Consistent and inconsistent inequality indices for ordinal variables

Gaston Yalonetzky

Economics Letters, 2022, vol. 219, issue C

Abstract: Should inequality comparisons with ordinal variables be sensitive to alternative sorting of the categories? We introduce the consistency property whereby an inequality or bipolarisation index regards frequency distribution r less unequal than s if and only if it ranks the reverse-ordered distribution r′ less unequal than s′ for every pair of comparable frequency distributions. We characterise the class of consistent indices with a functional equation that serves as a useful test of the property. Applying the test to the most popular indices in the literature, we identify the respective consistent and inconsistent sets.

Keywords: Ordinal variables; Inequality; Bipolarisation; Consistency (search for similar items in EconPapers)
JEL-codes: D63 I14 I31 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:219:y:2022:i:c:s0165176522003123

DOI: 10.1016/j.econlet.2022.110833

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