9 NAMEA and the Input–Output Framework
Sensitivity of Environmental Variables to Changes in the Production Structure
Introduction
NAMEA is a methodology which allows integration of economic and environmental information in a coherent manner. The satellite accounts of the national accounting systems in European countries have been built using NAMEA methodology.
One of the advantages of using NAMEA to build environmental satellite account systems is that it offers the possibility of analysing the impact of productive activities at a disaggregated level per sector or per economic activity branch (de Haan and Keuning, 1996). In order to do so, the aforementioned environmental account systems should be linked to the national accounts dedicated to more disaggregated economic information, i.e. to the input–output framework.
The input–output framework is basically made up of supply-and-use tables, symmetric input–output tables and other complementary tables. These tables show the flow of goods and services between the different production activities and between these activities and the economic agents which make up the final demand of the economy for a given period and in monetary terms.
Input–output techniques can be used for a detailed and coherent analysis of the production flows of an economy and their environmental consequences. In this chapter, the symmetrical input–output table will be used since it allows us to analyse both the direct and indirect flows that stem from changes in final demand.
Accordingly, the chapter is structured as follows. The foundations of the input–output model applied to environmental issues are provided in next section, together with a classification of applications in the context of changes in the input–output coefficients. The third section goes deeper into the analysis of the variability of the coefficients and different techniques to analyse the sensitivity of NAMEA variables to changes in the productive structure of activity branches are reviewed. The advantages and drawbacks of the sensitivity analysis as well as several extensions to the environmental area are discussed in the final section.
Basic Model and Literature
There is an abundant literature linking the input–output framework to environmental issues and, thus, to environmental accounts. Leontief himself considered this possibility in the 1970s (Leontief, 1970) as a further development of his mathematical model, particularly through the inclusion of information on air pollutants (Leontief and Ford, 1972).
Before reviewing the different possibilities of using the input–output techniques in the environmental realm, the basic model is delineated.
Let us assume that the production activity of an economic system is made up of n productive sectors which interact in order to produce goods and services that meet final demand (private and public consumption, investment, net exports). Each productive sector consumes water and other natural resources and emits air pollutants and other residues. NAMEA allows us to identify the amount of resources, gases or residues which can be attributed to each production branch and to include them in the environmental satellite accounts. These substances, either consumed or generated, will be referred to as NAMEA substances from now on.
It will be assumed that the amount of the NAMEA substance consumed or generated e of the m sector can be broken down into the following two factors:
where: cm represents the intensity coefficient (i.e. substance per unit of output of sector m) and xm is the quantity of output produced by m (in monetary terms). The level of xm will depend on demand for the products of m by the rest of the sectors and by final demand:
where xmj represent the sales of sector m to sector j, and ym are the sales of m to the final demand.
On the other hand, the technical coefficients amj can be defined as the output of sector m required to produce a unit of product by sector j:
We know that activity j will have a direct requirement for the products of sector m but it will also have an indirect requirement for those products. This is due to the fact that the requirements of sector j for the products of a third sector k will lead to a requirement for the product of sector m by k, since k needs those (intermediate) products for its own production. This chain of additional production induced by sector m in order to produce the products of sector j may be extended indefinitely through the inclusion of other intermediate activities. The total requirements of a sector for the goods and services produced by the rest of the sectors can be picked up by the coefficients of the inverse Leontief matrix. Therefore, equation (2) can be rewritten as follows:
where bmq are the elements of the row m of the inverse Leontief matrix 
which includes the direct and indirect purchases of the good or service produced by m made by sector q. A is the matrix (n × n) of technical coefficients which includes all the elements defined in (3).1
Furthermore, the vector of the coefficients of final demand can be defined per sector as:
where 
represents the overall final demand which is an indicator of general economic activity. Equation (4) will then be transformed into:
Then,
To sum up, three factors are behind the level of the NAMEA substance e of the m sector, including:
Once the basic model has been specified, we can distinguish three main lines of research which use the aforementioned framework in order to assess the environmental impacts of the economic system, with a disaggregation per sector.
A first group of authors have analysed the impact of changes in the final demand of the different sectors on either the global or the sectoral level of generation/consumption of a NAMEA substance through the analysis of demand multipliers (columns of coefficients of the Leontief matrix). This approach assumes structural stability of the productive relationships, i.e. the technical coefficients are considered fixed and only the ‘flow’ variables change.3 If (7) is expressed in a disaggregated manner, then the following expression results:
In other words, the impact of a sector on the NAMEA substance generation/ consumption e due to changes in the final demand vector is assessed. In turn, these changes depend on variations in the level of economic activity (scale factor) and/or on changes in the expenditure and investment habits of actors (hi coefficients). Several articles follow this approach, including: Proops (1988), Lenzen (1998), Munksgaard and Pedersen (2001), Machado et al. (2001), Ferng (2003), Sánchez-Chóliz and Duarte (2004), Gallego and Lenzen (2005), Mongelli et al. (2006), Peters and Hertwich (2006), Butnar and Llop (2007), Alcántara and Padilla (2009), Alcántara et al. (2010) and Chen and Zhang (2010).
A second set of studies within an input–output framework are based on structural decomposition techniques. The changes experienced by the level of generation/consumption of a NAMEA substance between two periods are explained by the changes in final demand and structural coefficients, within a comparative static approach:
In contrast to the first set of studies, this approach analyses the impact of changes in the technical coefficients (7) on the level of the NAMEA polluting element under investigation. In other words, it involves a relaxation of the structural stability assumption. The drawback is that the distribution of the impacts between different factors (structure and demand flows) involves some arbitrariness and ad-hoc solutions are proposed (Dietzenbacher and Los, 1998; Rose and Chen, 1991; Chang and Lin, 1998; Wier, 1998; Kagawa and Inamura, 2001; de Haan, 2001; Hoen and Mulder, 2003; Alcántara and Duarte, 2004; Llop, 2007; Roca and Serrano, 2007; Tarancón and del Río, 2007c; and Liu et al., 2010 belong to this stream of the literature).
A third group of approaches analyses the impact of changes in the technical coefficients in (7) on the level of the generation/consumption of a NAMEA substance from different activity branches. In contrast to the previous approach, the analysis does not focus on changes between two input–output tables in two different periods, but it simulates small variations taking place in the mathematical model which relates demand and NAMEA substance levels. The aim is to analyse the sensitivity of variations in the quantity of the NAMEA substance under investigation caused by those small changes. Therefore, it is worth looking at the following expression in more depth:
Obviously, changes in the bmj elements are the result of changes in the technical coefficients aik which represent the technological mix of each sector. Weber and Schnabl (1998), Tarancón and del Río (2007a, b) are relevant papers in this literature.
Analysis of the Sensitivity of the Coefficients
An analysis of the sensitivity of coefficients allows us to identify the transactions between activity branches which lead to the highest growth in the generation/ consumption of a NAMEA substance. Accordingly, we can identify which production technologies (represented by the columns of technical coefficients) have the greatest impact on emissions.
Identification of Structurally and Technologically Relevant Coefficients
From equation (10) we can see that the quantity of em will depend on the production of sector m, xm for a fixed factor cm. For a level of fixed final demand (hi fixed 
, and g fixed), the only variation in production will stem from a change in the coefficients of the inverse Leontief matrix (b) which belong to row m. In other words:
The changes in the b coefficients are obviously linked to changes in the technical coefficients of production which, if read per column, made up the technological mix of each sector. This relationship can be quantified through the Sherman and Morrison formula (see Sherman and Morrison, 1950). In particular, a change in the technical coefficient aik will induce the following changes in the elements of the inverse Leontief matrix bmj:
Therefore, if (12) is substituted in (11), then:
since 
.
Finally, this can be expressed as elasticities in this way:
Therefore, the elasticity of the generation/consumption of a NAMEA substance under investigation with respect to the change in the technical coefficient aik will be determined by the technological characteristics of the global production system and the output volume of activity branch k with respect to the output of sector m. This last factor depends on the demand for the products of sector k and, thus, it depends on final demand. Therefore, since this elasticity also depends on the composition of final demand in the economy, which determines the output of sector k, it does not only measure the relevance of the technological changes in the sector. Accordingly, we can call this the structural relevance factor since it is affected by the structure of the final demand vector.
On the other hand, we could identify the technological relevance of a coefficient (transaction) which is independent of the specific composition of the final demand vector. This is so because this composition does not depend on the firms in the activity branch but on the consumption and investment habits of economic actors and on the external sector (imports/exports).
To do this, we propose a uniform final demand vector as an alternative measure, i.e. 
. The changes in the generation/consumption of the NAMEA substance under investigation will result from the aggregation of the changes in the elements of row m of the Leontief matrix caused by the change in aik. Thus, the effect of the change of the row of the Leontief matrix can be expressed as follows:
If the value reached by (15) is high, then the generation/consumption of a NAMEA substance under investigation will be highly sensitive to a change in the technological mix of sector k, independently of the structure of final demand. The only difference between (13) and (15) is that each of the bkq coefficients is weighted by the final demand of sector q. (15) could be expressed as elasticities (relative increase in the aggregation of the elements of row m of matrix B due to a variation of the aik coefficient) in the following manner:
Equation (16) provides information on the capacity that the technology of sector k has to induce the generation/consumption of the NAMEA substance in the whole production system when the coefficient aik changes, independently of the composition of final demand. In other words, (16) informs on the technological relevance of sector k due to a change in this coefficient.
Identification of Relevant Coefficients as a Function of the Global Impact on the System
In the previous section, the relevance of the technical coefficients (and thus, the transactions between associated activity branches) has been identified depending on the impact that changes in the quantity of those technical coefficients have on the generation/consumption of a NAMEA substance by sector m. Alternatively, we could identify the most relevant coefficients depending on how their changes affect the generation/consumption of a NAMEA substance in the whole system, i.e. in all the sectors combined.
Accordingly, we propose an alternative measure for evaluating the relevance of a coefficient based on the concept of elasticity. This measure is based on a coefficient’s capacity (elasticity) to change the overall output. This elasticity would be expressed as:
If we integrate (12) into (17) and take into account 
, then:
The most structurally important coefficients are those with the highest elasticity. Changes in those coefficients will generate the greatest variations in the overall amount of the generation/consumption of a NAMEA substance.
Discussion and Conclusions
This chapter has highlighted the role of input–output analysis as a tool for exploiting the information provided by the NAMEA methodology. Several approaches allow us to use input–output tables to derive relevant economic and environmental results. These approaches fall broadly into two groups.
On the one hand, several techniques are based on the structural stability hypothesis and, thus, aim to assess the consequences of changes in the flow variables of the system (especially, components of final demand by activity branches) for a given technological structure.
On the other hand, other techniques focus on the changes in the production structure of the system. This structure materializes in the matrix of technical coefficients for the input–output system.
In this second group, the chapter has aimed to provide an overview of sensitivity analyses in input–output techniques applied to the generation/consumption of the NAMEA substance. Sensitivity analyses allow us to assess the environmental impact of the different coefficients which make up the productive structure of the economic system. They allow us to obtain a map of the hot-points of the production system, i.e. to identify the transactions between sectors which have the greatest impact on the generation/consumption of the NAMEA substance. This approach is deemed highly relevant in the context of environmental impact assessment since it is able to identify the degree of importance of a sector in the generation of emissions by taking into account both direct and indirect impacts.
However, at least four limitations in this approach are worth mentioning.
First, the input–output approach assumes linearity of productive relationships (i.e. constant returns to scale), which is not very realistic. Nonetheless, this assumption does not significantly distort the results when the focus of the analysis is small structural changes.
Second, the sensitivity analysis assumes that the rest of technical coefficients remain constant. This ceteris paribus assumption is very restrictive since it rules out the impact of joint changes in the coefficients. Fortunately, empirical studies have shown that the impact of those joint effects is of minor importance compared with the individual effects.
Third, the quantity input–output model considers the final demand vector as an exogenous variable. The consideration of the distribution coefficients of final demand (hi) allows us to analyse the structure of final demand. However, this does not imply that the scale factor (g) changes in an endogenous manner. One alternative to make those effects endogenous is to use the modelling framework of the social accounting matrix (SAM) and to build models in which the structure of final demand is endogenous within an extended inverse Leontief matrix. Examples of this alternative are Manresa and Sancho (2004), Sánchez-Chóliz et al. (2007), Hartono and Resosudarmo (2008), Parikh et al. (2009) and Duarte et al. (2010) who use a SAM to make private consumption and their impact on greenhouse emissions endogenous. In turn, Rodríguez-Morilla et al. (2007) use the matrix of multipliers of a SAM in order to analyse the economic and social efficiency of the productive system.
Fourth, the aforementioned techniques use quantities produced. In contrast, the impact of prices on the generation/consumption of the NAMEA substance is not explicitly considered. Although there is a price version in the input–output model (see, among others, Førsund, 1985; Llop and Pié, 2008; Tarancón et al. 2010a), a joint treatment of quantities and prices requires a more flexible modelling framework. In this context, the literature has advanced through the construction of general computable equilibrium (CGE) models which use information from the previously built SAM. Examples of these models include Li and Rose (1995), Naqvi (1998), Zhang (1998), Allan et al. (2007), Guivarch et al. (2009) and Kretschmer and Peterson (2010).
Finally, we should go beyond the analysis of the interactions between the activity branches of an economic system, as in this chapter. The interactions between the activity branches of different economic systems should also be analysed. One stream of the literature on input–output analysis has gone deeply into these aspects through the creation of multi-regional input–output models (MRIO) which require information on international trade flows. For example, Reinert and Roland-Holst (2001) build a model based on the SAM for Canada, Mexico and the United States. Other environmental and multi-regional applications of the input–output framework are Liang et al. (2006), Ackerman et al. (2007), Li and Hewitt (2008) and McGregor et al. (2008). A detailed review of these models is provided by Wiedmann et al. (2007) and Wiedmann (2009).
Notes
1 The Leontief model can be expressed as follows. Let x be the vector (nx1) of sector production, A the matrix of technical coefficients defined in (3) and y the vector (nx1) of final demand. Therefore: 
, with B = (I – A)–1 being the Leontief inverse matrix.
2 The terms sector and branch are used interchangeably.
3 Several applications use this approach in order to assess the impacts of foreign trade on energy consumption and CO2 emissions.
References
Ackerman, F., Ishikawa, M. and Suga, M. (2007) ‘The carbon content of Japan-US trade’, Energy Policy, 35: 4455–4462.
Alcántara, V. and Duarte, R. (2004) ‘Comparison of energy intensities in European Union countries: results of a structural decomposition analysis’, Energy Policy, 32: 177–189.
Alcántara, V. and Padilla, E. (2009) ‘Input–output subsystems and pollution: an application to the service sector and CO2 emissions in Spain’, Ecological Economics, 6: 905–914.
Alcántara, V., del Río, P. and Hernández, F. (2010) ‘Structural analysis of electricity consumption by productive sectors: the Spanish case’, Energy, 35: 2088–2098.
Allan, G., Hanley, N., McGregor, P., Swales, K. and Turner, K. (2007) ‘The impact of increased efficiency in the industrial use of energy: a computable general equilibrium analysis for the United Kingdom’, Energy Economics, 29: 779–798.
Butnar, I. and Llop, M. (2007) ‘Composition of greenhouse gas emissions in Spain: an Input–Output analysis’, Ecological Economics, 61: 388–395.
Chang, Y.F. and Lin, S.J. (1998) ‘Structural decomposition of industrial CO2 emissions in Taiwan: an Input–Output approach’, Energy Policy, 26: 5–12.
Chen, G.Q. and Zhang, B. (2010) ‘Greenhouse gas emissions in China 2007: inventory and Input–Output analysis’, Energy Policy, 38: 6180–6193.
de Haan, M. (2001) ‘A structural decomposition analysis of pollution in the Netherlands’, Economic Systems Research, 13: 181–196.
de Haan, M. and Keuning, S.J. (1996) ‘Taking the environment into account: the NAMEA approach’, Review of Income and Wealth, 42: 131–148.
Dietzenbacher, E. and Los, B. (1998) ‘Structural decomposition techniques: sense and sensitivity’, Economic Systems Research, 4: 307–323.
Duarte, R., Mainar, A. and Sánchez-Chóliz, J. (2010) ‘The impact of household consumption patterns on emissions in Spain’, Energy Economics, 32: 176–185.
Ferng, J.J. (2003) ‘Allocating the responsibility of CO2 over-emissions from the perspectives of benefit principle and ecological deficit’, Ecological Economics, 46: 121–141.
Fontela, E. (2005) ‘Conferencia inaugural’, Spanish Input–Output Conference, University of Oviedo, mimeo.
Førsund, F.R. (1985) ‘Input–Output models, national economic models, and the environment’, in A.V. Kneese and J.L. Sweeney (eds), Handbook of Natural Resource and Energy Economics, Amsterdam: Elsevier, pp. 325–344.
Gallego, B. and Lenzen, M. (2005) ‘A consistent Input–Output formulation of shared producer and consumer responsibility’, Economic Systems Research, 17: 365–391.
Guivarch, C., Hallegatte, S. and Crassous, R. (2009) ‘The resilience of the Indian economy to rising oil prices as a validation test for a global energy–environment–economy CGE model’, Energy Policy, 37: 4259–4266.
Hartono, D. and Resosudarmo, B.P. (2008) ‘The economy-wide impact of controlling energy consumption in Indonesia: an analysis using a Social Accounting Matrix framework’, Energy Policy, 36: 1404–1419.
Hoen, A. and Mulder, M. (2003) ‘Explaining Dutch emissions of CO2: a decomposition analysis’, CPB discussion paper, The Hague: Netherlands Bureau for Economic Policy Analysis.
Kagawa, S. and Inamura, H. (2001) ‘A structural decomposition of energy consumption based on a hybrid rectangular Input–Output framework: Japan’s case’, Economic Systems Research, 13: 339–363.
Kretschmer, B. and Peterson, S. (2010) ‘Integrating bioenergy into computable general equilibrium models: a survey’, Energy Economics, 32: 673–686.
Lenzen, M. (1998) ‘Primary energy and greenhouse gases embodied in Australian final consumption: an Input–Output analysis’, Energy Policy, 26: 496–506.
Leontief, W. (1970) ‘Environmental repercussions and the economic structure: an input–output approach’, Review of Economics and Statistics, 52: 262–271.
Leontief, W. and Ford, D. (1972) ‘Air pollution and the economic structure: empirical results of Input–Output computations’, in A. Brody and A. Carter (eds), Input–Output Techniques, Amsterdam: North-Holland.
Li, P. and Rose, A. (1995) ‘Global warming policy and the Pennsylvania economy: a computable general equilibrium analysis’, Economic Systems Research, 7: 151–171.
Li, Y. and Hewitt, C.N. (2008) ‘The effect of trade between China and the UK on national and global carbon dioxide emission’, Energy Policy, 36: 1907–1914.
Liang, Q.M., Fan, Y. and Wei, Y.M. (2006) ‘Multi-regional Input–Output model for regional energy requirements and CO2 emissions in China’, Energy Policy, 35: 1685–1700.
Liu, H., Xi, Y., Guo, J. and Li, X. (2010) ‘Energy embodied in the international trade of China: an energy Input–Output analysis’, Energy Policy, 38: 3957–3964.
Llop, M. (2007) ‘Economic structure and pollution intensity within the environmental Input–Output framework’, Energy policy, 35: 3410–3417.
Llop, M. and Pié, L. (2008) ‘Input–Output analysis of alternative policies implemented on the energy activities: an application for Catalonia’, Energy Policy, 36: 1642–1648.
McGregor, P.G., Swales, J.K. and Turner, K. (2008) ‘The CO2 trade balance between Scotland and the rest of the UK: performing a multi-region environmental Input–Output analysis with limited data’, Ecological Economics, 66: 662–673.
Machado, G., Schaeffer, R. and Worrell, E. (2001) ‘Energy and carbon embodied in the International Trade of Brazil: an Input–Output approach’, Ecological Economics, 39: 409–424.
Manresa, A. and Sancho, F. (2004) ‘Energy intensive and CO2 emissions in Catalonia: a SAM analysis’, International Journal of Environment, Workforce and Employment, 1: 91–106.
Mongelli, I., Tassielli, G. and Notarnicola, B. (2006) ‘Global warming agreements, international trade and energy/carbon embodiments: an Input–Output approach to the Italian case’, Energy Policy, 34: 88–100.
Munksgaard, J. and Pedersen, K.A. (2001) ‘CO2 accounts for open economies: producer or consumer responsibility’, Energy Policy, 29: 327–334.
Naqvi, F. (1998) ‘A computable general equilibrium model of energy, economy and equity interactions in Pakistan’, Energy Economics, 20 (4): 347–373.
Parikh, J., Panda, M., Ganesh-Kumar, A. and Singh, V. (2009) ‘CO2 emissions structure of Indian economy’, Energy, 34: 1024–1031.
Peters, G.P. and Hertwich, E.G. (2006) ‘Pollution embodied in trade: the Norwegian case’, Global Environmental Change, 16: 379–387.
Proops, J.L.R. (1988) ‘Energy intensities, Input–Output analysis and economic development’, in M. Ciaschini (ed.), Input–Output Analysis: Current Developments, London: Chapman and Hall.
Reinert, K.A. and Roland-Holst, D.W. (2001) ‘Industrial pollution linkages in North America: a linear analysis’, Economic Systems Research, 13: 197–208.
Roca, J. and Serrano, M. (2007) ‘Income growth and atmospheric pollution in Spain: an Input–Output approach’, Ecological Economics, 63: 230–242.
Rodríguez-Morilla, C., Llanes, G. and Cardenete, M.A. (2007) ‘Economic and environmental efficiency using a social accounting matrix’, Ecological Economics, 60: 774–786.
Rose, A. and Chen, C.Y. (1991) ‘Sources of change in energy use in the U.S. economy, 1972–1982’, Resources and Energy Economics, 13: 1–21.
Sánchez-Chóliz, J. and Duarte, R. (2004) ‘CO2 emissions embodied in international trade: evidence for Spain’, Energy Policy, 32: 1999–2005.
Sánchez-Chóliz, J., Duarte, R. and Mainar, A. (2007) ‘Environmental impact of household activity in Spain’, Ecological Economics, 62: 308–318.
Sherman, J. and 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.
Tarancón Morán, M.A. and Del Río González, P. (2007a) ‘CO2 emissions and intersectoral linkages: the case of Spain’, Energy Policy, 35: 1100–1116.
Tarancón Morán, M.A. and Del Río González, P. (2007b) ‘A combined Input–Output and sensitivity analysis approach to analyse sector linkages and CO2 emissions’, Energy Economics, 29.
Tarancón Morán, M.A. and Del Río González, P. (2007c) ‘Structural factors affecting land-transport CO2 emissions: a European comparison’, Transportation Research Part D: Transport and Environment, 12.
Tarancón Morán, M.A., Callejas Albiñana, F., Dietzenbacher, E. and Lahr, M.L. (2008a) ‘A revision of the tolerable limits approach: searching for the important coefficients’, Economic Systems Research, 20.
Tarancón Morán, M.A., Del Río González, P. and Callejas Albiñana, F. (2008b) ‘Tracking the genealogy of CO2 emissions in the electricity sector: an intersectoral approach applied to the Spanish case’, Energy Policy, 36: 1915–1926.
Tarancón Morán, M.A., Del Río González, P. and Callejas Albiñana, F. (2010) ‘Assessing the influence of manufacturing sectors on electricity demand: a cross-country Input–Output approach’, Energy Policy, 38: 1900–1908.
Tarancón Morán, M.A., Del Río González, P. and Callejas Albiñana, F. (in press) ‘Determining the responsibility of manufacturing sectors regarding electricity consumption: the Spanish case’, Energy.
Weber, C. and Schnabl, H. (1998) ‘Environmentally important intersectoral flows: insights from main contributions identification and minimal flow analysis’, Economic Systems Research, 10: 337–356.
Wiedmann, T. (2009) ‘A review of recent multi-region Input–Output models used for consumption-based emission and resource accounting’, Ecological Economics, 69: 211–222.
Wiedmann, T., Lenzen, B., Turner, K. and Barretta, J. (2007) ‘Examining the global environmental impact of regional consumption activities – part 2: review of Input–Output models for the assessment of environmental impacts embodied in trade’, Ecological Economics, 61: 15–26.
Wier, M. (1998) ‘Sources of changes in emissions from energy: a structural decomposition analysis’, Economic Systems Research, 10: 99–112.
Zhang, Z. (1998) ‘Macro-economic and sectoral effects of carbon taxes: a general equilibrium analysis for China’, Economic Systems Research, 10: 135–159.