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Negatives in symmetric input–output tables: the impossible quest for the Holy Grail


  • Louis Mesnard



In the Supply-Use (or Make-Use) input-output model, “product-technology” (PT) or “fixed-industry-sales-structure” (FISS) assumptions are more widely adopted (SNA, Eurostat) for deriving symmetric input-output tables (SIOT) than “industry-technology” or “fixed-product-sales-structure” assumptions, but generate negatives in the SIOT. A SIOT deduced from the Supply-Use model is considered as satisfactory as soon as it contains no more negatives: scholars have focused on the negatives in the SIOT and on how to remove them. However, as a SIOT may include no negatives even if there are some negatives in the inverse Supply matrix, we have completely reversed the reasoning. A counter-example demonstrates that computing the inverse Supply matrix, as imposed by PT or FISS assumptions, is mathematically a nonsense operation even when the SIOT does not include any negative; this result is new. Hence, deriving a SIOT under PT or FISS assumptions must be rejected. Three applications are provided: Austria 2000 and 2005 and USA 2007.
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Suggested Citation

  • Louis Mesnard, 2011. "Negatives in symmetric input–output tables: the impossible quest for the Holy Grail," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 46(2), pages 427-454, April.
  • Handle: RePEc:spr:anresc:v:46:y:2011:i:2:p:427-454
    DOI: 10.1007/s00168-009-0332-5

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    References listed on IDEAS

    1. Lars Bohlin & Lars Widell, 2006. "Estimation of commodity-by-commodity input-output matrices," Economic Systems Research, Taylor & Francis Journals, vol. 18(2), pages 205-215.
    2. Joe Mattey, 1993. "Evidence on IO Technology Assumptions From the Longitudinal Research Database," Working Papers 93-8, Center for Economic Studies, U.S. Census Bureau.
    3. Joe Mattey & Thijs ten Raa, 2009. "Primary Versus Secondary Production Techniques in U.S. Manufacturing," World Scientific Book Chapters,in: Input–Output Economics: Theory And Applications Featuring Asian Economies, chapter 16, pages 285-305 World Scientific Publishing Co. Pte. Ltd..
    4. Richard Harris & Aying Liu, 1998. "Input-Output Modelling of the Urban and Regional Economy: The Importance of External Trade," Regional Studies, Taylor & Francis Journals, vol. 32(9), pages 851-862.
    5. Rutger Hoekstra, 2005. "Economic Growth, Material Flows and the Environment," Books, Edward Elgar Publishing, number 3700.
    6. Jose Rueda-Cantuche & Joerg Beutel & Frederik Neuwahl & Ignazio Mongelli & Andreas Loeschel, 2009. "A Symmetric Input-Output Table For Eu27: Latest Progress," Economic Systems Research, Taylor & Francis Journals, vol. 21(1), pages 59-79.
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    Cited by:

    1. Reyno Seymore & Martin Combrinck, 2016. "Alternative Growth Industries In Gabon: An Input-Output Analysis," EcoMod2016 9076, EcoMod.
    2. Rodrigues, João F.D. & Rueda-Cantuche, José M., 2013. "A two-stage econometric method for the estimation of carbon multipliers with rectangular supply and use tables," Ecological Economics, Elsevier, vol. 95(C), pages 206-212.

    More about this item


    C67; D57;

    JEL classification:

    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • D57 - Microeconomics - - General Equilibrium and Disequilibrium - - - Input-Output Tables and Analysis


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