IDEAS home Printed from
   My bibliography  Save this article

Matrix Balancing Under Conflicting Information


  • Manfred Lenzen
  • Blanca Gallego
  • Richard Wood


We have developed a generalised iterative scaling method (KRAS) that is able to balance and reconcile input-output tables and SAMs under conflicting external information and inconsistent constraints. Like earlier RAS variants, KRAS can: (a) handle constraints on arbitrarily sized and shaped subsets of matrix elements; (b) include reliability of the initial estimate and the external constraints; and (c) deal with negative values, and preserve the sign of matrix elements. Applying KRAS in four case studies, we find that, as with constrained optimisation, KRAS is able to find a compromise solution between inconsistent constraints. This feature does not exist in conventional RAS variants such as GRAS. KRAS can constitute a major advance for the practice of balancing input-output tables and Social Accounting Matrices, in that it removes the necessity of manually tracing inconsistencies in external information. This quality does not come at the expense of substantial programming and computational requirements (of conventional constrained optimisation techniques).

Suggested Citation

  • Manfred Lenzen & Blanca Gallego & Richard Wood, 2009. "Matrix Balancing Under Conflicting Information," Economic Systems Research, Taylor & Francis Journals, vol. 21(1), pages 23-44.
  • Handle: RePEc:taf:ecsysr:v:21:y:2009:i:1:p:23-44
    DOI: 10.1080/09535310802688661

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Han-Shen Chen, 2015. "Using Water Footprints for Examining the Sustainable Development of Science Parks," Sustainability, MDPI, Open Access Journal, vol. 7(5), pages 1-21, May.
    2. Guangwu Chen & Thomas Wiedmann & Michalis Hadjikakou & Hazel Rowley, 2016. "City Carbon Footprint Networks," Energies, MDPI, Open Access Journal, vol. 9(8), pages 1-16, July.
    3. Jakub Boratyński, 2016. "A Bayesian Approach to Matrix Balancing: Transformation of Industry-Level Data under NACE Revision," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 8(4), pages 219-239, December.
    4. Coleman, Charles, 2016. "A SAS® Macro for the Generalized RAS Algorithm," MPRA Paper 77651, University Library of Munich, Germany, revised 19 Mar 2017.
    5. Chen, Guangwu & Wiedmann, Thomas & Wang, Yafei & Hadjikakou, Michalis, 2016. "Transnational city carbon footprint networks – Exploring carbon links between Australian and Chinese cities," Applied Energy, Elsevier, vol. 184(C), pages 1082-1092.
    6. Wiedmann, Thomas, 2009. "A review of recent multi-region input-output models used for consumption-based emission and resource accounting," Ecological Economics, Elsevier, vol. 69(2), pages 211-222, December.
    7. Hiramatsu, Tomoru & Inoue, Hiroki & Kato, Yasuhiko, 2016. "Estimation of interregional input–output table using hybrid algorithm of the RAS method and real-coded genetic algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 385-402.
    8. Edward F. Baranov & Igor A. Kim & Dmitri I. Piontkovski & Elena A. Staritsyna, 2015. "Constructing Retrospective Time Series of Russian Input-Output Accounts Based on the Nace/Cpa Classifications," HSE Working papers WP BRP 108/EC/2015, National Research University Higher School of Economics.
    9. Dietzenbacher, Erik & Pei, Jiansuo & Yang, Cuihong, 2012. "Trade, production fragmentation, and China's carbon dioxide emissions," Journal of Environmental Economics and Management, Elsevier, vol. 64(1), pages 88-101.
    10. repec:eee:touman:v:40:y:2014:i:c:p:90-101 is not listed on IDEAS
    11. Coleman, Charles, 2015. "SAS® Macros for Constraining Arrays of Numbers," MPRA Paper 77650, University Library of Munich, Germany.
    12. Thomas Wiedmann & John Barrett, 2010. "A Review of the Ecological Footprint Indicator—Perceptions and Methods," Sustainability, MDPI, Open Access Journal, vol. 2(6), pages 1-49, June.
    13. Stefan Giljum & Hanspeter Wieland & Stephan Lutter & Martin Bruckner & Richard Wood & Arnold Tukker & Konstantin Stadler, 2016. "Identifying priority areas for European resource policies: a MRIO-based material footprint assessment," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 5(1), pages 1-24, December.
    14. Malik, Arunima & Lenzen, Manfred & Ely, Rômulo Neves & Dietzenbacher, Erik, 2014. "Simulating the impact of new industries on the economy: The case of biorefining in Australia," Ecological Economics, Elsevier, vol. 107(C), pages 84-93.
    15. repec:eee:appene:v:206:y:2017:i:c:p:531-540 is not listed on IDEAS


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:ecsysr:v:21:y:2009:i:1:p:23-44. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.