Inequality measurement for bounded variables

Inaki Permanyer, Suman Seth and Gaston Yalonetzky

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Many health indicators are bounded, that is, their values lie between a lower and an upper bound. Inequality measurement with bounded variables faces two normative challenges well‐known in the health inequality literature. One is that inequality rankings may or may not be consistent across admissible attainment and shortfall representations of the variable. The other is that the set of maximum‐inequality distributions for bounded variables is different from the respective set for variables with no upper bound. Therefore, the ethical criteria for ranking maximum‐inequality distributions with unbounded variables may not be appropriate for bounded variables. In a novel proposal, we justify an axiom requiring maximum‐inequality distributions of bounded variables to be ranked equally, irrespective of their means. Then, our axiomatic characterization naturally leads to indices that measure inequality as an increasing function of the observed proportion of maximum attainable inequality for a given mean. Additionally, our inequality indices rank distributions consistently when switching between attainment and shortfall representations. In our empirical illustration with three health indicators, a starkly different picture of cross‐country inter‐temporal inequality emerges when traditional inequality indices give way to our proposed normalized inequality indices.

Keywords: bounded variables; inequality measurement; consistency (search for similar items in EconPapers)
JEL-codes: D63 I31 O57 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2025-04-19
New Economics Papers: this item is included in nep-inv
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Published in Health Economics, 19, April, 2025. ISSN: 1057-9230

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:127974

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