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

S Subramanian ()
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S Subramanian: Independent Scholar (formerly, Madras Institute of Development Studies)

Economics Bulletin, 2021, vol. 41, issue 4, 2309-2319

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.

Keywords: Gini index; Fibonacci index; rank-order weight; Fibonacci sequence; Pell sequence; golden ratio; silver ratio (search for similar items in EconPapers)
JEL-codes: D3 D6 (search for similar items in EconPapers)
Date: 2021-12-29
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Citations: View citations in EconPapers (1)

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