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GRAS versus minimizing absolute and squared differences: a comment

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  • Jan Oosterhaven

Abstract

Junius and Oosterhaven (2003) developed the GRAS algorithm that minimizes the information gain when updating input-output tables with both positive and negative signs. Jackson and Murray (2004), however, claim that minimizing squared differences in coefficients produces a smaller information gain, which is theoretically impossible. In this comment, calculation errors are sorted out from differences in measures, and it is shown that the information gain needs to be taken in absolute terms when increasing and decreasing cell values occur together. The numerical results show that GRAS outperforms both sign-preserving alternatives in all but one comparison of lesser economic importance. Moreover, as opposed to the result of Jackson and Murray, they show that minimizing absolute differences consistently outperforms minimizing squared differences, which overweighs large errors in small coefficients.

Suggested Citation

  • Jan Oosterhaven, 2005. "GRAS versus minimizing absolute and squared differences: a comment," Economic Systems Research, Taylor & Francis Journals, vol. 17(3), pages 327-331.
    • Handle: RePEc:taf:ecsysr:v:17:y:2005:i:3:p:327-331
    DOI: 10.1080/09535310500221864
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    Citations

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    Cited by:

    1. Pieters, Janneke, 2010. "Growth and Inequality in India: Analysis of an Extended Social Accounting Matrix," World Development, Elsevier, vol. 38(3), pages 270-281, March.
    2. Rachel C. Reyes & Arne Geschke & Arjan de Koning & Richard Wood & Tatyana Bulavskaya & Konstantin Stadler & Hagen Schulte in den Bäumen & Arnold Tukker, 2017. "The Virtual IELab – an exercise in replicating part of the EXIOBASE V.2 production pipeline in a virtual laboratory," Economic Systems Research, Taylor & Francis Journals, vol. 29(2), pages 209-233, April.
    3. repec:ilo:ilowps:464252 is not listed on IDEAS
    4. Manfred Lenzen & Arne Geschke & Muhammad Daaniyall Abd Rahman & Yanyan Xiao & Jacob Fry & Rachel Reyes & Erik Dietzenbacher & Satoshi Inomata & Keiichiro Kanemoto & Bart Los & Daniel Moran & Hagen Sch, 2017. "The Global MRIO Lab – charting the world economy," Economic Systems Research, Taylor & Francis Journals, vol. 29(2), pages 158-186, April.
    5. Wenfeng Huang & Shintaro Kobayashi & Hajime Tanji, 2008. "Updating an Input-Output Matrix with Sign-preservation: Some Improved Objective Functions and their Solutions," Economic Systems Research, Taylor & Francis Journals, vol. 20(1), pages 111-123.
    6. Andre Lemelin, 2009. "A Gras Variant Solving For Minimum Information Loss," Economic Systems Research, Taylor & Francis Journals, vol. 21(4), pages 399-408.
    7. Tamas Revesz, 2023. "A not sign-preserving iteration algorithm for the ‘Improved Normalized Squared Differences’ matrix adjustment model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(1), pages 49-71, March.
    8. Roberto Mínguez & Jan Oosterhaven & Fernando Escobedo, 2009. "Cell‐Corrected Ras Method (Cras) For Updating Or Regionalizing An Input–Output Matrix," Journal of Regional Science, Wiley Blackwell, vol. 49(2), pages 329-348, May.
    9. Anders Hammer Strømman, 2009. "A Multi-Objective Assessment Of Input-Output Matrix Updating Methods," Economic Systems Research, Taylor & Francis Journals, vol. 21(1), pages 81-88.
    10. Erik Dietzenbacher & Ronald E. Miller, 2009. "Ras‐Ing The Transactions Or The Coefficients: It Makes No Difference," Journal of Regional Science, Wiley Blackwell, vol. 49(3), pages 555-566, August.

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