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The Informational Index of Income Inequality

Author

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  • Paulo L. dos Santos

    (Department of Economics, New School for Social Research)

Abstract

A new informational index of income inequality is proposed. Based on a combinatorial characterisation of entropy and on its generalisation by multivariate measures of co-information, the index addresses a limiting analytical choice embedded in Theil's two indices of income inequality. This yields a positive measure of inequality of opportunity in income-generating processes, defined in relation to probabilities that the population-wide distribution of income describes the set of possible income levels facing specified sub-groups of that population. Its measure across a population is given when sub-groups consist of each individual. This can be successively decomposed linearly by sub-groups defined by covariates of income. In those instances, the index also provides informational measures of phenomenological association and interaction between income and those covariates. On those bases the index improves on mean-log deviations as measures of "luck egalitarian" notions of equity; casts new light on and uncovers new properties in the Theil-Finezza index of segregation; offers a non-parametric generalisation of the Kitagawa-Oaxaca-Blinder decomposition; and lays new conceptual foundations for work on the determinants and normative content of patterns of income differentiation in decentralised market economies.

Suggested Citation

  • Paulo L. dos Santos, 2022. "The Informational Index of Income Inequality," Working Papers 2211, New School for Social Research, Department of Economics.
    • Handle: RePEc:new:wpaper:2211
    as

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    File URL: http://www.economicpolicyresearch.org/econ/2022/NSSR_WP_112022.pdf
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    References listed on IDEAS

    as
    1. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    2. Amartya K. Sen, 1997. "From Income Inequality to Economic Inequality," Southern Economic Journal, John Wiley & Sons, vol. 64(2), pages 384-401, October.
    3. Fleurbaey, Marc, 1995. "Equal Opportunity or Equal Social Outcome?," Economics and Philosophy, Cambridge University Press, vol. 11(1), pages 25-55, April.
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    More about this item

    Keywords

    Inequality indices; income distribution; information theory;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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