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A Gras Variant Solving For Minimum Information Loss

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  • Andre Lemelin

Abstract

The fundamental idea in Junius and Oosterhaven (2003) is to break down the information contained in the a priori data into two parts: algebraic signs, and absolute values. This approach is well grounded in information theory, and provides a basis on which to solve the problem of adjusting matrices with negative entries. However, Junius and Oosterhaven (2003) have formulated a target function that is not equivalent to the Kullback and Leibler (1951) cross-entropy measure, and so is not a representation of the minimum information loss principle. Neither is the alternative target function proposed by Lenzen et al. (2007). This paper develops the exact Kullback and Leibler cross-entropy measure. In addition, following the constrained optimization approach, this paper applies the same principle to solve adjustment problems where row-sums, column-sums or both are constrained to zero.

Suggested Citation

  • Andre Lemelin, 2009. "A Gras Variant Solving For Minimum Information Loss," Economic Systems Research, Taylor & Francis Journals, vol. 21(4), pages 399-408.
    • Handle: RePEc:taf:ecsysr:v:21:y:2009:i:4:p:399-408
    DOI: 10.1080/09535311003589310
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    References listed on IDEAS

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    1. Randall Jackson & Alan Murray, 2004. "Alternative Input-Output Matrix Updating Formulations," Economic Systems Research, Taylor & Francis Journals, vol. 16(2), pages 135-148.
    2. Jan Oosterhaven, 2005. "GRAS versus minimizing absolute and squared differences: a comment," Economic Systems Research, Taylor & Francis Journals, vol. 17(3), pages 327-331.
    3. 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.
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