diamond (1974) and Sonis and Hewings (1992)). In this work, three alternative key sector and linkage concepts */forward and backward linkages, field of influence and structural path analysis */will be generalised in the sense that they operate in terms of the usage of production factors.2 The latter term shall be understood in a broader meaning as to include economic quantities (for example labour, income, imports), environmental degradation (land disturbance, emissions) and resources (energy, water, land). In the following, the mathematical description of the generalisation for all three approaches and for arbitrary production factors will be presented (Sections 2.1, 2.2 and 2.3). The generalised concepts will then be applied to recent Australian data on specific factors, which are identified in Section 3. Finally, the results will be discussed and interpreted.

2. Methodology 2.1. Input /output theory The assessment of key sectors and linkages is based on input/output analysis, which is a top-down macroeconomic technique using sectoral monetary transactions data X /{Xij }i ,j1,...,N to account for the complex interdependencies of industries in modern economies. For an introduction to the generalised input /output theory and further details and reviews, see Leontief and Ford (1970), Isard et al. (1972), Herendeen (1978), Miller and Blair (1985), Proops (1988), Miller et al. (1989), Hawdon and Pearson (1995) and Forssell (1998). 2.1.1. The Leontief model The most widely known and used input /output application is the static quantity model of Leontief (1936, 1941, 1966), which is based on a N /N matrix
 Xij A fAij g (1) xj

2 A more recent key sector approach is the ‘Pure Linkage’ concept of Sonis and Hewings (1995). This concept is based on a decomposition of the Leontief inverse into submatrices describing the disjoined interdependence of two sector subgroups in terms of internal and external multipliers, which was introduced by Miyazawa (1966) and then further developed by Cella (1984) (see also Cella, 1986; Guccione, 1986) and Clements (1990). A generalisation of this decomposition approach to environmental factors has been presented by Fritz et al. (1998) and will therefore not be treated in this work.

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of ‘direct requirements’ coefficients, where the N /1 vector x represents total output. The fundamental equation of this model links exogenous final demands y (N /1) with total output via x(IA)1 yBy;

(2)

where I is the N /N unity matrix and B is called the ‘Leontief inverse’. An element Bij of B measures the output of industry i that is necessary to satisfy a unit of final demand from industry j. A ‘generalised’ Leontief model features a 1 /N vector m of demand-driven ‘factor multipliers’, that is requirements of production factors per monetary unit of final demand of commodities produced by N industry sectors. m can be calculated from a 1 /N vector q containing sectoral production factor usage per unit of total output according to m q(IA)1 qB:

(3)

The total factor requirement Q (scalar) of a final demand bundle y can then be written as Q my q(IA)1 y qx:

(4)

The Leontief input/output system represents a situation that is characterised by (1) no factor scarcity and perfectly quantity-elastic supply; (2) idle capacity; and (3) fixed prices that are unaffected by changes in final demand. This situation is dominated by consumers’ demand, with producers adjusting to an optimal input structure reflected by the fixed requirements coefficients Aij . A main drawback of the Leontief model is that it postulates a linear relationship between inputs and output, or in other words, zero fixed costs and constant returns to scale. Furthermore, the fixed technological coefficients do not allow input substitution. Real-world production responses to final demand changes can be considerably different from those predicted from input /output calculations, for example, due to potential slackness of production capacity. Moreover, production increases are likely to be facilitated using or installing the most recent and not average current technology. Similarly, production decreases will most probably put old and inefficient equipment out of service, but not average current equipment (compare Tiebout (1960), p. 402). Finally, demand changes generate effects on production via employment /income /consumption loops, which are beyond the feedback loops within intermediate demand.

2.1.2. The Ghosh model An alternative formulation of the inter-industry model was suggested by Ghosh (1958), featuring a N /N matrix
 Xij ˜ ˜ (5) A fAij g xi of ‘direct sales’ coefficients. The fundamental equation of this model links exogenous

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primary inputs v (1 /N ) with total output via ˜ 1  vB; ˜ x?v(I A)

(6)

where ? denotes transposition and B˜ is called the ‘Ghosh inverse’. Elements B˜ij of B˜ ˜ measure the and m˜ i aj1 N B˜ij qj of the supply-driven factor multipliers m? ˜ Bq? output of industry j and the factor usage, respectively, that is necessary to utilise a unit of primary input into industry i. The total factor usage Q accompanying this output is ˜ Q vBq?qBy:

(7)

An interesting feature of the Ghosh formulation is that the sales coefficients A˜ ij are independent of prices and valuation (Augustinovics, 1970).3 There has been considerable debate on the correct economic interpretation of the Ghosh model. Ghosh (1958) imagines a monopolistic or centrally planned market with scarce resources, where allocation rather than production functions govern and where shortages lead to price increases and rationing. Although Ghosh perceived the A˜ij as value coefficients, these were subsequently employed as quantity coefficients, such as by Bon (1988) for multi-regional analysis and in the studies of Giarratani (1976) and Davis and Salkin (1984) of the potential impacts of supply constraints in energy and water resources, respectively. This conception, in turn, was heavily criticised, for example on the grounds that a situation where all inputs are nonessential and where production recipes can vary and input substitution can occur perfectly, depending on the availability of supply, is implausible (Cella, 1988; Oosterhaven, 1988) and cannot be derived from any economic theory of production or optimisation behaviour (Cronin, 1984).4 The perception of the sales matrix as a price model to be used for analysing costpush inflationary processes was revived by Oosterhaven (1996) and Dietzenbacher (1997). In this interpretation, primary input ‘prices’ change exogenously, are entirely passed on to price-taking purchasers and change only output ‘values’, while quantities are fixed. As a consequence, supply is perfectly price-elastic, while demand is perfectly price-inelastic. Dietzenbacher (1997) shows that the Ghosh and Leontief price models yield the same results, as do their dual quantity models. Another strain of criticism focused on the fact that (assumed fixed) requirements and sales coefficients cannot be simultaneously independent of total output as required (since A˜  xA ˆ xˆ 1 ; see Cella, 1984, 1988) and therefore the Leontief and Ghosh models cannot be used in conjunction.5 This issue has since become known as the ‘joint stability problem’, a term coined by Chen and Rose (1986, 1989), who showed that requirements and sales coefficients can only be jointly stable if the 3 ˜ xˆ 1 ) to present the primary inputs Augustinovics (1970) uses the balance equation (vxˆ 1 )ByvB(y structure of final demand and the final allocation structure of primary inputs for the Hungarian economy. 4 Note that the matrices of requirements and sales coefficients are extreme cases of the constantelasticity-of-substitution production function for zero and infinite elasticity, respectively. 5 Loviscek (1982), for example, suggests a weighted measure of total linkage combining both Ghosh and Leontief inverses.

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M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

relative change in total outputs is the same across all industries (see also Dietzenbacher, 1989). However, empirical evidence seems to support that both requirements and sales coefficients vary equally in time and hence, with scale (Augustinovics, 1970). In summary, Eq. (6) cannot be interpreted in a physical, causal sense: supply-side multipliers B˜ij do not quantify the amount of output generated by an injection of primary inputs, but instead indicate how primary inputs depend on further processing. The consensus seems that the Ghosh model is justified as a descriptive tool for international comparative studies and for linkage and key sector identification, but not suitable for impact studies (Oosterhaven, 1988). 2.1.3. Methodological qualifications for both models As Jones (1976) and McGilvray (1977) point out, there exists a choice for A (and ˜ /6 between the domestic flow and technology matrices, the former describing intraA) regional interdependence and the latter including imports.7 Since the focus in this work is on depletable resources and emissions to air, a global perspective was adopted. The direct requirements (and sales) matrices therefore comprises domestically produced as well as imported current and capital intermediate demand (see Lenzen, 2001b): A Adom;cur
Aimp;cur
Adom;cap
Aimp;cap  A1
A2
A3
A4 :

(8)

A represents an input /output system, which is partially closed with regard to capital demand, but private final consumption is not internalised. All key sector measures calculated in the following are therefore of type I, which means that they consider indirect effects, but not feedback from household consumption into industrial production (induced effects). For examples of type-II linkages, see Diamond (1974) and Cochrane (1990). A shortcoming of the formulations in Eqs. (1) /(8) is that they represent singleregion input/output models. An inherent assumption in this model is that imports are produced using the domestic recipe of production factor inputs. Another conceptual problem that arises out of the assumption of a perfectly homogenous sectoral output is the interpretation of industry/internal transactions, which are represented in the direct matrices by the elements on the diagonal. Firstly, the magnitude of industry/internal deliveries depends on the boundary chosen for the collection of the statistical data (that is, for example, whether only transactions between enterprises are counted, or also transactions between different establishments of the same enterprise) and are therefore arbitrary (Australian Bureau of Statistics, 1999). Secondly, Georgescu-Roegen (1971) argued that industry/internal 6 The critique in the following paragraphs applies equally to the Leontief and the Ghosh model, unless explicitly stated otherwise. 7 In this context, McGilvray criticises that, although the proposed linkage-growth mechanism relies partly on potential imports substitution, there is no consideration of comparative advantages in any of the linkage measures. Key sectors obtained from linkage rankings might therefore be unrealistic, especially in the case of small and highly trade-dependent developing countries (see also Bulmer-Thomas, 1982).

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deliveries cannot be explained if all parts of the industry produce identical commodities and that a correct input /output table has zeroes on its diagonal (a ‘net’ table). However, based on this observation, Weber (1998) proved that multipliers, as in Eq. (2), are independent of the diagonal elements in the direct requirements matrix. The usage of gross or net tables in this work will be indicated along with the corresponding results. Finally, capital expenditure can vary significantly from one year to the following due to the low frequency of purchases of long-lived and expensive structures and equipment. Hence, the capital component in multipliers might be mis-estimated in years with atypical capital expenditure.8 2.2. Forward and backward linkages 2.2.1. Measures based on the Leontief inverse The row averages (over outputs) Bi + /Sj bij /N and the column averages (over inputs) B+ j /Si bij /N of the Leontief inverse B form the elements of the forward and backward linkages (Ui + and U+ j ) suggested by Rasmussen (1956) and Hirschman (1958). For normalisation, and to allow inter-industry comparisons, Hazari (1970) suggests relating these row and column sums to the global average b/ /Sij bij /N2: Ui+ 

Bi+ b

;

U+ j 

B+ j b

:

(9)

Ui+
/1 indicates strong forward linkages or ‘sensitivity of dispersion’, of sector i , meaning that a unit change in all sectors’ final demand would cause an aboveaverage production increase in sector i, that is sector i ’s products would be in greater demand. U+ j
/1 indicates strong backward linkages, or ‘power of dispersion’, of sector j , meaning that a unit change in the final demand of sector j would create an above-average increase in the activity of the whole economy, that is sector j would draw more heavily on the rest of the system. A key sector is characterised by Ui+
/ 1 ffl/U+ j
/1 and exhibits both above-average dependence and influence on other sectors. The Ui+ and U+ j are normalised to Si Ui+ /N /1 and Sj U+ j /N /1. Bharadwaj (1966) and Hazari (1970) recommend taking into account column and row ‘coefficients of variation’ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Varj (bij ) Vari (bij ) Vi+  and V+ j  with Bi+ B+ j (10)   N N X X 1 2 bkl  bmn =N ; Vark=l (bkl ) N  1 k=l1 m=n1 because high linkage values can result from either many high bij (reflected in low Vi+ 8

Casler (1983) suggested determining a representative mix of capital stock held by industries through time and calculating a capital corrections matrix from the depreciation rates of capital stock items. This matrix, however, would not comprise a growth component of investment.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

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and V+ j ), or only a few very high bij (reflected in high Vi+ and V+ j ). An example for the latter is the Korean rice sector, as cited by Jones (1976). Intermediate rice deliveries were a mere 14% of total output, but formed a large fraction for a few small industries, hence exaggerating the key role of the rice sector. An additional criterion for key sectors is therefore that coefficients of variation are relatively low (see also Hazari, 1970). Hirschman (1958) pointed out that linkages have to include information about the level of sectoral economic activity if they are to indicate investment. Once again, the example of Jones (1976) of the Korean rice sector serves to illustrate the artificial importance of linkages that are attached to small sectors. An obvious remedy to this problem is to introduce a weighting scheme using the weighted row averages Bi+ d/ / Sj bij dj , column averages B+ j d/ /Si bij dj /dj NB+ j and global averages bd/ /Sij bij dj /N with final-demand weights dj /yj /y /yj /Sj yj and to define linkages and coefficients of variation pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Varj (bij dj ) Bi× d B+ j d d d d Ui+  ; U+ j  ; Vi +  ; and d d 1 b b Bi+ d N (11) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vari (bij dj ) d V+ j  V+ j : 1 d B+ j N While the linkages Ui+ and U+ j in Eq. (9) describe responses to a unit change (in Australian Dollars, A$) in sectoral final demand, the weighted linkages in Eq. (11) describe responses to a fractional change (in %) in sectoral final demand yi .9 They are normalised according to Si/Ui+ d//N /1 and Si/U+ j d//N /1.10 While these measures incorporate the level, or the importance, of each sector in the total final demand, they rest on the assumption of a peculiar and unrealistic economic stimulus that homogeneously affects the final demand from all industries (Jones, 1976; Heimler, 1991). Note also that, considering the fundamental input /output relationship in Eq. (2), we find for the forward linkages Bi+ d/ /xi /y, bd/ /x /Ny and Ui+ d/ /Nxi /x . Ui+ d hence merely reflects sectoral shares in total output and is therefore not a good measure for indirect effects (see Jones (1976 pp. 328/329) for a hypothetical example of fertiliser and caprolacdam utilisation). Cuello et al. (1992) recommended an alternative weighting scheme based on sectoral output xi . Their empirical analysis of Washington State, USA, revealed that the weighting improved the capability of identifying key sectors. They define jj /xj / x /xi /Sk xk as sectoral weights, with weighted row and column averages Bi+ j/ / 9

While the definition by Hazari (1970) of backward weighted linkages corresponds to the one used in Eq. (6), his forward weighted linkage uses weighted row averages Bi+ d di aj bij : The forward linkages in Eq. (6) are the same as those proposed by Laumas (1976). 10 Note that replacing the ji , jj , di and dj in Eq. (11) and Eq. (12) with a constant weight of 1/N yields the Ui+ , U+ j , Vi+ and V+ j as in Eq. (9) and Eq. (10).

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Sj bij jj and B+ j j/ /Si ji bij . Weighted linkages and coefficients of variation are then Bi+ j B+ j j j Ui+  ; U ; +j  N N 1X 1X j j Bi+ B+ j N i1 N j1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vari (ji bij ) V+ j j  1 B+ j j N j

Vi+

j

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Varj (bij jj )  1 Bi+ j N

and (12)

with normalisation Si/Ui+ j/N /1 and Sj/U+ j j//N /1.11 A disadvantage of the outputweight approach is that the linkages have no intuitively simple meaning. Moreover, as shown in Fig. 1, the forward averages Bi+ j are positively correlated to the output weight j. Therefore, as a number of calculations for the Australian case (the results of which are not reproduced here) showed, forward linkages Ui+ and Ui+ j are not significantly different: it appears that industries with a large total output have also above-average intermediate output (compare Schultz (1977) and Clements and Rossi

Fig. 1. Relationship between forward averages and final-demand (j) and output (k) weights. Linear regressions and their R2-coefficients are shown in the inserts. 11 Rao and Harmston (1979) introduce output-weighted linkages with B+ j j/ /ji Bi+ and B+ j j/ /jj B+ j , that is with weights outside the sum.

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(1991)). This correlation cannot be observed between final demand and intermediate output.12 As a consequence, output weights were not applied in this work. After this examination of linkages based on the Leontief inverse B, it can be concluded that neither Ui+ , nor Ui+ d and Ui+ j in Eq. (4), Eq. (6) and Eq. (7) are a satisfactory measure of forward linkage. Most of the shortcomings mentioned above were already elaborated by Jones (1976) and Beyers (1976). These and other authors (Miller and Lahr, 2000) argue that the Ghosh inverse B˜ remains the only reasonable candidate for measuring forward linkages. 2.2.2. Measures based on the Ghosh inverse Considering the stream of criticism described in Section 2.1.2 and, in particular on the work of Oosterhaven (1988, 1996) and Dietzenbacher (1997), it must be concluded that a forward-looking model is only plausible if formulated as a price model with quantities fixed. In a causal sense, such a model only captures price effects of an exogenously specified cost-push, but not quantity effects (which are examined as an exogenously specified demand-pull under fixed prices, using the Leontief model). This has implications for the interpretation of forward quantitylinkages: the Ghosh inverse can only be employed as a descriptive, ‘ex-post’, static device, that measures the amount of output that is necessary to utilise or absorb, or that accompanies primary inputs. The same (non-causal) interpretation must be applied to environmentally extended forward linkages. Given these qualifications and using primary-input weights si /vi /v/vi /Si vi , row ¯˜ a b˜ =N 2 averages B˜i+ aj b˜ij =N and B˜i+ s  aj si b˜ij si N B˜i+ and global averages b ij ij s ¯ and b˜  aij si b˜ij =N of the Ghosh inverse, forward linkages and their variances can be readily defined by following Eqs. (9) /(11): qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Varj (b˜ij ) B˜i+ B˜ + s U˜ i+  ; U˜ i+ s  i and ; V˜ i+  B˜i+ b˜ b˜s (13) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ˜ (s ) Var b j i ij  V˜ i+ : V˜ i+ s  s ˜ Bi+

2.2.3. Generalised forward and backward linkages In generalised input /output models, the flow of production factor embodiments is described according to Eq. (3) and Eq. (7) as multipliers qi bij and b˜ij qj : Replacing bij with qi bij and b˜ij with b˜ij qj ; so that B˜i+ q aj b˜ij qj =N; B+ j q/ /Si qi bij /N , b¯˜q aij b˜ij qj =N 2 ;

12

A regression between backward averages and weights yielded no correlation at all. This indicates that industries with large output can have small intermediate input if they draw significantly on primary inputs such as labour.

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2

/b / /Sij qi bij /N , B˜i+ qs aj si b˜ij qj si N B˜i+ q ; B+ j qd/ /Si qi bij dj /N /dj N/B+ j q ; b˜qs  aij si b˜ij qj =N and bqd/ /Sij qi bij dj /N , it is straightforward to define unweighted and weighted linkages

q

U˜ i+ q=s 

B˜i+ q=s b˜q=s

U+ j q=d 

and

B+ j q=d bq=d

;

(14)

which indicate above-average effects in terms of factor requirements (q /d and q/s denote indices q , qs or qd). Their coefficients of variation are qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ˜ij qj ) ( b Var Varj (si b˜ij qj ) Var (q b ) j i i ij ; V+ j q  ; V˜ i+ qs   V˜ i+ q V˜ i+ q  1 B+ j q B˜i+ q qs ˜ Bi+ N (15) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Var (q b d ) i i ij j and V+ j qd   V+ j q : 1 qd B+ j N Note that, as the U˜ i+ ; U+ j , the U˜ i+ q=s and U+ j q=d are normalised to ai U˜ i× q=s =N 1 and aj U˜ ×j q=d =N 1: Replacing the si and dj in Eq. (14) and Eq. (15) with a constant weight of 1/N yields the U˜ i+ q and U+ j q : Further replacing the qi with 1 yields the U˜ i+ and U+ j . 2.3. Field of influence Following early work by Sherman and Morrison (1950) and by Bullard and Sebald (1977, 1988), Sonis and Hewings (1989) developed the concept of a field of influence of a change in a transaction aij contained in a direct requirements matrix A. This influence is represented by the change in the Leontief inverse B resulting from a small change o in one of the elements of A. Sherman and Morrison (1950) provided the analytical solution bkl  (o) bkl


bki bjl o 1  bji o

;

(16)

where b kl (o) denotes the elements of the disturbed Leontief inverse B(o)[I (A
E)]1 and (E)kl /o if k /i ffl/l/j and 0 otherwise. Eq. (16) can be written in matrix form as B(o)B


o 1  bji o

Fij ;

(17)

where the matrix Fij with elements (Fij )kl /bki bjl is called the ‘field of influence’ of 13

Sonis and Hewings (1992), Sonis et al. (1995a) and Sonis et al. (1995b) have generalised the Sherman /Morrison formula to incremental changes in two and more elements of the direct requirements matrix, leading to second- and higher-order fields of influence.

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the transaction aij .13 In order to enable ranking of transactions, the Fij can be reduced to scalars N X N X (Fij )kl

Sij 

k1 l1 N X N X N X N X

N X N X

 k1 ij

(F )kl =N

2

bki bjl

l1 N 2 b2

;

(18)

i1 j1 k1 l1

which are normalised according to Si ,j Sij /N2 /1. aij with Sij
/1 are said to be ‘inverse important coefficients’, since their changes have the greatest impact on the rest of the economy.14 It is straightforward to derive the relationship between the field of influence intensity and Hirschman’s and Rasmussen’s forward and backward linkages, since N X N X

N 1X

bki bjl

Sij  k1 l1 N 2 b2



N k1

bki

N 1X

N

l1

b2

bjl U+ i Uj+ :

(19)

It can be seen from Eq. (19) that Fij contains a description of the constituents of the forward linkage Uj+ of industry j and the backward linkage U+ i of industry i (both based on the Leontief inverse). From Eq. (19) the coefficients of variation follow as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  N X N  N N u 1 X 1 XX t bki bjl  bmi bjn 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N 2  1 k1 l1 N 2 m1 n1 Vark;l (bki bjl )  : (20) Vij  N X N X B+ i Bj+ 1 bmi bjn N 2 m1 n1 The Sij refer to a unit change (o ) in a transaction aij . In order to describe the responses Sij d to fractional changes in the aij , while retaining the normalisation Si,j/ Sij d//N2 /1, o has to be replaced with o /dij /o /aij/b2 =S d with S d/ / Skmnl bkm amn bnl /N4 /Sk,l (BAB)kl /N4, leading to Sij d U+ i dij Uj+

and

Vij d Vij :

(21)

The generalisation of the field of influence approach towards production factor embodiments can be taken directly from Eq. (14), Eq. (19) and Eq. (21): Sij q U+ i q Uj+ q

and

Sij qd U+ i q dij q Uj+ q ;

(22)

with dqij /aij/bq2 =S qd ; S qd/ /Skmnl qk bkm amn qn bnl /N4 /Sl {(q BA#q)B}l /N4, where # 14

Note that, as Sonis and Hewings (1992) point out, the rank sequence of coefficients depends on the matrix norm chosen for Fij . An alternative to the formulation in Eq. (10) is using the maximum norm as Sij /jjFij jj /maxk ,l j(Fij )kl j.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

13

denotes element-wise multiplication. The normalisations Si ,j/Sij q//N2 /1 and Si ,j/Sij qd// N2 /1 hold and coefficients of variation are vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N X N u 1 X t (qk bki qj bjl  B+ i q Bj+ q )2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 N Var (q b q b ) k1 l1 k;l k ki j jl Vij q   and (23) B+ i q Bj+ q B+ i q Bj+ q Vij qd Vij q : Replacing the dij and/or the qi with 1 in Eq. (21) and Eq. (22) yields the Sij q ; Sij d and Sij , respectively. Rather than using Eq. (23), computing the Vij q is more easily carried out by approximating with qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (24) Vij : V+ i 2
Vj+ 2 and Vij q : V+ i q2
Vj+ q2 : A major weakness of the field of influence Fij as in Eq. (17) is that it does not exactly describe the relative changes B(o)  B o



1 1  bji o

Fij

(25)

in the Leontief inverse. Since, in addition to Fij , they are also a function of bji and o , a ranking in terms of these relative changes may look considerably different to one of the Sij . Furthermore, as evident from Eq. (19), Eq. (21) and Eq. (22), fields of influence refer only to the Leontief inverse and therefore do not adequately reflect forward linkages. One way to incorporate both the Leontief and the Ghosh linkages into a field-of-influence measure is S˜ij q  P

U+ i q Xij U˜ j+ q q ˜ q k;l U+ k Xkl U l +

(26)

with both forward and backward linkages weighted according to the transactions ˜ Xij , which are common in both measures. Note that, since A˜  xA ˆ xˆ 1 ; we find B 1 ij 1 q ˜ ˜ xB ˆ xˆ and also F  xF ˆ xˆ : Sij is therefore related to the separate fields of influence of both the requirements and the sales matrix: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X x x q bij b˜kl bij b˜kl ql  q bij bkl l b˜ij i b˜kl ql S˜jk q  il i il i xk xj X qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  q xi (F jk )il (F˜jk )il xl ql : (27) il i In this work, S˜ij q shall be referred to as the ‘field of influence intensity’.15 15

In contrast, Sonis et al. (1995b) and Sonis et al. (2000) termed the matrix M with mij /Skl bki bjl / Skl bkl the ‘first-order intensity matrix of the field of influence’ or the ‘multiplier product matrix’. The column and row sums of M are equal to those of the Leontief inverse B.

14

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

2.4. Structural path analysis The decomposition of multipliers into paths was introduced into economics and regional science by Crama et al. (1984) and Defourny and Thorbecke (1984). In order to systematically determine environmentally important input /output paths, the total factor multipliers as in Eq. (2) can be decomposed by ‘unravelling’ the Leontief inverse using its series expansion (IA)1 I
A
A2
A3
  

(28)

Combining Eq. (2) and Eq. (28), a factor multiplier for final demand supplied by industry i can then be written as

mi 

N X

qj (Iji
Aji
(A2 )ji
(A3 )ji
  )

j1



N X

  N N X N X X qj Iji
Aji
Ajk Aki
Ajl Alk Aki
  

j1

k1

l1 k1

 N 4 N X 4 X 4 N X N X 4 X 4 X X X X qj Iji
Aa;ji
Ab;jk Aa;ki
 j1



a1

4 X

k1 b1 a1

Ag;jl Ab;lk Aa;ki
  

l1 k1 g1 b1



a1

qi


N X

qj

j1



4 X N X b1 j1

4 X

Aa;ji


a1

Ab;kj

N X k1

4 X

qk

4 X N X b1 j1

Aa;ji
   ;

Ab;kj

4 X a1

Aa;ji


N X l1

ql

4 X N X

Ag;lk

g1 k1

(29)

a1

where i, j, k and l denote industries, a , b and g denote components of A as in Eq. (8) and Iij /1 if i/j and Iij /0 otherwise. mi is thus a sum over a direct factor input qi , occurring in industry i itself and higher-order paths. A path from industry j (domestic or foreign) via industry i into final demand of first order is represented by a product qj Aa ,ji , while a path from industry k via industry j and industry i into final demand is represented by a product qk Ab ,kj Aa ,ji and so on. An index triplet (a ,ij) shall be referred to as a ‘vertex’. Each product describes the factor usage response of industry i noted in the first vertex to a unit change in final demand from industry j in the last vertex along one particular path. There are 4 /N paths of first order, (4 / N )2 paths of second order, and, in general, (4 /N )n paths of n th order. Replacing the qi with 1 in Eq. (29) yields a decomposition of multipliers mi in monetary terms.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

15

Let yyhh
ygov
yst
yexp y1
y2
y3
y4 

4 X

(30)

ym

m1

be N /1 components of final demand taken up by households, governments, changes in stocks and exports. The factor usage responses qm ,j /mi dm ,j of industry i to a fractional change in final demand segment ym ,j can then be described using finaldemand weights dm ,i /ym ,i /y /ym ,i /Sk Sn yn ,k . The total factor requirement Q can then be decomposed into sectoral contributions according to Q my 

N X N X

mk ym;k 

k1 m1

N X N X

mk dm;k y

k1 m1

N X N X

qm;k y:

(31)

k1 m1

Inserting Eq. (29) into qm ,i /mi dm ,i yields qm;i qi dm;i


N X j1

qj

4 X a1

Aa;ji dm;i


N X k1

qk

4 X N X b1 j1

Ab;kj

4 X

Aa;ji dm;i
   : (32)

a1

The term qk Ab ,kj Aa ,ji dm,i , for example, describes the factor usage response in industry k to a fractional change in final demand of segment m from industry i, along the path Ab ,kj Aa ,ji , leading from the factor-using industry k via the intermediate industry j to industry i supplying the final demand segment m. Replacing the dm,i with 1 in Eq. (29) yields the decomposition in Eq. (29). Eq. (29) and Eq. (32) contain descriptions of the many constituents of both forward and backward linkages and field-of-influence elements and thus provide the most detailed picture of inter-industry influence and dependence. The same decomposition technique can be applied to the direct sales matrix and the Ghosh inverse, but this shall not be exercised here because of limited journal space. In this work, an algorithm for scanning, extracting and ranking input paths will be employed, which is similar to an extraction technique used by Treloar (1997), but extended to input paths from imported commodities as well as domestically produced and imported capital. In this algorithm, Eq. (26) and Eq. (29) are evaluated by sequential backwards scanning of the production chain tree from final demand to the various locations of production factor usage. Since the value of input paths decreases with path length, the scanning only proceeds up to a specified maximum order. Furthermore, branches of the tree are ‘pruned’ when the respective path value becomes lower than a specified threshold (Treloar, 1997). While Treloar compiled both top-ranking paths and the number of paths necessary to achieve a specified degree of system completeness, only the top 20 paths for each factor are calculated in this work. For the latter task, computing times can be significantly reduced with regard to the algorithm used by Treloar by setting the threshold to the value of the 20th-ranking path for each factor. During the scanning of a tree, the 20th-ranking path value is continuously replaced as higher-valued paths are found, thus facilitating a dynamic upward adjustment of the pruning threshold.

16

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

3. Application to the Australian economy of 1995 This study deals with Australian energy consumption, land disturbance, water use and emissions of greenhouse gases NOx and SO2. This selection is based purely on data availability and quality and does not necessarily reflect the importance of environmental and health impacts. Nevertheless, land disturbance, water use and greenhouse gas emissions are among the most crucial environmental factors in the case of Australia (Whetton et al., 1993; Glanznig, 1995; Murray-Darling Basin Ministerial Council, 1995). The term ‘energy consumption’ is used in this work to denote the combustion of non-renewable fossil fuels in units of megajoules (MJ). This definition covers, for example, coal, natural gas, fuel oil, petrol, diesel and kerosene. However, items such as crude oil for refinery feedstock and wood are not included, since they are either not combusted or renewable. A measure of land disturbance in units of hectares (ha) can be obtained by a weighted sum containing products of the affected area and a land condition factor. The latter is a weight between 0 and 1, which is based on vegetation coverage, species diversity and bioproductivity. A detailed assessment of Australian land disturbance can be found in Lenzen and Murray (2001). ‘Water use’ includes the consumption of self-extracted water (surface water from rivers or lakes, mainly extracted by farmers for irrigation) as well as mains water in units of litres (l) (see Lenzen and Foran, 2001). In accordance to guidelines set out by the Intergovernmental Panel on Climate Change (IPCC), greenhouse gas emissions are expressed in CO2-equivalents (CO2-e), which are calculated as a weighted sum of nominal emissions using gas-specific global warming potentials of 1 (CO2), 21 (CH4), 310 (N2O), 6500 (CF4) and 9200 (C2F6). Vectors q containing sectoral production factor usage were obtained partly from well-documented sources, such as the National Greenhouse Gas Inventory Committee (1998a), energy statistics (Australian Bureau of Agricultural and Resource Economics, 1997a) and water accounts (Australian Bureau of Statistics, 2000b). Further sectoral disaggregation was achieved by using supplementary reports (Wilkenfeld and Associates Pty Ltd., 1998) and unpublished estimates on these factors (Australian Bureau of Agricultural and Resource Economics, 1997b, 1999; Australian Bureau of Statistics, 2000a). However, no comprehensive data exists for Australian land use, let alone land disturbance, so that a range of disparate sources had to be appraised (Lenzen and Murray, 2001). The matrices A1 and A2 can be derived from supply, use and imports matrices published by the Australian Bureau of Statistics (1999, see Lenzen, 2001b), while A3 and A4 were constructed by the author (Lenzen, 2001b). Multipliers mi as in Eq. (3) and hence unweighted and weighted linkages and fields of influence are not affected by whether net or gross matrices are used, but this does not hold for structural paths (compare also Schultz (1977) and Weber and Schnabl (1998)). In this work, in order to illustrate both options, linkages and fields of influence were calculated using net tables, while paths were determined using gross tables. As a consequence, industry/internal transactions are only shown in Table 3 in Section 3.3, but not in the figures in Section 3.2. For the sake of brevity,

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34 Table 1 Codes assigned to 134 industry sectors specified in the Australian input /output classification Symbol

Industry

Ac Ai Al Ap At Ba Bc Bk Bl Bm Bp Br Bs Bt Bu Bv Bx Cc Ce Cg Ch Cl Cm Cn Co Cp Cr Cs Ct Cu Dc De Df Dp Dw Ed Ee El En Eq Et Fc Fd Fe Fi Fm Fn Fo Fp

Insecticides, pesticides and other agricultural chemicals Aircraft Alumina, aluminium alloys and aluminium recovery Automotive petrol Air and space transport Barley, unmilled Beef cattle Banking Black coal Beer and malt Bread, cakes, biscuits and other bakery products Brown coal, lignite Typing, copying, staff placement and other business services Bus and tramway transport services Prefabricated buildings Soft drinks, cordials and syrups Bauxite Concrete and mortar Cement Services to agriculture, ginned cotton, shearing and hunting Basic chemicals Clothing Communication services Confectionery Copper Plaster and other concrete products Bricks and other ceramic products Childminding and other community care services Cosmetics and toiletry preparations Libraries, parks, museums and the arts Dairy cattle and untreated whole milk Soap and other detergents Defence Dairy products Ownership of dwellings Education Cable, wire, batteries, lights and other electrical equipment Electricity supply Electronic equipment, photocopying, gaming machines Pumps, bearings, air conditioning and other equipment Motion picture, radio and television services Flour, cereal foods, rice, pasta and other flour mill products Raw sugar, animal feeds, seafoods, coffee and other foods Mixed fertilisers Commercial fishing Nuts, bolts, nails, tools and other fabricated metal products Money market corporation and other non-bank finance Gas oil, fuel oil Vegetables, fruit, juices and other fruit and vegetable products

17

18

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

Table 1 (Continued ) Symbol

Industry

Fr Fu Fw Ga Gd Gl Gp Gv Hh Ho Hs Hw In Io Is Ke Kn Lg Lm Lp Ma Mi Mn Mp Ms Mv Nb Ne Nf Ng Oc Oe Of Oi Om Os Ot Pa Pc Pd Pe Pg Ph Pi Pl Pp Pr Ps Pt Rb

Forestry and services to forestry Furniture Footwear Gas production and distribution Sanitary and garbage disposal services Gold and lead Glass and glass products Government administration Household appliances and hot water systems Accommodation, cafes and restaurants Health services Hardwoods, brushwoods, scrubwoods, hewn and other timber Insurance Iron ores Basic iron and steel, pipes, tubes, sheets, rods, bars and rails Kerosene and aviation jet fuel Knitting mill products Liquified natural gas, liquifued natural petrol Lime Leather and leather products Agricultural, mining and construction machinery Mineral and glass wool and other non-metallic mineral products Exploration and services to mining Meat and meat products Legal, accounting, marketing and business management services Motor vehicles and parts, other transport equipment Non-residential buildings, roads, and other construction Newspapers, books, recorded media and other publishing Non-ferrous metal recovery and basic products Natural gas Adhesives, inks, polishes and other chemical products Photographic, optical, medical and radio equipment, watches Oils and fats Crude oil Coins, jewellery, sporting goods and other manufacturing Police, interest groups, fire brigade and other services Cable car, chair lift, monorail and over-snow transport Paper containers and products Petroleum bitumen, refinery LPG and other refinery products Property developer, real estate and other property services Poultry and eggs Pigs Pharmaceutical goods for human use Pipeline transport services Plastic products Pulp, paper and paperboard Printing, stationery and services to printing Hairdressing, goods hiring, laundry and other personal services Paints Residential building, construction, repair and maintenance

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

19

Table 1 (Continued ) Symbol

Industry

Rd Rf Rh Ri Rp Rs Rt Ru Rv Rw Sb Sc Sf Sg Sh Sm Sp St Su Sw Sz Ta Ti To Tp Ts Tx Uo Vf Wa Wh Wo Wp Ws Wt

Road freight transport services Railway freight transport services Repairs of household and business equipment Rice, in the husk Railway passenger transport services Sport, gambling and recreational services Retail trade Rubber products Repairs of motor vehicles, agricultural and other machinery Railway equipment Ships and boats Seed cotton Security broking and dealing and other services to finance Sand, gravel and other construction materials mining Sheet containers and other sheet metal products Frames, mesh and other structural metal products Water transport Travel agencies, forwarding and other services to transport Sugar cane Softwoods, conifers Silver and zinc ores Taxi and hired car with driver Sawn timer, woodchips and other sawmill products Tobacco products Carpets, curtains, tarpaulins, sails, tents and other textiles Scientific research, technical and computer services Processed wool, textile fibres, yarns and woven fabrics Uranium, nickel, tin, and other non-ferrous metal ores Vegetable and fruit growing, hay, plant nurseries, flowers Water supply, sewerage and drainage services Wheat, legumes for grain, oilseeds, oats and other grains Sheep and shorn wool Plywood, window frames, doors and other wood products Wine and spirits Wholesale trade

abbreviations for 134 industry sectors (Table 1) listed in the Australian input /output classification will be used in the following. 3.1. Forward and backward linkages Fig. 2 shows linkages in monetary terms (left column of diagrams) and for the example of water use (right column), calculated using different weight combinations. All diagrams are organised showing forward linkages on the vertical, and backward linkages on the horizontal axis, so that key sectors can readily be identified in the upper right corner of the diagrams. Comparing all four diagrams clearly

20

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

Fig. 2. Unweighted and weighted forward and backward linkages in monetary and water use terms. Sector abbreviations are listed in Table 1. For further details see text.

demonstrates that any weighting or factor generalisation considerably increases the scatter and range of linkages. Diagram (a) shows (grey-filled circles) electronic equipment (En), basic chemicals (Ch), pine plantation (Sw) and petrol refining (Ap) with above-average monetary linkages. For comparison, these industries are also represented by the grey circles in diagram (b). The black-filled circles mark cotton (Cg, Sc) and food products (Fd) as above-average-linked industries in terms of water use. Note that the monetary key sectors from diagram (a) are mostly buried amongst the bulk of sectors. This demonstrates that a translation of the key sector concept from monetary into factor use terms can generate considerably different rankings. Diagram (c) shows that a weighting with final demand and primary input shares also substantially changes the picture: wholesale and retail trade (Wt, Rt), nonresidential building (Nb), communication (Cm), government administration (Gv), hospitality (Ho) and business management services (Ms) have gained in importance simply due to their large share in primary input and final demand (black circles).16 Again, key sectors from diagram (a) are shown as grey circles. In water use as well as weighted terms (d), key sectors are wholesale trade (Wt), fruit and vegetable growing (Vf), food products (Fd), government administration (Gv) and hospitality (Ho), but also meat and dairy products (Mp, Dp) and retail trade (Rt), the latter mostly backward-linked. Once again, some key sectors from diagram (c), shown in diagram (d) as black circles, recede towards the bulk of the sectors.

Table 2 Industries with top ten unweighted and weighted forward and backward linkages, including coefficients of variation (C.o.v.), in monetary and environmental terms Type

Rank

Intermediate demand Industry

q

/Vi+ /

Forward weighted /Ui+ qs/ /Vi+ qs/

Backward /U+ j q/ /V+ j q/

Backward weighted /U+ j qd/ /V+ j qd/

Energy consumption C.o.v.

Industry

Land disturbance

Water use

Value

C.o.v.

Industry

Value

C.o.v.

Industry

Value

C.o.v.

Greenhouse gas emissions

NOx emissions

Industry

Industry

Value

C.o.v.

Value

SO2 emissions C.o.v.

Industry

Value

C.o.v.

1 2 3 4 5 6 7 8 9 10

En Eq Ch Ai Pp Oe Ee Ma Sw Ru

4.49 3.59 3.18 3.14 3.02 2.92 2.54 2.39 2.28 2.24

1.66 1.19 1.40 2.64 2.38 1.57 1.53 1.32 2.49 1.56

Br Eq Oi Ch Ai Ee En Bl Pc Bx

6.01 4.34 3.83 3.54 3.50 3.30 3.28 3.08 2.98 2.53

8.72 5.64 3.90 5.22 6.11 7.61 5.30 10.74 3.85 8.95

Fe Ma Sc Cg Ac Ba Ch Wo Fr Wh

15.02 12.06 7.24 7.16 5.84 4.03 3.51 3.21 2.74 2.30

7.44 7.69 7.88 7.88 8.21 4.08 7.97 3.31 8.24 6.47

Fe Ma Sc Ac Cg Ch Wh Eq Fo En

16.50 9.57 4.89 4.86 4.83 4.03 3.04 2.66 2.59 2.41

4.24 4.42 4.40 4.55 4.41 3.79 5.74 3.42 3.81 3.58

Ma Fr Fe Eq Br Ch En Ee Sc Ac

8.01 6.49 5.73 4.39 3.36 3.08 2.75 2.65 2.53 2.49

5.93 8.45 7.50 4.27 7.38 4.45 3.96 5.11 7.48 8.14

Sp Br Ai Eq Oi Ch En Pc Ma Ee

4.38 3.97 3.92 3.88 3.79 3.50 3.14 2.85 2.76 2.69

7.97 7.15 5.89 3.59 3.52 4.48 3.30 3.09 2.59 5.07

Bx Co Uo Sz Nf Ot Br Eq Gl Mn

15.31 11.85 6.97 6.19 4.45 4.32 4.02 3.53 3.25 3.02

11.19 11.20 11.17 11.18 10.90 10.64 7.76 9.02 11.17 10.04

1 2 3 4 5 6 7 8 9 10

Wt Ms Nb Pd Ts Cm St Rd Sf Is

10.55 8.57 7.80 7.64 7.23 5.03 4.50 3.98 3.57 3.52

1.24 2.11 1.66 2.70 1.66 1.96 2.13 1.59 2.61 1.60

Nb Wt Bl El Ms Ts Pd Oi St Is

12.93 9.47 7.74 7.35 5.94 5.73 5.68 5.04 4.54 3.84

7.94 4.85 10.74 7.97 4.22 4.81 4.90 3.90 3.91 5.33

Wt Ms Ma Nb Ts Rd Mv Pd Cm Is

11.67 7.10 6.98 6.33 5.55 4.93 4.57 4.14 4.09 3.70

7.42 7.76 7.69 7.63 7.84 7.84 7.64 7.59 7.87 7.60

Wt Nb Ms Ts Ma Rd Pd Mv St Cm

11.96 8.97 6.81 5.60 5.37 4.78 4.38 4.16 3.72 3.71

3.65 4.24 3.74 3.57 4.42 3.86 3.53 3.91 3.57 3.80

Wt Nb Ms Ts El Pd Bl Ma Rd Is

10.78 10.25 6.16 5.63 5.08 4.95 4.37 4.15 4.14 4.09

3.94 5.59 3.97 3.96 6.21 3.83 10.01 5.93 3.97 4.09

Nb Wt Ms St Ts Pd El Oi Bl Rd

10.51 9.84 6.64 6.34 6.18 5.77 5.59 5.21 4.65 4.03

5.52 2.96 2.86 4.52 3.11 3.20 5.94 3.52 9.96 2.44

Nb El Wt Pd Ts Nf Ms Bl Gl Uo

9.44 9.21 8.28 5.76 5.21 4.50 4.45 4.24 4.18 3.66

7.93 8.87 8.73 9.01 8.88 10.90 8.77 8.59 11.17 11.17

1 2 3 4 5 6 7 8 9 10

Pg Lp Pe Dp Mp Ap Hw De Fe Ch

1.53 1.38 1.37 1.35 1.32 1.31 1.27 1.27 1.26 1.26

1.74 2.34 1.79 2.51 2.35 3.61 2.22 2.52 2.61 2.61

Nf Fe Pl Pt De Pp Sh Oc Is Sm

2.22 2.20 2.00 1.96 1.86 1.81 1.80 1.73 1.69 1.59

6.46 6.79 7.09 7.49 6.96 5.94 5.53 6.71 5.76 5.54

Mp Tx Lp Cl Tp Pe Pg Kn Fw Bc

25.12 16.89 10.18 7.53 6.36 6.06 4.43 4.39 4.30 3.86

10.21 11.37 8.26 11.15 11.23 8.93 7.87 11.20 8.17 8.55

Dp Cg Fc Mp Pg Fd Ws Pe Tx Bp

13.57 11.83 11.44 7.57 5.14 4.52 3.90 3.36 3.18 2.88

10.79 11.14 10.10 8.84 5.23 8.02 6.26 5.04 7.07 6.18

Mp Sw Fr Lp Pp Pe Ti Tx Pg Bc

7.50 5.32 5.32 2.84 2.55 2.37 2.22 2.11 1.97 1.87

9.86 10.23 10.23 7.34 4.86 6.64 6.02 8.09 5.20 5.54

Sp Fe Nf Is Pt Pl De Sh Mp Oc

3.14 2.01 1.93 1.87 1.85 1.83 1.75 1.74 1.66 1.61

9.50 6.65 4.75 5.02 7.52 7.07 6.84 4.92 5.18 6.59

Nf Al Sh Ee Sm Bu Fm Sb Hh Oe

6.44 6.44 4.45 4.41 3.66 3.38 3.24 2.85 2.76 2.49

10.24 10.24 9.75 10.64 9.66 9.70 9.60 9.71 9.44 10.12

1 2 3 4 5 6 7 8 9 10

Rt Ho Gv Dw Wt Hs Df Ed Rs Cs

18.74 9.97 9.33 7.71 6.16 5.40 4.40 4.25 3.89 3.55

1.96 1.71 1.96 2.60 2.25 1.89 1.88 2.11 1.92 1.71

Rt Ho Gv Dw Hs Ed El Wt Df Cs

15.83 10.11 8.89 6.41 5.27 5.18 4.99 4.89 4.32 4.29

5.51 5.88 5.45 4.86 5.71 6.70 8.66 4.79 4.54 6.33

Mp Rt Cl Ho Tx Fd Tp Dp Bp Cs

55.63 13.93 13.68 11.19 3.93 3.59 2.62 2.22 2.09 1.76

10.21 8.64 11.15 7.80 11.37 6.90 11.23 8.09 7.78 8.35

Dp Mp Ho Rt Fd Fc Bp Gv Cl Rs

23.25 17.28 15.42 12.36 9.44 7.44 3.87 3.12 2.97 2.58

10.79 8.84 3.99 3.89 8.02 10.10 6.18 3.55 6.28 5.80

Mp Rt Ho Gv Dw Cs El Hs Dp Ed

20.83 15.82 10.25 6.58 4.76 3.91 3.77 3.71 3.60 3.58

9.86 4.26 4.54 4.48 3.93 4.73 7.16 4.85 6.41 5.87

Rt Ho Gv Dw Wt Hs Mp Ed Df Cs

15.15 10.00 8.39 6.41 5.17 4.85 4.65 4.57 4.34 3.99

3.77 3.79 3.85 3.58 3.43 4.17 5.18 4.73 3.49 4.37

Rt Gv Ho Dw Df Hs Hs Ed Mv Wt

14.81 11.82 8.42 7.74 5.84 5.35 5.35 4.98 4.98 4.21

8.01 9.01 7.70 8.49 8.95 8.28 8.28 7.82 9.15 8.06

21

Sector abbreviations are listed in Table 1.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

Forward /Ui+ q/

Value

22

Table 3 Paths with top 20 unweighted and weighted factor multipliers and factor embodiments Type

Rank

Path value (order, coverage) Energy consumption

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(MJ/A$) El1 112.38 Nf1 27.92 Ch1 27.42 Sp1 23.22 Is1 19.38 Fo1 17.63 Cr1 15.91 Mi1 15.60 At1 13.06 Pc1 11.51 Ce1 11.02 Ap1 10.26 Ke1 10.17 El1 El1 9.89 Ta1 9.52 Ga1 9.51 Pp1 9.10 Gp1 8.78 Bt1 7.94 El1 Nf1 6.78

(ha/’000A$) (0; (0; (0; (0; (0; (0; (0; (0; (0; (0; (0; (0; (0; (1; (0; (0; (0; (0; (0; (1;

86.7%) 52.4%) 52.2%) 59.5%) 49.9%) 56.3%) 57.3%) 54.5%) 57.4%) 45.7%) 44.4%) 42.8%) 42.6%) 7.6%) 57.7%) 64.8%) 30.5%) 35.8%) 53.2%) 12.7%)

(0; (0; (0; (1; (0; (0; (0; (1; (1; (0; (0; (1; (1; (1; (0; (1; (0; (0; (1; (0;

83.2%) 49.8%) 18.9%) 7.3%) 50.1%) 30.6%) 26.7%) 18.6%) 10.5%) 46.1%) 46.3%) 24.3%) 12.1%) 14.7%) 13.6%) 22.6%) 40.4%) 21.5%) 32.6%) 2.9%)

(PJ)

qm,i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

El1 -pr 503.54 Nf1 -ex 91.45 Rt1 -pr 62.45 El1 El1 -pr 44.33 Sp1 -ex 42.64 At1 -ex 42.58 At1 -pr 37.07 El1 Ho1 -pr 36.16 El1 Rt1 -pr 34.76 Is1 -ex 31.03 Ch1 -ex 30.85 El1 Al1 -ex 29.09 El1 Nf1 -ex 22.20 El1 Gv1 -gv 21.92 Wt1 -pr 21.57 El1 Ed1 -gv 20.45 Ap1 -pr 20.24 Df1 -gv 19.92 El1 Gl1 -ex 19.40 El1 -gv 17.82

Water use

Bc1 18.68 Wo1 15.69 Bc1 Mp1 7.16 Wo1 Tx1 4.63 Fr1 2.87 Ba1 2.72 Wh1 2.68 Bc1 Mp1 Lp1 1.48 Sw1 1.29 Wo1 Tx2 Cl1 1.00 Wo1 Tx1 Cl1 0.90 Bc3 Bc1 0.88 Bc3 Pg1 0.88 Wo1 Mp1 0.88 Wo1 Tx2 Tp1 0.88 Wo1 Lp1 0.84 Wo1 Tx1 Tx1 0.83 Wo1 Tx1 Tp1 0.76 Bc1 Mp1 Pe1 0.72 Bc3 Pe1 0.72

(L/A$)

NOx emissions

(0; (0; (1; (1; (0; (0; (0; (2; (0; (2; (2; (1; (1; (1; (2; (1; (2; (2; (2; (1;

93.1%) 97.6%) 79.2%) 76.1%) 90.4%) 84.4%) 84.2%) 40.4%) 80.8%) 37.0%) 33.3%) 4.4%) 52.7%) 9.7%) 38.4%) 22.8%) 13.7%) 33.4%) 33.1%) 33.0%)

Ri1 7397.99 Sc1 1528.04 Dc1 1381.02 Su1 1167.10 Bc1 677.35 Sc1 Cg1 551.03 Dc1 Dp1 544.58 Ri1 Fc1 436.33 Bx1 350.31 Wa1 332.59 Ws1 307.68 Vf1 306.53 Bc1 Mp1 259.63 Ba1 230.63 Wo1 211.56 Wh1 183.83 Su1 Fd1 136.84 Su1 Bv1 77.57 Dc1 Dp1 Dp1 70.18 Ri1 Ws1 69.26

(0; (0; (0; (0; (0; (1; (1; (1; (0; (0; (0; (0; (1; (0; (0; (0; (1; (1; (2; (1;

99.2%) 95.5%) 94.0%) 94.2%) 83.4%) 93.3%) 80.0%) 76.1%) 95.7%) 96.6%) 61.3%) 80.9%) 68.1%) 79.1%) 70.7%) 75.1%) 56.6%) 67.4%) 10.3%) 13.8%)

(kg CO2-e/A$) Fr1 89.41 Bc1 25.70 Sw1 16.42 Gd1 14.14 Lm1 13.20 El1 9.90 Bc1 Mp1 9.85 Hw1 7.25 Fr1 Fr1 7.10 Wo1 6.54 Ce1 3.83 Ri1 3.69 Dc1 3.43 Ga1 2.74 Ng1 2.36 Pg1 2.26 Bc1 Mp1 Lp1 2.04 Bl1 2.03 Wo1 Tx1 1.93 Ba1 1.92

(0; (0; (0; (0; (0; (0; (1; (0; (1; (0; (0; (0; (0; (0; (0; (0; (2; (0; (1; (0;

90.8%) 89.0%) 64.4%) 95.8%) 86.6%) 83.9%) 76.7%) 44.4%) 7.2%) 82.8%) 65.3%) 77.8%) 67.1%) 83.4%) 72.0%) 40.2%) 41.9%) 68.9%) 53.5%) 64.6%)

(0; (1; (1; (1; (1; (0; (1; (0; (2; (0; (1; (0; (2; (2; (1; (2; (0; (1; (2; (0;

97.5%) 40.5%) 37.8%) 53.7%) 5.0%) 99.4%) 4.7%) 49.2%) 28.0%) 32.3%) 22.3%) 87.3%) 21.6%) 38.2%) 38.8%) 9.7%) 11.5%) 0.9%) 16.6%) 92.4%)

(GL) Dc1 Dp1 -pr 1554.36 Wa1 -pr 1067.42 Bc1 Mp1 -ex 1056.89 Bc1 Mp1 -pr 987.25 Dc1 Dp1 -ex 825.40 Vf1 -pr 721.62 Su1 Fd1 -pr 475.88 Ri1 Fc1 -pr 472.72 Wo1 -ex 448.04 Su1 Fd1 -ex 367.51 Sc1 Cg1 -ex 326.35 El1 -pr 248.38 Wh1 -ex 233.78 Dc1 Dp1 Dp1 -pr 200.32 Ri1 Fc1 -ex 195.97 Ws1 Ho1 -pr 179.70 Bc1 Mp1 Rt1 -pr 178.92 Vf1 -ex 161.20 Ws1 -ex 144.95 Su1 Bv1 -pr 140.72

(1; (0; (1; (1; (1; (0; (1; (1; (0; (1; (1; (0; (0; (2; (1; (1; (2; (0; (0; (1;

53.0%) 94.1%) 34.8%) 32.5%) 28.1%) 67.8%) 32.0%) 53.1%) 82.9%) 24.7%) 74.3%) 71.9%) 88.8%) 6.8%) 22.0%) 12.3%) 16.0%) 15.1%) 42.4%) 62.8%)

(Mt CO2-e) El1 -pr 44.35 Bc1 Mp1 -ex 40.10 Bc1 Mp1 -pr 37.46 Fr1 -gv 31.57 Bl1 -ex 13.95 Wo1 -ex 13.84 Bc1 Mp1 Rt1 -pr 6.79 Nf1 -ex 6.12 Bc1 Mp1 Ho1 -pr 4.89 Bc1 -ex 4.59 Rt1 -pr 4.20 El1 El1 -pr 3.90 Fd1 -pr 3.89 Dc1 Dp1 -pr 3.86 El1 Ho1 -pr 3.19 Sp1 -ex 3.18 Al1 -ex 3.17 El1 Rt1 -pr 3.06 Bc1 -st 3.01 Fd1 -ex 3.00

(0; (1; (1; (0; (0; (0; (2; (0; (2; (0; (0; (1; (0; (1; (1; (0; (0; (1; (0; (0;

80.6%) 39.2%) 36.6%) 87.7%) 72.3%) 97.1%) 15.9%) 42.3%) 17.7%) 47.1%) 9.8%) 7.1%) 22.1%) 29.4%) 11.5%) 46.9%) 25.8%) 7.2%) 30.9%) 17.1%)

(Mha) Wo1 -ex 33.24 Bc1 Mp1 -ex 29.15 Bc1 Mp1 -pr 27.23 Wo1 Tx1 -ex 4.47 Wo1 Mp1 -ex 3.59 Wh1 -ex 3.41 Wo1 Mp1 -pr 3.35 Bc1 -ex 3.34 Wo1 Tx1 Cl1 -pr 2.81 Bc1 -st 2.19 Wo1 Tx1 -pr 1.85 Fr1 -gv 1.02 Bc1 Mp1 Fd1 -pr 0.85 Bc1 Mp1 Lp1 -ex 0.84 Dc1 Dp1 -pr 0.81 Wo1 Tx1 Tx1 -ex 0.80 Bc1 -pr 0.78 Bc1 Mp1 -st 0.68 Bc1 Mp1 Fd1 -ex 0.65 Ba1 -ex 0.55

Greenhouse gas emissions

SO2 emissions

(g/A$)

(g/A$)

Sp1 41.80 El1 28.00 Cr1 15.27 Ch1 11.71 Nf1 11.25 Sp2 Sp1 9.45 Su1 9.39 Ta1 9.32 Gp1 8.64 Mi1 8.31 Bc1 8.26 Ce1 7.74 Is1 7.73 Fo1 7.65 Rf1 7.44 At1 6.80 Ba1 6.73 Fi1 5.41 Fr1 4.66 Sw1 4.66

(0; (0; (0; (0; (0; (1; (0; (0; (0; (0; (0; (0; (0; (0; (0; (0; (0; (0; (0; (0;

72.0%) 82.9%) 75.8%) 53.7%) 53.7%) 16.3%) 64.0%) 75.0%) 55.6%) 60.4%) 61.0%) 55.6%) 45.1%) 55.4%) 62.2%) 62.0%) 58.2%) 51.3%) 46.6%) 46.6%)

El1 -pr 125.47 Sp1 -ex 76.77 Rt1 -pr 40.04 Nf1 -ex 36.85 At1 -ex 22.18 At1 -pr 19.31 Sp1 -pr 15.02 Wt1 -pr 13.53 Ch1 -ex 13.18 Bc1 Mp1 -ex 12.89 Is1 -ex 12.38 Bc1 Mp1 -pr 12.04 Df1 -gv 11.71 El1 El1 -pr 11.05 Bl1 -ex 9.72 El1 Ho1 -pr 9.01 Ap1 -pr 8.79 El1 Rt1 -pr 8.66 Vf1 -pr 8.66 Wt1 -ex 7.38

(0; (0; (0; (0; (0; (0; (0; (0; (0; (1; (0; (1; (0; (1; (0; (1; (0; (1; (0; (0;

79.6%) 60.7%) 26.8%) 51.0%) 33.1%) 28.9%) 11.9%) 17.5%) 47.7%) 19.1%) 41.7%) 17.8%) 27.3%) 7.0%) 25.9%) 11.2%) 39.6%) 5.8%) 34.3%) 9.5%)

(kt)

Nf1 158.65 El1 25.01 Nf1 Nf1 18.63 Nf1 Bu1 6.65 Al1 6.55 Is1 6.11 Nf2 Nf1 2.47 El1 El1 2.20 Nf1 Nf1 Nf1 2.19 Nf1 Om1 2.15 Ce1 2.07 Nf1 Fu1 1.81 Mi1 1.71 Nf1 Is1 1.64 El1 Al1 1.51 El1 Nf1 1.51 Is1 Is1 1.40 Nf1 Al1 Al1 1.34 Nf1 Al1 Nf1 1.34 Nf2 Bu1 1.31

(0; (0; (1; (1; (0; (0; (1; (1; (2; (1; (0; (1; (0; (1; (1; (1; (1; (2; (2; (1;

82.2%) 68.8%) 9.6%) 37.4%) 16.2%) 39.0%) 1.3%) 6.1%) 1.1%) 25.0%) 31.6%) 27.5%) 27.5%) 10.5%) 3.7%) 0.8%) 9.0%) 3.3%) 0.7%) 7.4%)

Nf1 -ex 519.59 El1 -pr 112.07 Nf1 Al1 -ex 79.93 Nf1 Nf1 -ex 61.00 Nf1 -pr 35.73 Al1 -ex 28.12 El1 El1 -pr 9.87 Is1 -ex 9.78 Nf1 Nf1 Al1 -ex 9.38 El1 Ho1 -pr 8.05 Nf1 Nf1 Nf1 -ex 7.16 El1 Al1 -ex 6.47 Nf1 Al1 Al1 -ex 5.75 El1 Nf1 -ex 4.94 El1 Ed1 -gv 4.55 Nf1 Al1 Nf1 -ex 4.39 Nf1 Nf1 -pr 4.19 El1 -gv 3.96 Nf1 Fu1 -pr 2.79 Nf1 Is1 -ex 2.63

(0; (0; (1; (1; (0; (0; (1; (0; (2; (1; (2; (1; (2; (1; (1; (2; (1; (0; (1; (1;

78.1%) 66.1%) 45.2%) 9.2%) 5.4%) 15.9%) 5.8%) 36.0%) 5.3%) 11.7%) 1.1%) 3.7%) 3.3%) 0.7%) 11.9%) 0.7%) 0.6%) 2.3%) 25.1%) 9.7%)

(kt)

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

mi

Land disturbance

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

23

Table 2 shows the ten top-ranking unweighted and weighted forward and backward linkages, including coefficients of variation, in monetary and environmental terms. A value of 10.0 with coefficient of variation 0.5 means that the respective linkage is ten times stronger than the average over all industries and that this value has a S.D. of 50%. First of all it can be observed that for all linkage types, the rank sequences in monetary terms (describing effects on intermediate demand) are different from those describing factors. Weighted linkages are more similar across factors because they are strongly determined by primary inputs {vi } and final demands {yi }. Finally, linkages in terms of resource use and emissions span a wider range of values than monetary linkages. As an example, forward unweighted land and water linkages are strong for industries producing fertilisers (Fe) and agricultural machinery (Ma) and chemicals (Ac) because their products are utilised by land- and water-intensive agricultural industries. Seed cotton (Sc) and cotton ginning (Cg) appear high-ranking only because cotton ginning is aggregated with other agricultural services, which serve land- and water-intensive cattle and sheep grazing. This shortcoming establishes a case for further disaggregation. Bauxite mining (Bx) has strong forward SO2 links because of emissions occurring through the oxidisation of the sulphur-containing carbon anode in aluminium smelting. The SO2 forward link of copper mining (Co) is facilitated by the oxidisation of copper and iron sulphides during the downstream purification of copper ore (National Greenhouse Gas Inventory Committee, 1998b, pp. 93/97). Once again, the processing of uranium, nickel, tin, silver, zinc, gold and lead ores is aggregated in the ‘non-ferrous basic metals’ (Nf) sector and therefore the forward SO2 links of the corresponding mining sectors (Uo, Sz, Gl) are probably overstated. As a final example, brown and black coal (Br, Bl) are utilised in energyand greenhouse-gas-intensive electricity generation, and aircraft (Ai) in energy- and NOx -intensive transportation. Some of the sectors mentioned above are small in terms of their value added and therefore disappear in weighted forward linkages. The latter are dominated by wholesale trade Wt), non-residential building (Nb) and business management and technical services (Ms, Ts). The products of these industries are utilised by almost all industries in the economy. Unweighted backward linkages comprise a different set: industries dependent on agriculture (meat and dairy products (Mp, Dp), textiles (Tx), leather products (Lp) and cotton ginning (Cg)) have strong backwards linkages in terms of land and water. Similarly, non-ferrous metals (Nf), pulp and paper (Pp) and iron and steel (Is) depend strongly on energy, and are therefore also linked in terms of greenhouse gas and NOx emissions. Once the importance of final demand is taken into account, retail trade (Rt), meat and dairy products (Mp, Dp), restaurants and accommoda-

16

This result is consistent with rankings obtained for the Brazilian economy by Sonis et al. (1995a) who report that weighting of linkages produced rankings that were quite different from those of unweighted linkages.

24

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

tion (Ho), rent for dwellings (Dw) and government final demand (Gv) are strongly linked to their upstream suppliers. 3.2. Field of influence As suggested by Sonis et al. (1995b), Sonis and Hewings (1999) and Sonis et al. (2000), the field of influence intensities S˜ij q can be visualised as an ‘economic landscape’ (Figs. 3 and 4). The floor underlying the landscape is organised in the same way as an Australian input/output table: starting in the upper left corner with inter-agricultural transactions, primary (agriculture and mining), secondary (food and manufacturing) and tertiary (wholesale, retail, repairing, electricity, gas, water, transport, communication, services and administration) are arranged along both horizontal axes. Blocks of sectors are marked in one horizontal direction by separating lines of black bars. Commodity flow proceeds inwards from the left

Fig. 3. Economic landscape representing the field of influence intensity S˜ij q of intermediate transactions in value terms. Agr, agriculture; Min, mining; Fd, food; Man, manufacturing; Trd, wholesale and retail trade; util, electricity, gas and water utilities; tra, transport; Serv, services; sector abbreviations in Table 1.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

25

Fig. 4. Economic landscape representing the field of influence intensity S˜ij q of intermediate transactions in terms of greenhouse gas emissions. Abbreviations as in Fig. 3.

(supplying industries, backward linkages attached) and outwards to the top (using industries, forward linkages attached). The vertical axis carries the normalised field of influence intensity as in Eq. (26). Each vertical bar then represents the relative importance of the industries involved in the respective transaction: a value of 100 means that the combined product of forward and backward linkage and of the transaction value is 100 times larger than the average over all intermediate demand. Fig. 3 depicts S˜ij q in terms of intermediate demand (qi /1
/i ). Important requirements and sales coefficients appear in clusters mostly above the diagonal, thus tracing the natural flow of commodities from primary to secondary to tertiary industries. The clusters with the strongest fields of influence comprise material (Cc, Sm, En, Ee) and service (Pd, Ms, Cm, St, At, Rd, Pr) inputs into non-residential building (Nb) and wholesale trade (Wt), followed by business-oriented services (Ms, Pd, Ts, Cm) and iron and steel (Is) for vehicles, equipment and metal products. Important primary suppliers are involved in crude oil (Oi) for refining products (Ap, Fo), and cattle (Bc, Dc) for meat (Mp) and dairy (Dp).

26

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

Switching to greenhouse gas emissions (Fig. 4) changes the picture considerably: services and trade have diminished, while new fields of influence have sprung up for material (hay and fodder in Vf and Ch) and service (rail and road transport Rf, Rd) inputs into primary industries (Bc, Fr, Bl), shipping (Sp) of iron ore and electricity supply for heavy industries (Is, Ch, Al, Nf). Important in both monetary and greenhouse gas terms are beef cattle (Bc) for meat (Mp), the paper production chain (Sw 0/Pp 0/Pr, Pa), crude oil (Oi) for refining (Ap, Fo, Pc) and iron and steel (Is) for vehicles, equipment and metal products. 3.3. Structural path analysis The algorithm described in Section 3.2 was run in order to obtain a decomposition of multipliers mi according to Eq. (29) and of absolute factor requirements mi yi according to Eq. (32). The latter reflect */as the weighted multiplier in Eq. (23) */ responses to fractional changes in final demand. Both can easily be obtained from each other by dividing/multiplying by total final demand y . Note that instead of representing unit-less deviations from an average value (as for linkages and fields of influence), path values carry the units of multipliers (Eq. (29)) and of factors (Eq. (32)). In the following, each path will be characterised by a code, consisting of (1) a description of the path vertices (a ,ij ); (2) the path value; (3) the path order; and (4) the path coverage, that is, the relative contribution (in %) to the total factor multiplier referring to the final demand from the industry denoted by the second index (j ) in the last vertex. In the presentation of the results, vertex indices ij are assigned the codes listed in Table 1. These codes are then supplemented by the vertex types a as in Eq. (8) and, in the case of Eq. (32), further complemented by the final demand segment type m as in Eq. (30). For example, the hypothetical multiplier path Pl1 En4 Sf1 10.00 (2; 2.50%), describes the specific factor inputs for plastic (Pl) produced outside Australia for the foreign manufacture of electronical equipment (En) which is imported for capital investment (4) by domestic providers of services to finance (Sf1). The path value is 10.00 (factor-specific units) per Australian Dollar at 1995 basic prices (1995A$). The path is of second order and constitutes a coverage of 2.50% of the total factor multiplier of the ‘services to finance’ industry. The fourth-order path denoted by Is1 Sh1 Mv2 Mv3 Rd1 -gv describes the total factor inputs for basic iron and steel (Is) made into sheet metal products (Sh) for motor vehicle parts (Mv) imported (2) by domestic assemblers of motor vehicles (Mv) sold for capital investment (3) to the road freight industry (Rd1) servicing the government (-gv). The vertex Mv2 Mv is called an ‘internal transaction’ because the transaction occurs within the same sector (Mv). Internal deliveries must be understood by considering sector inhomogeneity: some establishments in the ‘motor vehicle and parts’ industry may produce only particular parts, while other mainly assemble vehicles. All procedures were run with a maximum depth of ten orders, with thresholds chosen to be :/1% of the average multiplier value. Note that the number of decimal places used for printing path values in Table 3 does not indicate an uncertainty level, but was only chosen in order to be able to show values which are slightly above the threshold.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

27

On-site energy consumption (zeroth-order paths) of electricity generation and some manufacturing industries represent the most important multiplier paths (see upper half of Table 3). Within land disturbance and water use, agricultural industries (Bc, Wo, Su, Dc, Ri, Sc, Wh), as well as food and textile industries (Mp, Tx, Dp, Cg) are predominant. In contrast to energy consumption and emissions, second-order paths are common, such as grazing beef cattle (Bc1) for meat producers (Mp1) delivering into the leather industry (Lp1). The commodity delivered by meat producers into the leather industry is skins, which are not a primary, but a ‘secondary’ or a ‘joint product’. An important path involving capital investment is Bc3 Bc1, describing an internal delivery of livestock between beef cattle grazers for breeding. Significant imported land disturbance appears for example in the path Wo1 Tx2 Cl1. Note that this ranking assumes Australian per-value land disturbance in foreign production (see Section 2). In the case of imported fibres, this assumption is unrealistic, so that the respective intensity value has to be treated cautiously. The zeroth-order linkage paths often comprise primary industries with relatively small final demand and hence, they are not important constituents of total requirements. Here, as a consequence, a larger number of first- and second-order paths can be found. Electricity generation for private final consumption dominates the energy requirement paths (see lower half). The remainder are paths leading to either important private final consumption (retail, Rt, and hospitality, Ho) or important export commodities (non-ferrous metal products, Nf, or international shipping, Sp and air transport, At). Since NOx and SO2 emissions are strongly correlated with energy consumption, the above industries are also found to generate important paths in terms of these factors. However, the ranking differs and firstorder paths are more common. In Australia, both energy and non-energy greenhouse gas sources contribute significantly to the total greenhouse gas emissions, so that both agricultural and manufacturing industries, as well as forestry and electricity generation, can be found participating in top-ranking requirement paths. Paths are mostly of zero or first order. Again, within land disturbance and water use, agricultural industries as well as food and textile industries are predominant. Note that, once again industries listed in Table 3 coincide with top-ranking industries in Figs. 3 and 4, demonstrating that paths provide detailed information about the content of fields of influence. It appears that a considerable amount of environmental and resource pressure is exerted in Australia for the sake of providing income from exports. Beef cattle for exported meat products (Bc1 Mp1 -ex) alone, for example, is responsible for 29.2 Mha of land disturbance, 1057 GL of water use, 37.5 Mt CO2-e of greenhouse gases (mostly through extensive land clearing in the state of Queensland) and 12.9 kt of NOx emissions. Similarly, the export of non-ferrous metal products (Nf1 -ex) generates 6.1 Mt CO2-e of greenhouse gases, 36.9 kt of NOx , 519.6 kt of SO2 and needs 91.5 PJ of energy, while exported sheep and wool (Wo1 -ex) causes 33.2 Mha of land disturbance, 13.8 Mt CO2-e of greenhouse gas emissions (mostly CH4 from enteric fermentation) and requires 448 GL of water.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

28

4. Discussion The three concepts treated in this work address the structure of environmental pressure associated with economic activity at different levels of detail. While Hirschman /Rasmussen-type linkages provide information on a N -sector level, the field-of-influence approach deals with N2 transactions between two sectors and structural path analysis appraises an (in principle) infinite number of input /output paths.17 Hence, the more detailed approaches yield information about the content of aggregate measures calculated in less detailed approaches. Some measures refer to either unit or fractional primary input or final demand. Since each of these addresses a different issue, it depends on the question to be examined, whether weighted or unweighted, or more or less detailed measures are employed, and results from different approaches should be seen as complementary. A shortcoming of the rank sequences presented in the previous sections is that they depend on the sector classification in the respective input /output table, which was already noted by Bharadwaj (1966 p. 318) (see also Hewings, 1974). In addition, important internal transactions may enter top ranks if a gross instead of a net table is used. Moreover, generalised multipliers mi carry a range of stochastic uncertainties, which are caused by potential errors due to the aggregation of input/output data over firms, the mis-allocation of a specific product in an aggregated sector, source data uncertainty, the imports assumption (Bullard et al., 1978) or the mis-estimation of capital flow values (Lenzen, 2001a). S.E. estimates for such uncertainties have not been studied extensively, but are mostly B/20% in the cases reported in the literature (Bullard and Sebald, 1977, 1988). These uncertainties affect detailed measures, such as paths, more than aggregated measures, such as fields of influence or linkages. In order to reduce these uncertainties, the following improvements in the underlying data are desirable: (1) environmentally important industry sectors should not be classified within another aggregate, but separately, in order to reduce the allocation error; (2) a multi-region input /output framework could be set up, including national data on resource use and pollution in order to reduce the error associated with the imports assumption; and (3) an input /output table for domestically produced as well as imported capital flow could be estimated by statistical offices regularly.

5. Conclusions In this work, three traditional key sector concepts were formulated in terms of environmentally important production factors and extended in order to account for the level of primary input and final demand. The results emerging from these generalised linkages yield insights about forward and backward resource use and pollutant emission effects associated with sectoral inputs and outputs. Generalised fields of influence characterise single intermediate transactions that exhibit above17

In this context, Sonis et al. (1994) use the terms macro-, meso- and micro-level perspective.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

29

average importance for the rest of the economy. Finally, by enabling the identification and ranking of paths, generalised structural path analysis supplies detailed decompositions into the ‘contents’ of both linkages and fields of influence. Naturally, primary industries, such as grazing or mining, have strong forward linkages, while secondary industries, such as meat and dairy products, metals and textiles, have strong backwards linkages. Weighting with primary input and final demand has a stronger influence on linkages than weighting with production factor usage. Economic landscapes mapping fields of influence are useful to capture in one image the interdependence of industries in economies, the key requirements and sales and also the shifts that occur when different production factors are appraised. Comparing the topology of intermediate demand with that of greenhouse gas emissions, for example, illustrates where the various tiers of the economy come into play. The largest constituents of linkages and fields of influence are represented by structural paths of zeroth order, but first- and second-order paths also occupy top ranks. A remarkable result of the structural path analysis is that a considerable part of environmental and resource pressure is exerted along paths that ultimately lead into exports. Comparative key sector analysis in monetary and environmental terms can be applied in environmental policy design and analysis. An example for such a policy is given by Daniels (1992): since the 1980s Australia has sought to escape from the predicament of increasing foreign debt and falling primary commodity prices by expanding the volume of primary exports such as meat, wool, wheat and non-ferrous metals in order to maintain total export revenues and living standards. Since these exports are associated with a high level of environmental degradation (see Tables 2 and 3), Australia has become locked into an environmental /economic dilemma through increasing dependency on degrading production and further erosion of environmental quality. Daniels argued that, in order to avoid long-term losses of productivity, biodiversity and real income, Australia has to re-direct its domestic production towards more value-adding and less land- and emissions-intensive commodities. A similar conflict of interests is a current Australian water policy issue: in order to reduce the irrigation-induced stress on the Murray-Darling river system in South-Eastern Australia, shifts in production from water-intensive industries towards more value-adding sectors have been recommended (Australian Academy of Technological Sciences and Engineering, 1999). The analytical techniques described in this article can provide valuable information for decisionmaking in both cases.

Acknowledgements This work was financially supported by CSIRO Sustainable Ecosystems, Canberra. The author wishes to thank an anonymous reviewer for helpful comments

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and Vicki Moore from the School of Physics’ Library for her patience and help in obtaining the relevant literature.

References Augustinovics, M., 1970. Methods of international and intertemporal comparison of structure. In: Contributions to Input /Output Analysis: Fourth International Conference on Input /Output Techniques. North-Holland, Geneva, Switzerland. Australian Academy of Technological Sciences and Engineering, Institution of Engineers, Australia, 1999. Water and the Australian Economy. Australian Academy of Technological Sciences and Engineering, Parkville, Vic., Australia. Australian Bureau of Agricultural and Resource Economics, 1997a. Australian energy consumption and production. ABARE Research Report 97.2, Commonwealth of Australia, Canberra, Australia. Australian Bureau of Agricultural and Resource Economics, 1997b. Australian energy consumption and production. Table C1AUST 1973 /74 to 1994 /95. Electronic file (unpublished). Australian Bureau of Agricultural and Resource Economics, 1999. Personal communication. Australian Bureau of Statistics, 1999. Australian National Accounts, Input /Output. Tables, 1994 /95. ABS Catalogue No. 5209.0, Australian Bureau of Statistics, Canberra, Australia. Australian Bureau of Statistics, 2000a. Water Account Data 1993 /94 to 1996 /97. Electronic file (unpublished). Australian Bureau of Statistics, 2000b. Water Account for Australia. ABS Catalogue No. 4610.0, Australian Bureau of Statistics, Canberra, Australia. Beyers, W.B., 1976. Empirical identification of key sectors: some further evidence. Environment and Planning A 8, 231 /236. Bharadwaj, K.R., 1966. A note on structural interdependence and the concept of a key sector. Kyklos 19, 315 /319. Bon, R., 1988. Supply-side multiregional input /output models. Journal of Regional Science 28, 41 /50. Boucher, M., 1976. Some further results on the linkage hypothesis. Quarterly Journal of Economics 90, 313 /318. Bullard, C.W., Sebald, A.V., 1977. Effects of parametric uncertainty and technological change on input / output models. Review of Economics and Statistics 59, 75 /81. Bullard, C.W., Sebald, A.V., 1988. Monte Carlo sensitivity analysis of input /output models. The Review of Economics and Statistics 70, 708 /712. Bullard, C.W., Penner, P.S., Pilati, D.A., 1978. Net energy analysis */handbook for combining process and input /output analysis. Resources and Energy 1, 267 /313. Bulmer-Thomas, V., 1982. Trade, structure and linkages in Costa Rica. Journal of Development Economics 5, 73 /86. Casler, S., 1983. Correcting input /output coefficients for capital depreciation. Energy Systems and Policy 7, 171 /193. Cella, G., 1984. The input /output measurement of interindustry linkages. Oxford Bulletin of Economics and Statistics 46, 73 /84. Cella, G., 1986. The input /output measurement of interindustry linkages: a reply. Oxford Bulletin of Economics and Statistics 48, 379 /384. Cella, G., 1988. The supply-side approaches to input /output analysis: an assessment. Ricerche Economiche 42, 433 /451. Chen, J.C., Rose, A., 1986. The joint stability of input /output production and allocation coefficients. Modelling and Simulation 17, 251 /255. Chen, J.C., Rose, A., 1989. The absolute and relative joint stability of input /output production and allocation coefficients. In: Peterson, W.A. (Ed.), Advances in Input /Output Analysis. Oxford University Press, New York, USA, pp. 25 /36.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

31

Clements, B.J., 1990. On the decomposition and normalization of interindustry linkages. Economics Letters 33, 337 /340. Clements, B.J., Rossi, J.W., 1991. Interindustry linkages and economic development: the case of Brazil reconsidered. Developing Economies 29, 166 /187. Cochrane, S.G., 1990. Input /output linkages in a frontier region of Indonesia. International Regional Science Review 13, 183 /203. Crama, Y., Defourny, J., Gazon, J., 1984. Structural decomposition of multipliers in input /output or social accounting matrix analysis. Economie Applique´e 37, 215 /222. Cronin, F.J., 1984. Analytical assumptions and causal ordering in interindustry modeling. Southern Economic Journal 51, 521 /529. Cuello, F.A., Mansouri, F., Hewings, G.J.D., 1992. The identification of structure at the sectoral level: a reformulation of the Hirschman /Rasmussen key sector indices. Economic Systems Research 4, 285 / 296. Daniels, P.L., 1992. Barriers to sustainable development in natural resource-based economies: Australia as a case study. Society and Natural Resources 5, 247 /262. Davis, H.C., Salkin, E.L., 1984. Alternative approaches to the estimation of economic impacts resulting from supply constraints. Annals of Regional Science 18, 25 /34. Defourny, J., Thorbecke, E., 1984. Structural path analysis and multiplier decomposition within a social accounting matrix framework. Economic Journal 94, 111 /136. Diamond, J., 1974. The analysis of structural constraints in developing economies: a case study. Oxford Bulletin of Economics and Statistics 36, 95 /108. Diamond, J., 1975a. Inter-industry indicators of employment potential. Applied Economics 7, 265 /273. Diamond, J., 1975b. Key sectors in some underdeveloped countries: a comment. Kyklos 29, 762 /764. Dietzenbacher, E., 1989. On the relationship between the supply-driven and the demand-driven input / output model. Environment and Planning A 21, 1533 /1539. Dietzenbacher, E., 1997. In vindication of the Ghosh model: a reinterpretation as a price model. Journal of Regional Science 37, 629 /651. Forssell, O., 1998. Extending economy-wide models with environment-related parts. Economic Systems Research 10, 183 /199. Fritz, O.M., Sonis, M., Hewings, G.J.D., 1998. A Miyazawa analysis of interactions between polluting and non-polluting sectors. Structural Change and Economic Dynamics 9, 289 /305. Georgescu-Roegen, N., 1971. The Entropy Law and the Economic Process. Harvard University Press, Cambridge, MA, USA. Ghosh, A., 1958. Input /output approach in an allocation system. Economica XXV, 58 /64. Giarratani, F., 1976. Application of an interindustry supply model to energy issues. Environment and Planning A 8, 447 /454. Glanznig A, 1995. Native vegetation clearance, habitat loss and biodiversity decline. Biodiversity Series, Paper No. 6. Department of the Environment, Sport and Territories Biodiversity Unit, Canberra, Australia. Gould, B.W., Kulshreshtha, S.N., 1986. An interindustry analysis of structural change and energy use linkages in the Saskatchewan economy. Energy Economics 8, 186 /196. Groenewold, N., Hagger, A.J., Madden, J.R., 1987. The measurement of industry employment contribution in an input /output model. Regional Studies 21, 255 /263. Groenewold, N., Hagger, A.J., Madden, J.R., 1993. Measuring industry importance: an Australian application. Annals of Regional Science 27, 175 /182. Guccione, A., 1986. The input /output measurement of interindustry linkages: a comment. Oxford Bulletin of Economics and Statistics 48, 373 /377. Hawdon, D., Pearson, P., 1995. Input /output simulations of energy, environment, economy interactions in the UK. Energy Economics 17, 73 /86. Hazari, B., 1970. Empirical identification of key-sectors in the Indian economy. Review of Economics and Statistics 52, 301 /305. Heimler, A., 1991. Linkages and vertical integration in the Chinese economy. Review of Economics and Statistics 73, 261 /267.

32

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

Herendeen, R.A., 1978. Input /output techniques and energy cost of commodities. Energy Policy 6, 162 / 165. Hewings, G.J.D., 1974. The effect of aggregation on the empirical identification of key-sectors in a regional economy: a partial evaluation of alternative techniques. Environment and Planning A 6, 439 / 453. Hewings, G., 1982. The empirical identification of key-sectors in an economy: a regional perspective. Developing Economies 20, 173 /195. Hewings, G.J.D., Merrifield, J., Schneider, J.C., 1984. Regional tests of the linkage hypothesis. Revue d’Economie Re´gionale et Urbaine 2, 275 /289. Hirschman, A.O., 1958. The Strategy of Economic Development. Yale University Press, New Haven, CT, USA. Isard, W., Choguill, C.L., Kissin, J., Seyfarth, R.H., Tatlock, R., Bassett, K.E., Furtado, J.G., Izumita, R.M., 1972. Ecologic /Economic Analysis for Regional Development. The Free Press, New York, NY, USA. Jones, L.P., 1976. The measurement of Hirschmanian linkages. Quarterly Journal of Economics 90, 323 / 333. Kol, J., 1991. Key sectors, comparative advantage, and international shifts in employment: a case study for Indonesia, South Korea, Mexico and Pakistan and their trade relations with the European Community. In: Peterson, W. (Ed.), Advances in Input /Output Analysis. Oxford University Press, New York, NY, USA, pp. 199 /210. Laumas, P.S., 1975a. Key sectors in some underdeveloped countries. Kyklos 28, 62 /79. Laumas, P.S., 1975b. Key sectors in some underdeveloped countries: a reply. Kyklos 29, 767 /769. Laumas, P.S., 1976. The weighting problem in testing the linkage hypothesis. Quarterly Journal of Economics 90, 308 /312. Lenzen, M., 2001a. Errors in conventional and input /output-based life-cycle inventories. Journal of Industrial Ecology 4, 127 /148. Lenzen, M., 2001b. A generalised input /output multiplier calculus for Australia. Economic Systems Research 13, 65 /92. Lenzen, M., Foran, B., 2001. An input /output analysis of Australian water usage. Water Policy 3, 321 / 340. Lenzen, M., Murray, S.A., 2001. A modified ecological footprint method and its application to Australia. Ecological Economics 37, 229 /255. Leontief, W., 1936. Quantitative input and output relations in the economic system of the United States. Review of Economics and Statistics 18, 105 /125. Leontief, W., 1941. The Structure of the American Economy, 1919 /1939. Oxford University Press, Oxford, UK. Leontief, W., 1966. Input /Output Economics. Oxford University Press, New York, NY, USA. Leontief, W., Ford, D., 1970. Environmental repercussions and the economic structure: an input /output approach. Review of Economics and Statistics 52, 262 /271. Loviscek, A.J., 1982. Industrial cluster analysis */backward or forward linkages? Annals of Regional Science 16, 36 /47. McGilvray, J., 1977. Linkages, key-sectors and development strategy. In: Leontief, W. (Ed.), Structure, System and Economic Policy. Cambridge University Press, Cambridge, UK, pp. 49 /56. Meller, P., Marfa´n, M., 1981. Small and large industry: employment generation, linkages, and key sectors. Economic Development and Cultural Change 29, 263 /274. Miller, R.E., Blair, P.D., 1985. Input /Output Analysis: Foundations and Extensions. Prentice-Hall, Englewood Cliffs, NJ, USA. Miller RE, Lahr ML, 2000. A taxonomy of extractions. In: Proceedings of the Twelfth International Conference on Input /Output Techniques, Macerata, Italy. http://policy.rutgers.edu/cupr/iioa/iioa.htm Miller, R.E., Polenske, K.R., Rose, A.Z., 1989. Frontiers of Input /Output Analysis. Oxford University Press, New York, NY, USA. Miyazawa, K., 1966. Internal and external matrix multipliers in the input /output model. Hitotsubashi Journal of Economics 7, 38 /55.

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

33

Murray-Darling Basin Ministerial Council, 1995. An audit of water use in the Murray-Darling Basin. Murray-Darling Basin Ministerial Council, Canberra, Australia. National Greenhouse Gas Inventory Committee, 1998a. Australian Methodology for the Estimation of Greenhouse Gas Emissions and Sinks. Workbooks 1.1 /8.1, Australian Greenhouse Office, Canberra, Australia. National Greenhouse Gas Inventory Committee, 1998b. Australian Methodology for the Estimation of Greenhouse Gas Emissions and Sinks, Land Use Change and Forestry; Industrial emissions. Workbook 7.1, Australian Greenhouse Office, Canberra, Australia. Oosterhaven, J., 1988. On the plausibility of the supply-driven input /output model. Journal of Regional Science 28, 203 /217. Oosterhaven, J., 1996. Leontief versus Ghoshian price and quantity models. Southern Economic Journal 62, 750 /759. Panchamukhi, V.R., 1975. Linkages in industrialization: a study of selected developing countries in Asia. UN Journal of Development Planning 8, 121 /165. Proops, J.L.R., 1988. Energy intensities, input /output analysis and economic development. In: Ciaschini, M. (Ed.), Input /Output Analysis */Current Developments. Chapman and Hall, London, UK, pp. 201 /216. Rao, V., Harmston, F.K., 1979. Identification of key sectors in a region of a developed economy. Annals of Regional Science 13, 78 /90. Rasmussen, P.N., 1956. Studies in Intersectoral Relations. North-Holland, Amsterdam, Netherlands. Riedel, J., 1976. A balanced-growth version of the linkage hypothesis: a comment. Quarterly Journal of Economics 90, 319 /322. Schultz, S., 1977. Approaches to identifying key-sectors empirically by means of input /output analysis. Journal of Development Studies 14, 77 /96. Schultz, S., Schumacher, D., 1975. Key sectors in some underdeveloped countries: a comment. Kyklos 29, 765 /766. Sherman, J., Morrison, W.J., 1950. Adjustment of an inverse matrix corresponding to a change in one element of a given matrix. Annals of Mathematical Statistics 21, 124 /127. Sonis, M., Hewings, J.J.D., 1989. Error and sensitivity input /output analysis: a new approach. In: Miller, R.E., Polenske, K.R., Rose, A.Z. (Eds.), Frontiers of Input /Output Analysis. Oxford University Press, New York, USA, pp. 232 /244. Sonis, M., Hewings, G., 1992. Coefficient change in input /output models: theory and applications. Economic Systems Research 4, 143 /157. Sonis, M., Hewings, G.J.D., 1995. Matrix sensitivity, error analysis and internal/external multiregional multipliers. Hitotsubashi Journal of Economics 36, 61 /70. Sonis, M., Hewings, G.J.D., 1999. Economic landscapes: multiplier product matrix analysis for multiregional IO systems. Hitotsubashi Journal of Economics 40, 59 /74. Sonis, M., Hewings, G.J.D., Lee, J.K., 1994. Interpreting spatial economic structure and spatial multipliers: three perspectives. Geographical Analysis 26, 124 /151. Sonis, M., Guilhoto, J.J.M., Hewings, G.J.D., Martins, E.B., 1995a. Linkages, key sectors, and structural change: some new perspectives. Developing Economies 33, 233 /270. Sonis, M., Hewings, G.J.D., Guo, J.M., 1995b. Evaluation of Economic Structure: the Multiplier Product Matrix. Regional Economics Applications Laboratory, Urbana-Champaign, IL, USA. Sonis, M., Hewings, G.J.D., Guo, J., 2000. A new image of classical key sector analysis: minimum information decomposition of the Leontief inverse. Economic Systems Research 12, 401 /423. Tiebout, C.M., 1960. Regional and interregional input /output models: an appraisal. In: Pfouts, R.W. (Ed.), The Techniques of Urban Economic Analysis. Chandler-Davis, West Trenton, NJ, USA, pp. 95 /407. Treloar, G., 1997. Extracting embodied energy paths from input /output tables: towards an input /outputbased hybrid energy analysis method. Economic Systems Research 9, 375 /391. Weber, C., 1998. Zerlegung kumulierter energieaufwendungen als instrument der umweltorientierten verflechtungsanalyse. Jahrbu¨cher fu¨r Nationalo¨konomie und Statistik 217, 273 /291. Weber, C., Schnabl, H., 1998. Environmentally important intersectoral flows: insights from main contributions identification and minimal flow analysis. Economic Systems Research 10, 337 /356.

34

M. Lenzen / Structural Change and Economic Dynamics 14 (2003) 1 /34

Whetton, P.H., Fowler, A.M., Haylock, M.R., Pittock, A.B., 1993. Implications of climate change due to the enhanced greenhouse effect on floods and droughts in Australia. Climatic Change 25, 289 /317. Wilkenfeld and Associates Pty Ltd., 1998. Australia’s National Greenhouse Gas Inventory 1990 and 1995: cross-sectoral analysis of emissions, Australian Greenhouse Office, Killara, NSW, Australia. Yotopoulos, P.A., Nugent, J.B., 1973. A balanced-growth version of the linkage hypothesis: a test. Quarterly Journal of Economics 87, 157 /171. Yotopoulos, P.A., Nugent, J.B., 1976. In defense of a test of the linkage hypothesis. Quarterly Journal of Economics 90, 334 /343.