Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references

TL;DR

This paper introduces a unified framework for measuring economic inequality and risk by combining societal reference points and personal gamble distributions, bridging classical and modern indices.

Contribution

It proposes a novel approach that unifies classical and contemporary inequality and risk measures through societal references and personal gambles.

Findings

A new risk measure accounting for the relativity of large and small risks.

Unification of classical and modern inequality indices.

Illustration of the approach with a specific risk measure.

Abstract

The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or median, or curves like the hypotenuse of the right triangle where every Lorenz curve falls into. In this paper we argue that by appropriately choosing population-based references, called societal references, and distributions of personal positions, called gambles, which are random, we can meaningfully unify classical and contemporary indices of economic inequality, as well as various measures of risk. To illustrate the herein proposed approach, we put forward and explore a risk measure that takes into account the relativity of large risks with respect to small ones.