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Basic analytical tool-kit for input-output tables with multiple related outputs: Applications to physical input-output tables with disposals to nature


  • Aleix Altimiras-Martin

    () (Cambridge Centre for Climate Change Mitigation Research, Department of Land Economy, University of Cambridge
    NEREUS, Faculty of Economics and Administration, University of Sao Paulo)


Physical Input-Output Tables (PIOTs) are a powerful accounting framework since they trace simultaneously all physical flows of the economy, including goods and emission. However, there is no IO model able to operate them and, thus, they cannot be used for analytical purposes - only descriptive. A series of papers suggested different methods to operate them but without clearly identifying a IO model matching the specificities of PIOTs (Hubacek and Giljum 2003; Giljum and Hubacek 2004; Suh 2004; Giljum, Hubacek, and Sun 2004; Dietzenbacher 2005; Dietzenbacher et al. 2009; Xu and Zhang 2009). This paper aims to develop an output-driven and an input-driven IO model to operate PIOTs, which would constitute the basic analytical tool-kit to analyse such tables. First, section 2 compares the operation of the traditional Input-Output Tables (IOTs) with PIOTs. It identifies a new type of table - a multiple related outputs IOT - that matches the specificities of a PIOT: it has several outputs (goods and emissions) and one of the outputs - the emissions - is related to the total sectoral throughput by the technology of production. Then, it is shown that the related output causes traditional output-driven IO models such as the Leontief one to underestimate the total outputs. Then, section 3 devises a new IO model by assuming a linear relationship between the related outputs (emissions) and the total throughput (total output or input); consequently, the related outputs such as the emissions can be endogenised in the structure of production and, thus, the model can be driven with final goods alone. Section 3.2 generalises the model for any number of multiple related outputs and shows how to operate a PIOT with five types of simultaneous emissions. Then, section 3.3 shows that Suh's (2004) method is in fact a change of total output units that transforms the PIOT - a multiple related outputs IOT - into a single output IOT that can then be operated with traditional IO models. For completeness, section 4 examines the use of input-driven models with multiple related output tables and finds that no special modification of the input-driven model is required. Thus, this paper provides the theoretical background to analyse PIOTs and any other multiple related outputs IOTs. It is expected that this new model will revive the momentum in PIOT development and analysis which had been lost because of the lack of robust analytical tools.

Suggested Citation

  • Aleix Altimiras-Martin, 2012. "Basic analytical tool-kit for input-output tables with multiple related outputs: Applications to physical input-output tables with disposals to nature," 4CMR Working Paper Series 001, University of Cambridge, Department of Land Economy, Cambridge Centre for Climate Change Mitigation Research.
  • Handle: RePEc:ccc:wpaper:001

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    References listed on IDEAS

    1. Stefan Giljum & Klaus Hubacek, 2004. "Alternative Approaches of Physical Input-Output Analysis to Estimate Primary Material Inputs of Production and Consumption Activities," Economic Systems Research, Taylor & Francis Journals, vol. 16(3), pages 301-310.
    2. Giorgio Nebbia, 2000. "Contabilità monetaria e contabilità ambientale," ECONOMIA PUBBLICA, FrancoAngeli Editore, vol. 2000(6).
    3. Erik Dietzenbacher & Esther Velazquez, 2007. "Analysing Andalusian Virtual Water Trade in an Input-Output Framework," Regional Studies, Taylor & Francis Journals, vol. 41(2), pages 185-196.
    4. Bullard, Clark W. & Herendeen, Robert A., 1975. "The energy cost of goods and services," Energy Policy, Elsevier, vol. 3(4), pages 268-278, December.
    5. Giljum, Stefan & Hubacek, Klaus & Sun, Laixiang, 2004. "Beyond the simple material balance: a reply to Sangwon Suh's note on physical input-output analysis," Ecological Economics, Elsevier, vol. 48(1), pages 19-22, January.
    6. Kirsten S. Wiebe & Martin Bruckner & Stefan Giljum & Christian Lutz, 2012. "Calculating Energy-Related Co 2 Emissions Embodied In International Trade Using A Global Input--Output Model," Economic Systems Research, Taylor & Francis Journals, vol. 24(2), pages 113-139, November.
    7. Dietzenbacher, Erik, 2005. "Waste treatment in physical input-output analysis," Ecological Economics, Elsevier, vol. 55(1), pages 11-23, October.
    8. Hubacek, Klaus & Giljum, Stefan, 2003. "Applying physical input-output analysis to estimate land appropriation (ecological footprints) of international trade activities," Ecological Economics, Elsevier, vol. 44(1), pages 137-151, February.
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    More about this item


    Physical input-output tables; Input-output analysis; Environmental Accounts; Waste; Emission; Material Flow Analysis; EW-MFA;

    JEL classification:

    • Q57 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Ecological Economics
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models

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