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A note on the indeterminacy and arbitrariness of pena’s method of construction of synthetic indicators

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Abstract

In this paper we demonstrate that Pena’s method of construction of a synthetic indicator is very sensitive to the order in which the constituent variables (whose linear aggregation yields the synthetic indicator) are arranged. Since m number of constituent variables may be arranged in m-factorial ways, even a moderately large m can give rise to a very large number of synthetic indicators from which one cannot choose the one which best represents the constituent variables. Given that an analyst has too little information as to the order in which a sizeable number of constituent variables must be arranged so as to obtain the best representative synthetic indicator, Pena’s method can give only an arbitrary synthetic indicator whose representativeness is indeterminate and uncertain.

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  • Mishra, SK, 2012. "A note on the indeterminacy and arbitrariness of pena’s method of construction of synthetic indicators," MPRA Paper 37534, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:37534
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    References listed on IDEAS

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    1. José-María Montero & Coro Chasco & Beatriz Larraz, 2010. "Building an environmental quality index for a big city: a spatial interpolation approach combined with a distance indicator," Journal of Geographical Systems, Springer, vol. 12(4), pages 435-459, December.
    2. Mishra, SK, 2007. "A Note on Human Development Indices with Income Equalities," MPRA Paper 3513, University Library of Munich, Germany.
    3. Mishra, SK, 2008. "On construction of robust composite indices by linear aggregation," MPRA Paper 9232, University Library of Munich, Germany.
    4. Nayak, Purusottam & Ray, Santanu, 2010. "Human development in North East India: a critical appraisal," MPRA Paper 26494, University Library of Munich, Germany.
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    Cited by:

    1. Mishra, SK, 2012. "A note on construction of heuristically optimal Pena’s synthetic indicators by the particle swarm method of global optimization," MPRA Paper 37625, University Library of Munich, Germany.
    2. Enrico Ivaldi & Guido Bonatti & Riccardo Soliani, 2017. "An Indicator for the Measurement of Political Participation: The Case of Italy," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 132(2), pages 605-620, June.
    3. Nayak, Purusottam & Mishra, SK, 2012. "Efficiency of Pena’s P2 Distance in Construction of Human Development Indices," MPRA Paper 39022, University Library of Munich, Germany.
    4. Mishra, SK, 2012. "A comparative study of trends in globalization using different synthetic indicators," MPRA Paper 38028, University Library of Munich, Germany.
    5. Mishra, SK, 2012. "A maximum entropy perspective of Pena’s synthetic indicators," MPRA Paper 37797, University Library of Munich, Germany.

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    More about this item

    Keywords

    Synthetic indicators; Composite Indices; Human development; NP-Hard problem;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration

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