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A single-parameter generalization of Gini based on the 'metallic' sequences of number theory

Author

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  • S Subramanian

    (Independent Scholar (formerly, Madras Institute of Development Studies))

Abstract

The best-known and most-widely studied generalization of the Gini coefficient of inequality is the single-parameter extension due to authors such as David Donaldson, John Weymark, Nanak Kakwani, Shlomo Yitzhaki, and Satya Chakravarti. The ‘S-Gini' parametrization is essentially in the form of a scalar employed as an exponent on Gini's income-weight, which is the Borda rank-order. The present note considers an alternative single-parameter generalization in which income-weights are derived from Fibonacci-like sequences of numbers, each sequence being indexed by a non-negative integer. The Gini coefficient is a special case of the resulting series of indices, another of which—the ‘Fibonacci' index—is introduced, and shown to be a transfer-sensitive extension of Gini.

Suggested Citation

  • S Subramanian, 2021. "A single-parameter generalization of Gini based on the 'metallic' sequences of number theory," Economics Bulletin, AccessEcon, vol. 41(4), pages 2309-2319.
  • Handle: RePEc:ebl:ecbull:eb-21-00819
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    File URL: http://www.accessecon.com/Pubs/EB/2021/Volume41/EB-21-V41-I4-P199.pdf
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    Cited by:

    1. S Subramanian, 2023. "Using the zeta function to explain 'downside' and 'upside' inequality aversion," Economics Bulletin, AccessEcon, vol. 43(1), pages 8-17.

    More about this item

    Keywords

    Gini index; Fibonacci index; rank-order weight; Fibonacci sequence; Pell sequence; golden ratio; silver ratio;
    All these keywords.

    JEL classification:

    • D3 - Microeconomics - - Distribution
    • D6 - Microeconomics - - Welfare Economics

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